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Sample records for simulating complex reaction-diffusion

  1. Meredys, a multi-compartment reaction-diffusion simulator using multistate realistic molecular complexes

    Directory of Open Access Journals (Sweden)

    Le Novère Nicolas

    2010-03-01

    Full Text Available Abstract Background Most cellular signal transduction mechanisms depend on a few molecular partners whose roles depend on their position and movement in relation to the input signal. This movement can follow various rules and take place in different compartments. Additionally, the molecules can form transient complexes. Complexation and signal transduction depend on the specific states partners and complexes adopt. Several spatial simulator have been developed to date, but none are able to model reaction-diffusion of realistic multi-state transient complexes. Results Meredys allows for the simulation of multi-component, multi-feature state molecular species in two and three dimensions. Several compartments can be defined with different diffusion and boundary properties. The software employs a Brownian dynamics engine to simulate reaction-diffusion systems at the reactive particle level, based on compartment properties, complex structure, and hydro-dynamic radii. Zeroth-, first-, and second order reactions are supported. The molecular complexes have realistic geometries. Reactive species can contain user-defined feature states which can modify reaction rates and outcome. Models are defined in a versatile NeuroML input file. The simulation volume can be split in subvolumes to speed up run-time. Conclusions Meredys provides a powerful and versatile way to run accurate simulations of molecular and sub-cellular systems, that complement existing multi-agent simulation systems. Meredys is a Free Software and the source code is available at http://meredys.sourceforge.net/.

  2. Reaction-diffusion controlled growth of complex structures

    Science.gov (United States)

    Noorduin, Willem; Mahadevan, L.; Aizenberg, Joanna

    2013-03-01

    Understanding how the emergence of complex forms and shapes in biominerals came about is both of fundamental and practical interest. Although biomineralization processes and organization strategies to give higher order architectures have been studied extensively, synthetic approaches to mimic these self-assembled structures are highly complex and have been difficult to emulate, let alone replicate. The emergence of solution patterns has been found in reaction-diffusion systems such as Turing patterns and the BZ reaction. Intrigued by this spontaneous formation of complexity we explored if similar processes can lead to patterns in the solid state. We here identify a reaction-diffusion system in which the shape of the solidified products is a direct readout of the environmental conditions. Based on insights in the underlying mechanism, we developed a toolbox of engineering strategies to deterministically sculpt patterns and shapes, and combine different morphologies to create a landscape of hierarchical multi scale-complex tectonic architectures with unprecedented levels of complexity. These findings may hold profound implications for understanding, mimicking and ultimately expanding upon nature's morphogenesis strategies, allowing the synthesis of advanced highly complex microscale materials and devices. WLN acknowledges the Netherlands Organization for Scientific Research for financial support

  3. Accurate numerical simulation of reaction-diffusion processes for heavy oil recovery

    Energy Technology Data Exchange (ETDEWEB)

    Govind, P.A.; Srinivasan, S. [Society of Petroleum Engineers, Richardson, TX (United States)]|[Texas Univ., Austin, TX (United States)

    2008-10-15

    This study evaluated a reaction-diffusion simulation tool designed to analyze the displacement of carbon dioxide (CO{sub 2}) in a simultaneous injection of carbon dioxide and elemental sodium in a heavy oil reservoir. Sodium was used due to the exothermic reaction of sodium with in situ that occurs when heat is used to reduce oil viscosity. The process also results in the formation of sodium hydroxide that reduces interfacial tension at the bitumen interface. A commercial simulation tool was used to model the sodium transport mechanism to the reaction interface through diffusion as well as the reaction zone's subsequent displacement. The aim of the study was to verify if the in situ reaction was able to generate sufficient heat to reduce oil viscosity and improve the displacement of the heavy oil. The study also assessed the accuracy of the reaction front simulation tool, in which an alternate method was used to model the propagation front as a moving heat source. The sensitivity of the simulation results were then evaluated in relation to the diffusion coefficient in order to understand the scaling characteristics of the reaction-diffusion zone. A pore-scale simulation was then up-scaled to grid blocks. Results of the study showed that when sodium suspended in liquid CO{sub 2} is injected into reservoirs, it diffuses through the carrier phase and interacts with water. A random walk diffusion algorithm with reactive dissipation was implemented to more accurately characterize reaction and diffusion processes. It was concluded that the algorithm modelled physical dispersion while neglecting the effect of numerical dispersion. 10 refs., 3 tabs., 24 figs.

  4. Step-by-Step Simulation of Radiation Chemistry Using Green Functions for Diffusion-Influenced Reactions

    Science.gov (United States)

    Plante, Ianik; Cucinotta, Francis A.

    2011-01-01

    Radiolytic species are formed approximately 1 ps after the passage of ionizing radiation through matter. After their formation, they diffuse and chemically react with other radiolytic species and neighboring biological molecules, leading to various oxidative damage. Therefore, the simulation of radiation chemistry is of considerable importance to understand how radiolytic species damage biological molecules [1]. The step-by-step simulation of chemical reactions is difficult, because the radiolytic species are distributed non-homogeneously in the medium. Consequently, computational approaches based on Green functions for diffusion-influenced reactions should be used [2]. Recently, Green functions for more complex type of reactions have been published [3-4]. We have developed exact random variate generators of these Green functions [5], which will allow us to use them in radiation chemistry codes. Moreover, simulating chemistry using the Green functions is which is computationally very demanding, because the probabilities of reactions between each pair of particles should be evaluated at each timestep [2]. This kind of problem is well adapted for General Purpose Graphic Processing Units (GPGPU), which can handle a large number of similar calculations simultaneously. These new developments will allow us to include more complex reactions in chemistry codes, and to improve the calculation time. This code should be of importance to link radiation track structure simulations and DNA damage models.

  5. An adaptive algorithm for simulation of stochastic reaction-diffusion processes

    International Nuclear Information System (INIS)

    Ferm, Lars; Hellander, Andreas; Loetstedt, Per

    2010-01-01

    We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reaction-diffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the domain is treated macroscopically, in other parts with the tau-leap method and in the remaining parts with Gillespie's stochastic simulation algorithm (SSA) as implemented in the next subvolume method (NSM). The chemical reactions are handled by SSA everywhere in the computational domain. A trajectory of the process is advanced in time by an operator splitting technique and the timesteps are chosen adaptively. The spatial adaptation is based on estimates of the errors in the tau-leap method and the macroscopic diffusion. The accuracy and efficiency of the method are demonstrated in examples from molecular biology where the domain is discretized by unstructured meshes.

  6. Event-triggered synchronization for reaction-diffusion complex networks via random sampling

    Science.gov (United States)

    Dong, Tao; Wang, Aijuan; Zhu, Huiyun; Liao, Xiaofeng

    2018-04-01

    In this paper, the synchronization problem of the reaction-diffusion complex networks (RDCNs) with Dirichlet boundary conditions is considered, where the data is sampled randomly. An event-triggered controller based on the sampled data is proposed, which can reduce the number of controller and the communication load. Under this strategy, the synchronization problem of the diffusion complex network is equivalently converted to the stability of a of reaction-diffusion complex dynamical systems with time delay. By using the matrix inequality technique and Lyapunov method, the synchronization conditions of the RDCNs are derived, which are dependent on the diffusion term. Moreover, it is found the proposed control strategy can get rid of the Zeno behavior naturally. Finally, a numerical example is given to verify the obtained results.

  7. Multi-scale simulation of reaction-diffusion systems

    NARCIS (Netherlands)

    Vijaykumar, A.

    2017-01-01

    In many reaction-diffusion processes, ranging from biochemical networks, catalysis, to complex self-assembly, the spatial distribution of the reactants and the stochastic character of their interactions are crucial for the macroscopic behavior. The recently developed mesoscopic Green’s Function

  8. Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.

    Science.gov (United States)

    Chen, Minghan; Li, Fei; Wang, Shuo; Cao, Young

    2017-03-14

    Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity. In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method. Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.

  9. Stochastic reaction-diffusion algorithms for macromolecular crowding

    Science.gov (United States)

    Sturrock, Marc

    2016-06-01

    Compartment-based (lattice-based) reaction-diffusion algorithms are often used for studying complex stochastic spatio-temporal processes inside cells. In this paper the influence of macromolecular crowding on stochastic reaction-diffusion simulations is investigated. Reaction-diffusion processes are considered on two different kinds of compartmental lattice, a cubic lattice and a hexagonal close packed lattice, and solved using two different algorithms, the stochastic simulation algorithm and the spatiocyte algorithm (Arjunan and Tomita 2010 Syst. Synth. Biol. 4, 35-53). Obstacles (modelling macromolecular crowding) are shown to have substantial effects on the mean squared displacement and average number of molecules in the domain but the nature of these effects is dependent on the choice of lattice, with the cubic lattice being more susceptible to the effects of the obstacles. Finally, improvements for both algorithms are presented.

  10. URDME: a modular framework for stochastic simulation of reaction-transport processes in complex geometries.

    Science.gov (United States)

    Drawert, Brian; Engblom, Stefan; Hellander, Andreas

    2012-06-22

    Experiments in silico using stochastic reaction-diffusion models have emerged as an important tool in molecular systems biology. Designing computational software for such applications poses several challenges. Firstly, realistic lattice-based modeling for biological applications requires a consistent way of handling complex geometries, including curved inner- and outer boundaries. Secondly, spatiotemporal stochastic simulations are computationally expensive due to the fast time scales of individual reaction- and diffusion events when compared to the biological phenomena of actual interest. We therefore argue that simulation software needs to be both computationally efficient, employing sophisticated algorithms, yet in the same time flexible in order to meet present and future needs of increasingly complex biological modeling. We have developed URDME, a flexible software framework for general stochastic reaction-transport modeling and simulation. URDME uses Unstructured triangular and tetrahedral meshes to resolve general geometries, and relies on the Reaction-Diffusion Master Equation formalism to model the processes under study. An interface to a mature geometry and mesh handling external software (Comsol Multiphysics) provides for a stable and interactive environment for model construction. The core simulation routines are logically separated from the model building interface and written in a low-level language for computational efficiency. The connection to the geometry handling software is realized via a Matlab interface which facilitates script computing, data management, and post-processing. For practitioners, the software therefore behaves much as an interactive Matlab toolbox. At the same time, it is possible to modify and extend URDME with newly developed simulation routines. Since the overall design effectively hides the complexity of managing the geometry and meshes, this means that newly developed methods may be tested in a realistic setting already at

  11. Mathematical analysis and numerical simulation of patterns in fractional and classical reaction-diffusion systems

    International Nuclear Information System (INIS)

    Owolabi, Kolade M.

    2016-01-01

    The aim of this paper is to examine pattern formation in the sub— and super-diffusive scenarios and compare it with that of classical or standard diffusive processes in two-component fractional reaction-diffusion systems that modeled a predator-prey dynamics. The focus of the work concentrates on the use of two separate mathematical techniques, we formulate a Fourier spectral discretization method as an efficient alternative technique to solve fractional reaction-diffusion problems in higher-dimensional space, and later advance the resulting systems of ODEs in time with the adaptive exponential time-differencing solver. Obviously, the fractional Fourier approach is able to achieve spectral convergence up to machine precision regardless of the fractional order α, owing to the fact that our approach is able to give full diagonal representation of the fractional operator. The complexity of the dynamics in this system is theoretically discussed and graphically displayed with some examples and numerical simulations in one, two and three dimensions.

  12. Diffusive instabilities in hyperbolic reaction-diffusion equations

    Science.gov (United States)

    Zemskov, Evgeny P.; Horsthemke, Werner

    2016-03-01

    We investigate two-variable reaction-diffusion systems of the hyperbolic type. A linear stability analysis is performed, and the conditions for diffusion-driven instabilities are derived. Two basic types of eigenvalues, real and complex, are described. Dispersion curves for both types of eigenvalues are plotted and their behavior is analyzed. The real case is related to the Turing instability, and the complex one corresponds to the wave instability. We emphasize the interesting feature that the wave instability in the hyperbolic equations occurs in two-variable systems, whereas in the parabolic case one needs three reaction-diffusion equations.

  13. Turing Patterns in a Reaction-Diffusion System

    International Nuclear Information System (INIS)

    Wu Yanning; Wang Pingjian; Hou Chunju; Liu Changsong; Zhu Zhengang

    2006-01-01

    We have further investigated Turing patterns in a reaction-diffusion system by theoretical analysis and numerical simulations. Simple Turing patterns and complex superlattice structures are observed. We find that the shape and type of Turing patterns depend on dynamical parameters and external periodic forcing, and is independent of effective diffusivity rate σ in the Lengyel-Epstein model. Our numerical results provide additional insight into understanding the mechanism of development of Turing patterns and predicting new pattern formations.

  14. Flexible single molecule simulation of reaction-diffusion processes

    International Nuclear Information System (INIS)

    Hellander, Stefan; Loetstedt, Per

    2011-01-01

    An algorithm is developed for simulation of the motion and reactions of single molecules at a microscopic level. The molecules diffuse in a solvent and react with each other or a polymer and molecules can dissociate. Such simulations are of interest e.g. in molecular biology. The algorithm is similar to the Green's function reaction dynamics (GFRD) algorithm by van Zon and ten Wolde where longer time steps can be taken by computing the probability density functions (PDFs) and then sample from the distribution functions. Our computation of the PDFs is much less complicated than GFRD and more flexible. The solution of the partial differential equation for the PDF is split into two steps to simplify the calculations. The sampling is without splitting error in two of the coordinate directions for a pair of molecules and a molecule-polymer interaction and is approximate in the third direction. The PDF is obtained either from an analytical solution or a numerical discretization. The errors due to the operator splitting, the partitioning of the system, and the numerical approximations are analyzed. The method is applied to three different systems involving up to four reactions. Comparisons with other mesoscopic and macroscopic models show excellent agreement.

  15. Reaction Diffusion and Chemotaxis for Decentralized Gathering on FPGAs

    Directory of Open Access Journals (Sweden)

    Bernard Girau

    2009-01-01

    and rapid simulations of the complex dynamics of this reaction-diffusion model. Then we describe the FPGA implementation of the environment together with the agents, to study the major challenges that must be solved when designing a fast embedded implementation of the decentralized gathering model. We analyze the results according to the different goals of these hardware implementations.

  16. Pattern dynamics of the reaction-diffusion immune system.

    Science.gov (United States)

    Zheng, Qianqian; Shen, Jianwei; Wang, Zhijie

    2018-01-01

    In this paper, we will investigate the effect of diffusion, which is ubiquitous in nature, on the immune system using a reaction-diffusion model in order to understand the dynamical behavior of complex patterns and control the dynamics of different patterns. Through control theory and linear stability analysis of local equilibrium, we obtain the optimal condition under which the system loses stability and a Turing pattern occurs. By combining mathematical analysis and numerical simulation, we show the possible patterns and how these patterns evolve. In addition, we establish a bridge between the complex patterns and the biological mechanism using the results from a previous study in Nature Cell Biology. The results in this paper can help us better understand the biological significance of the immune system.

  17. Step-by-Step Simulation of Radiation of Radiation Chemistry Using Green Functions for Diffusion-Influenced Reactions

    Science.gov (United States)

    Plante, Ianik; Cucinotta, Francis A.

    2011-01-01

    The irradiation of biological systems leads to the formation of radiolytic species such as H(raised dot), (raised dot)OH, H2, H2O2, e(sup -)(sub aq), etc.[1]. These species react with neighboring molecules, which result in damage in biological molecules such as DNA. Radiation chemistry is there for every important to understand the radiobiological consequences of radiation[2]. In this work, we discuss an approach based on the exact Green Functions for diffusion-influenced reactions which may be used to simulate radiation chemistry and eventually extended to study more complex systems, including DNA.

  18. Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK.

    Science.gov (United States)

    Wang, Kaier; Steyn-Ross, Moira L; Steyn-Ross, D Alistair; Wilson, Marcus T; Sleigh, Jamie W; Shiraishi, Yoichi

    2014-04-11

    Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requires numerical solution of the system's set of defining differential equations. Traditionally, this would be done by selecting an appropriate differential equation solver from a library of such solvers, then writing computer codes (in a programming language such as C or Matlab) to access the selected solver and display the integrated results as a function of space and time. This "code-based" approach is flexible and powerful, but requires a certain level of programming sophistication. A modern alternative is to use a graphical programming interface such as Simulink to construct a data-flow diagram by assembling and linking appropriate code blocks drawn from a library. The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution. As a tutorial introduction, we first demonstrate application of the Simulink data-flow technique to the classical van der Pol nonlinear oscillator, and compare Matlab and Simulink coding approaches to solving the van der Pol ordinary differential equations. We then show how to introduce space (in one and two dimensions) by solving numerically the partial differential equations for two different reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuum model for a two-dimensional sheet of human cortex whose neurons are linked by both chemical and electrical (diffusive) synapses. We compare the relative performances of the Matlab and Simulink implementations. The pattern simulations by Simulink are in good agreement with theoretical predictions. Compared with traditional coding approaches, the Simulink block-diagram paradigm reduces the time and programming burden required to implement a solution for reaction-diffusion systems of equations. Construction of the block-diagram does not require high-level programming

  19. STEPS: efficient simulation of stochastic reaction–diffusion models in realistic morphologies

    Directory of Open Access Journals (Sweden)

    Hepburn Iain

    2012-05-01

    Full Text Available Abstract Background Models of cellular molecular systems are built from components such as biochemical reactions (including interactions between ligands and membrane-bound proteins, conformational changes and active and passive transport. A discrete, stochastic description of the kinetics is often essential to capture the behavior of the system accurately. Where spatial effects play a prominent role the complex morphology of cells may have to be represented, along with aspects such as chemical localization and diffusion. This high level of detail makes efficiency a particularly important consideration for software that is designed to simulate such systems. Results We describe STEPS, a stochastic reaction–diffusion simulator developed with an emphasis on simulating biochemical signaling pathways accurately and efficiently. STEPS supports all the above-mentioned features, and well-validated support for SBML allows many existing biochemical models to be imported reliably. Complex boundaries can be represented accurately in externally generated 3D tetrahedral meshes imported by STEPS. The powerful Python interface facilitates model construction and simulation control. STEPS implements the composition and rejection method, a variation of the Gillespie SSA, supporting diffusion between tetrahedral elements within an efficient search and update engine. Additional support for well-mixed conditions and for deterministic model solution is implemented. Solver accuracy is confirmed with an original and extensive validation set consisting of isolated reaction, diffusion and reaction–diffusion systems. Accuracy imposes upper and lower limits on tetrahedron sizes, which are described in detail. By comparing to Smoldyn, we show how the voxel-based approach in STEPS is often faster than particle-based methods, with increasing advantage in larger systems, and by comparing to MesoRD we show the efficiency of the STEPS implementation. Conclusion STEPS simulates

  20. Diffusion-controlled reaction. V. Effect of concentration-dependent diffusion coefficient on reaction rate in graft polymerization

    International Nuclear Information System (INIS)

    Imre, K.; Odian, G.

    1979-01-01

    The effect of diffusion on radiation-initiated graft polymerization has been studied with emphasis on the single- and two-penetrant cases. When the physical properties of the penetrants are similar, the two-penetrant problems can be reduced to the single-penetrant problem by redefining the characteristic parameters of the system. The diffusion-free graft polymerization rate is assumed to be proportional to the upsilon power of the monomer concentration respectively, and, in which the proportionality constant a = k/sub p/R/sub i//sup w//k/sub t//sup z/, where k/sub p/ and k/sub t/ are the propagation and termination rate constants, respectively, and R/sub i/ is the initiation rate. The values of upsilon, w, and z depend on the particular reaction system. The results of earlier work were generalized by allowing a non-Fickian diffusion rate which predicts an essentially exponential dependence on the monomer concentration of the diffusion coefficient, D = D 0 [exp(deltaC/M)], where M is the saturation concentration. A reaction system is characterized by the three dimensionless parameters, upsilon, delta, and A = (L/2)[aM/sup (upsilon--1)//D 0 ]/sup 1/2/, where L is the polymer film thickness. Graft polymerization tends to become diffusion controlled as A increases. Larger values of delta and ν cause a reaction system to behave closer to the diffusion-free regime. Transition from diffusion-free to diffusion-controlled reaction involves changes in the dependence of the reaction rate on film thickness, initiation rate, and monomer concentration. Although the diffusion-free rate is w order in initiation rate, upsilon order in monomer, and independent of film thickness, the diffusion-controlled rate is w/2 order in initiator rate and inverse first-order in film thickness. Dependence of the diffusion-controlled rate on monomer is dependent in a complex manner on the diffusional characteristics of the reaction system. 11 figures, 4 tables

  1. Accurate reaction-diffusion operator splitting on tetrahedral meshes for parallel stochastic molecular simulations

    Energy Technology Data Exchange (ETDEWEB)

    Hepburn, I.; De Schutter, E., E-mail: erik@oist.jp [Computational Neuroscience Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904 0495 (Japan); Theoretical Neurobiology & Neuroengineering, University of Antwerp, Antwerp 2610 (Belgium); Chen, W. [Computational Neuroscience Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904 0495 (Japan)

    2016-08-07

    Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realistic biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.

  2. Parametric spatiotemporal oscillation in reaction-diffusion systems.

    Science.gov (United States)

    Ghosh, Shyamolina; Ray, Deb Shankar

    2016-03-01

    We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnold's tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.

  3. Inertial effects in diffusion-limited reactions

    International Nuclear Information System (INIS)

    Dorsaz, N; Foffi, G; De Michele, C; Piazza, F

    2010-01-01

    Diffusion-limited reactions are commonly found in biochemical processes such as enzyme catalysis, colloid and protein aggregation and binding between different macromolecules in cells. Usually, such reactions are modeled within the Smoluchowski framework by considering purely diffusive boundary problems. However, inertial effects are not always negligible in real biological or physical media on typical observation time frames. This is all the more so for non-bulk phenomena involving physical boundaries, that introduce additional time and space constraints. In this paper, we present and test a novel numerical scheme, based on event-driven Brownian dynamics, that allows us to explore a wide range of velocity relaxation times, from the purely diffusive case to the underdamped regime. We show that our algorithm perfectly reproduces the solution of the Fokker-Planck problem with absorbing boundary conditions in all the regimes considered and is thus a good tool for studying diffusion-guided reactions in complex biological environments.

  4. Field theory of propagating reaction-diffusion fronts

    International Nuclear Information System (INIS)

    Escudero, C.

    2004-01-01

    The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean-field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to be taken into account. Here, we construct an analytic theory connecting the first principles of the reaction-diffusion process to an effective equation of motion via field-theoretic arguments, and we arrive at results already confirmed by numerical simulations

  5. The two-regime method for optimizing stochastic reaction-diffusion simulations

    KAUST Repository

    Flegg, M. B.

    2011-10-19

    Spatial organization and noise play an important role in molecular systems biology. In recent years, a number of software packages have been developed for stochastic spatio-temporal simulation, ranging from detailed molecular-based approaches to less detailed compartment-based simulations. Compartment-based approaches yield quick and accurate mesoscopic results, but lack the level of detail that is characteristic of the computationally intensive molecular-based models. Often microscopic detail is only required in a small region (e.g. close to the cell membrane). Currently, the best way to achieve microscopic detail is to use a resource-intensive simulation over the whole domain. We develop the two-regime method (TRM) in which a molecular-based algorithm is used where desired and a compartment-based approach is used elsewhere. We present easy-to-implement coupling conditions which ensure that the TRM results have the same accuracy as a detailed molecular-based model in the whole simulation domain. Therefore, the TRM combines strengths of previously developed stochastic reaction-diffusion software to efficiently explore the behaviour of biological models. Illustrative examples and the mathematical justification of the TRM are also presented.

  6. 4D Biofabrication of Branching Multicellular Structures: A Morphogenesis Simulation Based on Turing’s Reaction-Diffusion Dynamics

    Science.gov (United States)

    Zhu, Xiaolu; Yang, Hao

    2017-12-01

    The recently emerged four-dimensional (4D) biofabrication technique aims to create dynamic three-dimensional (3D) biological structures that can transform their shapes or functionalities with time when an external stimulus is imposed or when cell postprinting self-assembly occurs. The evolution of 3D pattern of branching geometry via self-assembly of cells is critical for 4D biofabrication of artificial organs or tissues with branched geometry. However, it is still unclear that how the formation and evolution of these branching pattern are biologically encoded. We study the 4D fabrication of lung branching structures utilizing a simulation model on the reaction-diffusion mechanism, which is established using partial differential equations of four variables, describing the reaction and diffusion process of morphogens with time during the development process of lung branching. The simulation results present the forming process of 3D branching pattern, and also interpret the behaviors of side branching and tip splitting as the stalk growing, through 3D visualization of numerical simulation.

  7. Combining molecular dynamics with mesoscopic Green’s function reaction dynamics simulations

    Energy Technology Data Exchange (ETDEWEB)

    Vijaykumar, Adithya, E-mail: vijaykumar@amolf.nl [FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam (Netherlands); van ’t Hoff Institute for Molecular Sciences, University of Amsterdam, P.O. Box 94157, 1090 GD Amsterdam (Netherlands); Bolhuis, Peter G. [van ’t Hoff Institute for Molecular Sciences, University of Amsterdam, P.O. Box 94157, 1090 GD Amsterdam (Netherlands); Rein ten Wolde, Pieter, E-mail: p.t.wolde@amolf.nl [FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam (Netherlands)

    2015-12-07

    In many reaction-diffusion processes, ranging from biochemical networks, catalysis, to complex self-assembly, the spatial distribution of the reactants and the stochastic character of their interactions are crucial for the macroscopic behavior. The recently developed mesoscopic Green’s Function Reaction Dynamics (GFRD) method enables efficient simulation at the particle level provided the microscopic dynamics can be integrated out. Yet, many processes exhibit non-trivial microscopic dynamics that can qualitatively change the macroscopic behavior, calling for an atomistic, microscopic description. We propose a novel approach that combines GFRD for simulating the system at the mesoscopic scale where particles are far apart, with a microscopic technique such as Langevin dynamics or Molecular Dynamics (MD), for simulating the system at the microscopic scale where reactants are in close proximity. This scheme defines the regions where the particles are close together and simulated with high microscopic resolution and those where they are far apart and simulated with lower mesoscopic resolution, adaptively on the fly. The new multi-scale scheme, called MD-GFRD, is generic and can be used to efficiently simulate reaction-diffusion systems at the particle level.

  8. Combining molecular dynamics with mesoscopic Green’s function reaction dynamics simulations

    International Nuclear Information System (INIS)

    Vijaykumar, Adithya; Bolhuis, Peter G.; Rein ten Wolde, Pieter

    2015-01-01

    In many reaction-diffusion processes, ranging from biochemical networks, catalysis, to complex self-assembly, the spatial distribution of the reactants and the stochastic character of their interactions are crucial for the macroscopic behavior. The recently developed mesoscopic Green’s Function Reaction Dynamics (GFRD) method enables efficient simulation at the particle level provided the microscopic dynamics can be integrated out. Yet, many processes exhibit non-trivial microscopic dynamics that can qualitatively change the macroscopic behavior, calling for an atomistic, microscopic description. We propose a novel approach that combines GFRD for simulating the system at the mesoscopic scale where particles are far apart, with a microscopic technique such as Langevin dynamics or Molecular Dynamics (MD), for simulating the system at the microscopic scale where reactants are in close proximity. This scheme defines the regions where the particles are close together and simulated with high microscopic resolution and those where they are far apart and simulated with lower mesoscopic resolution, adaptively on the fly. The new multi-scale scheme, called MD-GFRD, is generic and can be used to efficiently simulate reaction-diffusion systems at the particle level

  9. Reaction-Diffusion Automata Phenomenology, Localisations, Computation

    CERN Document Server

    Adamatzky, Andrew

    2013-01-01

    Reaction-diffusion and excitable media are amongst most intriguing substrates. Despite apparent simplicity of the physical processes involved the media exhibit a wide range of amazing patterns: from target and spiral waves to travelling localisations and stationary breathing patterns. These media are at the heart of most natural processes, including morphogenesis of living beings, geological formations, nervous and muscular activity, and socio-economic developments.   This book explores a minimalist paradigm of studying reaction-diffusion and excitable media using locally-connected networks of finite-state machines: cellular automata and automata on proximity graphs. Cellular automata are marvellous objects per se because they show us how to generate and manage complexity using very simple rules of dynamical transitions. When combined with the reaction-diffusion paradigm the cellular automata become an essential user-friendly tool for modelling natural systems and designing future and emergent computing arch...

  10. ReaDDy--a software for particle-based reaction-diffusion dynamics in crowded cellular environments.

    Directory of Open Access Journals (Sweden)

    Johannes Schöneberg

    Full Text Available We introduce the software package ReaDDy for simulation of detailed spatiotemporal mechanisms of dynamical processes in the cell, based on reaction-diffusion dynamics with particle resolution. In contrast to other particle-based reaction kinetics programs, ReaDDy supports particle interaction potentials. This permits effects such as space exclusion, molecular crowding and aggregation to be modeled. The biomolecules simulated can be represented as a sphere, or as a more complex geometry such as a domain structure or polymer chain. ReaDDy bridges the gap between small-scale but highly detailed molecular dynamics or Brownian dynamics simulations and large-scale but little-detailed reaction kinetics simulations. ReaDDy has a modular design that enables the exchange of the computing core by efficient platform-specific implementations or dynamical models that are different from Brownian dynamics.

  11. Modeling of the interplay between single-file diffusion and conversion reaction in mesoporous systems

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Jing [Iowa State Univ., Ames, IA (United States)

    2013-01-11

    We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. A strict single-file (no passing) constraint occurs in the diffusion within such narrow pores. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice–gas model for this reaction–diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction–diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction–diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion (SFD) in this multispecies system. Noting the shortcomings of mf-RDE and h-RDE, we then develop a generalized hydrodynamic (GH) formulation of appropriate gh-RDE which incorporates an unconventional description of chemical diffusion in mixed-component quasi-single-file systems based on a refined picture of tracer diffusion for finite-length pores. The gh-RDE elucidate the non-exponential decay of the steady-state reactant concentration into the pore and the non-mean-field scaling of the reactant penetration depth. Then an extended model of a catalytic conversion reaction within a functionalized nanoporous material is developed to assess the effect of varying the reaction product – pore interior interaction from attractive to repulsive. The analysis is performed utilizing the generalized hydrodynamic formulation of the reaction-diffusion equations which can reliably capture the complex interplay between reaction and restricted transport for both irreversible and reversible reactions.

  12. Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

    Science.gov (United States)

    Owolabi, Kolade M.

    2018-03-01

    In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

  13. Effective reaction rates in diffusion-limited phosphorylation-dephosphorylation cycles

    Science.gov (United States)

    Szymańska, Paulina; Kochańczyk, Marek; Miekisz, Jacek; Lipniacki, Tomasz

    2015-02-01

    We investigate the kinetics of the ubiquitous phosphorylation-dephosphorylation cycle on biological membranes by means of kinetic Monte Carlo simulations on the triangular lattice. We establish the dependence of effective macroscopic reaction rate coefficients as well as the steady-state phosphorylated substrate fraction on the diffusion coefficient and concentrations of opposing enzymes: kinases and phosphatases. In the limits of zero and infinite diffusion, the numerical results agree with analytical predictions; these two limits give the lower and the upper bound for the macroscopic rate coefficients, respectively. In the zero-diffusion limit, which is important in the analysis of dense systems, phosphorylation and dephosphorylation reactions can convert only these substrates which remain in contact with opposing enzymes. In the most studied regime of nonzero but small diffusion, a contribution linearly proportional to the diffusion coefficient appears in the reaction rate. In this regime, the presence of opposing enzymes creates inhomogeneities in the (de)phosphorylated substrate distributions: The spatial correlation function shows that enzymes are surrounded by clouds of converted substrates. This effect becomes important at low enzyme concentrations, substantially lowering effective reaction rates. Effective reaction rates decrease with decreasing diffusion and this dependence is more pronounced for the less-abundant enzyme. Consequently, the steady-state fraction of phosphorylated substrates can increase or decrease with diffusion, depending on relative concentrations of both enzymes. Additionally, steady states are controlled by molecular crowders which, mostly by lowering the effective diffusion of reactants, favor the more abundant enzyme.

  14. Towards reaction-diffusion computing devices based on minority-carrier transport in semiconductors

    International Nuclear Information System (INIS)

    Asai, Tetsuya; Adamatzky, Andrew; Amemiya, Yoshihito

    2004-01-01

    Reaction-diffusion (RD) chemical systems are known to realize sensible computation when both data and results of the computation are encoded in concentration profiles of chemical species; the computation is implemented via spreading and interaction of either diffusive or phase waves. Thin-layer chemical systems are thought of therefore as massively-parallel locally-connected computing devices, where micro-volume of the medium is analogous to an elementary processor. Practical applications of the RD chemical systems are reduced however due to very low speed of traveling waves which makes real-time computation senseless. To overcome the speed-limitations while preserving unique features of RD computers we propose a semiconductor RD computing device where minority carriers diffuse as chemical species and reaction elements are represented by p-n-p-n diodes. We offer blue-prints of the RD semiconductor devices, and study in computer simulation propagation phenomena of the density wave of minority carriers. We then demonstrate what computational problems can be solved in RD semiconductor devices and evaluate space-time complexity of computation in the devices

  15. Diffusive epidemic process: theory and simulation

    International Nuclear Information System (INIS)

    Maia, Daniel Souza; Dickman, Ronald

    2007-01-01

    We study the continuous absorbing-state phase transition in the one-dimensional diffusive epidemic process via mean-field theory and Monte Carlo simulation. In this model, particles of two species (A and B) hop on a lattice and undergo reactions B → A and A+B → 2B; the total particle number is conserved. We formulate the model as a continuous-time Markov process described by a master equation. A phase transition between the (absorbing) B-free state and an active state is observed as the parameters (reaction and diffusion rates, and total particle density) are varied. Mean-field theory reveals a surprising, nonmonotonic dependence of the critical recovery rate on the diffusion rate of B particles. A computational realization of the process that is faithful to the transition rates defining the model is devised, allowing for direct comparison with theory. Using the quasi-stationary simulation method we determine the order parameter and the survival time in systems of up to 4000 sites. Due to strong finite-size effects, the results converge only for large system sizes. We find no evidence for a discontinuous transition. Our results are consistent with the existence of three distinct universality classes, depending on whether A particles diffusive more rapidly, less rapidly or at the same rate as B particles. We also perform quasi-stationary simulations of the triplet creation model, which yield results consistent with a discontinuous transition at high diffusion rates

  16. Simulation of reaction diffusion processes over biologically relevant size and time scales using multi-GPU workstations.

    Science.gov (United States)

    Hallock, Michael J; Stone, John E; Roberts, Elijah; Fry, Corey; Luthey-Schulten, Zaida

    2014-05-01

    Simulation of in vivo cellular processes with the reaction-diffusion master equation (RDME) is a computationally expensive task. Our previous software enabled simulation of inhomogeneous biochemical systems for small bacteria over long time scales using the MPD-RDME method on a single GPU. Simulations of larger eukaryotic systems exceed the on-board memory capacity of individual GPUs, and long time simulations of modest-sized cells such as yeast are impractical on a single GPU. We present a new multi-GPU parallel implementation of the MPD-RDME method based on a spatial decomposition approach that supports dynamic load balancing for workstations containing GPUs of varying performance and memory capacity. We take advantage of high-performance features of CUDA for peer-to-peer GPU memory transfers and evaluate the performance of our algorithms on state-of-the-art GPU devices. We present parallel e ciency and performance results for simulations using multiple GPUs as system size, particle counts, and number of reactions grow. We also demonstrate multi-GPU performance in simulations of the Min protein system in E. coli . Moreover, our multi-GPU decomposition and load balancing approach can be generalized to other lattice-based problems.

  17. Reaction-diffusion pulses: a combustion model

    International Nuclear Information System (INIS)

    Campos, Daniel; Llebot, Josep Enric; Fort, Joaquim

    2004-01-01

    We focus on a reaction-diffusion approach proposed recently for experiments on combustion processes, where the heat released by combustion follows first-order reaction kinetics. This case allows us to perform an exhaustive analytical study. Specifically, we obtain the exact expressions for the speed of the thermal pulses, their maximum temperature and the condition of self-sustenance. Finally, we propose two generalizations of the model, namely, the case of several reactants burning together, and that of time-delayed heat conduction. We find an excellent agreement between our analytical results and simulations

  18. Reaction-diffusion pulses: a combustion model

    Energy Technology Data Exchange (ETDEWEB)

    Campos, Daniel [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Llebot, Josep Enric [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Fort, Joaquim [Dept. de FIsica, Univ. de Girona, Campus de Montilivi, 17071 Girona, Catalonia (Spain)

    2004-07-02

    We focus on a reaction-diffusion approach proposed recently for experiments on combustion processes, where the heat released by combustion follows first-order reaction kinetics. This case allows us to perform an exhaustive analytical study. Specifically, we obtain the exact expressions for the speed of the thermal pulses, their maximum temperature and the condition of self-sustenance. Finally, we propose two generalizations of the model, namely, the case of several reactants burning together, and that of time-delayed heat conduction. We find an excellent agreement between our analytical results and simulations.

  19. Agent-based simulation of reactions in the crowded and structured intracellular environment: Influence of mobility and location of the reactants

    Directory of Open Access Journals (Sweden)

    Lapin Alexei

    2011-05-01

    Full Text Available Abstract Background In this paper we apply a novel agent-based simulation method in order to model intracellular reactions in detail. The simulations are performed within a virtual cytoskeleton enriched with further crowding elements, which allows the analysis of molecular crowding effects on intracellular diffusion and reaction rates. The cytoskeleton network leads to a reduction in the mobility of molecules. Molecules can also unspecifically bind to membranes or the cytoskeleton affecting (i the fraction of unbound molecules in the cytosol and (ii furthermore reducing the mobility. Binding of molecules to intracellular structures or scaffolds can in turn lead to a microcompartmentalization of the cell. Especially the formation of enzyme complexes promoting metabolic channeling, e.g. in glycolysis, depends on the co-localization of the proteins. Results While the co-localization of enzymes leads to faster reaction rates, the reduced mobility decreases the collision rate of reactants, hence reducing the reaction rate, as expected. This effect is most prominent in diffusion limited reactions. Furthermore, anomalous diffusion can occur due to molecular crowding in the cell. In the context of diffusion controlled reactions, anomalous diffusion leads to fractal reaction kinetics. The simulation framework is used to quantify and separate the effects originating from molecular crowding or the reduced mobility of the reactants. We were able to define three factors which describe the effective reaction rate, namely f diff for the diffusion effect, f volume for the crowding, and f access for the reduced accessibility of the molecules. Conclusions Molecule distributions, reaction rate constants and structural parameters can be adjusted separately in the simulation allowing a comprehensive study of individual effects in the context of a realistic cell environment. As such, the present simulation can help to bridge the gap between in vivo and in vitro

  20. Diffusion-controlled reactions modeling in Geant4-DNA

    Energy Technology Data Exchange (ETDEWEB)

    Karamitros, M., E-mail: matkara@gmail.com [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France); CNRS, INCIA, UMR 5287, F-33400 Talence (France); Luan, S. [University of New Mexico, Department of Computer Science, Albuquerque, NM (United States); Bernal, M.A. [Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, SP (Brazil); Allison, J. [Geant4 Associates International Ltd (United Kingdom); Baldacchino, G. [CEA Saclay, IRAMIS, LIDYL, Radiation Physical Chemistry Group, F-91191 Gif sur Yvette Cedex (France); CNRS, UMR3299, SIS2M, F-91191 Gif sur Yvette Cedex (France); Davidkova, M. [Nuclear Physics Institute of the ASCR, Prague (Czech Republic); Francis, Z. [Saint Joseph University, Faculty of Sciences, Department of Physics, Mkalles, Beirut (Lebanon); Friedland, W. [Helmholtz Zentrum München, German Research Center for Environmental Health, Institute of Radiation Protection, Ingolstädter Landstr. 1, 85764 Neuherberg (Germany); Ivantchenko, V. [Ecoanalytica, 119899 Moscow (Russian Federation); Geant4 Associates International Ltd (United Kingdom); Ivantchenko, A. [Geant4 Associates International Ltd (United Kingdom); Mantero, A. [SwHaRD s.r.l., via Buccari 9, 16153 Genova (Italy); Nieminem, P.; Santin, G. [ESA-ESTEC, 2200 AG Noordwijk (Netherlands); Tran, H.N. [Division of Nuclear Physics and Faculty of Applied Sciences, Ton Duc Thang University, Tan Phong Ward, District 7, Ho Chi Minh City (Viet Nam); Stepan, V. [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France); Nuclear Physics Institute of the ASCR, Prague (Czech Republic); Incerti, S., E-mail: incerti@cenbg.in2p3.fr [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France)

    2014-10-01

    Context Under irradiation, a biological system undergoes a cascade of chemical reactions that can lead to an alteration of its normal operation. There are different types of radiation and many competing reactions. As a result the kinetics of chemical species is extremely complex. The simulation becomes then a powerful tool which, by describing the basic principles of chemical reactions, can reveal the dynamics of the macroscopic system. To understand the dynamics of biological systems under radiation, since the 80s there have been on-going efforts carried out by several research groups to establish a mechanistic model that consists in describing all the physical, chemical and biological phenomena following the irradiation of single cells. This approach is generally divided into a succession of stages that follow each other in time: (1) the physical stage, where the ionizing particles interact directly with the biological material; (2) the physico-chemical stage, where the targeted molecules release their energy by dissociating, creating new chemical species; (3) the chemical stage, where the new chemical species interact with each other or with the biomolecules; (4) the biological stage, where the repairing mechanisms of the cell come into play. This article focuses on the modeling of the chemical stage. Method This article presents a general method of speeding-up chemical reaction simulations in fluids based on the Smoluchowski equation and Monte-Carlo methods, where all molecules are explicitly simulated and the solvent is treated as a continuum. The model describes diffusion-controlled reactions. This method has been implemented in Geant4-DNA. The keys to the new algorithm include: (1) the combination of a method to compute time steps dynamically with a Brownian bridge process to account for chemical reactions, which avoids costly fixed time step simulations; (2) a k–d tree data structure for quickly locating, for a given molecule, its closest reactants. The

  1. Synchronization criteria for generalized reaction-diffusion neural networks via periodically intermittent control.

    Science.gov (United States)

    Gan, Qintao; Lv, Tianshi; Fu, Zhenhua

    2016-04-01

    In this paper, the synchronization problem for a class of generalized neural networks with time-varying delays and reaction-diffusion terms is investigated concerning Neumann boundary conditions in terms of p-norm. The proposed generalized neural networks model includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks as its special cases. By establishing a new inequality, some simple and useful conditions are obtained analytically to guarantee the global exponential synchronization of the addressed neural networks under the periodically intermittent control. According to the theoretical results, the influences of diffusion coefficients, diffusion space, and control rate on synchronization are analyzed. Finally, the feasibility and effectiveness of the proposed methods are shown by simulation examples, and by choosing different diffusion coefficients, diffusion spaces, and control rates, different controlled synchronization states can be obtained.

  2. Diffusion limited reactions in crystalline solids

    International Nuclear Information System (INIS)

    Fastenau, R.

    1982-01-01

    Diffusion limited reactions in crystal lattices are studied with diffusion and random walk theory. First the random walk on a crystal lattice is studied. These results are used in a formal study of diffusion limited reactions in which the following simplified traps are discussed: planes, cylinders, spheres, disks and rings. The traps are either present at the start of the process (annealing) or fed into the crystal at a constant rate (continuous production). For the study of trapping processes occurring in real crystals it was necessary to investigate the interaction of the reacting species on the atomic level. Using lattice relaxation calculations, several reactions were studied. These calculations result in a model for the potential energy of the crystal versus the separation of the reaction partners. This model is used in Monte Carlo simulations of the trapping process, which are made at a high trap density, since the extrapolation to the low density regime can be made using the formal part of this work. The following reactions were studied: the trapping of interstitial helium atoms by vacancies, self interstitial vacancy recombination, the trapping of vacancies by immobile, helium filled, vacancies and the capture of self interstitials and vacancies by dislocations. A part of these results is used in two models for the low temperature nucleation and growth of bubbles due to helium bombardment. The models described give the right bubble density versus helium dose, but differ widely in the fraction of helium present in the bubbles found. A mechanism of blistering based on a percolation effect is also discussed. (Auth.)

  3. Numerical simulation of alteration of sodium bentonite by diffusion of ionic groundwater components

    International Nuclear Information System (INIS)

    Jacobsen, J.S.; Carnahan, C.L.

    1987-12-01

    Experiments measuring the movement of trace amounts of radionuclides through compacted bentonite have typically used unaltered bentonite. Models based on experiments such as these may not lead to accurate predictions of the migration through altered or partially altered bentonite of radionuclides that undergo ion exchange. To address this problem, we have modified an existing transport code to include ion exchange and aqueous complexation reactions. The code is thus able to simulate the diffusion of major ionic groundwater components through bentonite and reactions between the bentonite and groundwater. Numerical simulations have been made to investigate the conversion of sodium bentonite to calcium bentonite for a reference groundwater characteristic of deep granitic formations. 20 refs., 2 figs., 2 tabs

  4. External boundary effects on simultaneous diffusion and reaction processes

    International Nuclear Information System (INIS)

    Le Roux, M.N.; Wilhelmsson, H.

    1989-01-01

    External boundaries influence the spatial and temporal structure of evolution of dynamic systems governed by reaction-diffusion equations. Critical limits, i.e. thresholds for explosive growth or onset of diffusion dominated decay, are found to be caused by the presence of the boundary and to depend on: the position of the boundary, where the density is assumed to be zero at any instant of time: the mutual weights (coefficients) and powers of the nonlinear reaction and diffusion processes; and the initial spatial distribution. However, for particular relations between the nonlinear powers of the reaction and diffusion terms the critical limits do not depend on the initial conditions. The results are obtained by simulation experiment for one, two and three dimensions. Trends in the dynamic evolution of the system with an external boundary imposed are compared with the corresponding analytic results obtained for free boundary. Interesting applications are found in various areas, e.g. in the field of high temperature fusion plasma where the evolution of the temperature profile for the so-called H-mode (constant plasma density) is described

  5. Reaction-diffusion systems in intracellular molecular transport and control.

    Science.gov (United States)

    Soh, Siowling; Byrska, Marta; Kandere-Grzybowska, Kristiana; Grzybowski, Bartosz A

    2010-06-07

    Chemical reactions make cells work only if the participating chemicals are delivered to desired locations in a timely and precise fashion. Most research to date has focused on active-transport mechanisms, although passive diffusion is often equally rapid and energetically less costly. Capitalizing on these advantages, cells have developed sophisticated reaction-diffusion (RD) systems that control a wide range of cellular functions-from chemotaxis and cell division, through signaling cascades and oscillations, to cell motility. These apparently diverse systems share many common features and are "wired" according to "generic" motifs such as nonlinear kinetics, autocatalysis, and feedback loops. Understanding the operation of these complex (bio)chemical systems requires the analysis of pertinent transport-kinetic equations or, at least on a qualitative level, of the characteristic times of the constituent subprocesses. Therefore, in reviewing the manifestations of cellular RD, we also describe basic theory of reaction-diffusion phenomena.

  6. Delay-induced wave instabilities in single-species reaction-diffusion systems

    Science.gov (United States)

    Otto, Andereas; Wang, Jian; Radons, Günter

    2017-11-01

    The Turing (wave) instability is only possible in reaction-diffusion systems with more than one (two) components. Motivated by the fact that a time delay increases the dimension of a system, we investigate the presence of diffusion-driven instabilities in single-species reaction-diffusion systems with delay. The stability of arbitrary one-component systems with a single discrete delay, with distributed delay, or with a variable delay is systematically analyzed. We show that a wave instability can appear from an equilibrium of single-species reaction-diffusion systems with fluctuating or distributed delay, which is not possible in similar systems with constant discrete delay or without delay. More precisely, we show by basic analytic arguments and by numerical simulations that fast asymmetric delay fluctuations or asymmetrically distributed delays can lead to wave instabilities in these systems. Examples, for the resulting traveling waves are shown for a Fisher-KPP equation with distributed delay in the reaction term. In addition, we have studied diffusion-induced instabilities from homogeneous periodic orbits in the same systems with variable delay, where the homogeneous periodic orbits are attracting resonant periodic solutions of the system without diffusion, i.e., periodic orbits of the Hutchinson equation with time-varying delay. If diffusion is introduced, standing waves can emerge whose temporal period is equal to the period of the variable delay.

  7. Amplitude equations for a sub-diffusive reaction-diffusion system

    International Nuclear Information System (INIS)

    Nec, Y; Nepomnyashchy, A A

    2008-01-01

    A sub-diffusive reaction-diffusion system with a positive definite memory operator and a nonlinear reaction term is analysed. Amplitude equations (Ginzburg-Landau type) are derived for short wave (Turing) and long wave (Hopf) bifurcation points

  8. Internal Diffusion-Controlled Enzyme Reaction: The Acetylcholinesterase Kinetics.

    Science.gov (United States)

    Lee, Sangyun; Kim, Ji-Hyun; Lee, Sangyoub

    2012-02-14

    Acetylcholinesterase is an enzyme with a very high turnover rate; it quenches the neurotransmitter, acetylcholine, at the synapse. We have investigated the kinetics of the enzyme reaction by calculating the diffusion rate of the substrate molecule along an active site channel inside the enzyme from atomic-level molecular dynamics simulations. In contrast to the previous works, we have found that the internal substrate diffusion is the determinant of the acetylcholinesterase kinetics in the low substrate concentration limit. Our estimate of the overall bimolecular reaction rate constant for the enzyme is in good agreement with the experimental data. In addition, the present calculation provides a reasonable explanation for the effects of the ionic strength of solution and the mutation of surface residues of the enzyme. The study suggests that internal diffusion of the substrate could be a key factor in understanding the kinetics of enzymes of similar characteristics.

  9. Reaction-diffusion fronts with inhomogeneous initial conditions

    Energy Technology Data Exchange (ETDEWEB)

    Bena, I [Departement de Physique Theorique, Universite de Geneve, CH-1211 Geneva 4 (Switzerland); Droz, M [Departement de Physique Theorique, Universite de Geneve, CH-1211 Geneva 4 (Switzerland); Martens, K [Departement de Physique Theorique, Universite de Geneve, CH-1211 Geneva 4 (Switzerland); Racz, Z [Institute for Theoretical Physics, Eoetvoes University, 1117 Budapest (Hungary)

    2007-02-14

    Properties of reaction zones resulting from A+B {yields} C type reaction-diffusion processes are investigated by analytical and numerical methods. The reagents A and B are separated initially and, in addition, there is an initial macroscopic inhomogeneity in the distribution of the B species. For simple two-dimensional geometries, exact analytical results are presented for the time evolution of the geometric shape of the front. We also show using cellular automata simulations that the fluctuations can be neglected both in the shape and in the width of the front.

  10. Aerosol simulation including chemical and nuclear reactions

    International Nuclear Information System (INIS)

    Marwil, E.S.; Lemmon, E.C.

    1985-01-01

    The numerical simulation of aerosol transport, including the effects of chemical and nuclear reactions presents a challenging dynamic accounting problem. Particles of different sizes agglomerate and settle out due to various mechanisms, such as diffusion, diffusiophoresis, thermophoresis, gravitational settling, turbulent acceleration, and centrifugal acceleration. Particles also change size, due to the condensation and evaporation of materials on the particle. Heterogeneous chemical reactions occur at the interface between a particle and the suspending medium, or a surface and the gas in the aerosol. Homogeneous chemical reactions occur within the aersol suspending medium, within a particle, and on a surface. These reactions may include a phase change. Nuclear reactions occur in all locations. These spontaneous transmutations from one element form to another occur at greatly varying rates and may result in phase or chemical changes which complicate the accounting process. This paper presents an approach for inclusion of these effects on the transport of aerosols. The accounting system is very complex and results in a large set of stiff ordinary differential equations (ODEs). The techniques for numerical solution of these ODEs require special attention to achieve their solution in an efficient and affordable manner. 4 refs

  11. Turbulent diffusion of chemically reacting flows: Theory and numerical simulations.

    Science.gov (United States)

    Elperin, T; Kleeorin, N; Liberman, M; Lipatnikov, A N; Rogachevskii, I; Yu, R

    2017-11-01

    The theory of turbulent diffusion of chemically reacting gaseous admixtures developed previously [T. Elperin et al., Phys. Rev. E 90, 053001 (2014)PLEEE81539-375510.1103/PhysRevE.90.053001] is generalized for large yet finite Reynolds numbers and the dependence of turbulent diffusion coefficient on two parameters, the Reynolds number and Damköhler number (which characterizes a ratio of turbulent and reaction time scales), is obtained. Three-dimensional direct numerical simulations (DNSs) of a finite-thickness reaction wave for the first-order chemical reactions propagating in forced, homogeneous, isotropic, and incompressible turbulence are performed to validate the theoretically predicted effect of chemical reactions on turbulent diffusion. It is shown that the obtained DNS results are in good agreement with the developed theory.

  12. The time dependent propensity function for acceleration of spatial stochastic simulation of reaction–diffusion systems

    International Nuclear Information System (INIS)

    Fu, Jin; Wu, Sheng; Li, Hong; Petzold, Linda R.

    2014-01-01

    The inhomogeneous stochastic simulation algorithm (ISSA) is a fundamental method for spatial stochastic simulation. However, when diffusion events occur more frequently than reaction events, simulating the diffusion events by ISSA is quite costly. To reduce this cost, we propose to use the time dependent propensity function in each step. In this way we can avoid simulating individual diffusion events, and use the time interval between two adjacent reaction events as the simulation stepsize. We demonstrate that the new algorithm can achieve orders of magnitude efficiency gains over widely-used exact algorithms, scales well with increasing grid resolution, and maintains a high level of accuracy

  13. Control of transversal instabilities in reaction-diffusion systems

    Science.gov (United States)

    Totz, Sonja; Löber, Jakob; Totz, Jan Frederik; Engel, Harald

    2018-05-01

    In two-dimensional reaction-diffusion systems, local curvature perturbations on traveling waves are typically damped out and vanish. However, if the inhibitor diffuses much faster than the activator, transversal instabilities can arise, leading from flat to folded, spatio-temporally modulated waves and to spreading spiral turbulence. Here, we propose a scheme to induce or inhibit these instabilities via a spatio-temporal feedback loop. In a piecewise-linear version of the FitzHugh–Nagumo model, transversal instabilities and spiral turbulence in the uncontrolled system are shown to be suppressed in the presence of control, thereby stabilizing plane wave propagation. Conversely, in numerical simulations with the modified Oregonator model for the photosensitive Belousov–Zhabotinsky reaction, which does not exhibit transversal instabilities on its own, we demonstrate the feasibility of inducing transversal instabilities and study the emerging wave patterns in a well-controlled manner.

  14. Soft tissue deformation modelling through neural dynamics-based reaction-diffusion mechanics.

    Science.gov (United States)

    Zhang, Jinao; Zhong, Yongmin; Gu, Chengfan

    2018-05-30

    Soft tissue deformation modelling forms the basis of development of surgical simulation, surgical planning and robotic-assisted minimally invasive surgery. This paper presents a new methodology for modelling of soft tissue deformation based on reaction-diffusion mechanics via neural dynamics. The potential energy stored in soft tissues due to a mechanical load to deform tissues away from their rest state is treated as the equivalent transmembrane potential energy, and it is distributed in the tissue masses in the manner of reaction-diffusion propagation of nonlinear electrical waves. The reaction-diffusion propagation of mechanical potential energy and nonrigid mechanics of motion are combined to model soft tissue deformation and its dynamics, both of which are further formulated as the dynamics of cellular neural networks to achieve real-time computational performance. The proposed methodology is implemented with a haptic device for interactive soft tissue deformation with force feedback. Experimental results demonstrate that the proposed methodology exhibits nonlinear force-displacement relationship for nonlinear soft tissue deformation. Homogeneous, anisotropic and heterogeneous soft tissue material properties can be modelled through the inherent physical properties of mass points. Graphical abstract Soft tissue deformation modelling with haptic feedback via neural dynamics-based reaction-diffusion mechanics.

  15. TrackArt: the user friendly interface for single molecule tracking data analysis and simulation applied to complex diffusion in mica supported lipid bilayers.

    Science.gov (United States)

    Matysik, Artur; Kraut, Rachel S

    2014-05-01

    Single molecule tracking (SMT) analysis of fluorescently tagged lipid and protein probes is an attractive alternative to ensemble averaged methods such as fluorescence correlation spectroscopy (FCS) or fluorescence recovery after photobleaching (FRAP) for measuring diffusion in artificial and plasma membranes. The meaningful estimation of diffusion coefficients and their errors is however not straightforward, and is heavily dependent on sample type, acquisition method, and equipment used. Many approaches require advanced computing and programming skills for their implementation. Here we present TrackArt software, an accessible graphic interface for simulation and complex analysis of multiple particle paths. Imported trajectories can be filtered to eliminate spurious or corrupted tracks, and are then analyzed using several previously described methodologies, to yield single or multiple diffusion coefficients, their population fractions, and estimated errors. We use TrackArt to analyze the single-molecule diffusion behavior of a sphingolipid analog SM-Atto647N, in mica supported DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) bilayers. Fitting with a two-component diffusion model confirms the existence of two separate populations of diffusing particles in these bilayers on mica. As a demonstration of the TrackArt workflow, we characterize and discuss the effective activation energies required to increase the diffusion rates of these populations, obtained from Arrhenius plots of temperature-dependent diffusion. Finally, TrackArt provides a simulation module, allowing the user to generate models with multiple particle trajectories, diffusing with different characteristics. Maps of domains, acting as impermeable or permeable obstacles for particles diffusing with given rate constants and diffusion coefficients, can be simulated or imported from an image. Importantly, this allows one to use simulated data with a known diffusion behavior as a comparison for results

  16. Delay-induced Turing-like waves for one-species reaction-diffusion model on a network

    Science.gov (United States)

    Petit, Julien; Carletti, Timoteo; Asllani, Malbor; Fanelli, Duccio

    2015-09-01

    A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous perturbation. These are generalized Turing-like waves that materialize in a single-species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time-delayed differential equations. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz network and with the inclusion of the delay.

  17. Innovation Diffusion: Learner Benefits and Instructor Insights with the DIFFUSION SIMULATION GAME

    Science.gov (United States)

    Kovalik, Cindy L.; Kuo, Chia-Ling

    2012-01-01

    This research project investigated student reaction to playing the DIFFUSION SIMULATION GAME (DSG) and how an instructor, who is a novice in playing online games, implemented the DSG in an online higher education course. The goal of this research project was to determine whether playing the DSG helps students learn and apply course content. In…

  18. Investigation of the complex reaction coordinate of acid catalyzed amide hydrolysis from molecular dynamics simulations

    International Nuclear Information System (INIS)

    Zahn, Dirk

    2004-01-01

    The rate-determining step of acid catalyzed peptide hydrolysis is the nucleophilic attack of a water molecule to the carbon atom of the amide group. Therein the addition of the hydroxyl group to the amide carbon atom involves the association of a water molecule transferring one of its protons to an adjacent water molecule. The protonation of the amide nitrogen atom follows as a separate reaction step. Since the nucleophilic attack involves the breaking and formation of several bonds, the underlying reaction coordinate is rather complex. We investigate this reaction step from path sampling Car-Parrinello molecular dynamics simulations. This approach does not require the predefinition of reaction coordinates and is thus particularly suited for investigating reaction mechanisms. From our simulations the most relevant components of the reaction coordinate are elaborated. Though the C···O distance of the oxygen atom of the water molecule performing the nucleophilic attack and the corresponding amide carbon atom is a descriptor of the reaction progress, a complete picture of the reaction coordinate must include all three molecules taking part in the reaction. Moreover, the proton transfer is found to depend on favorable solvent configurations. Thus, also the arrangement of non-reacting, i.e. solvent water molecules needs to be considered in the reaction coordinate

  19. Dichotomous-noise-induced pattern formation in a reaction-diffusion system

    Science.gov (United States)

    Das, Debojyoti; Ray, Deb Shankar

    2013-06-01

    We consider a generic reaction-diffusion system in which one of the parameters is subjected to dichotomous noise by controlling the flow of one of the reacting species in a continuous-flow-stirred-tank reactor (CSTR) -membrane reactor. The linear stability analysis in an extended phase space is carried out by invoking Furutzu-Novikov procedure for exponentially correlated multiplicative noise to derive the instability condition in the plane of the noise parameters (correlation time and strength of the noise). We demonstrate that depending on the correlation time an optimal strength of noise governs the self-organization. Our theoretical analysis is corroborated by numerical simulations on pattern formation in a chlorine-dioxide-iodine-malonic acid reaction-diffusion system.

  20. Rigorous Multicomponent Reactive Separations Modelling: Complete Consideration of Reaction-Diffusion Phenomena

    International Nuclear Information System (INIS)

    Ahmadi, A.; Meyer, M.; Rouzineau, D.; Prevost, M.; Alix, P.; Laloue, N.

    2010-01-01

    This paper gives the first step of the development of a rigorous multicomponent reactive separation model. Such a model is highly essential to further the optimization of acid gases removal plants (CO 2 capture, gas treating, etc.) in terms of size and energy consumption, since chemical solvents are conventionally used. Firstly, two main modelling approaches are presented: the equilibrium-based and the rate-based approaches. Secondly, an extended rate-based model with rigorous modelling methodology for diffusion-reaction phenomena is proposed. The film theory and the generalized Maxwell-Stefan equations are used in order to characterize multicomponent interactions. The complete chain of chemical reactions is taken into account. The reactions can be kinetically controlled or at chemical equilibrium, and they are considered for both liquid film and liquid bulk. Thirdly, the method of numerical resolution is described. Coupling the generalized Maxwell-Stefan equations with chemical equilibrium equations leads to a highly non-linear Differential-Algebraic Equations system known as DAE index 3. The set of equations is discretized with finite-differences as its integration by Gear method is complex. The resulting algebraic system is resolved by the Newton- Raphson method. Finally, the present model and the associated methods of numerical resolution are validated for the example of esterification of methanol. This archetype non-electrolytic system permits an interesting analysis of reaction impact on mass transfer, especially near the phase interface. The numerical resolution of the model by Newton-Raphson method gives good results in terms of calculation time and convergence. The simulations show that the impact of reactions at chemical equilibrium and that of kinetically controlled reactions with high kinetics on mass transfer is relatively similar. Moreover, the Fick's law is less adapted for multicomponent mixtures where some abnormalities such as counter-diffusion

  1. Neutron-induced complex reaction analysis with 3D nuclear track simulation

    International Nuclear Information System (INIS)

    Sajo-Bohus, L.; Palfalvi, J.K.; Akatov, Yu.; Arevalo, O.; Greaves, E.D.; Nemeth, P.; Palacios, D.; Szabo, J.; Eoerdoegh, I.

    2005-01-01

    Complex (multiple) etched tracks are analysed through digitised images and 3D simulation by a purpose-built algorithm. From a binary track image an unfolding procedure is followed to generate a 3D track model, from which several track parameters are estimated. The method presented here allows the deposited energy, that originated from particle fragmentation or carbon spallation by means of induced tracks in commercially available PADC detectors, to be estimated. Results of evaluated nuclear tracks related to 12 C (n,3αn ' ) reaction are presented here. The detectors were exposed on the ISS in 2001

  2. Critical behavior in reaction-diffusion systems exhibiting absorbing phase transition

    CERN Document Server

    Ódor, G

    2003-01-01

    Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n>1 parents and where explicit diffusion of single particles (A) exists are reviewed. Arguments based on mean-field approximation and simulations are given which support novel kind of non-equilibrium criticality. These are in contradiction with the implications of a suggested phenomenological, multiplicative noise Langevin equation approach and with some of recent numerical analysis. Simulation results for the one and two dimensional binary spreading 2A -> 4A, 4A -> 2A model display a new type of mean-field criticality characterized by alpha=1/3 and beta=1/2 critical exponents suggested in cond-mat/0210615.

  3. GRIZZLY Model of Multi-Reactive Species Diffusion, Moisture/Heat Transfer and Alkali-Silica Reaction for Simulating Concrete Aging and Degradation

    Energy Technology Data Exchange (ETDEWEB)

    Huang, Hai [Idaho National Lab. (INL), Idaho Falls, ID (United States); Spencer, Benjamin W. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Cai, Guowei [Vanderbilt Univ., Nashville, TN (United States)

    2015-09-01

    Concrete is widely used in the construction of nuclear facilities because of its structural strength and its ability to shield radiation. The use of concrete in nuclear power plants for containment and shielding of radiation and radioactive materials has made its performance crucial for the safe operation of the facility. As such, when life extension is considered for nuclear power plants, it is critical to have accurate and reliable predictive tools to address concerns related to various aging processes of concrete structures and the capacity of structures subjected to age-related degradation. The goal of this report is to document the progress of the development and implementation of a fully coupled thermo-hydro-mechanical-chemical model in GRIZZLY code with the ultimate goal to reliably simulate and predict long-term performance and response of aged NPP concrete structures subjected to a number of aging mechanisms including external chemical attacks and volume-changing chemical reactions within concrete structures induced by alkali-silica reactions and long-term exposure to irradiation. Based on a number of survey reports of concrete aging mechanisms relevant to nuclear power plants and recommendations from researchers in concrete community, we’ve implemented three modules during FY15 in GRIZZLY code, (1) multi-species reactive diffusion model within cement materials; (2) coupled moisture and heat transfer model in concrete; and (3) anisotropic, stress-dependent, alkali-silica reaction induced swelling model. The multi-species reactive diffusion model was implemented with the objective to model aging of concrete structures subjected to aggressive external chemical attacks (e.g., chloride attack, sulfate attack, etc.). It considers multiple processes relevant to external chemical attacks such as diffusion of ions in aqueous phase within pore spaces, equilibrium chemical speciation reactions and kinetic mineral dissolution/precipitation. The moisture

  4. Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains

    KAUST Repository

    Madzvamuse, Anotida; Gaffney, Eamonn A.; Maini, Philip K.

    2009-01-01

    By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth. © Springer-Verlag 2009.

  5. Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains

    KAUST Repository

    Madzvamuse, Anotida

    2009-08-29

    By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth. © Springer-Verlag 2009.

  6. Probing the type of anomalous diffusion with single-particle tracking.

    Science.gov (United States)

    Ernst, Dominique; Köhler, Jürgen; Weiss, Matthias

    2014-05-07

    Many reactions in complex fluids, e.g. signaling cascades in the cytoplasm of living cells, are governed by a diffusion-driven encounter of reactants. Yet, diffusion in complex fluids often exhibits an anomalous characteristic ('subdiffusion'). Since different types of subdiffusion have distinct effects on timing and equilibria of chemical reactions, a thorough determination of the reactants' type of random walk is key to a quantitative understanding of reactions in complex fluids. Here we introduce a straightforward and simple approach for determining the type of subdiffusion from single-particle tracking data. Unlike previous approaches, our method also is sensitive to transient subdiffusion phenomena, e.g. obstructed diffusion below the percolation threshold. We validate our strategy with data from experiment and simulation.

  7. RKC time-stepping for advection-diffusion-reaction problems

    International Nuclear Information System (INIS)

    Verwer, J.G.; Sommeijer, B.P.; Hundsdorfer, W.

    2004-01-01

    The original explicit Runge-Kutta-Chebyshev (RKC) method is a stabilized second-order integration method for pure diffusion problems. Recently, it has been extended in an implicit-explicit manner to also incorporate highly stiff reaction terms. This implicit-explicit RKC method thus treats diffusion terms explicitly and the highly stiff reaction terms implicitly. The current paper deals with the incorporation of advection terms for the explicit method, thus aiming at the implicit-explicit RKC integration of advection-diffusion-reaction equations in a manner that advection and diffusion terms are treated simultaneously and explicitly and the highly stiff reaction terms implicitly

  8. Rethinking pattern formation in reaction-diffusion systems

    Science.gov (United States)

    Halatek, J.; Frey, E.

    2018-05-01

    The present theoretical framework for the analysis of pattern formation in complex systems is mostly limited to the vicinity of fixed (global) equilibria. Here we present a new theoretical approach to characterize dynamical states arbitrarily far from (global) equilibrium. We show that reaction-diffusion systems that are driven by locally mass-conserving interactions can be understood in terms of local equilibria of diffusively coupled compartments. Diffusive coupling generically induces lateral redistribution of the globally conserved quantities, and the variable local amounts of these quantities determine the local equilibria in each compartment. We find that, even far from global equilibrium, the system is well characterized by its moving local equilibria. We apply this framework to in vitro Min protein pattern formation, a paradigmatic model for biological pattern formation. Within our framework we can predict and explain transitions between chemical turbulence and order arbitrarily far from global equilibrium. Our results reveal conceptually new principles of self-organized pattern formation that may well govern diverse dynamical systems.

  9. Reaction diffusion in chromium-zircaloy-2 system

    International Nuclear Information System (INIS)

    Xiang Wenxin; Ying Shihao

    2001-01-01

    Reaction diffusion in the chromium-zircaloy-2 diffusion couples is investigated in the temperature range of 1023 - 1123 K. Scanning electron microscope (SEM) and energy dispersive spectrum (EDS) were used to measure the thickness of the reaction layer and to determine the Zr, Fe and Cr concentration penetrate profile in reaction layer, respectively. The growth kinetics of reaction layer has been studied and the results show that the growth of intermetallic compound is controlled by the process of volume diffusion as the layer growth approximately obeys the parabolic law. Interdiffusion coefficients were calculated using Boltzmann-Matano-Heumann model. Calculated interdiffusion coefficients were compared with those obtained on the condition that Cr dissolves in Zr and merely forms dilute solid solution. The comparison indicates that Cr diffuses in dilute solid solution is five orders of magnitude faster than in Zr(Fe, Cr) 2 intermetallic compound

  10. Turing instability in reaction-diffusion systems with nonlinear diffusion

    Energy Technology Data Exchange (ETDEWEB)

    Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)

    2013-10-15

    The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.

  11. Modeling of Reaction Processes Controlled by Diffusion

    International Nuclear Information System (INIS)

    Revelli, Jorge

    2003-01-01

    Stochastic modeling is quite powerful in science and technology.The technics derived from this process have been used with great success in laser theory, biological systems and chemical reactions.Besides, they provide a theoretical framework for the analysis of experimental results on the field of particle's diffusion in ordered and disordered materials.In this work we analyze transport processes in one-dimensional fluctuating media, which are media that change their state in time.This fact induces changes in the movements of the particles giving rise to different phenomena and dynamics that will be described and analyzed in this work.We present some random walk models to describe these fluctuating media.These models include state transitions governed by different dynamical processes.We also analyze the trapping problem in a lattice by means of a simple model which predicts a resonance-like phenomenon.Also we study effective diffusion processes over surfaces due to random walks in the bulk.We consider different boundary conditions and transitions movements.We derive expressions that describe diffusion behaviors constrained to bulk restrictions and the dynamic of the particles.Finally it is important to mention that the theoretical results obtained from the models proposed in this work are compared with Monte Carlo simulations.We find, in general, excellent agreements between the theory and the simulations

  12. Reaction probability derived from an interpolation formula for diffusion processes with an absorptive boundary condition

    International Nuclear Information System (INIS)

    Misawa, T.; Itakura, H.

    1995-01-01

    The present article focuses on a dynamical simulation of molecular motion in liquids. In the simulation involving diffusion-controlled reaction with discrete time steps, lack of information regarding the trajectory within the time step may result in a failure to count the number of reactions of the particles within the step. In order to rectify this, an interpolated diffusion process is used. The process is derived from a stochastic interpolation formula recently developed by the first author [J. Math. Phys. 34, 775 (1993)]. In this method, the probability that reaction has occurred during the time step given the initial and final positions of the particles is calculated. Some numerical examples confirm that the theoretical result corresponds to an improvement over the Clifford-Green work [Mol. Phys. 57, 123 (1986)] on the same matter

  13. PhreeqcRM: A reaction module for transport simulators based on the geochemical model PHREEQC

    Science.gov (United States)

    Parkhurst, David L.; Wissmeier, Laurin

    2015-01-01

    PhreeqcRM is a geochemical reaction module designed specifically to perform equilibrium and kinetic reaction calculations for reactive transport simulators that use an operator-splitting approach. The basic function of the reaction module is to take component concentrations from the model cells of the transport simulator, run geochemical reactions, and return updated component concentrations to the transport simulator. If multicomponent diffusion is modeled (e.g., Nernst–Planck equation), then aqueous species concentrations can be used instead of component concentrations. The reaction capabilities are a complete implementation of the reaction capabilities of PHREEQC. In each cell, the reaction module maintains the composition of all of the reactants, which may include minerals, exchangers, surface complexers, gas phases, solid solutions, and user-defined kinetic reactants.PhreeqcRM assigns initial and boundary conditions for model cells based on standard PHREEQC input definitions (files or strings) of chemical compositions of solutions and reactants. Additional PhreeqcRM capabilities include methods to eliminate reaction calculations for inactive parts of a model domain, transfer concentrations and other model properties, and retrieve selected results. The module demonstrates good scalability for parallel processing by using multiprocessing with MPI (message passing interface) on distributed memory systems, and limited scalability using multithreading with OpenMP on shared memory systems. PhreeqcRM is written in C++, but interfaces allow methods to be called from C or Fortran. By using the PhreeqcRM reaction module, an existing multicomponent transport simulator can be extended to simulate a wide range of geochemical reactions. Results of the implementation of PhreeqcRM as the reaction engine for transport simulators PHAST and FEFLOW are shown by using an analytical solution and the reactive transport benchmark of MoMaS.

  14. An analytic algorithm for the space-time fractional reaction-diffusion equation

    Directory of Open Access Journals (Sweden)

    M. G. Brikaa

    2015-11-01

    Full Text Available In this paper, we solve the space-time fractional reaction-diffusion equation by the fractional homotopy analysis method. Solutions of different examples of the reaction term will be computed and investigated. The approximation solutions of the studied models will be put in the form of convergent series to be easily computed and simulated. Comparison with the approximation solution of the classical case of the studied modeled with their approximation errors will also be studied.

  15. On the Green's function of the partially diffusion-controlled reversible ABCD reaction for radiation chemistry codes

    Energy Technology Data Exchange (ETDEWEB)

    Plante, Ianik, E-mail: ianik.plante-1@nasa.gov [Wyle Science, Technology & Engineering, 1290 Hercules, Houston, TX 77058 (United States); Devroye, Luc, E-mail: lucdevroye@gmail.com [School of Computer Science, McGill University, 3480 University Street, Montreal H3A 0E9 (Canada)

    2015-09-15

    Several computer codes simulating chemical reactions in particles systems are based on the Green's functions of the diffusion equation (GFDE). Indeed, many types of chemical systems have been simulated using the exact GFDE, which has also become the gold standard for validating other theoretical models. In this work, a simulation algorithm is presented to sample the interparticle distance for partially diffusion-controlled reversible ABCD reaction. This algorithm is considered exact for 2-particles systems, is faster than conventional look-up tables and uses only a few kilobytes of memory. The simulation results obtained with this method are compared with those obtained with the independent reaction times (IRT) method. This work is part of our effort in developing models to understand the role of chemical reactions in the radiation effects on cells and tissues and may eventually be included in event-based models of space radiation risks. However, as many reactions are of this type in biological systems, this algorithm might play a pivotal role in future simulation programs not only in radiation chemistry, but also in the simulation of biochemical networks in time and space as well.

  16. On the Green's function of the partially diffusion-controlled reversible ABCD reaction for radiation chemistry codes

    International Nuclear Information System (INIS)

    Plante, Ianik; Devroye, Luc

    2015-01-01

    Several computer codes simulating chemical reactions in particles systems are based on the Green's functions of the diffusion equation (GFDE). Indeed, many types of chemical systems have been simulated using the exact GFDE, which has also become the gold standard for validating other theoretical models. In this work, a simulation algorithm is presented to sample the interparticle distance for partially diffusion-controlled reversible ABCD reaction. This algorithm is considered exact for 2-particles systems, is faster than conventional look-up tables and uses only a few kilobytes of memory. The simulation results obtained with this method are compared with those obtained with the independent reaction times (IRT) method. This work is part of our effort in developing models to understand the role of chemical reactions in the radiation effects on cells and tissues and may eventually be included in event-based models of space radiation risks. However, as many reactions are of this type in biological systems, this algorithm might play a pivotal role in future simulation programs not only in radiation chemistry, but also in the simulation of biochemical networks in time and space as well

  17. Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior.

    Science.gov (United States)

    Ackerman, David M; Wang, Jing; Wendel, Joseph H; Liu, Da-Jiang; Pruski, Marek; Evans, James W

    2011-03-21

    We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.

  18. Multiscale Reaction-Diffusion Algorithms: PDE-Assisted Brownian Dynamics

    KAUST Repository

    Franz, Benjamin

    2013-06-19

    Two algorithms that combine Brownian dynami cs (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface, which partitions the domain, and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that the overlap region is required to accurately compute variances using PBD simulations. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented. © 2013 Society for Industrial and Applied Mathematics.

  19. Efficient kinetic Monte Carlo method for reaction-diffusion problems with spatially varying annihilation rates

    Science.gov (United States)

    Schwarz, Karsten; Rieger, Heiko

    2013-03-01

    We present an efficient Monte Carlo method to simulate reaction-diffusion processes with spatially varying particle annihilation or transformation rates as it occurs for instance in the context of motor-driven intracellular transport. Like Green's function reaction dynamics and first-passage time methods, our algorithm avoids small diffusive hops by propagating sufficiently distant particles in large hops to the boundaries of protective domains. Since for spatially varying annihilation or transformation rates the single particle diffusion propagator is not known analytically, we present an algorithm that generates efficiently either particle displacements or annihilations with the correct statistics, as we prove rigorously. The numerical efficiency of the algorithm is demonstrated with an illustrative example.

  20. Externally controlled anisotropy in pattern-forming reaction-diffusion systems.

    Science.gov (United States)

    Escala, Dario M; Guiu-Souto, Jacobo; Muñuzuri, Alberto P

    2015-06-01

    The effect of centrifugal forces is analyzed in a pattern-forming reaction-diffusion system. Numerical simulations conducted on the appropriate extension of the Oregonator model for the Belousov-Zhabotinsky reaction show a great variety of dynamical behaviors in such a system. In general, the system exhibits an anisotropy that results in new types of patterns or in a global displacement of the previous one. We consider the effect of both constant and periodically modulated centrifugal forces on the different types of patterns that the system may exhibit. A detailed analysis of the patterns and behaviors observed for the different parameter values considered is presented here.

  1. A new multicompartmental reaction-diffusion modeling method links transient membrane attachment of E. coli MinE to E-ring formation.

    Science.gov (United States)

    Arjunan, Satya Nanda Vel; Tomita, Masaru

    2010-03-01

    Many important cellular processes are regulated by reaction-diffusion (RD) of molecules that takes place both in the cytoplasm and on the membrane. To model and analyze such multicompartmental processes, we developed a lattice-based Monte Carlo method, Spatiocyte that supports RD in volume and surface compartments at single molecule resolution. Stochasticity in RD and the excluded volume effect brought by intracellular molecular crowding, both of which can significantly affect RD and thus, cellular processes, are also supported. We verified the method by comparing simulation results of diffusion, irreversible and reversible reactions with the predicted analytical and best available numerical solutions. Moreover, to directly compare the localization patterns of molecules in fluorescence microscopy images with simulation, we devised a visualization method that mimics the microphotography process by showing the trajectory of simulated molecules averaged according to the camera exposure time. In the rod-shaped bacterium Escherichia coli, the division site is suppressed at the cell poles by periodic pole-to-pole oscillations of the Min proteins (MinC, MinD and MinE) arising from carefully orchestrated RD in both cytoplasm and membrane compartments. Using Spatiocyte we could model and reproduce the in vivo MinDE localization dynamics by accounting for the previously reported properties of MinE. Our results suggest that the MinE ring, which is essential in preventing polar septation, is largely composed of MinE that is transiently attached to the membrane independently after recruited by MinD. Overall, Spatiocyte allows simulation and visualization of complex spatial and reaction-diffusion mediated cellular processes in volumes and surfaces. As we showed, it can potentially provide mechanistic insights otherwise difficult to obtain experimentally. The online version of this article (doi:10.1007/s11693-009-9047-2) contains supplementary material, which is available to

  2. Matching the reaction-diffusion simulation to dynamic [18F]FMISO PET measurements in tumors: extension to a flow-limited oxygen-dependent model.

    Science.gov (United States)

    Shi, Kuangyu; Bayer, Christine; Gaertner, Florian C; Astner, Sabrina T; Wilkens, Jan J; Nüsslin, Fridtjof; Vaupel, Peter; Ziegler, Sibylle I

    2017-02-01

    Positron-emission tomography (PET) with hypoxia specific tracers provides a noninvasive method to assess the tumor oxygenation status. Reaction-diffusion models have advantages in revealing the quantitative relation between in vivo imaging and the tumor microenvironment. However, there is no quantitative comparison of the simulation results with the real PET measurements yet. The lack of experimental support hampers further applications of computational simulation models. This study aims to compare the simulation results with a preclinical [ 18 F]FMISO PET study and to optimize the reaction-diffusion model accordingly. Nude mice with xenografted human squamous cell carcinomas (CAL33) were investigated with a 2 h dynamic [ 18 F]FMISO PET followed by immunofluorescence staining using the hypoxia marker pimonidazole and the endothelium marker CD 31. A large data pool of tumor time-activity curves (TAC) was simulated for each mouse by feeding the arterial input function (AIF) extracted from experiments into the model with different configurations of the tumor microenvironment. A measured TAC was considered to match a simulated TAC when the difference metric was below a certain, noise-dependent threshold. As an extension to the well-established Kelly model, a flow-limited oxygen-dependent (FLOD) model was developed to improve the matching between measurements and simulations. The matching rate between the simulated TACs of the Kelly model and the mouse PET data ranged from 0 to 28.1% (on average 9.8%). By modifying the Kelly model to an FLOD model, the matching rate between the simulation and the PET measurements could be improved to 41.2-84.8% (on average 64.4%). Using a simulation data pool and a matching strategy, we were able to compare the simulated temporal course of dynamic PET with in vivo measurements. By modifying the Kelly model to a FLOD model, the computational simulation was able to approach the dynamic [ 18 F]FMISO measurements in the investigated

  3. Feynman-Kac equations for reaction and diffusion processes

    Science.gov (United States)

    Hou, Ru; Deng, Weihua

    2018-04-01

    This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.

  4. Distributed order reaction-diffusion systems associated with Caputo derivatives

    Science.gov (United States)

    Saxena, R. K.; Mathai, A. M.; Haubold, H. J.

    2014-08-01

    This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation of distributed order associated with the Caputo derivatives as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the joint Laplace and Fourier transforms in compact and closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by other authors, notably by Mainardi et al. ["The fundamental solution of the space-time fractional diffusion equation," Fractional Calculus Appl. Anal. 4, 153-202 (2001); Mainardi et al. "Fox H-functions in fractional diffusion," J. Comput. Appl. Math. 178, 321-331 (2005)] for the fundamental solution of the space-time fractional equation, including Haubold et al. ["Solutions of reaction-diffusion equations in terms of the H-function," Bull. Astron. Soc. India 35, 681-689 (2007)] and Saxena et al. ["Fractional reaction-diffusion equations," Astrophys. Space Sci. 305, 289-296 (2006a)] for fractional reaction-diffusion equations. The advantage of using the Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation, containing this derivative, includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of fractional diffusion, space-time fraction diffusion, and time-fractional diffusion, see Schneider and Wyss ["Fractional diffusion and wave equations," J. Math. Phys. 30, 134-144 (1989)]. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-function in compact forms. The convergence conditions for the double series occurring in the solutions are investigated. It is interesting to observe that the double series comes out to be a special case of the Srivastava-Daoust hypergeometric function of two variables

  5. Simulation of multivariate diffusion bridges

    DEFF Research Database (Denmark)

    Bladt, Mogens; Finch, Samuel; Sørensen, Michael

    We propose simple methods for multivariate diffusion bridge simulation, which plays a fundamental role in simulation-based likelihood and Bayesian inference for stochastic differential equations. By a novel application of classical coupling methods, the new approach generalizes a previously...... proposed simulation method for one-dimensional bridges to the mulit-variate setting. First a method of simulating approzimate, but often very accurate, diffusion bridges is proposed. These approximate bridges are used as proposal for easily implementable MCMC algorithms that produce exact diffusion bridges...

  6. Diffusion dynamics and concentration of toxic materials from quantum dots-based nanotechnologies: an agent-based modeling simulation framework

    Energy Technology Data Exchange (ETDEWEB)

    Agusdinata, Datu Buyung, E-mail: bagusdinata@niu.edu; Amouie, Mahbod [Northern Illinois University, Department of Industrial & Systems Engineering and Environment, Sustainability, & Energy Institute (United States); Xu, Tao [Northern Illinois University, Department of Chemistry and Biochemistry (United States)

    2015-01-15

    Due to their favorable electrical and optical properties, quantum dots (QDs) nanostructures have found numerous applications including nanomedicine and photovoltaic cells. However, increased future production, use, and disposal of engineered QD products also raise concerns about their potential environmental impacts. The objective of this work is to establish a modeling framework for predicting the diffusion dynamics and concentration of toxic materials released from Trioctylphosphine oxide-capped CdSe. To this end, an agent-based model simulation with reaction kinetics and Brownian motion dynamics was developed. Reaction kinetics is used to model the stability of surface capping agent particularly due to oxidation process. The diffusion of toxic Cd{sup 2+} ions in aquatic environment was simulated using an adapted Brownian motion algorithm. A calibrated parameter to reflect sensitivity to reaction rate is proposed. The model output demonstrates the stochastic spatial distribution of toxic Cd{sup 2+} ions under different values of proxy environmental factor parameters. With the only chemistry considered was oxidation, the simulation was able to replicate Cd{sup 2+} ion release from Thiol-capped QDs in aerated water. The agent-based method is the first to be developed in the QDs application domain. It adds both simplicity of the solubility and rate of release of Cd{sup 2+} ions and complexity of tracking of individual atoms of Cd at the same time.

  7. Diffusion dynamics and concentration of toxic materials from quantum dots-based nanotechnologies: an agent-based modeling simulation framework

    International Nuclear Information System (INIS)

    Agusdinata, Datu Buyung; Amouie, Mahbod; Xu, Tao

    2015-01-01

    Due to their favorable electrical and optical properties, quantum dots (QDs) nanostructures have found numerous applications including nanomedicine and photovoltaic cells. However, increased future production, use, and disposal of engineered QD products also raise concerns about their potential environmental impacts. The objective of this work is to establish a modeling framework for predicting the diffusion dynamics and concentration of toxic materials released from Trioctylphosphine oxide-capped CdSe. To this end, an agent-based model simulation with reaction kinetics and Brownian motion dynamics was developed. Reaction kinetics is used to model the stability of surface capping agent particularly due to oxidation process. The diffusion of toxic Cd 2+ ions in aquatic environment was simulated using an adapted Brownian motion algorithm. A calibrated parameter to reflect sensitivity to reaction rate is proposed. The model output demonstrates the stochastic spatial distribution of toxic Cd 2+ ions under different values of proxy environmental factor parameters. With the only chemistry considered was oxidation, the simulation was able to replicate Cd 2+ ion release from Thiol-capped QDs in aerated water. The agent-based method is the first to be developed in the QDs application domain. It adds both simplicity of the solubility and rate of release of Cd 2+ ions and complexity of tracking of individual atoms of Cd at the same time

  8. Kinetic Monte Carlo Simulation of Cation Diffusion in Low-K Ceramics

    Science.gov (United States)

    Good, Brian

    2013-01-01

    Low thermal conductivity (low-K) ceramic materials are of interest to the aerospace community for use as the thermal barrier component of coating systems for turbine engine components. In particular, zirconia-based materials exhibit both low thermal conductivity and structural stability at high temperature, making them suitable for such applications. Because creep is one of the potential failure modes, and because diffusion is a mechanism by which creep takes place, we have performed computer simulations of cation diffusion in a variety of zirconia-based low-K materials. The kinetic Monte Carlo simulation method is an alternative to the more widely known molecular dynamics (MD) method. It is designed to study "infrequent-event" processes, such as diffusion, for which MD simulation can be highly inefficient. We describe the results of kinetic Monte Carlo computer simulations of cation diffusion in several zirconia-based materials, specifically, zirconia doped with Y, Gd, Nb and Yb. Diffusion paths are identified, and migration energy barriers are obtained from density functional calculations and from the literature. We present results on the temperature dependence of the diffusivity, and on the effects of the presence of oxygen vacancies in cation diffusion barrier complexes as well.

  9. Computation of short-time diffusion using the particle simulation method

    International Nuclear Information System (INIS)

    Janicke, L.

    1983-01-01

    The method of particle simulation allows a correct description of turbulent diffusion even in areas near the source and the computation of overall average values (anticipated values). The model is suitable for dealing with complex situation. It is derived from the K-model which describes the dispersion of noxious matter using the diffusion formula. (DG) [de

  10. Numerical simulation of reaction-diffusion systems by modified cubic B-spline differential quadrature method

    International Nuclear Information System (INIS)

    Mittal, R.C.; Rohila, Rajni

    2016-01-01

    In this paper, we have applied modified cubic B-spline based differential quadrature method to get numerical solutions of one dimensional reaction-diffusion systems such as linear reaction-diffusion system, Brusselator system, Isothermal system and Gray-Scott system. The models represented by these systems have important applications in different areas of science and engineering. The most striking and interesting part of the work is the solution patterns obtained for Gray Scott model, reminiscent of which are often seen in nature. We have used cubic B-spline functions for space discretization to get a system of ordinary differential equations. This system of ODE’s is solved by highly stable SSP-RK43 method to get solution at the knots. The computed results are very accurate and shown to be better than those available in the literature. Method is easy and simple to apply and gives solutions with less computational efforts.

  11. A fractional reaction-diffusion description of supply and demand

    Science.gov (United States)

    Benzaquen, Michael; Bouchaud, Jean-Philippe

    2018-02-01

    We suggest that the broad distribution of time scales in financial markets could be a crucial ingredient to reproduce realistic price dynamics in stylised Agent-Based Models. We propose a fractional reaction-diffusion model for the dynamics of latent liquidity in financial markets, where agents are very heterogeneous in terms of their characteristic frequencies. Several features of our model are amenable to an exact analytical treatment. We find in particular that the impact is a concave function of the transacted volume (aka the "square-root impact law"), as in the normal diffusion limit. However, the impact kernel decays as t-β with β = 1/2 in the diffusive case, which is inconsistent with market efficiency. In the sub-diffusive case the decay exponent β takes any value in [0, 1/2], and can be tuned to match the empirical value β ≈ 1/4. Numerical simulations confirm our theoretical results. Several extensions of the model are suggested. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

  12. High-fidelity meshes from tissue samples for diffusion MRI simulations.

    Science.gov (United States)

    Panagiotaki, Eleftheria; Hall, Matt G; Zhang, Hui; Siow, Bernard; Lythgoe, Mark F; Alexander, Daniel C

    2010-01-01

    This paper presents a method for constructing detailed geometric models of tissue microstructure for synthesizing realistic diffusion MRI data. We construct three-dimensional mesh models from confocal microscopy image stacks using the marching cubes algorithm. Random-walk simulations within the resulting meshes provide synthetic diffusion MRI measurements. Experiments optimise simulation parameters and complexity of the meshes to achieve accuracy and reproducibility while minimizing computation time. Finally we assess the quality of the synthesized data from the mesh models by comparison with scanner data as well as synthetic data from simple geometric models and simplified meshes that vary only in two dimensions. The results support the extra complexity of the three-dimensional mesh compared to simpler models although sensitivity to the mesh resolution is quite robust.

  13. Unified path integral approach to theories of diffusion-influenced reactions

    Science.gov (United States)

    Prüstel, Thorsten; Meier-Schellersheim, Martin

    2017-08-01

    Building on mathematical similarities between quantum mechanics and theories of diffusion-influenced reactions, we develop a general approach for computational modeling of diffusion-influenced reactions that is capable of capturing not only the classical Smoluchowski picture but also alternative theories, as is here exemplified by a volume reactivity model. In particular, we prove the path decomposition expansion of various Green's functions describing the irreversible and reversible reaction of an isolated pair of molecules. To this end, we exploit a connection between boundary value and interaction potential problems with δ - and δ'-function perturbation. We employ a known path-integral-based summation of a perturbation series to derive a number of exact identities relating propagators and survival probabilities satisfying different boundary conditions in a unified and systematic manner. Furthermore, we show how the path decomposition expansion represents the propagator as a product of three factors in the Laplace domain that correspond to quantities figuring prominently in stochastic spatially resolved simulation algorithms. This analysis will thus be useful for the interpretation of current and the design of future algorithms. Finally, we discuss the relation between the general approach and the theory of Brownian functionals and calculate the mean residence time for the case of irreversible and reversible reactions.

  14. Simple simulation of diffusion bridges with application to likelihood inference for diffusions

    DEFF Research Database (Denmark)

    Bladt, Mogens; Sørensen, Michael

    2014-01-01

    the accuracy and efficiency of the approximate method and compare it to exact simulation methods. In the study, our method provides a very good approximation to the distribution of a diffusion bridge for bridges that are likely to occur in applications to statistical inference. To illustrate the usefulness......With a view to statistical inference for discretely observed diffusion models, we propose simple methods of simulating diffusion bridges, approximately and exactly. Diffusion bridge simulation plays a fundamental role in likelihood and Bayesian inference for diffusion processes. First a simple......-dimensional diffusions and is applicable to all one-dimensional diffusion processes with finite speed-measure. One advantage of the new approach is that simple simulation methods like the Milstein scheme can be applied to bridge simulation. Another advantage over previous bridge simulation methods is that the proposed...

  15. One-dimensional isothermal multicomponent diffusion-reaction model and its application to methanol synthesis over commercial Cu-based catalyst

    Directory of Open Access Journals (Sweden)

    Lei Kun

    2015-03-01

    Full Text Available The present work was a study on global reaction rate of methanol synthesis. We measured experimentally the global reaction rate in the internal recycle gradientless reactor over catalyst SC309. The diffusion-reaction model of methanol synthesis was suggested. For model we chose the hydrogenation of CO and CO2 as key reaction. CO and CO2 were key components in our model. The internal diffusion effectiveness factors of CO and CO2 in the catalyst were calculated by the numerical integration. A comparison with the experiment showed that all the absolute values of the relative error were less than 10%. The simulation results showed that decreasing reaction temperature and catalyst diameter were conducive to reduce the influence of the internal diffusion on the methanol synthesis.

  16. Nonlinear analysis of a reaction-diffusion system: Amplitude equations

    Energy Technology Data Exchange (ETDEWEB)

    Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)

    2012-10-15

    A reaction-diffusion system with a nonlinear diffusion term is considered. Based on nonlinear analysis, the amplitude equations are obtained in the cases of the Hopf and Turing instabilities in the system. Turing pattern-forming regions in the parameter space are determined for supercritical and subcritical instabilities in a two-component reaction-diffusion system.

  17. A diffusion-limited reaction model for self-propagating Al/Pt multilayers with quench limits

    Science.gov (United States)

    Kittell, D. E.; Yarrington, C. D.; Hobbs, M. L.; Abere, M. J.; Adams, D. P.

    2018-04-01

    A diffusion-limited reaction model was calibrated for Al/Pt multilayers ignited on oxidized silicon, sapphire, and tungsten substrates, as well as for some Al/Pt multilayers ignited as free-standing foils. The model was implemented in a finite element analysis code and used to match experimental burn front velocity data collected from several years of testing at Sandia National Laboratories. Moreover, both the simulations and experiments reveal well-defined quench limits in the total Al + Pt layer (i.e., bilayer) thickness. At these limits, the heat generated from atomic diffusion is insufficient to support a self-propagating wave front on top of the substrates. Quench limits for reactive multilayers are seldom reported and are found to depend on the thermal properties of the individual layers. Here, the diffusion-limited reaction model is generalized to allow for temperature- and composition-dependent material properties, phase change, and anisotropic thermal conductivity. Utilizing this increase in model fidelity, excellent overall agreement is shown between the simulations and experimental results with a single calibrated parameter set. However, the burn front velocities of Al/Pt multilayers ignited on tungsten substrates are over-predicted. Possible sources of error are discussed and a higher activation energy (from 41.9 kJ/mol.at. to 47.5 kJ/mol.at.) is shown to bring the simulations into agreement with the velocity data observed on tungsten substrates. This higher activation energy suggests an inhibited diffusion mechanism present at lower heating rates.

  18. Exact analytical solutions for nonlinear reaction-diffusion equations

    International Nuclear Information System (INIS)

    Liu Chunping

    2003-01-01

    By using a direct method via the computer algebraic system of Mathematica, some exact analytical solutions to a class of nonlinear reaction-diffusion equations are presented in closed form. Subsequently, the hyperbolic function solutions and the triangular function solutions of the coupled nonlinear reaction-diffusion equations are obtained in a unified way

  19. Speed ot travelling waves in reaction-diffusion equations

    International Nuclear Information System (INIS)

    Benguria, R.D.; Depassier, M.C.; Mendez, V.

    2002-01-01

    Reaction diffusion equations arise in several problems of population dynamics, flame propagation and others. In one dimensional cases the systems may evolve into travelling fronts. Here we concentrate on a reaction diffusion equation which arises as a simple model for chemotaxis and present results for the speed of the travelling fronts. (Author)

  20. Synchronous parallel kinetic Monte Carlo for continuum diffusion-reaction systems

    International Nuclear Information System (INIS)

    Martinez, E.; Marian, J.; Kalos, M.H.; Perlado, J.M.

    2008-01-01

    A novel parallel kinetic Monte Carlo (kMC) algorithm formulated on the basis of perfect time synchronicity is presented. The algorithm is intended as a generalization of the standard n-fold kMC method, and is trivially implemented in parallel architectures. In its present form, the algorithm is not rigorous in the sense that boundary conflicts are ignored. We demonstrate, however, that, in their absence, or if they were correctly accounted for, our algorithm solves the same master equation as the serial method. We test the validity and parallel performance of the method by solving several pure diffusion problems (i.e. with no particle interactions) with known analytical solution. We also study diffusion-reaction systems with known asymptotic behavior and find that, for large systems with interaction radii smaller than the typical diffusion length, boundary conflicts are negligible and do not affect the global kinetic evolution, which is seen to agree with the expected analytical behavior. Our method is a controlled approximation in the sense that the error incurred by ignoring boundary conflicts can be quantified intrinsically, during the course of a simulation, and decreased arbitrarily (controlled) by modifying a few problem-dependent simulation parameters

  1. Glider-based computing in reaction-diffusion hexagonal cellular automata

    International Nuclear Information System (INIS)

    Adamatzky, Andrew; Wuensche, Andrew; De Lacy Costello, Benjamin

    2006-01-01

    A three-state hexagonal cellular automaton, discovered in [Wuensche A. Glider dynamics in 3-value hexagonal cellular automata: the beehive rule. Int J Unconvention Comput, in press], presents a conceptual discrete model of a reaction-diffusion system with inhibitor and activator reagents. The automaton model of reaction-diffusion exhibits mobile localized patterns (gliders) in its space-time dynamics. We show how to implement the basic computational operations with these mobile localizations, and thus demonstrate collision-based logical universality of the hexagonal reaction-diffusion cellular automaton

  2. Multiscale simulations of anisotropic particles combining molecular dynamics and Green's function reaction dynamics

    NARCIS (Netherlands)

    Vijaykumar, A.; Ouldridge, T.E.; ten Wolde, P.R.; Bolhuis, P.G.

    2017-01-01

    The modeling of complex reaction-diffusion processes in, for instance, cellular biochemical networks or self-assembling soft matter can be tremendously sped up by employing a multiscale algorithm which combines the mesoscopic Green's Function Reaction Dynamics (GFRD) method with explicit stochastic

  3. Study of ODE limit problems for reaction-diffusion equations

    Directory of Open Access Journals (Sweden)

    Jacson Simsen

    2018-01-01

    Full Text Available In this work we study ODE limit problems for reaction-diffusion equations for large diffusion and we study the sensitivity of nonlinear ODEs with respect to initial conditions and exponent parameters. Moreover, we prove continuity of the flow and weak upper semicontinuity of a family of global attractors for reaction-diffusion equations with spatially variable exponents when the exponents go to 2 in \\(L^{\\infty}(\\Omega\\ and the diffusion coefficients go to infinity.

  4. Diffusion microscopist simulator - The development and application of a Monte Carlo simulation system for diffusion MRI

    International Nuclear Information System (INIS)

    Yeh, C.H.

    2011-09-01

    Diffusion magnetic resonance imaging (dMRI) has made a significant breakthrough in neurological disorders and brain research thanks to its exquisite sensitivity to tissue cyto-architecture. However, as the water diffusion process in neuronal tissues is a complex biophysical phenomena at molecular scale, it is difficult to infer tissue microscopic characteristics on a voxel scale from dMRI data. The major methodological contribution of this thesis is the development of an integrated and generic Monte Carlo simulation framework, 'Diffusion Microscopist Simulator' (DMS), which has the capacity to create 3D biological tissue models of various shapes and properties, as well as to synthesize dMRI data for a large variety of MRI methods, pulse sequence design and parameters. DMS aims at bridging the gap between the elementary diffusion processes occurring at a micrometric scale and the resulting diffusion signal measured at millimetric scale, providing better insights into the features observed in dMRI, as well as offering ground-truth information for optimization and validation of dMRI acquisition protocols for different applications. We have verified the performance and validity of DMS through various benchmark experiments, and applied to address particular research topics in dMRI. Based on DMS, there are two major application contributions in this thesis. First, we use DMS to investigate the impact of finite diffusion gradient pulse duration (delta) on fibre orientation estimation in dMRI. We propose that current practice of using long delta, which is enforced by the hardware limitation of clinical MRI scanners, is actually beneficial for mapping fibre orientations, even though it violates the underlying assumption made in q-space theory. Second, we employ DMS to investigate the feasibility of estimating axon radius using a clinical MRI system. The results suggest that the algorithm for mapping the direct microstructures is applicable to dMRI data acquired from

  5. Nonlinear variational models for reaction and diffusion systems

    International Nuclear Information System (INIS)

    Tanyi, G.E.

    1983-08-01

    There exists a natural metric w.r.t. which the density dependent diffusion operator is harmonic in the sense of Eells and Sampson. A physical corollary of this statement is the property that any two regular points on the orbit of a reaction or diffusion operator can be connected by a path along which the reaction rate is constant. (author)

  6. Computer simulation for sodium-concrete reactions

    International Nuclear Information System (INIS)

    Zhang Bin; Zhu Jizhou

    2006-01-01

    In the liquid metal cooled fast breeder reactors (LMFBRs), direct contacts between sodium and concrete is unavoidable. Due to sodium's high chemical reactivity, sodium would react with concrete violently. Lots of hydrogen gas and heat would be released then. This would harm the ignorantly of the containment. This paper developed a program to simualte sodium-conrete reactions across-the-board. It could give the reaction zone temperature, pool temperature, penetration depth, penetration rate, hydrogen flux and reaction heat and so on. Concrete was considered to be composed of silica and water only in this paper. The variable, the quitient of sodium hydroxide, was introduced in the continuity equation to simulate the chemical reactions more realistically. The product of the net gas flux and boundary depth was ably transformed to that of penetration rate and boundary depth. The complex chemical kinetics equations was simplified under some hypothesises. All the technique applied above simplified the computer simulation consumedly. In other words, they made the computer simulation feasible. Theoretics models that applied in the program and the calculation procedure were expatiated in detail. Good agreements of an overall transient behavior were obtained in the series of sodium-concrete reaction experiment analysis. The comparison between the analytical and experimental results showed the program presented in this paper was creditable and reasonable for simulating the sodium-concrete reactions. This program could be used for nuclear safety judgement. (authors)

  7. Use of ion beams to simulate reaction of reactor fuels with their cladding

    International Nuclear Information System (INIS)

    Birtcher, R.C.; Baldo, P.

    2006-01-01

    Processes occurring within reactor cores are not amenable to direct experimental observation. Among major concerns are damage, fission gas accumulation and reaction between the fuel and its cladding all of which lead to swelling. These questions can be investigated through simulation with ion beams. As an example, we discuss the irradiation driven interaction of uranium-molybdenum alloys, intended for use as low-enrichment reactor fuels, with aluminum, which is used as fuel cladding. Uranium-molybdenum coated with a 100 nm thin film of aluminum was irradiated with 3 MeV Kr ions to simulate fission fragment damage. Mixing and diffusion of aluminum was followed as a function of irradiation with RBS and nuclear reaction analysis using the 27 Al(p,γ) 28 Si reaction which occurs at a proton energy of 991.9 keV. During irradiation at 150 deg. C, aluminum diffused into the uranium alloy at a irradiation driven diffusion rate of 30 nm 2 /dpa. At a dose of 90 dpa, uranium diffusion into the aluminum layer resulted in formation of an aluminide phase at the initial interface. The thickness of this phase grew until it consumed the aluminum layer. The rapid diffusion of Al into these reactor fuels may offer explanation of the observation that porosity is not observed in the fuel particles but on their periphery

  8. A Multilevel Adaptive Reaction-splitting Simulation Method for Stochastic Reaction Networks

    KAUST Repository

    Moraes, Alvaro; Tempone, Raul; Vilanova, Pedro

    2016-01-01

    In this work, we present a novel multilevel Monte Carlo method for kinetic simulation of stochastic reaction networks characterized by having simultaneously fast and slow reaction channels. To produce efficient simulations, our method adaptively classifies the reactions channels into fast and slow channels. To this end, we first introduce a state-dependent quantity named level of activity of a reaction channel. Then, we propose a low-cost heuristic that allows us to adaptively split the set of reaction channels into two subsets characterized by either a high or a low level of activity. Based on a time-splitting technique, the increments associated with high-activity channels are simulated using the tau-leap method, while those associated with low-activity channels are simulated using an exact method. This path simulation technique is amenable for coupled path generation and a corresponding multilevel Monte Carlo algorithm. To estimate expected values of observables of the system at a prescribed final time, our method bounds the global computational error to be below a prescribed tolerance, TOL, within a given confidence level. This goal is achieved with a computational complexity of order O(TOL-2), the same as with a pathwise-exact method, but with a smaller constant. We also present a novel low-cost control variate technique based on the stochastic time change representation by Kurtz, showing its performance on a numerical example. We present two numerical examples extracted from the literature that show how the reaction-splitting method obtains substantial gains with respect to the standard stochastic simulation algorithm and the multilevel Monte Carlo approach by Anderson and Higham. © 2016 Society for Industrial and Applied Mathematics.

  9. A Multilevel Adaptive Reaction-splitting Simulation Method for Stochastic Reaction Networks

    KAUST Repository

    Moraes, Alvaro

    2016-07-07

    In this work, we present a novel multilevel Monte Carlo method for kinetic simulation of stochastic reaction networks characterized by having simultaneously fast and slow reaction channels. To produce efficient simulations, our method adaptively classifies the reactions channels into fast and slow channels. To this end, we first introduce a state-dependent quantity named level of activity of a reaction channel. Then, we propose a low-cost heuristic that allows us to adaptively split the set of reaction channels into two subsets characterized by either a high or a low level of activity. Based on a time-splitting technique, the increments associated with high-activity channels are simulated using the tau-leap method, while those associated with low-activity channels are simulated using an exact method. This path simulation technique is amenable for coupled path generation and a corresponding multilevel Monte Carlo algorithm. To estimate expected values of observables of the system at a prescribed final time, our method bounds the global computational error to be below a prescribed tolerance, TOL, within a given confidence level. This goal is achieved with a computational complexity of order O(TOL-2), the same as with a pathwise-exact method, but with a smaller constant. We also present a novel low-cost control variate technique based on the stochastic time change representation by Kurtz, showing its performance on a numerical example. We present two numerical examples extracted from the literature that show how the reaction-splitting method obtains substantial gains with respect to the standard stochastic simulation algorithm and the multilevel Monte Carlo approach by Anderson and Higham. © 2016 Society for Industrial and Applied Mathematics.

  10. Spatiotemporal Patterns in a Ratio-Dependent Food Chain Model with Reaction-Diffusion

    Directory of Open Access Journals (Sweden)

    Lei Zhang

    2014-01-01

    Full Text Available Predator-prey models describe biological phenomena of pursuit-evasion interaction. And this interaction exists widely in the world for the necessary energy supplement of species. In this paper, we have investigated a ratio-dependent spatially extended food chain model. Based on the bifurcation analysis (Hopf and Turing, we give the spatial pattern formation via numerical simulation, that is, the evolution process of the system near the coexistence equilibrium point (u2*,v2*,w2*, and find that the model dynamics exhibits complex pattern replication. For fixed parameters, on increasing the control parameter c1, the sequence “holes → holes-stripe mixtures → stripes → spots-stripe mixtures → spots” pattern is observed. And in the case of pure Hopf instability, the model exhibits chaotic wave pattern replication. Furthermore, we consider the pattern formation in the case of which the top predator is extinct, that is, the evolution process of the system near the equilibrium point (u1*,v1*,0, and find that the model dynamics exhibits stripes-spots pattern replication. Our results show that reaction-diffusion model is an appropriate tool for investigating fundamental mechanism of complex spatiotemporal dynamics. It will be useful for studying the dynamic complexity of ecosystems.

  11. Instability induced by cross-diffusion in reaction-diffusion systems

    DEFF Research Database (Denmark)

    Tian, Canrong; Lin, Zhigui; Pedersen, Michael

    2010-01-01

    In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficient conditions for the instability are obtained respectively. The conclusion is applied to the ecosystem, it is shown that cros...... can induce the instability of an equilibrium which is stable for the kinetic system and for the self-diffusion–reaction system.......In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficient conditions for the instability are obtained respectively. The conclusion is applied to the ecosystem, it is shown that cross-diffusion...

  12. Modeling and simulation of diffusion-convection-reaction in heterogeneous nanochannels using OpenFOAM

    NARCIS (Netherlands)

    Pimpalgaonkar, H.G.; van Steijn, V.; Kreutzer, M.T.; Kleijn, C.R.; Simos, Theodore; Tsitouras, Charalambos

    2016-01-01

    We present a finite volume implementation of a phase field method in OpenFOAM as a tool to simulate reactive multiphase flows on heterogeneous surfaces. Using this tool, we simulate the formation and growth of a droplet due to a chemical reaction on a hydrophilic catalytic patch surrounded by a

  13. Laser spot detection based on reaction diffusion

    Czech Academy of Sciences Publication Activity Database

    Vázquez-Otero, Alejandro; Khikhlukha, Danila; Solano-Altamirano, J. M.; Dormido, R.; Duro, N.

    2016-01-01

    Roč. 16, č. 3 (2016), s. 1-11, č. článku 315. ISSN 1424-8220 R&D Projects: GA MŠk EF15_008/0000162 Grant - others:ELI Beamlines(XE) CZ.02.1.01/0.0/0.0/15_008/0000162 Institutional support: RVO:68378271 Keywords : laser spot detection * laser beam detection * reaction diffusion models * Fitzhugh-Nagumo model * reaction diffusion computation * Turing patterns Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 2.677, year: 2016

  14. Reaction time for trimolecular reactions in compartment-based reaction-diffusion models

    Science.gov (United States)

    Li, Fei; Chen, Minghan; Erban, Radek; Cao, Yang

    2018-05-01

    Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modeling. The formulae for the first collision time and the mean reaction time are derived for the case where three molecules are present in the solution under periodic boundary conditions. For the case of reflecting boundary conditions, similar formulae are obtained using a computer-assisted approach. The accuracy of these formulae is further verified through comparison with numerical results. The presented derivation is based on the first passage time analysis of Montroll [J. Math. Phys. 10, 753 (1969)]. Montroll's results for two-dimensional lattice-based random walks are adapted and applied to compartment-based models of trimolecular reactions, which are studied in one-dimensional or pseudo one-dimensional domains.

  15. Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

    KAUST Repository

    Woolley, Thomas E.; Baker, Ruth E.; Gaffney, Eamonn A.; Maini, Philip K.; Seirin-Lee, Sungrim

    2012-01-01

    Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases. © 2012 American Physical Society.

  16. Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

    KAUST Repository

    Woolley, Thomas E.

    2012-05-22

    Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases. © 2012 American Physical Society.

  17. Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations

    KAUST Repository

    Alzahrani, Hasnaa H.

    2016-01-01

    A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge

  18. Impact of porosity variation on diffusive transport: experimentation vs simulation

    International Nuclear Information System (INIS)

    Fatnassi, Ikram

    2015-01-01

    Reactions induced by the diffusion of reactants from different sources may alter rock confinement properties, and are therefore critical processes to assess short-term and long-term behaviour of rocks displaying a low permeability, such as argillites which are used as barriers in underground storage installation. In order to test transport-chemistry codes based on a continuous approach, the author of this research thesis reports the development and performance of simplest as possible experiments of sealing/dissolution diffusion, by using porous media of increasing complexity: compact sand, sintered glass, stoneware, chalk, until a material close to that envisaged within the frame of a storage like a Tournemire argillite. The principle of these experiments relies on the characterisation of the diffusive behaviour of an inert tracer within a porous medium submitted to dissolution reactions (attack of a carbonate matrix by an acid solution) and/or precipitation of mineral compounds (calcium oxalate, gypsum or barite) which results in an evolution of porosity and a modification of the diffusive transport of the studied tracer. At the end of the experiment, porous media and precipitates are characterised by SEM-EDS [fr

  19. A reaction-diffusion model of CO2 influx into an oocyte

    Science.gov (United States)

    Somersalo, Erkki; Occhipinti, Rossana; Boron, Walter F.; Calvetti, Daniela

    2012-01-01

    We have developed and implemented a novel mathematical model for simulating transients in surface pH (pHS) and intracellular pH (pHi) caused by the influx of carbon dioxide (CO2) into a Xenopus oocyte. These transients are important tools for studying gas channels. We assume that the oocyte is a sphere surrounded by a thin layer of unstirred fluid, the extracellular unconvected fluid (EUF), which is in turn surrounded by the well-stirred bulk extracellular fluid (BECF) that represents an infinite reservoir for all solutes. Here, we assume that the oocyte plasma membrane is permeable only to CO2. In both the EUF and intracellular space, solute concentrations can change because of diffusion and reactions. The reactions are the slow equilibration of the CO2 hydration-dehydration reactions and competing equilibria among carbonic acid (H2CO3)/bicarbonate ( HCO3-) and a multitude of non-CO2/HCO3- buffers. Mathematically, the model is described by a coupled system of reaction-diffusion equations that—assuming spherical radial symmetry—we solved using the method of lines with appropriate stiff solvers. In agreement with experimental data (Musa-Aziz et al, PNAS 2009, 106:5406–5411), the model predicts that exposing the cell to extracellular 1.5% CO2/10 mM HCO3- (pH 7.50) causes pHi to fall and pHS to rise rapidly to a peak and then decay. Moreover, the model provides insights into the competition between diffusion and reaction processes when we change the width of the EUF, membrane permeability to CO2, native extra-and intracellular carbonic anhydrase-like activities, the non-CO2/HCO3- (intrinsic) intracellular buffering power, or mobility of intrinsic intracellular buffers. PMID:22728674

  20. Restrictive liquid-phase diffusion and reaction in bidispersed catalysts

    International Nuclear Information System (INIS)

    Lee, S.Y.; Seader, J.D.; Tsai, C.H.; Massoth, F.E.

    1991-01-01

    In this paper, the effect of bidispersed pore-size distribution on liquid-phase diffusion and reaction in NiMo/Al 2 O 3 catalysts is investigated by applying two bidispersed-pore-structure models, the random-pore model and a globular-structure model, to extensive experimental data, which were obtained from sorptive diffusion measurements at ambient conditions and catalytic reaction rate measurements on nitrogen-containing compounds. Transport of the molecules in the catalysts was found to be controlled by micropore diffusion, in accordance with the random-pore model, rather than macropore diffusion as predicted by the globular-structure model. A qualitative criterion for micropore-diffusion control is proposed: relatively small macroporosity and high catalyst pellet density. Since most hydrotreating catalysts have high density, diffusion in these types of catalysts may be controlled by micropore diffusion. Accordingly, it is believed in this case that increasing the size of micropores may be more effective to reduce intraparticle diffusion resistance than incorporating macropores alone

  1. Splitting Schemes & Segregation In Reaction-(Cross-)Diffusion Systems

    OpenAIRE

    Carrillo, José A.; Fagioli, Simone; Santambrogio, Filippo; Schmidtchen, Markus

    2017-01-01

    One of the most fascinating phenomena observed in reaction-diffusion systems is the emergence of segregated solutions, i.e. population densities with disjoint supports. We analyse such a reaction cross-diffusion system. In order to prove existence of weak solutions for a wide class of initial data without restriction about their supports or their positivity, we propose a variational splitting scheme combining ODEs with methods from optimal transport. In addition, this approach allows us to pr...

  2. Rapid calculation of maximum particle lifetime for diffusion in complex geometries

    Science.gov (United States)

    Carr, Elliot J.; Simpson, Matthew J.

    2018-03-01

    Diffusion of molecules within biological cells and tissues is strongly influenced by crowding. A key quantity to characterize diffusion is the particle lifetime, which is the time taken for a diffusing particle to exit by hitting an absorbing boundary. Calculating the particle lifetime provides valuable information, for example, by allowing us to compare the timescale of diffusion and the timescale of the reaction, thereby helping us to develop appropriate mathematical models. Previous methods to quantify particle lifetimes focus on the mean particle lifetime. Here, we take a different approach and present a simple method for calculating the maximum particle lifetime. This is the time after which only a small specified proportion of particles in an ensemble remain in the system. Our approach produces accurate estimates of the maximum particle lifetime, whereas the mean particle lifetime always underestimates this value compared with data from stochastic simulations. Furthermore, we find that differences between the mean and maximum particle lifetimes become increasingly important when considering diffusion hindered by obstacles.

  3. Analytically solvable models of reaction-diffusion systems

    Energy Technology Data Exchange (ETDEWEB)

    Zemskov, E P; Kassner, K [Institut fuer Theoretische Physik, Otto-von-Guericke-Universitaet, Universitaetsplatz 2, 39106 Magdeburg (Germany)

    2004-05-01

    We consider a class of analytically solvable models of reaction-diffusion systems. An analytical treatment is possible because the nonlinear reaction term is approximated by a piecewise linear function. As particular examples we choose front and pulse solutions to illustrate the matching procedure in the one-dimensional case.

  4. Numerical simulation of flow in De-NOx catalyst honeycomb with NOx reduction reaction

    Energy Technology Data Exchange (ETDEWEB)

    Tanno, K.; Makino, H. [Electric Power Industry, Kanagawa (Japan). Energy Engineering Research Lab.; Kurose, R.; Komori, S. [Kyoto Univ. (Japan). Dept. of Mechanical Engineering and Science

    2013-07-01

    The effect of flow behavior in a De-NOx honeycomb with NOx reduction reaction is investigated by direct numerical simulation (DNS). As the inlet flow, fully developed turbulent or laminar flow is given. The results show that the surface reaction is strongly affected by inner flow behavior. The surface reaction rate for the turbulent flow is higher than that for the laminar flow. This is due to the difference of inner flow behavior that the diffusion of NOx in the vicinity of the wall is dominated only by molecular diffusion for the laminar flow, whereas it is enhanced by turbulent motions for the turbulent flow. Moreover, surface reaction is suppressed towards downstream even though inlet flow is turbulent. This is due to the flow transition from turbulent to laminar.

  5. Decay to Equilibrium for Energy-Reaction-Diffusion Systems

    KAUST Repository

    Haskovec, Jan

    2018-02-06

    We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow. The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer (thermodynamical equilibrium) given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential. We prove corresponding entropy-entropy production inequalities with explicitly calculable constants and establish the convergence to thermodynamical equilibrium, first in entropy and later in L norm using Cziszár–Kullback–Pinsker type inequalities.

  6. Decay to Equilibrium for Energy-Reaction-Diffusion Systems

    KAUST Repository

    Haskovec, Jan; Hittmeir, Sabine; Markowich, Peter A.; Mielke, Alexander

    2018-01-01

    We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow. The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer (thermodynamical equilibrium) given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential. We prove corresponding entropy-entropy production inequalities with explicitly calculable constants and establish the convergence to thermodynamical equilibrium, first in entropy and later in L norm using Cziszár–Kullback–Pinsker type inequalities.

  7. A method of simulating and visualizing nuclear reactions

    International Nuclear Information System (INIS)

    Atwood, C.H.; Paul, K.M.

    1994-01-01

    Teaching nuclear reactions to students is difficult because the mechanisms are complex and directly visualizing them is impossible. As a teaching tool, the authors have developed a method of simulating nuclear reactions using colliding water droplets. Videotaping of the collisions, taken with a high shutter speed camera and run frame-by-frame, shows details of the collisions that are analogous to nuclear reactions. The method for colliding the water drops and videotaping the collisions are shown

  8. Analysis of diffusivity of the oscillating reaction components in a microreactor system

    Directory of Open Access Journals (Sweden)

    Martina Šafranko

    2017-01-01

    Full Text Available When performing oscillating reactions, periodical changes in the concentrations of reactants, intermediaries, and products take place. Due to the mentioned periodical changes of the concentrations, the information about the diffusivity of the components included into oscillating reactions is very important for the control of the oscillating reactions. Non-linear dynamics makes oscillating reactions very interesting for analysis in different reactor systems. In this paper, the analysis of diffusivity of the oscillating reaction components was performed in a microreactor, with the aim of identifying the limiting component. The geometry of the microreactor microchannel and a well defined flow profile ensure optimal conditions for the diffusion phenomena analysis, because diffusion profiles in a microreactor depend only on the residence time. In this paper, the analysis of diffusivity of the oscillating reaction components was performed in a microreactor equipped with 2 Y-shape inlets and 2 Y-shape outlets, with active volume of V = 4 μL at different residence times.

  9. Considerations for the independent reaction times and step-by-step methods for radiation chemistry simulations

    Science.gov (United States)

    Plante, Ianik; Devroye, Luc

    2017-10-01

    Ionizing radiation interacts with the water molecules of the tissues mostly by ionizations and excitations, which result in the formation of the radiation track structure and the creation of radiolytic species such as H.,.OH, H2, H2O2, and e-aq. After their creation, these species diffuse and may chemically react with the neighboring species and with the molecules of the medium. Therefore radiation chemistry is of great importance in radiation biology. As the chemical species are not distributed homogeneously, the use of conventional models of homogeneous reactions cannot completely describe the reaction kinetics of the particles. Actually, many simulations of radiation chemistry are done using the Independent Reaction Time (IRT) method, which is a very fast technique to calculate radiochemical yields but which do not calculate the positions of the radiolytic species as a function of time. Step-by-step (SBS) methods, which are able to provide such information, have been used only sparsely because these are time-consuming in terms of calculation. Recent improvements in computer performance now allow the regular use of the SBS method in radiation chemistry. The SBS and IRT methods are both based on the Green's functions of the diffusion equation (GFDE). In this paper, several sampling algorithms of the GFDE and for the IRT method are presented. We show that the IRT and SBS methods are exactly equivalent for 2-particles systems for diffusion and partially diffusion-controlled reactions between non-interacting particles. We also show that the results obtained with the SBS simulation method with periodic boundary conditions are in agreement with the predictions by classical reaction kinetics theory, which is an important step towards using this method for modelling of biochemical networks and metabolic pathways involved in oxidative stress. Finally, the first simulation results obtained with the code RITRACKS (Relativistic Ion Tracks) are presented.

  10. Nonlinear reaction-diffusion systems conditional symmetry, exact solutions and their applications in biology

    CERN Document Server

    Cherniha, Roman

    2017-01-01

    This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems  and those developing the theoretical aspects of conditional symmetry conception,...

  11. Multiscale simulations of anisotropic particles combining molecular dynamics and Green's function reaction dynamics

    Science.gov (United States)

    Vijaykumar, Adithya; Ouldridge, Thomas E.; ten Wolde, Pieter Rein; Bolhuis, Peter G.

    2017-03-01

    The modeling of complex reaction-diffusion processes in, for instance, cellular biochemical networks or self-assembling soft matter can be tremendously sped up by employing a multiscale algorithm which combines the mesoscopic Green's Function Reaction Dynamics (GFRD) method with explicit stochastic Brownian, Langevin, or deterministic molecular dynamics to treat reactants at the microscopic scale [A. Vijaykumar, P. G. Bolhuis, and P. R. ten Wolde, J. Chem. Phys. 143, 214102 (2015)]. Here we extend this multiscale MD-GFRD approach to include the orientational dynamics that is crucial to describe the anisotropic interactions often prevalent in biomolecular systems. We present the novel algorithm focusing on Brownian dynamics only, although the methodology is generic. We illustrate the novel algorithm using a simple patchy particle model. After validation of the algorithm, we discuss its performance. The rotational Brownian dynamics MD-GFRD multiscale method will open up the possibility for large scale simulations of protein signalling networks.

  12. Permanganate diffusion and reaction in sedimentary rocks.

    Science.gov (United States)

    Huang, Qiuyuan; Dong, Hailiang; Towne, Rachael M; Fischer, Timothy B; Schaefer, Charles E

    2014-04-01

    In situ chemical oxidation using permanganate has frequently been used to treat chlorinated solvents in fractured bedrock aquifers. However, in systems where matrix back-diffusion is an important process, the ability of the oxidant to migrate and treat target contaminants within the rock matrix will likely determine the overall effectiveness of this remedial approach. In this study, a series of diffusion experiments were performed to measure the permanganate diffusion and reaction in four different types of sedimentary rocks (dark gray mudstone, light gray mudstone, red sandstone, and tan sandstone). Results showed that, within the experimental time frame (~2 months), oxidant migration into the rock was limited to distances less than 500 μm. The observed diffusivities for permanganate into the rock matrices ranged from 5.3 × 10(-13) to 1.3 × 10(-11) cm(2)/s. These values were reasonably predicted by accounting for both the rock oxidant demand and the effective diffusivity of the rock. Various Mn minerals formed as surface coatings from reduction of permanganate coupled with oxidation of total organic carbon (TOC), and the nature of the formed Mn minerals was dependent upon the rock type. Post-treatment tracer testing showed that these Mn mineral coatings had a negligible impact on diffusion through the rock. Overall, our results showed that the extent of permanganate diffusion and reaction depended on rock properties, including porosity, mineralogy, and organic carbon. These results have important implications for our understanding of long-term organic contaminant remediation in sedimentary rocks using permanganate. Copyright © 2014 Elsevier B.V. All rights reserved.

  13. Chaotic advection, diffusion, and reactions in open flows

    International Nuclear Information System (INIS)

    Tel, Tamas; Karolyi, Gyoergy; Pentek, Aron; Scheuring, Istvan; Toroczkai, Zoltan; Grebogi, Celso; Kadtke, James

    2000-01-01

    We review and generalize recent results on advection of particles in open time-periodic hydrodynamical flows. First, the problem of passive advection is considered, and its fractal and chaotic nature is pointed out. Next, we study the effect of weak molecular diffusion or randomness of the flow. Finally, we investigate the influence of passive advection on chemical or biological activity superimposed on open flows. The nondiffusive approach is shown to carry some features of a weak diffusion, due to the finiteness of the reaction range or reaction velocity. (c) 2000 American Institute of Physics

  14. Modelling non-homogeneous stochastic reaction-diffusion systems: the case study of gemcitabine-treated non-small cell lung cancer growth.

    Science.gov (United States)

    Lecca, Paola; Morpurgo, Daniele

    2012-01-01

    Reaction-diffusion based models have been widely used in the literature for modeling the growth of solid tumors. Many of the current models treat both diffusion/consumption of nutrients and cell proliferation. The majority of these models use classical transport/mass conservation equations for describing the distribution of molecular species in tumor spheroids, and the Fick's law for describing the flux of uncharged molecules (i.e oxygen, glucose). Commonly, the equations for the cell movement and proliferation are first order differential equations describing the rate of change of the velocity of the cells with respect to the spatial coordinates as a function of the nutrient's gradient. Several modifications of these equations have been developed in the last decade to explicitly indicate that the tumor includes cells, interstitial fluids and extracellular matrix: these variants provided a model of tumor as a multiphase material with these as the different phases. Most of the current reaction-diffusion tumor models are deterministic and do not model the diffusion as a local state-dependent process in a non-homogeneous medium at the micro- and meso-scale of the intra- and inter-cellular processes, respectively. Furthermore, a stochastic reaction-diffusion model in which diffusive transport of the molecular species of nutrients and chemotherapy drugs as well as the interactions of the tumor cells with these species is a novel approach. The application of this approach to he scase of non-small cell lung cancer treated with gemcitabine is also novel. We present a stochastic reaction-diffusion model of non-small cell lung cancer growth in the specification formalism of the tool Redi, we recently developed for simulating reaction-diffusion systems. We also describe how a spatial gradient of nutrients and oncological drugs affects the tumor progression. Our model is based on a generalization of the Fick's first diffusion law that allows to model diffusive transport in non

  15. Square Turing patterns in reaction-diffusion systems with coupled layers

    Energy Technology Data Exchange (ETDEWEB)

    Li, Jing [State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871 (China); Wang, Hongli, E-mail: hlwang@pku.edu.cn, E-mail: qi@pku.edu.cn [State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871 (China); Center for Quantitative Biology, Peking University, Beijing 100871 (China); Ouyang, Qi, E-mail: hlwang@pku.edu.cn, E-mail: qi@pku.edu.cn [State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871 (China); Center for Quantitative Biology, Peking University, Beijing 100871 (China); The Peking-Tsinghua Center for Life Sciences, Beijing 100871 (China)

    2014-06-15

    Square Turing patterns are usually unstable in reaction-diffusion systems and are rarely observed in corresponding experiments and simulations. We report here an example of spontaneous formation of square Turing patterns with the Lengyel-Epstein model of two coupled layers. The squares are found to be a result of the resonance between two supercritical Turing modes with an appropriate ratio. Besides, the spatiotemporal resonance of Turing modes resembles to the mode-locking phenomenon. Analysis of the general amplitude equations for square patterns reveals that the fixed point corresponding to square Turing patterns is stationary when the parameters adopt appropriate values.

  16. Information diffusion, Facebook clusters, and the simplicial model of social aggregation: a computational simulation of simplicial diffusers for community health interventions.

    Science.gov (United States)

    Kee, Kerk F; Sparks, Lisa; Struppa, Daniele C; Mannucci, Mirco A; Damiano, Alberto

    2016-01-01

    By integrating the simplicial model of social aggregation with existing research on opinion leadership and diffusion networks, this article introduces the constructs of simplicial diffusers (mathematically defined as nodes embedded in simplexes; a simplex is a socially bonded cluster) and simplicial diffusing sets (mathematically defined as minimal covers of a simplicial complex; a simplicial complex is a social aggregation in which socially bonded clusters are embedded) to propose a strategic approach for information diffusion of cancer screenings as a health intervention on Facebook for community cancer prevention and control. This approach is novel in its incorporation of interpersonally bonded clusters, culturally distinct subgroups, and different united social entities that coexist within a larger community into a computational simulation to select sets of simplicial diffusers with the highest degree of information diffusion for health intervention dissemination. The unique contributions of the article also include seven propositions and five algorithmic steps for computationally modeling the simplicial model with Facebook data.

  17. Solutes and cells - aspects of advection-diffusion-reaction phenomena in biochips

    DEFF Research Database (Denmark)

    Vedel, Søren

    2012-01-01

    the dependencies on density. This shows that the varied single-cell behavior including the overall modulations imposed by density arise as a natural consequence of pseudopod-driven motility in a social context. The final subproject concerns the combined effects of advection, diffusion and reaction of several......Cell’), and the overall title of the project is Solutes and cells — aspects of advection-diffusion-reaction phenomena in biochips. The work has consisted of several projects focusing on theory, and to some extend analysis of experimental data, with advection-diffusion-reaction phenomena of solutes as the recurring theme...... quantitatively interpret the proximal concentration of specific solutes, and integrate this to achieve biological functions. In three specific examples, the author and co-workers have investigated different aspects of the influence of advection, diffusion and reaction on solute distributions, as well...

  18. 1D to 3D diffusion-reaction kinetics of defects in crystals

    DEFF Research Database (Denmark)

    Trinkaus, H.; Heinisch, H.L.; Barashev, A.V.

    2002-01-01

    Microstructural features evolving in crystalline solids from diffusion-reaction kinetics of mobile components depend crucially on the dimension of the underlying diffusion process which is commonly assumed to be three-dimensional (3D). In metals, irradiation-induced displacement cascades produce...... clusters of self-interstitials performing 1D diffusion. Changes between equivalent 1D diffusion paths and transversal diffusion result in diffusion-reaction kinetics between one and three dimensions. An analytical approach suggests a single-variable function (master curve) interpolating between the 1D...

  19. Similarity solutions of reaction–diffusion equation with space- and time-dependent diffusion and reaction terms

    Energy Technology Data Exchange (ETDEWEB)

    Ho, C.-L. [Department of Physics, Tamkang University, Tamsui 25137, Taiwan (China); Lee, C.-C., E-mail: chieh.no27@gmail.com [Center of General Education, Aletheia University, Tamsui 25103, Taiwan (China)

    2016-01-15

    We consider solvability of the generalized reaction–diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction–diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction–diffusion systems. Several representative examples of exactly solvable reaction–diffusion equations are presented.

  20. Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes II: Size Effects on Ionic Distributions and Diffusion-Reaction Rates

    Science.gov (United States)

    Lu, Benzhuo; Zhou, Y.C.

    2011-01-01

    The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations. PMID:21575582

  1. Numerical solution of a reaction-diffusion equation

    International Nuclear Information System (INIS)

    Moyano, Edgardo A.; Scarpettini, Alberto F.

    2000-01-01

    The purpose of the present work to continue the observations and the numerical experiences on a reaction-diffusion model, that is a simplified form of the neutronic flux equation. The model is parabolic, nonlinear, with Dirichlet boundary conditions. The purpose is to approximate non trivial solutions, asymptotically stables for t → ∞, that is solutions that tend to the elliptic problem, in the Lyapunov sense. It belongs to the so-called reaction-diffusion equations of semi linear kind, that is, linear equations in the heat operator and they have a nonlinear reaction function, in this case f (u, a, b) = u (a - b u), being u concentration, a and b parameters. The study of the incidence of these parameters take an interest to the neutronic flux physics. So that we search non trivial, positive and bounded solutions. The used algorithm is based on the concept of monotone and ordered sequences, and on the existence theorem of Amann and Sattinger. (author)

  2. Spectroscopy and dynamics of chemical reactions in van der Waals complexes

    International Nuclear Information System (INIS)

    Soorkia, Satchin

    2008-09-01

    Transition metal elements have d valence electrons and are characterized by a great variety of electronic configurations responsible for their specific reactivity. The elements of the second row in particular have 4d and 5s atomic orbitals of similar size and energy which can be both involved in chemical processes. We have been interested in the reactivity of a transition metal element, zirconium, combined with a simple organic functionalized molecule in a van der Waals complex formed in a supersonic molecular beam in the model reaction Zr + CH 3 F. In this context, one of the chemicals reactions that we are interested in leads to the formation of ZrF. The electronic spectroscopy of ZrF in the spectral domain 400 - 470 nm is extremely rich and surprising for a diatomic molecule. With this study, we have been able to identify the ground state of ZrF (X 2 Δ) by simulating the observed rotational structures and obtain essential information on the electronic structure. These experimental results are in agreement with ab initio calculations. The excited states of the complex Zr...F-CH 3 have been studied with a depopulation method. The spectral domain 615 - 700 nm is particularly interesting because it reveals a group of diffuse bands red-shifted and broadened with respect to the transition a 3 F → z 3 F in the metal. This transition is forbidden from the ground state a 3 F 2 of zirconium but allowed from the a 3 F 4 state. Complexation of the metal atom with a CH 3 F molecule allows coupling of these two states to occur which ensures the optical transition from the ground state of the complex. (author)

  3. Estimation and prediction of convection-diffusion-reaction systems from point measurement

    NARCIS (Netherlands)

    Vries, D.

    2008-01-01

    Different procedures with respect to estimation and prediction of systems characterized by convection, diffusion and reactions on the basis of point measurement data, have been studied. Two applications of these convection-diffusion-reaction (CDR) systems have been used as a case study of the

  4. Interface methods for hybrid Monte Carlo-diffusion radiation-transport simulations

    International Nuclear Information System (INIS)

    Densmore, Jeffery D.

    2006-01-01

    Discrete diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Monte Carlo simulations in diffusive media. An important aspect of DDMC is the treatment of interfaces between diffusive regions, where DDMC is used, and transport regions, where standard Monte Carlo is employed. Three previously developed methods exist for treating transport-diffusion interfaces: the Marshak interface method, based on the Marshak boundary condition, the asymptotic interface method, based on the asymptotic diffusion-limit boundary condition, and the Nth-collided source technique, a scheme that allows Monte Carlo particles to undergo several collisions in a diffusive region before DDMC is used. Numerical calculations have shown that each of these interface methods gives reasonable results as part of larger radiation-transport simulations. In this paper, we use both analytic and numerical examples to compare the ability of these three interface techniques to treat simpler, transport-diffusion interface problems outside of a more complex radiation-transport calculation. We find that the asymptotic interface method is accurate regardless of the angular distribution of Monte Carlo particles incident on the interface surface. In contrast, the Marshak boundary condition only produces correct solutions if the incident particles are isotropic. We also show that the Nth-collided source technique has the capacity to yield accurate results if spatial cells are optically small and Monte Carlo particles are allowed to undergo many collisions within a diffusive region before DDMC is employed. These requirements make the Nth-collided source technique impractical for realistic radiation-transport calculations

  5. Cross-diffusional effect in a telegraph reaction diffusion Lotka-Volterra two competitive system

    International Nuclear Information System (INIS)

    Abdusalam, H.A; Fahmy, E.S.

    2003-01-01

    It is known now that, telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion in several branches of sciences. Telegraph reaction diffusion Lotka-Volterra two competitive system is considered. We observed that this system can give rise to diffusive instability only in the presence of cross-diffusion. Local and global stability analysis in the cross-diffusional effect are studied by considering suitable Lyapunov functional

  6. Substitution reactions of technetium complexes

    International Nuclear Information System (INIS)

    Omori, T.

    1997-01-01

    Substitution reactions of a series of technetium complexes are considered in comparison with corresponding reactions of rhenium. Rhenium and technetium complexes are rather inert in substitution reactions, the latter are characterized by greater rate constants when they proceed according to dissociative mechanism. In rare cases when k Tc /k Re id little it is assumed that the reaction proceeds according to the associative mechanism. (author)

  7. Liquid Film Diffusion on Reaction Rate in Submerged Biofilters

    DEFF Research Database (Denmark)

    Christiansen, Pia; Hollesen, Line; Harremoës, Poul

    1995-01-01

    Experiments were carried out in order to investigate the influence of liquid film diffusion on reaction rate in a submerged biofilter with denitrification and in order to compare with a theoretical study of the mass transfer coefficient. The experiments were carried out with varied flow, identified...... by the empty bed velocity of inflow and recirculation, respectively 1.3, 2.8, 5.6 and 10.9 m/h. The filter material consisted of 3 mm biostyren spheres. The results indicate that the influence of liquid film diffusion on reaction rate can be ignored....

  8. Microtubule self-organisation by reaction-diffusion processes causes collective transport and organisation of cellular particles

    Directory of Open Access Journals (Sweden)

    Demongeot Jacques

    2004-06-01

    Full Text Available Abstract Background The transport of intra-cellular particles by microtubules is a major biological function. Under appropriate in vitro conditions, microtubule preparations behave as a 'complex' system and show 'emergent' phenomena. In particular, they form dissipative structures that self-organise over macroscopic distances by a combination of reaction and diffusion. Results Here, we show that self-organisation also gives rise to a collective transport of colloidal particles along a specific direction. Particles, such as polystyrene beads, chromosomes, nuclei, and vesicles are carried at speeds of several microns per minute. The process also results in the macroscopic self-organisation of these particles. After self-organisation is completed, they show the same pattern of organisation as the microtubules. Numerical simulations of a population of growing and shrinking microtubules, incorporating experimentally realistic reaction dynamics, predict self-organisation. They forecast that during self-organisation, macroscopic parallel arrays of oriented microtubules form which cross the reaction space in successive waves. Such travelling waves are capable of transporting colloidal particles. The fact that in the simulations, the aligned arrays move along the same direction and at the same speed as the particles move, suggest that this process forms the underlying mechanism for the observed transport properties. Conclusions This process constitutes a novel physical chemical mechanism by which chemical energy is converted into collective transport of colloidal particles along a given direction. Self-organisation of this type provides a new mechanism by which intra cellular particles such as chromosomes and vesicles can be displaced and simultaneously organised by microtubules. It is plausible that processes of this type occur in vivo.

  9. Microtubule self-organisation by reaction-diffusion processes causes collective transport and organisation of cellular particles

    Science.gov (United States)

    Glade, Nicolas; Demongeot, Jacques; Tabony, James

    2004-01-01

    Background The transport of intra-cellular particles by microtubules is a major biological function. Under appropriate in vitro conditions, microtubule preparations behave as a 'complex' system and show 'emergent' phenomena. In particular, they form dissipative structures that self-organise over macroscopic distances by a combination of reaction and diffusion. Results Here, we show that self-organisation also gives rise to a collective transport of colloidal particles along a specific direction. Particles, such as polystyrene beads, chromosomes, nuclei, and vesicles are carried at speeds of several microns per minute. The process also results in the macroscopic self-organisation of these particles. After self-organisation is completed, they show the same pattern of organisation as the microtubules. Numerical simulations of a population of growing and shrinking microtubules, incorporating experimentally realistic reaction dynamics, predict self-organisation. They forecast that during self-organisation, macroscopic parallel arrays of oriented microtubules form which cross the reaction space in successive waves. Such travelling waves are capable of transporting colloidal particles. The fact that in the simulations, the aligned arrays move along the same direction and at the same speed as the particles move, suggest that this process forms the underlying mechanism for the observed transport properties. Conclusions This process constitutes a novel physical chemical mechanism by which chemical energy is converted into collective transport of colloidal particles along a given direction. Self-organisation of this type provides a new mechanism by which intra cellular particles such as chromosomes and vesicles can be displaced and simultaneously organised by microtubules. It is plausible that processes of this type occur in vivo. PMID:15176973

  10. A minimally-resolved immersed boundary model for reaction-diffusion problems

    OpenAIRE

    Pal Singh Bhalla, A; Griffith, BE; Patankar, NA; Donev, A

    2013-01-01

    We develop an immersed boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a minimally-resolved "blob" using many fewer degrees of freedom per particle than standard discretization approaches. More complicated or more highly resolved particle shapes can be built out of a collection of reactive blobs. We demonstrate numerically that the blo...

  11. The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems

    KAUST Repository

    Di Francesco, M.

    2008-12-08

    We study the long-time asymptotics of reaction-diffusion-type systems that feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimizing) equilibrium state in terms of the constants of diffusion and reaction and with respect to conserved quantities. Our method, the so-called entropy approach, seeks to quantify convergence to equilibrium by using functional inequalities, which relate quantitatively the entropy and its dissipation in time. The entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model variations. It has already been widely applied to scalar diffusion-convection equations, and the main goal of this paper is to study its generalization to systems of partial differential equations that contain diffusion and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid-state physics as a paradigm for general nonlinear systems. © 2008 The Royal Society.

  12. Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)

    2013-01-01

    In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

  13. Oscillatory pulses and wave trains in a bistable reaction-diffusion system with cross diffusion.

    Science.gov (United States)

    Zemskov, Evgeny P; Tsyganov, Mikhail A; Horsthemke, Werner

    2017-01-01

    We study waves with exponentially decaying oscillatory tails in a reaction-diffusion system with linear cross diffusion. To be specific, we consider a piecewise linear approximation of the FitzHugh-Nagumo model, also known as the Bonhoeffer-van der Pol model. We focus on two types of traveling waves, namely solitary pulses that correspond to a homoclinic solution, and sequences of pulses or wave trains, i.e., a periodic solution. The effect of cross diffusion on wave profiles and speed of propagation is analyzed. We find the intriguing result that both pulses and wave trains occur in the bistable cross-diffusive FitzHugh-Nagumo system, whereas only fronts exist in the standard bistable system without cross diffusion.

  14. Flow-Injection Responses of Diffusion Processes and Chemical Reactions

    DEFF Research Database (Denmark)

    Andersen, Jens Enevold Thaulov

    2000-01-01

    tool of automated analytical chemistry. The need for an even lower consumption of chemicals and for computer analysis has motivated a study of the FIA peak itself, that is, a theoretical model was developed, that provides detailed knowledge of the FIA profile. It was shown that the flow in a FIA...... manifold may be characterised by a diffusion coefficient that depends on flow rate, denoted as the kinematic diffusion coefficient. The description was applied to systems involving species of chromium, both in the case of simple diffusion and in the case of chemical reactions. It is suggested that it may...... be used in the resolution of FIA profiles to obtain information about the content of interference’s, in the study of chemical reaction kinetics and to measure absolute concentrations within the FIA-detector cell....

  15. An incomplete assembly with thresholding algorithm for systems of reaction-diffusion equations in three space dimensions IAT for reaction-diffusion systems

    International Nuclear Information System (INIS)

    Moore, Peter K.

    2003-01-01

    Solving systems of reaction-diffusion equations in three space dimensions can be prohibitively expensive both in terms of storage and CPU time. Herein, I present a new incomplete assembly procedure that is designed to reduce storage requirements. Incomplete assembly is analogous to incomplete factorization in that only a fixed number of nonzero entries are stored per row and a drop tolerance is used to discard small values. The algorithm is incorporated in a finite element method-of-lines code and tested on a set of reaction-diffusion systems. The effect of incomplete assembly on CPU time and storage and on the performance of the temporal integrator DASPK, algebraic solver GMRES and preconditioner ILUT is studied

  16. Lattice Boltzmann simulation of endothermal catalytic reaction in catalyst porous media

    International Nuclear Information System (INIS)

    Li Xunfeng; Cai Jun; Xin Fang; Huai Xiulan; Guo Jiangfeng

    2013-01-01

    Gas catalytic reaction in a fixed bed reactor is a general process in chemical industry. The chemical reaction process involves the complex multi-component flow, heat and mass transfer coupling chemical reaction in the catalyst porous structure. The lattice Boltzmann method is developed to simulate the complex process of the surface catalytic reaction in the catalyst porous media. The non-equilibrium extrapolation method is used to treat the boundaries. The porous media is structured by Sierpinski carpet fractal structure. The velocity correction is adopted on the reaction surface. The flow, temperature and concentration fields calculated by the lattice Boltzmann method are compared with those computed by the CFD software. The effects of the inlet velocity, porosity and inlet components ratio on the conversion are also studied. Highlights: ► LBM is developed to simulate the surface catalytic reaction. ► The Sierpinski carpet structure is used to construct the porous media. ► The LBM results are in agreement with the CFD predictions. ► Velocity, temperature and concentration fields are obtained. ► Effects of the velocity, porosity and concentration on conversion are analyzed.

  17. Characterising Complex Enzyme Reaction Data.

    Directory of Open Access Journals (Sweden)

    Handan Melike Dönertaş

    Full Text Available The relationship between enzyme-catalysed reactions and the Enzyme Commission (EC number, the widely accepted classification scheme used to characterise enzyme activity, is complex and with the rapid increase in our knowledge of the reactions catalysed by enzymes needs revisiting. We present a manual and computational analysis to investigate this complexity and found that almost one-third of all known EC numbers are linked to more than one reaction in the secondary reaction databases (e.g., KEGG. Although this complexity is often resolved by defining generic, alternative and partial reactions, we have also found individual EC numbers with more than one reaction catalysing different types of bond changes. This analysis adds a new dimension to our understanding of enzyme function and might be useful for the accurate annotation of the function of enzymes and to study the changes in enzyme function during evolution.

  18. A reaction-diffusion model of ROS-induced ROS release in a mitochondrial network.

    Directory of Open Access Journals (Sweden)

    Lufang Zhou

    2010-01-01

    Full Text Available Loss of mitochondrial function is a fundamental determinant of cell injury and death. In heart cells under metabolic stress, we have previously described how the abrupt collapse or oscillation of the mitochondrial energy state is synchronized across the mitochondrial network by local interactions dependent upon reactive oxygen species (ROS. Here, we develop a mathematical model of ROS-induced ROS release (RIRR based on reaction-diffusion (RD-RIRR in one- and two-dimensional mitochondrial networks. The nodes of the RD-RIRR network are comprised of models of individual mitochondria that include a mechanism of ROS-dependent oscillation based on the interplay between ROS production, transport, and scavenging; and incorporating the tricarboxylic acid (TCA cycle, oxidative phosphorylation, and Ca(2+ handling. Local mitochondrial interaction is mediated by superoxide (O2.- diffusion and the O2.(--dependent activation of an inner membrane anion channel (IMAC. In a 2D network composed of 500 mitochondria, model simulations reveal DeltaPsi(m depolarization waves similar to those observed when isolated guinea pig cardiomyocytes are subjected to a localized laser-flash or antioxidant depletion. The sensitivity of the propagation rate of the depolarization wave to O(2.- diffusion, production, and scavenging in the reaction-diffusion model is similar to that observed experimentally. In addition, we present novel experimental evidence, obtained in permeabilized cardiomyocytes, confirming that DeltaPsi(m depolarization is mediated specifically by O2.-. The present work demonstrates that the observed emergent macroscopic properties of the mitochondrial network can be reproduced in a reaction-diffusion model of RIRR. Moreover, the findings have uncovered a novel aspect of the synchronization mechanism, which is that clusters of mitochondria that are oscillating can entrain mitochondria that would otherwise display stable dynamics. The work identifies the

  19. Modeling the Influence of Diffusion-Controlled Reactions and Residual Termination and Deactivation on the Rate and Control of Bulk ATRP at High Conversions

    Directory of Open Access Journals (Sweden)

    Ali Mohammad Rabea

    2015-04-01

    Full Text Available In high-conversion atom transfer radical polymerization (ATRP, all the reactions, such as radical termination, radical deactivation, dormant chain activation, monomer propagation, etc. could become diffusion controlled sooner or later, depending on relative diffusivities of the involved reacting species. These diffusion-controlled reactions directly affect the rate of polymerization and the control of polymer molecular weight. A model is developed to investigate the influence of diffusion-controlled reactions on the high conversion ATRP kinetics. Model simulation reveals that diffusion-controlled termination slightly increases the rate, but it is the diffusion-controlled deactivation that causes auto-acceleration in the rate (“gel effect” and loss of control. At high conversions, radical chains are “trapped” because of high molecular weight. However, radical centers can still migrate through (1 radical deactivation–activation cycles and (2 monomer propagation, which introduce “residual termination” reactions. It is found that the “residual termination” does not have much influence on the polymerization kinetics. The migration of radical centers through propagation can however facilitate catalytic deactivation of radicals, which improves the control of polymer molecular weight to some extent. Dormant chain activation and monomer propagation also become diffusion controlled and finally stop the polymerization when the system approaches its glass state.

  20. Contribution to an effective design method for stationary reaction-diffusion patterns

    International Nuclear Information System (INIS)

    Szalai, István; Horváth, Judit; De Kepper, Patrick

    2015-01-01

    The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences

  1. Contribution to an effective design method for stationary reaction-diffusion patterns

    Energy Technology Data Exchange (ETDEWEB)

    Szalai, István; Horváth, Judit [Laboratory of Nonlinear Chemical Dynamics, Institute of Chemistry, Eötvös Loránd University, P.O. Box 32, H-1518 Budapest 112 (Hungary); De Kepper, Patrick [Centre de Recherche Paul Pascal, CNRS, University of Bordeaux, 115, Avenue Schweitzer, F-33600 Pessac (France)

    2015-06-15

    The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences.

  2. Hybrid approaches for multiple-species stochastic reaction-diffusion models

    Science.gov (United States)

    Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen

    2015-10-01

    Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

  3. Hybrid approaches for multiple-species stochastic reaction-diffusion models.

    KAUST Repository

    Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K; Byrne, Helen

    2015-01-01

    Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

  4. Hybrid approaches for multiple-species stochastic reaction-diffusion models.

    KAUST Repository

    Spill, Fabian

    2015-10-01

    Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

  5. Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation

    Directory of Open Access Journals (Sweden)

    Petr Stehlík

    2015-01-01

    Full Text Available We study reaction-diffusion equations with a general reaction function f on one-dimensional lattices with continuous or discrete time ux′  (or  Δtux=k(ux-1-2ux+ux+1+f(ux, x∈Z. We prove weak and strong maximum and minimum principles for corresponding initial-boundary value problems. Whereas the maximum principles in the semidiscrete case (continuous time exhibit similar features to those of fully continuous reaction-diffusion model, in the discrete case the weak maximum principle holds for a smaller class of functions and the strong maximum principle is valid in a weaker sense. We describe in detail how the validity of maximum principles depends on the nonlinearity and the time step. We illustrate our results on the Nagumo equation with the bistable nonlinearity.

  6. Wong-Zakai approximations and attractors for stochastic reaction-diffusion equations on unbounded domains

    Science.gov (United States)

    Wang, Xiaohu; Lu, Kening; Wang, Bixiang

    2018-01-01

    In this paper, we study the Wong-Zakai approximations given by a stationary process via the Wiener shift and their associated long term behavior of the stochastic reaction-diffusion equation driven by a white noise. We first prove the existence and uniqueness of tempered pullback attractors for the Wong-Zakai approximations of stochastic reaction-diffusion equation. Then, we show that the attractors of Wong-Zakai approximations converges to the attractor of the stochastic reaction-diffusion equation for both additive and multiplicative noise.

  7. Simulation of anisotropic diffusion by means of a diffusion velocity method

    CERN Document Server

    Beaudoin, A; Rivoalen, E

    2003-01-01

    An alternative method to the Particle Strength Exchange method for solving the advection-diffusion equation in the general case of a non-isotropic and non-uniform diffusion is proposed. This method is an extension of the diffusion velocity method. It is shown that this extension is quite straightforward due to the explicit use of the diffusion flux in the expression of the diffusion velocity. This approach is used to simulate pollutant transport in groundwater and the results are compared to those of the PSE method presented in an earlier study by Zimmermann et al.

  8. NMR diffusion simulation based on conditional random walk.

    Science.gov (United States)

    Gudbjartsson, H; Patz, S

    1995-01-01

    The authors introduce here a new, very fast, simulation method for free diffusion in a linear magnetic field gradient, which is an extension of the conventional Monte Carlo (MC) method or the convolution method described by Wong et al. (in 12th SMRM, New York, 1993, p.10). In earlier NMR-diffusion simulation methods, such as the finite difference method (FD), the Monte Carlo method, and the deterministic convolution method, the outcome of the calculations depends on the simulation time step. In the authors' method, however, the results are independent of the time step, although, in the convolution method the step size has to be adequate for spins to diffuse to adjacent grid points. By always selecting the largest possible time step the computation time can therefore be reduced. Finally the authors point out that in simple geometric configurations their simulation algorithm can be used to reduce computation time in the simulation of restricted diffusion.

  9. Multiscale simulations of patchy particle systems combining Molecular Dynamics, Path Sampling and Green's Function Reaction Dynamics

    Science.gov (United States)

    Bolhuis, Peter

    Important reaction-diffusion processes, such as biochemical networks in living cells, or self-assembling soft matter, span many orders in length and time scales. In these systems, the reactants' spatial dynamics at mesoscopic length and time scales of microns and seconds is coupled to the reactions between the molecules at microscopic length and time scales of nanometers and milliseconds. This wide range of length and time scales makes these systems notoriously difficult to simulate. While mean-field rate equations cannot describe such processes, the mesoscopic Green's Function Reaction Dynamics (GFRD) method enables efficient simulation at the particle level provided the microscopic dynamics can be integrated out. Yet, many processes exhibit non-trivial microscopic dynamics that can qualitatively change the macroscopic behavior, calling for an atomistic, microscopic description. The recently developed multiscale Molecular Dynamics Green's Function Reaction Dynamics (MD-GFRD) approach combines GFRD for simulating the system at the mesocopic scale where particles are far apart, with microscopic Molecular (or Brownian) Dynamics, for simulating the system at the microscopic scale where reactants are in close proximity. The association and dissociation of particles are treated with rare event path sampling techniques. I will illustrate the efficiency of this method for patchy particle systems. Replacing the microscopic regime with a Markov State Model avoids the microscopic regime completely. The MSM is then pre-computed using advanced path-sampling techniques such as multistate transition interface sampling. I illustrate this approach on patchy particle systems that show multiple modes of binding. MD-GFRD is generic, and can be used to efficiently simulate reaction-diffusion systems at the particle level, including the orientational dynamics, opening up the possibility for large-scale simulations of e.g. protein signaling networks.

  10. Large-eddy simulation of a turbulent piloted methane/air diffusion flame (Sandia flame D)

    International Nuclear Information System (INIS)

    Pitsch, H.; Steiner, H.

    2000-01-01

    The Lagrangian Flamelet Model is formulated as a combustion model for large-eddy simulations of turbulent jet diffusion flames. The model is applied in a large-eddy simulation of a piloted partially premixed methane/air diffusion flame (Sandia flame D). The results of the simulation are compared to experimental data of the mean and RMS of the axial velocity and the mixture fraction and the unconditional and conditional averages of temperature and various species mass fractions, including CO and NO. All quantities are in good agreement with the experiments. The results indicate in accordance with experimental findings that regions of high strain appear in layer like structures, which are directed inwards and tend to align with the reaction zone, where the turbulence is fully developed. The analysis of the conditional temperature and mass fractions reveals a strong influence of the partial premixing of the fuel. (c) 2000 American Institute of Physics

  11. Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps

    Science.gov (United States)

    Yi, Taishan; Chen, Yuming

    2017-12-01

    In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.

  12. Remodelling of cellular excitation (reaction) and intercellular coupling (diffusion) by chronic atrial fibrillation represented by a reaction-diffusion system

    Science.gov (United States)

    Zhang, Henggui; Garratt, Clifford J.; Kharche, Sanjay; Holden, Arun V.

    2009-06-01

    Human atrial tissue is an excitable system, in which myocytes are excitable elements, and cell-to-cell electrotonic interactions are via diffusive interactions of cell membrane potentials. We developed a family of excitable system models for human atrium at cellular, tissue and anatomical levels for both normal and chronic atrial fibrillation (AF) conditions. The effects of AF-induced remodelling of cell membrane ionic channels (reaction kinetics) and intercellular gap junctional coupling (diffusion) on atrial excitability, conduction of excitation waves and dynamics of re-entrant excitation waves are quantified. Both ionic channel and gap junctional coupling remodelling have rate dependent effects on atrial propagation. Membrane channel conductance remodelling allows the propagation of activity at higher rates than those sustained in normal tissue or in tissue with gap junctional remodelling alone. Membrane channel conductance remodelling is essential for the propagation of activity at rates higher than 300/min as seen in AF. Spatially heterogeneous gap junction coupling remodelling increased the risk of conduction block, an essential factor for the genesis of re-entry. In 2D and 3D anatomical models, the dynamical behaviours of re-entrant excitation waves are also altered by membrane channel modelling. This study provides insights to understand the pro-arrhythmic effects of AF-induced reaction and diffusion remodelling in atrial tissue.

  13. Defects and diffusion, theory & simulation II

    CERN Document Server

    Fisher, David J

    2010-01-01

    This second volume in a new series covering entirely general results in the fields of defects and diffusion includes 356 abstracts of papers which appeared between the end of 2009 and the end of 2010. As well as the abstracts, the volume includes original papers on theory/simulation, semiconductors and metals: ""Predicting Diffusion Coefficients from First Principles ..."" (Mantina, Chen & Liu), ""Gouge Assessment for Pipes ..."" (Meliani, Pluvinage & Capelle), ""Simulation of the Impact Behaviour of ... Hollow Sphere Structures"" (Ferrano, Speich, Rimkus, Merkel & Öchsner), ""Elastic-Plastic

  14. Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations

    KAUST Repository

    Alzahrani, Hasnaa H.

    2016-07-26

    A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge-Kutta- Chebyshev (RKC) scheme is adjusted to integrate diffusion. Spatial operator is de- scretised by second-order finite differences on a uniform grid. The overall solution is advanced over S fractional stiff integrations, where S corresponds to the number of RKC stages. The behavior of the scheme is analyzed by applying it to three simple problems. The results show that it achieves second-order accuracy, thus, preserving the formal accuracy of the original RKC. The presented development sets the stage for future extensions, particularly, to multidimensional reacting flows with detailed chemistry.

  15. Numerical simulation of impurities diffusion in a semiconductor. Application to the bore case in silicon

    International Nuclear Information System (INIS)

    Monnier, Joel

    1971-01-01

    To make a connection between technological parameters and electrical models it is necessary to know with a good accuracy the shape of the diffusion profiles. To do that we solve Fick's equations taking into account almost all physical phenomena known for diffusion in semiconductors: presence of an oxide layer, point defect diffusion coefficient dependence, impact of internal electric field, limited input flux, segregation coefficient... We have used DIFFUSI to predict diffusion profiles for device simulation programs; greater accuracy is then obtain to compute device properties and to optimize the device itself it is easy. Never accurate methods have still been studied like ionic probe and nuclear reactions to measure with an increased accuracy on the shape of the doping profiles. (author) [fr

  16. Experimental evidence of a diffusion process associated with the mass asymmetry degree of freedom in heavy ion reactions

    International Nuclear Information System (INIS)

    Moretto, L.G.; Babinet, R.P.; Galin, J.; Thompson, S.G.

    1975-01-01

    Dramatic changes of fragment angular distributions over a large range of atomic numbers in the reactions induced by 14 N, 20 Ne, and 40 Ar on natural Ag targets are interpreted as evidence of a diffusion-controlled evolution of an intermediate complex along the mass asymmetry degree of freedom. (Auth.)

  17. BlenX-based compositional modeling of complex reaction mechanisms

    Directory of Open Access Journals (Sweden)

    Judit Zámborszky

    2010-02-01

    Full Text Available Molecular interactions are wired in a fascinating way resulting in complex behavior of biological systems. Theoretical modeling provides a useful framework for understanding the dynamics and the function of such networks. The complexity of the biological networks calls for conceptual tools that manage the combinatorial explosion of the set of possible interactions. A suitable conceptual tool to attack complexity is compositionality, already successfully used in the process algebra field to model computer systems. We rely on the BlenX programming language, originated by the beta-binders process calculus, to specify and simulate high-level descriptions of biological circuits. The Gillespie's stochastic framework of BlenX requires the decomposition of phenomenological functions into basic elementary reactions. Systematic unpacking of complex reaction mechanisms into BlenX templates is shown in this study. The estimation/derivation of missing parameters and the challenges emerging from compositional model building in stochastic process algebras are discussed. A biological example on circadian clock is presented as a case study of BlenX compositionality.

  18. Relaxation and Diffusion in Complex Systems

    CERN Document Server

    Ngai, K L

    2011-01-01

    Relaxation and Diffusion in Complex Systems comprehensively presents a variety of experimental evidences of universal relaxation and diffusion properties in complex materials and systems. The materials discussed include liquids, glasses, colloids, polymers, rubbers, plastic crystals and aqueous mixtures, as well as carbohydrates, biomolecules, bioprotectants and pharmaceuticals. Due to the abundance of experimental data, emphasis is placed on glass-formers and the glass transition problem, a still unsolved problem in condensed matter physics and chemistry. The evidence for universal properties of relaxation and diffusion dynamics suggests that a fundamental physical law is at work. The origin of the universal properties is traced to the many-body effects of the interaction, rigorous theory of which does not exist at the present time. However, using solutions of simplified models as guides, key quantities have been identified and predictions of the universal properties generated. These predictions from Ngai’...

  19. Diffusion in Altered Tonalite Sample Using Time Domain Diffusion Simulations in Tomographic Images Combined with Lab-scale Diffusion Experiments

    Science.gov (United States)

    Voutilainen, M.; Sardini, P.; Togneri, L.; Siitari-Kauppi, M.; Timonen, J.

    2010-12-01

    In this work an effect of rock heterogeneity on diffusion was investigated. Time domain diffusion simulations were used to compare behavior of diffusion in homogeneous and heterogeneous 3D media. Tomographic images were used as heterogeneous rock media. One altered tonalite sample from Sievi, Finland, was chosen as test case for introduced analysis procedure. Effective diffusion coefficient of tonalite sample was determined with lab-scale experiments and the same coefficient was used also for homogeneous media. Somewhat technically complicated mathematical solution for analysis of through diffusion experiment is shortly described. Computed tomography (CT) is already quite widely used in many geological, petrological, and paleontological applications when the three-dimensional (3D) structure of the material is of interest, and is an excellent method for gaining information especially about its heterogeneity, grain size, or porosity. In addition to offering means for quantitative characterization, CT provides a lot of qualitative information [1]. A through -diffusion laboratory experiment using radioactive tracer was fitted using the Time Domain Diffusion (TDD) method. This rapid particle tracking method allows simulation of the heterogeneous diffusion based on pore-scale images and local values of diffusivities [2]. As a result we found out that heterogeneity has only a small effect to diffusion coefficient and in-diffusion profile for used geometry. Also direction dependency was tested and was found to be negligible. Whereas significant difference between generally accepted value and value obtained from simulations for constant m in Archie’s law was found. [1] Voutilainen, M., Siitari-Kauppi, M., Sardini, P., and Timonen, J., (2010). On pore-space characterization of an altered tonalite by X-ray µCT and the 14C-PMMA method (in progress). [2] Sardini, P., Robinet, J., Siitari-Kauppi, M., Delay, F., and Hellmuth, K-H, (2007). On direct simulation of heterogeneous

  20. Anomalous dimension in a two-species reaction-diffusion system

    Science.gov (United States)

    Vollmayr-Lee, Benjamin; Hanson, Jack; McIsaac, R. Scott; Hellerick, Joshua D.

    2018-01-01

    We study a two-species reaction-diffusion system with the reactions A+A\\to (0, A) and A+B\\to A , with general diffusion constants D A and D B . Previous studies showed that for dimensions d≤slant 2 the B particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the scaled B particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling \\tilde CBB(r, t) ˜ tφf(r/\\sqrt{t}) , where the exponent ϕ results from the renormalization of the square of the field associated with the B particles. We compute this exponent to first order in \

  1. Reaction effects in diffusive shock acceleration

    International Nuclear Information System (INIS)

    Drury, L.Oc.

    1984-01-01

    The effects of the reaction of accelerated particles back on the shock wave in the diffusive-shock-acceleration model of cosmic-ray generation are investigated theoretically. Effects examined include changes in the shock structure, modifications of the input and output spectra, scattering effects, and possible instabilities in the small-scale structure. It is pointed out that the latter two effects are applicable to any spatially localized acceleration mechanism. 14 references

  2. A Weak Comparison Principle for Reaction-Diffusion Systems

    Directory of Open Access Journals (Sweden)

    José Valero

    2012-01-01

    Full Text Available We prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation, and to a model of fractional-order chemical autocatalysis with decay. Moreover, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functions L∞ is proved for at least one solution of the problem.

  3. Pattern formation in reaction diffusion systems with finite geometry

    International Nuclear Information System (INIS)

    Borzi, C.; Wio, H.

    1990-04-01

    We analyze the one-component, one-dimensional, reaction-diffusion equation through a simple inverse method. We confine the system and fix the boundary conditions as to induce pattern formation. We analyze the stability of those patterns. Our goal is to get information about the reaction term out of the preknowledgment of the pattern. (author). 5 refs

  4. Analysis of Brownian Dynamics Simulations of Reversible Bimolecular Reactions

    KAUST Repository

    Lipková, Jana

    2011-01-01

    A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which include reversible bimolecular reactions is presented and analyzed. The method is a generalization of the λ-bcȳ model for irreversible bimolecular reactions which was introduced in [R. Erban and S. J. Chapman, Phys. Biol., 6(2009), 046001]. The formulae relating the experimentally measurable quantities (reaction rate constants and diffusion constants) with the algorithm parameters are derived. The probability of geminate recombination is also investigated. © 2011 Society for Industrial and Applied Mathematics.

  5. Large-time behavior of solutions to a reaction-diffusion system with distributed microstructure

    NARCIS (Netherlands)

    Muntean, A.

    2009-01-01

    Abstract We study the large-time behavior of a class of reaction-diffusion systems with constant distributed microstructure arising when modeling diffusion and reaction in structured porous media. The main result of this Note is the following: As t ¿ 8 the macroscopic concentration vanishes, while

  6. Exact solutions of certain nonlinear chemotaxis diffusion reaction ...

    Indian Academy of Sciences (India)

    constructed coupled differential equations. The results obtained ... Nonlinear diffusion reaction equation; chemotaxis; auxiliary equation method; solitary wave solutions. ..... fact limits the scope of applications of the derived results. ... Research Fellowship and AP acknowledges DU and DST for PURSE grant for financial.

  7. Computational Analyses of Complex Flows with Chemical Reactions

    Science.gov (United States)

    Bae, Kang-Sik

    The heat and mass transfer phenomena in micro-scale for the mass transfer phenomena on drug in cylindrical matrix system, the simulation of oxygen/drug diffusion in a three dimensional capillary network, and a reduced chemical kinetic modeling of gas turbine combustion for Jet propellant-10 have been studied numerically. For the numerical analysis of the mass transfer phenomena on drug in cylindrical matrix system, the governing equations are derived from the cylindrical matrix systems, Krogh cylinder model, which modeling system is comprised of a capillary to a surrounding cylinder tissue along with the arterial distance to veins. ADI (Alternative Direction Implicit) scheme and Thomas algorithm are applied to solve the nonlinear partial differential equations (PDEs). This study shows that the important factors which have an effect on the drug penetration depth to the tissue are the mass diffusivity and the consumption of relevant species during the time allowed for diffusion to the brain tissue. Also, a computational fluid dynamics (CFD) model has been developed to simulate the blood flow and oxygen/drug diffusion in a three dimensional capillary network, which are satisfied in the physiological range of a typical capillary. A three dimensional geometry has been constructed to replicate the one studied by Secomb et al. (2000), and the computational framework features a non-Newtonian viscosity model for blood, the oxygen transport model including in oxygen-hemoglobin dissociation and wall flux due to tissue absorption, as well as an ability to study the diffusion of drugs and other materials in the capillary streams. Finally, a chemical kinetic mechanism of JP-10 has been compiled and validated for a wide range of combustion regimes, covering pressures of 1atm to 40atm with temperature ranges of 1,200 K--1,700 K, which is being studied as a possible Jet propellant for the Pulse Detonation Engine (PDE) and other high-speed flight applications such as hypersonic

  8. Reaction diffusion equations with boundary degeneracy

    Directory of Open Access Journals (Sweden)

    Huashui Zhan

    2016-03-01

    Full Text Available In this article, we consider the reaction diffusion equation $$ \\frac{\\partial u}{\\partial t} = \\Delta A(u,\\quad (x,t\\in \\Omega \\times (0,T, $$ with the homogeneous boundary condition. Inspired by the Fichera-Oleinik theory, if the equation is not only strongly degenerate in the interior of $\\Omega$, but also degenerate on the boundary, we show that the solution of the equation is free from any limitation of the boundary condition.

  9. Synchronization of Reaction-Diffusion Neural Networks With Dirichlet Boundary Conditions and Infinite Delays.

    Science.gov (United States)

    Sheng, Yin; Zhang, Hao; Zeng, Zhigang

    2017-10-01

    This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.

  10. Traveling and Pinned Fronts in Bistable Reaction-Diffusion Systems on Networks

    Science.gov (United States)

    Kouvaris, Nikos E.; Kori, Hiroshi; Mikhailov, Alexander S.

    2012-01-01

    Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks. Here, we consider traveling and stationary patterns in bistable one-component systems on random Erdös-Rényi, scale-free and hierarchical tree networks. As revealed through numerical simulations, traveling fronts exist in network-organized systems. They represent waves of transition from one stable state into another, spreading over the entire network. The fronts can furthermore be pinned, thus forming stationary structures. While pinning of fronts has previously been considered for chains of diffusively coupled bistable elements, the network architecture brings about significant differences. An important role is played by the degree (the number of connections) of a node. For regular trees with a fixed branching factor, the pinning conditions are analytically determined. For large Erdös-Rényi and scale-free networks, the mean-field theory for stationary patterns is constructed. PMID:23028746

  11. Thermally activated reaction–diffusion-controlled chemical bulk reactions of gases and solids

    Directory of Open Access Journals (Sweden)

    S. Möller

    2015-01-01

    Full Text Available The chemical kinetics of the reaction of thin films with reactive gases is investigated. The removal of thin films using thermally activated solid–gas to gas reactions is a method to in-situ control deposition inventory in vacuum and plasma vessels. Significant scatter of experimental deposit removal rates at apparently similar conditions was observed in the past, highlighting the need for understanding the underlying processes. A model based on the presence of reactive gas in the films bulk and chemical kinetics is presented. The model describes the diffusion of reactive gas into the film and its chemical interaction with film constituents in the bulk using a stationary reaction–diffusion equation. This yields the reactive gas concentration and reaction rates. Diffusion and reaction rate limitations are depicted in parameter studies. Comparison with literature data on tokamak co-deposit removal results in good agreement of removal rates as a function of pressure, film thickness and temperature.

  12. Stochastic simulation of enzyme-catalyzed reactions with disparate timescales.

    Science.gov (United States)

    Barik, Debashis; Paul, Mark R; Baumann, William T; Cao, Yang; Tyson, John J

    2008-10-01

    Many physiological characteristics of living cells are regulated by protein interaction networks. Because the total numbers of these protein species can be small, molecular noise can have significant effects on the dynamical properties of a regulatory network. Computing these stochastic effects is made difficult by the large timescale separations typical of protein interactions (e.g., complex formation may occur in fractions of a second, whereas catalytic conversions may take minutes). Exact stochastic simulation may be very inefficient under these circumstances, and methods for speeding up the simulation without sacrificing accuracy have been widely studied. We show that the "total quasi-steady-state approximation" for enzyme-catalyzed reactions provides a useful framework for efficient and accurate stochastic simulations. The method is applied to three examples: a simple enzyme-catalyzed reaction where enzyme and substrate have comparable abundances, a Goldbeter-Koshland switch, where a kinase and phosphatase regulate the phosphorylation state of a common substrate, and coupled Goldbeter-Koshland switches that exhibit bistability. Simulations based on the total quasi-steady-state approximation accurately capture the steady-state probability distributions of all components of these reaction networks. In many respects, the approximation also faithfully reproduces time-dependent aspects of the fluctuations. The method is accurate even under conditions of poor timescale separation.

  13. First principles-based multiparadigm, multiscale strategy for simulating complex materials processes with applications to amorphous SiC films

    Energy Technology Data Exchange (ETDEWEB)

    Naserifar, Saber [Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211 (United States); Materials and Process Simulation Center, California Institute of Technology, Pasadena, California 91125 (United States); Goddard, William A. [Materials and Process Simulation Center, California Institute of Technology, Pasadena, California 91125 (United States); Tsotsis, Theodore T.; Sahimi, Muhammad, E-mail: moe@usc.edu [Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211 (United States)

    2015-05-07

    Progress has recently been made in developing reactive force fields to describe chemical reactions in systems too large for quantum mechanical (QM) methods. In particular, ReaxFF, a force field with parameters that are obtained solely from fitting QM reaction data, has been used to predict structures and properties of many materials. Important applications require, however, determination of the final structures produced by such complex processes as chemical vapor deposition, atomic layer deposition, and formation of ceramic films by pyrolysis of polymers. This requires the force field to properly describe the formation of other products of the process, in addition to yielding the final structure of the material. We describe a strategy for accomplishing this and present an example of its use for forming amorphous SiC films that have a wide variety of applications. Extensive reactive molecular dynamics (MD) simulations have been carried out to simulate the pyrolysis of hydridopolycarbosilane. The reaction products all agree with the experimental data. After removing the reaction products, the system is cooled down to room temperature at which it produces amorphous SiC film, for which the computed radial distribution function, x-ray diffraction pattern, and the equation of state describing the three main SiC polytypes agree with the data and with the QM calculations. Extensive MD simulations have also been carried out to compute other structural properties, as well the effective diffusivities of light gases in the amorphous SiC film.

  14. Variational methods applied to problems of diffusion and reaction

    CERN Document Server

    Strieder, William

    1973-01-01

    This monograph is an account of some problems involving diffusion or diffusion with simultaneous reaction that can be illuminated by the use of variational principles. It was written during a period that included sabbatical leaves of one of us (W. S. ) at the University of Minnesota and the other (R. A. ) at the University of Cambridge and we are grateful to the Petroleum Research Fund for helping to support the former and the Guggenheim Foundation for making possible the latter. We would also like to thank Stephen Prager for getting us together in the first place and for showing how interesting and useful these methods can be. We have also benefitted from correspondence with Dr. A. M. Arthurs of the University of York and from the counsel of Dr. B. D. Coleman the general editor of this series. Table of Contents Chapter 1. Introduction and Preliminaries . 1. 1. General Survey 1 1. 2. Phenomenological Descriptions of Diffusion and Reaction 2 1. 3. Correlation Functions for Random Suspensions 4 1. 4. Mean Free ...

  15. Distribution in flowing reaction-diffusion systems

    KAUST Repository

    Kamimura, Atsushi; Herrmann, Hans J.; Ito, Nobuyasu

    2009-01-01

    A power-law distribution is found in the density profile of reacting systems A+B→C+D and 2A→2C under a flow in two and three dimensions. Different densities of reactants A and B are fixed at both ends. For the reaction A+B, the concentration of reactants asymptotically decay in space as x-1/2 and x-3/4 in two dimensions and three dimensions, respectively. For 2A, it decays as log (x) /x in two dimensions. The decay of A+B is explained considering the effect of segregation of reactants in the isotropic case. The decay for 2A is explained by the marginal behavior of two-dimensional diffusion. A logarithmic divergence of the diffusion constant with system size is found in two dimensions. © 2009 The American Physical Society.

  16. Distribution in flowing reaction-diffusion systems

    KAUST Repository

    Kamimura, Atsushi

    2009-12-28

    A power-law distribution is found in the density profile of reacting systems A+B→C+D and 2A→2C under a flow in two and three dimensions. Different densities of reactants A and B are fixed at both ends. For the reaction A+B, the concentration of reactants asymptotically decay in space as x-1/2 and x-3/4 in two dimensions and three dimensions, respectively. For 2A, it decays as log (x) /x in two dimensions. The decay of A+B is explained considering the effect of segregation of reactants in the isotropic case. The decay for 2A is explained by the marginal behavior of two-dimensional diffusion. A logarithmic divergence of the diffusion constant with system size is found in two dimensions. © 2009 The American Physical Society.

  17. Hopf bifurcation in a delayed reaction-diffusion-advection population model

    Science.gov (United States)

    Chen, Shanshan; Lou, Yuan; Wei, Junjie

    2018-04-01

    In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator. Our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction-diffusion-advection model, and the model can exhibit oscillatory pattern through Hopf bifurcation. The effect of advection on Hopf bifurcation values is also considered, and our results suggest that Hopf bifurcation is more likely to occur when the advection rate increases.

  18. Multi-Algorithm Particle Simulations with Spatiocyte.

    Science.gov (United States)

    Arjunan, Satya N V; Takahashi, Koichi

    2017-01-01

    As quantitative biologists get more measurements of spatially regulated systems such as cell division and polarization, simulation of reaction and diffusion of proteins using the data is becoming increasingly relevant to uncover the mechanisms underlying the systems. Spatiocyte is a lattice-based stochastic particle simulator for biochemical reaction and diffusion processes. Simulations can be performed at single molecule and compartment spatial scales simultaneously. Molecules can diffuse and react in 1D (filament), 2D (membrane), and 3D (cytosol) compartments. The implications of crowded regions in the cell can be investigated because each diffusing molecule has spatial dimensions. Spatiocyte adopts multi-algorithm and multi-timescale frameworks to simulate models that simultaneously employ deterministic, stochastic, and particle reaction-diffusion algorithms. Comparison of light microscopy images to simulation snapshots is supported by Spatiocyte microscopy visualization and molecule tagging features. Spatiocyte is open-source software and is freely available at http://spatiocyte.org .

  19. Solitary wave solutions of selective nonlinear diffusion-reaction ...

    Indian Academy of Sciences (India)

    An auto-Bäcklund transformation derived in the homogeneous balance method is employed to obtain several new exact solutions of certain kinds of nonlin- ear diffusion-reaction (D-R) equations. These equations arise in a variety of problems in physical, chemical, biological, social and ecological sciences. Keywords.

  20. Diffusion of Sites versus Polymers in Polyelectrolyte Complexes and Multilayers.

    Science.gov (United States)

    Fares, Hadi M; Schlenoff, Joseph B

    2017-10-18

    It has long been assumed that the spontaneous formation of materials such as complexes and multilayers from charged polymers depends on (inter)diffusion of these polyelectrolytes. Here, we separately examine the mass transport of polymer molecules and extrinsic sites-charged polyelectrolyte repeat units balanced by counterions-within thin films of polyelectrolyte complex, PEC, using sensitive isotopic labeling techniques. The apparent diffusion coefficients of these sites within PEC films of poly(diallyldimethylammonium), PDADMA, and poly(styrenesulfonate), PSS, are at least 2 orders of magnitude faster than the diffusion of polyelectrolytes themselves. This is because site diffusion requires only local rearrangements of polyelectrolyte repeat units, placing far fewer kinetic limitations on the assembly of polyelectrolyte complexes in all of their forms. Site diffusion strongly depends on the salt concentration (ionic strength) of the environment, and diffusion of PDADMA sites is faster than that of PSS sites, accounting for the asymmetric nature of multilayer growth. Site diffusion is responsible for multilayer growth in the linear and into the exponential regimes, which explains how PDADMA can mysteriously "pass through" layers of PSS. Using quantitative relationships between site diffusion coefficient and salt concentration, conditions were identified that allowed the diffusion length to always exceed the film thickness, leading to full exponential growth over 3 orders of magnitude thickness. Both site and polymer diffusion were independent of molecular weight, suggesting that ion pairing density is a limiting factor. Polyelectrolyte complexes are examples of a broader class of dynamic bulk polymeric materials that (self-) assemble via the transport of cross-links or defects rather than actual molecules.

  1. Smoldyn on graphics processing units: massively parallel Brownian dynamics simulations.

    Science.gov (United States)

    Dematté, Lorenzo

    2012-01-01

    Space is a very important aspect in the simulation of biochemical systems; recently, the need for simulation algorithms able to cope with space is becoming more and more compelling. Complex and detailed models of biochemical systems need to deal with the movement of single molecules and particles, taking into consideration localized fluctuations, transportation phenomena, and diffusion. A common drawback of spatial models lies in their complexity: models can become very large, and their simulation could be time consuming, especially if we want to capture the systems behavior in a reliable way using stochastic methods in conjunction with a high spatial resolution. In order to deliver the promise done by systems biology to be able to understand a system as whole, we need to scale up the size of models we are able to simulate, moving from sequential to parallel simulation algorithms. In this paper, we analyze Smoldyn, a widely diffused algorithm for stochastic simulation of chemical reactions with spatial resolution and single molecule detail, and we propose an alternative, innovative implementation that exploits the parallelism of Graphics Processing Units (GPUs). The implementation executes the most computational demanding steps (computation of diffusion, unimolecular, and bimolecular reaction, as well as the most common cases of molecule-surface interaction) on the GPU, computing them in parallel on each molecule of the system. The implementation offers good speed-ups and real time, high quality graphics output

  2. The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems

    KAUST Repository

    Di Francesco, M.; Fellner, K.; Markowich, P. A

    2008-01-01

    and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid

  3. Turing patterns induced by cross-diffusion in a predator-prey system in presence of habitat complexity

    International Nuclear Information System (INIS)

    Ghorai, Santu; Poria, Swarup

    2016-01-01

    In this paper, we have investigated the phenomena of Turing pattern formation in a predator-prey model with habitat complexity in presence of cross diffusion. Using the linear stability analysis, the conditions for the existence of stationary pattern and the existence of Hopf bifurcation are obtained. It is shown analytically that the presence of cross diffusion in the system supports the formation of Turing pattern. Two parameter bifurcation analysis are done analytically and corresponding bifurcation diagrams are presented numerically. A series of simulation results are plotted for different biologically meaningful parameter values. Effects of variation of habitat complexity and the predator mortality rate and birth rate of prey on pattern formation are also reported. It is shown that cross-diffusion can lead to a wide variety of spatial and spatiotemporal pattern formation. It is found that the model exhibits spot and stripe pattern, and coexistence of both spot and strip patterns under the zero flux boundary condition. It is observed that cross-diffusion, habitat complexity, birth rate of prey and predator’s mortality rate play a significant role in the pattern formation of a distributed population system of predator-prey type.

  4. Explosive instabilities of reaction-diffusion equations including pinch effects

    International Nuclear Information System (INIS)

    Wilhelmsson, H.

    1992-01-01

    Particular solutions of reaction-diffusion equations for temperature are obtained for explosively unstable situations. As a result of the interplay between inertial, diffusion, pinch and source processes certain 'bell-shaped' distributions may grow explosively in time with preserved shape of the spatial distribution. The effect of the pinch, which requires a density inhomogeneity, is found to diminish the effect of diffusion, or inversely to support the inertial and source processes in creating the explosion. The results may be described in terms of elliptic integrals or. more simply, by means of expansions in the spatial coordinate. An application is the temperature evolution of a burning fusion plasma. (au) (18 refs.)

  5. Knowledge diffusion in complex networks by considering time-varying information channels

    Science.gov (United States)

    Zhu, He; Ma, Jing

    2018-03-01

    In this article, based on a model of epidemic spreading, we explore the knowledge diffusion process with an innovative mechanism for complex networks by considering time-varying information channels. To cover the knowledge diffusion process in homogeneous and heterogeneous networks, two types of networks (the BA network and the ER network) are investigated. The mean-field theory is used to theoretically draw the knowledge diffusion threshold. Numerical simulation demonstrates that the knowledge diffusion threshold is almost linearly correlated with the mean of the activity rate. In addition, under the influence of the activity rate and distinct from the classic Susceptible-Infected-Susceptible (SIS) model, the density of knowers almost linearly grows with the spreading rate. Finally, in consideration of the ubiquitous mechanism of innovation, we further study the evolution of knowledge in our proposed model. The results suggest that compared with the effect of the spreading rate, the average knowledge version of the population is affected more by the innovation parameter and the mean of the activity rate. Furthermore, in the BA network, the average knowledge version of individuals with higher degree is always newer than those with lower degree.

  6. Ponzi scheme diffusion in complex networks

    Science.gov (United States)

    Zhu, Anding; Fu, Peihua; Zhang, Qinghe; Chen, Zhenyue

    2017-08-01

    Ponzi schemes taking the form of Internet-based financial schemes have been negatively affecting China's economy for the last two years. Because there is currently a lack of modeling research on Ponzi scheme diffusion within social networks yet, we develop a potential-investor-divestor (PID) model to investigate the diffusion dynamics of Ponzi scheme in both homogeneous and inhomogeneous networks. Our simulation study of artificial and real Facebook social networks shows that the structure of investor networks does indeed affect the characteristics of dynamics. Both the average degree of distribution and the power-law degree of distribution will reduce the spreading critical threshold and will speed up the rate of diffusion. A high speed of diffusion is the key to alleviating the interest burden and improving the financial outcomes for the Ponzi scheme operator. The zero-crossing point of fund flux function we introduce proves to be a feasible index for reflecting the fast-worsening situation of fiscal instability and predicting the forthcoming collapse. The faster the scheme diffuses, the higher a peak it will reach and the sooner it will collapse. We should keep a vigilant eye on the harm of Ponzi scheme diffusion through modern social networks.

  7. A Reaction-Diffusion-Based Coding Rate Control Mechanism for Camera Sensor Networks

    Directory of Open Access Journals (Sweden)

    Naoki Wakamiya

    2010-08-01

    Full Text Available A wireless camera sensor network is useful for surveillance and monitoring for its visibility and easy deployment. However, it suffers from the limited capacity of wireless communication and a network is easily overflown with a considerable amount of video traffic. In this paper, we propose an autonomous video coding rate control mechanism where each camera sensor node can autonomously determine its coding rate in accordance with the location and velocity of target objects. For this purpose, we adopted a biological model, i.e., reaction-diffusion model, inspired by the similarity of biological spatial patterns and the spatial distribution of video coding rate. Through simulation and practical experiments, we verify the effectiveness of our proposal.

  8. A reaction-diffusion-based coding rate control mechanism for camera sensor networks.

    Science.gov (United States)

    Yamamoto, Hiroshi; Hyodo, Katsuya; Wakamiya, Naoki; Murata, Masayuki

    2010-01-01

    A wireless camera sensor network is useful for surveillance and monitoring for its visibility and easy deployment. However, it suffers from the limited capacity of wireless communication and a network is easily overflown with a considerable amount of video traffic. In this paper, we propose an autonomous video coding rate control mechanism where each camera sensor node can autonomously determine its coding rate in accordance with the location and velocity of target objects. For this purpose, we adopted a biological model, i.e., reaction-diffusion model, inspired by the similarity of biological spatial patterns and the spatial distribution of video coding rate. Through simulation and practical experiments, we verify the effectiveness of our proposal.

  9. Effects on nuclear fusion reaction on diffusion and thermal conduction in a magnetoplasma

    International Nuclear Information System (INIS)

    Sakai, Kazuo; Aono, Osamu.

    1976-12-01

    In spite of the well spread belief in the field of irreversible thermodynamics, vectorial phenomena couple thermodynamically with the scalar phenomena. Transport coefficients concerning the diffusion and the thermal conduction across a strong magnetic field are calculated in the presence of the deuteron-triton fusion reaction on the basis of the gas kinetic theory. When the reaction takes place, the diffusion increases and the thermal conduction decreases. Effects of the reaction exceed those of the Coulomb collision as the temperature is high enough. (auth.)

  10. Exact solutions of some coupled nonlinear diffusion-reaction ...

    Indian Academy of Sciences (India)

    certain coupled diffusion-reaction (D-R) equations of very general nature. In recent years, various direct methods have been proposed to find the exact solu- tions not only of nonlinear partial differential equations but also of their coupled versions. These methods include unified ansatz approach [3], extended hyperbolic func ...

  11. Simulation of diffusion in concentrated lattice gases

    International Nuclear Information System (INIS)

    Kehr, K.W.

    1986-01-01

    Recently the diffusion of particles in lattice gases was studied extensively by theoretical methods and numerical simulations. This paper reviews work on collective and, in particular, on tracer diffusion. The diffusion of tagged particles is characterized by a correlation factor whose behavior as a function of concentration is now well understood. Also the detailed kinetics of the tracer transitions was investigated. A special case is the one-dimensional lattice gas where the tracer diffusion coefficient vanishes. An interesting extension is the case of tagged atoms with a different transition rate. This model allows to study various physical situations, including impurity diffusion, percolation, and diffusion in partially blocked lattices. Finally some recent work on diffusion in lattice gases under the influence of a drift field will be reported. (author)

  12. Heat Diffusion in Gases, Including Effects of Chemical Reaction

    Science.gov (United States)

    Hansen, C. Frederick

    1960-01-01

    The diffusion of heat through gases is treated where the coefficients of thermal conductivity and diffusivity are functions of temperature. The diffusivity is taken proportional to the integral of thermal conductivity, where the gas is ideal, and is considered constant over the temperature interval in which a chemical reaction occurs. The heat diffusion equation is then solved numerically for a semi-infinite gas medium with constant initial and boundary conditions. These solutions are in a dimensionless form applicable to gases in general, and they are used, along with measured shock velocity and heat flux through a shock reflecting surface, to evaluate the integral of thermal conductivity for air up to 5000 degrees Kelvin. This integral has the properties of a heat flux potential and replaces temperature as the dependent variable for problems of heat diffusion in media with variable coefficients. Examples are given in which the heat flux at the stagnation region of blunt hypersonic bodies is expressed in terms of this potential.

  13. Physics of positronium acceptor complex formation reactions

    International Nuclear Information System (INIS)

    Gangopadhyay, Debarshi; Ganguly, Bichitra Nandi; Mukherjee, Tapas; Dutta-Roy, Binayak

    2002-01-01

    Positronium (P s ) reaction rates (κ) with weak Acceptors (Ac) leading to the formation of Ps-Ac complexes show several interesting features: non-monotonic temperature dependence of κ(departing from the usual Arrhenius behaviour), considerable variability of κ with respect to different solvents, and anomalies in response to external pressure at ambient temperature. The object of this work is to explain all these phenomena using a remarkably simple bubble model (the widely used model for the pick-off component of ortho-positronium decay in liquids), which has been revisited several times in the context and as a result smooth diffuse boundary of the bubble was suggested that yields reasonable agreement of the experimental data. The contractile force on the bubble relies much on the surface tension of the liquid, through our calculation the notion of critical surface tension emerges and enables us to explain the experimental observations satisfactorily. (author)

  14. Post-processing interstitialcy diffusion from molecular dynamics simulations

    Energy Technology Data Exchange (ETDEWEB)

    Bhardwaj, U., E-mail: haptork@gmail.com [Computational Analysis Division, BARC, Visakhapatnam, Andhra Pradesh, 530012 (India); Bukkuru, S. [Nuclear Physics Dept., Andhra University, Visakhapatnam, 530003 (India); Warrier, M. [Computational Analysis Division, BARC, Visakhapatnam, Andhra Pradesh, 530012 (India)

    2016-01-15

    An algorithm to rigorously trace the interstitialcy diffusion trajectory in crystals is developed. The algorithm incorporates unsupervised learning and graph optimization which obviate the need to input extra domain specific information depending on crystal or temperature of the simulation. The algorithm is implemented in a flexible framework as a post-processor to molecular dynamics (MD) simulations. We describe in detail the reduction of interstitialcy diffusion into known computational problems of unsupervised clustering and graph optimization. We also discuss the steps, computational efficiency and key components of the algorithm. Using the algorithm, thermal interstitialcy diffusion from low to near-melting point temperatures is studied. We encapsulate the algorithms in a modular framework with functionality to calculate diffusion coefficients, migration energies and other trajectory properties. The study validates the algorithm by establishing the conformity of output parameters with experimental values and provides detailed insights for the interstitialcy diffusion mechanism. The algorithm along with the help of supporting visualizations and analysis gives convincing details and a new approach to quantifying diffusion jumps, jump-lengths, time between jumps and to identify interstitials from lattice atoms. -- Graphical abstract:.

  15. Post-processing interstitialcy diffusion from molecular dynamics simulations

    International Nuclear Information System (INIS)

    Bhardwaj, U.; Bukkuru, S.; Warrier, M.

    2016-01-01

    An algorithm to rigorously trace the interstitialcy diffusion trajectory in crystals is developed. The algorithm incorporates unsupervised learning and graph optimization which obviate the need to input extra domain specific information depending on crystal or temperature of the simulation. The algorithm is implemented in a flexible framework as a post-processor to molecular dynamics (MD) simulations. We describe in detail the reduction of interstitialcy diffusion into known computational problems of unsupervised clustering and graph optimization. We also discuss the steps, computational efficiency and key components of the algorithm. Using the algorithm, thermal interstitialcy diffusion from low to near-melting point temperatures is studied. We encapsulate the algorithms in a modular framework with functionality to calculate diffusion coefficients, migration energies and other trajectory properties. The study validates the algorithm by establishing the conformity of output parameters with experimental values and provides detailed insights for the interstitialcy diffusion mechanism. The algorithm along with the help of supporting visualizations and analysis gives convincing details and a new approach to quantifying diffusion jumps, jump-lengths, time between jumps and to identify interstitials from lattice atoms. -- Graphical abstract:

  16. Non-Archimedean reaction-ultradiffusion equations and complex hierarchic systems

    Science.gov (United States)

    Zúñiga-Galindo, W. A.

    2018-06-01

    We initiate the study of non-Archimedean reaction-ultradiffusion equations and their connections with models of complex hierarchic systems. From a mathematical perspective, the equations studied here are the p-adic counterpart of the integro-differential models for phase separation introduced by Bates and Chmaj. Our equations are also generalizations of the ultradiffusion equations on trees studied in the 1980s by Ogielski, Stein, Bachas, Huberman, among others, and also generalizations of the master equations of the Avetisov et al models, which describe certain complex hierarchic systems. From a physical perspective, our equations are gradient flows of non-Archimedean free energy functionals and their solutions describe the macroscopic density profile of a bistable material whose space of states has an ultrametric structure. Some of our results are p-adic analogs of some well-known results in the Archimedean setting, however, the mechanism of diffusion is completely different due to the fact that it occurs in an ultrametric space.

  17. Simulation of diffusion-induced stress using reconstructed electrodes particle structures generated by micro/nano-CT

    International Nuclear Information System (INIS)

    Lim, Cheolwoong; Yan Bo; Yin Leilei; Zhu Likun

    2012-01-01

    Highlights: ► The microstructure of LIB electrodes was obtained by X-ray micro/nano-CT. ► We studied diffusion-induced stresses based on realistic 3D microstructures. ► Stresses depend on geometric characteristics of electrode particle. ► Stresses in a real particle are much higher than those in a spherical particle. - Abstract: Lithium ion batteries experience diffusion-induced stresses during charge and discharge processes which can cause electrode failure in the form of fracture. Previous diffusion-induced stress models and simulations are mainly based on simple active material particle structures, such as spheres and ellipsoids. However, the simple structure model cannot reveal the stress development in a real complex lithium ion battery electrode. In this paper, we studied the diffusion-induced stresses numerically based on a realistic morphology of reconstructed particles during the lithium ion intercalation process. The morphology of negative and positive active materials of a lithium ion battery was determined using X-ray micro/nano computed tomography technology. Diffusion-induced stresses were simulated at different C rates under galvonostatic conditions and compared with spherical particles. The simulation results show that the intercalation stresses of particles depend on their geometric characteristics. The highest von Mises stress and Tresca stress in a real particle are several times higher than the stresses in a spherical particle with the same volume.

  18. Global exponential stability of reaction-diffusion recurrent neural networks with time-varying delays

    International Nuclear Information System (INIS)

    Liang Jinling; Cao Jinde

    2003-01-01

    Employing general Halanay inequality, we analyze the global exponential stability of a class of reaction-diffusion recurrent neural networks with time-varying delays. Several new sufficient conditions are obtained to ensure existence, uniqueness and global exponential stability of the equilibrium point of delayed reaction-diffusion recurrent neural networks. The results extend and improve the earlier publications. In addition, an example is given to show the effectiveness of the obtained result

  19. Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions

    International Nuclear Information System (INIS)

    Lu Junguo

    2008-01-01

    In this paper, the global exponential stability and periodicity for a class of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions are addressed by constructing suitable Lyapunov functionals and utilizing some inequality techniques. We first prove global exponential converge to 0 of the difference between any two solutions of the original reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions, the existence and uniqueness of equilibrium is the direct results of this procedure. This approach is different from the usually used one where the existence, uniqueness of equilibrium and stability are proved in two separate steps. Furthermore, we prove periodicity of the reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions. Sufficient conditions ensuring the global exponential stability and the existence of periodic oscillatory solutions for the reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions are given. These conditions are easy to check and have important leading significance in the design and application of reaction-diffusion recurrent neural networks with delays. Finally, two numerical examples are given to show the effectiveness of the obtained results

  20. Simple computation of reaction–diffusion processes on point clouds

    KAUST Repository

    Macdonald, Colin B.

    2013-05-20

    The study of reaction-diffusion processes is much more complicated on general curved surfaces than on standard Cartesian coordinate spaces. Here we show how to formulate and solve systems of reaction-diffusion equations on surfaces in an extremely simple way, using only the standard Cartesian form of differential operators, and a discrete unorganized point set to represent the surface. Our method decouples surface geometry from the underlying differential operators. As a consequence, it becomes possible to formulate and solve rather general reaction-diffusion equations on general surfaces without having to consider the complexities of differential geometry or sophisticated numerical analysis. To illustrate the generality of the method, computations for surface diffusion, pattern formation, excitable media, and bulk-surface coupling are provided for a variety of complex point cloud surfaces.

  1. Simple computation of reaction–diffusion processes on point clouds

    KAUST Repository

    Macdonald, Colin B.; Merriman, Barry; Ruuth, Steven J.

    2013-01-01

    The study of reaction-diffusion processes is much more complicated on general curved surfaces than on standard Cartesian coordinate spaces. Here we show how to formulate and solve systems of reaction-diffusion equations on surfaces in an extremely simple way, using only the standard Cartesian form of differential operators, and a discrete unorganized point set to represent the surface. Our method decouples surface geometry from the underlying differential operators. As a consequence, it becomes possible to formulate and solve rather general reaction-diffusion equations on general surfaces without having to consider the complexities of differential geometry or sophisticated numerical analysis. To illustrate the generality of the method, computations for surface diffusion, pattern formation, excitable media, and bulk-surface coupling are provided for a variety of complex point cloud surfaces.

  2. A numerical study of one-dimensional replicating patterns in reaction-diffusion systems with non-linear diffusion coefficients

    International Nuclear Information System (INIS)

    Ferreri, J. C.; Carmen, A. del

    1998-01-01

    A numerical study of the dynamics of pattern evolution in reaction-diffusion systems is performed, although limited to one spatial dimension. The diffusion coefficients are nonlinear, based on powers of the scalar variables. The system keeps the dynamics of previous studies in the literature, but the presence of nonlinear diffusion generates a field of strong nonlinear interactions due to the presence of receding travelling waves. This field is limited by the plane of symmetry of the space domain and the last born outgoing travelling wave. These effects are discussed. (author). 10 refs., 7 figs

  3. Realistic multisite lattice-gas modeling and KMC simulation of catalytic surface reactions: Kinetics and multiscale spatial behavior for CO-oxidation on metal (1 0 0) surfaces

    Science.gov (United States)

    Liu, Da-Jiang; Evans, James W.

    2013-12-01

    data. Furthermore, we discuss the possible transition from traditional mean-field-type bistability and reaction kinetics for lower-pressure to multistability and enhanced fluctuation effects for moderate- or higher-pressure. Behavior in the latter regime reflects a stronger influence of adspecies interactions and also lower diffusivity in the higher-coverage mixed adlayer. We also analyze mesoscale spatiotemporal behavior including the propagation of reaction-diffusion fronts between bistable reactive and inactive states, and associated nucleation-mediated transitions between these states. This behavior is controlled by complex surface mass transport processes, specifically chemical diffusion in mixed reactant adlayers for which we provide a precise theoretical formulation. The msLG models together with an appropriate treatment of chemical diffusivity enable equation-free heterogeneous coupled lattice-gas (HCLG) simulations of spatiotemporal behavior. In addition, msLG + HCLG modeling can describe coverage variations across polycrystalline catalysts surfaces, pressure variations across catalyst surfaces in microreactors, and could be incorporated into a multiphysics framework to describe mass and heat transfer limitations for high-pressure catalysis.

  4. Dissociative diffusion mechanism in vacancy-rich materials according to mass action kinetics

    Directory of Open Access Journals (Sweden)

    N. J. Biderman

    2016-05-01

    Full Text Available Two sets of diffusion-reaction numerical simulations using a finite difference method (FDM were conducted to investigate fast impurity diffusion via interstitial sites in vacancy-rich materials such as Cu(In,GaSe2 (CIGS and Cu2ZnSn(S, Se4 (CZTSSe or CZTS via the dissociative diffusion mechanism where the interstitial diffuser ultimately reacts with a vacancy to produce a substitutional. The first set of simulations extends the standard interstitial-limited dissociative diffusion theory to vacancy-rich material conditions where vacancies are annihilated in large amounts, introducing non-equilibrium vacancy concentration profiles. The second simulation set explores the vacancy-limited dissociative diffusion where impurity incorporation increases the equilibrium vacancy concentration. In addition to diffusion profiles of varying concentrations and shapes that were obtained in all simulations, some of the profiles can be fitted with the constant- and limited-source solutions of Fick’s second law despite the non-equilibrium condition induced by the interstitial-vacancy reaction. The first set of simulations reveals that the dissociative diffusion coefficient in vacancy-rich materials is inversely proportional to the initial vacancy concentration. In the second set of numerical simulations, impurity-induced changes in the vacancy concentration lead to distinctive diffusion profile shapes. The simulation results are also compared with published data of impurity diffusion in CIGS. According to the characteristic properties of diffusion profiles from the two set of simulations, experimental detection of the dissociative diffusion mechanism in vacancy-rich materials may be possible.

  5. Diffusion in Liquids : Equilibrium Molecular Simulations and Predictive Engineering Models

    NARCIS (Netherlands)

    Liu, X.

    2013-01-01

    The aim of this thesis is to study multicomponent diffusion in liquids using Molecular Dynamics (MD) simulations. Diffusion plays an important role in mass transport processes. In binary systems, mass transfer processes have been studied extensively using both experiments and molecular simulations.

  6. Development of a quantum chemical molecular dynamics tribochemical simulator and its application to tribochemical reaction dynamics of lubricant additives

    International Nuclear Information System (INIS)

    Onodera, T; Tsuboi, H; Hatakeyama, N; Endou, A; Miyamoto, A; Miura, R; Takaba, H; Suzuki, A; Kubo, M

    2010-01-01

    Tribology at the atomistic and molecular levels has been theoretically studied by a classical molecular dynamics (MD) method. However, this method inherently cannot simulate the tribochemical reaction dynamics because it does not consider the electrons in nature. Although the first-principles based MD method has recently been used for understanding the chemical reaction dynamics of several molecules in the tribology field, the method cannot simulate the tribochemical reaction dynamics of a large complex system including solid surfaces and interfaces due to its huge computation costs. On the other hand, we have developed a quantum chemical MD tribochemical simulator on the basis of a hybrid tight-binding quantum chemical/classical MD method. In the simulator, the central part of the chemical reaction dynamics is calculated by the tight-binding quantum chemical MD method, and the remaining part is calculated by the classical MD method. Therefore, the developed tribochemical simulator realizes the study on tribochemical reaction dynamics of a large complex system, which cannot be treated by using the conventional classical MD or the first-principles MD methods. In this paper, we review our developed quantum chemical MD tribochemical simulator and its application to the tribochemical reaction dynamics of a few lubricant additives

  7. Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

    Science.gov (United States)

    Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

    2018-01-01

    This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0 . Furthermore, we prove the global existence and uniqueness of C^{α ,β } -solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1 -space. The exponential convergence rate is also derived.

  8. Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

    Science.gov (United States)

    Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

    2018-06-01

    This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0. Furthermore, we prove the global existence and uniqueness of C^{α ,β }-solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1-space. The exponential convergence rate is also derived.

  9. Numerical Simulation of Hydrogen Combustion: Global Reaction Model and Validation

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Yun [School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an (China); Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY (United States); Liu, Yinhe, E-mail: yinheliu@mail.xjtu.edu.cn [School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an (China)

    2017-11-20

    Due to the complexity of modeling the combustion process in nuclear power plants, the global mechanisms are preferred for numerical simulation. To quickly perform the highly resolved simulations with limited processing resources of large-scale hydrogen combustion, a method based on thermal theory was developed to obtain kinetic parameters of global reaction mechanism of hydrogen–air combustion in a wide range. The calculated kinetic parameters at lower hydrogen concentration (C{sub hydrogen} < 20%) were validated against the results obtained from experimental measurements in a container and combustion test facility. In addition, the numerical data by the global mechanism (C{sub hydrogen} > 20%) were compared with the results by detailed mechanism. Good agreement between the model prediction and the experimental data was achieved, and the comparison between simulation results by the detailed mechanism and the global reaction mechanism show that the present calculated global mechanism has excellent predictable capabilities for a wide range of hydrogen–air mixtures.

  10. Numerical Simulation of Hydrogen Combustion: Global Reaction Model and Validation

    International Nuclear Information System (INIS)

    Zhang, Yun; Liu, Yinhe

    2017-01-01

    Due to the complexity of modeling the combustion process in nuclear power plants, the global mechanisms are preferred for numerical simulation. To quickly perform the highly resolved simulations with limited processing resources of large-scale hydrogen combustion, a method based on thermal theory was developed to obtain kinetic parameters of global reaction mechanism of hydrogen–air combustion in a wide range. The calculated kinetic parameters at lower hydrogen concentration (C hydrogen < 20%) were validated against the results obtained from experimental measurements in a container and combustion test facility. In addition, the numerical data by the global mechanism (C hydrogen > 20%) were compared with the results by detailed mechanism. Good agreement between the model prediction and the experimental data was achieved, and the comparison between simulation results by the detailed mechanism and the global reaction mechanism show that the present calculated global mechanism has excellent predictable capabilities for a wide range of hydrogen–air mixtures.

  11. Reaction-diffusion modeling of hydrogen in beryllium

    Energy Technology Data Exchange (ETDEWEB)

    Wensing, Mirko; Matveev, Dmitry; Linsmeier, Christian [Forschungszentrum Juelich GmbH, Institut fuer Energie- und Klimaforschung - Plasmaphysik (Germany)

    2016-07-01

    Beryllium will be used as first-wall material for the future fusion reactor ITER as well as in the breeding blanket of DEMO. In both cases it is important to understand the mechanisms of hydrogen retention in beryllium. In earlier experiments with beryllium low-energy binding states of hydrogen were observed by thermal desorption spectroscopy (TDS) which are not yet well understood. Two candidates for these states are considered: beryllium-hydride phases within the bulk and surface effects. The retention of deuterium in beryllium is studied by a reaction rate approach using a coupled reaction diffusion system (CRDS)-model relying on ab initio data from density functional theory calculations (DFT). In this contribution we try to assess the influence of surface recombination.

  12. Two-dimensional numerical simulation of boron diffusion for pyramidally textured silicon

    International Nuclear Information System (INIS)

    Ma, Fa-Jun; Duttagupta, Shubham; Shetty, Kishan Devappa; Meng, Lei; Hoex, Bram; Peters, Ian Marius; Samudra, Ganesh S.

    2014-01-01

    Multidimensional numerical simulation of boron diffusion is of great relevance for the improvement of industrial n-type crystalline silicon wafer solar cells. However, surface passivation of boron diffused area is typically studied in one dimension on planar lifetime samples. This approach neglects the effects of the solar cell pyramidal texture on the boron doping process and resulting doping profile. In this work, we present a theoretical study using a two-dimensional surface morphology for pyramidally textured samples. The boron diffusivity and segregation coefficient between oxide and silicon in simulation are determined by reproducing measured one-dimensional boron depth profiles prepared using different boron diffusion recipes on planar samples. The established parameters are subsequently used to simulate the boron diffusion process on textured samples. The simulated junction depth is found to agree quantitatively well with electron beam induced current measurements. Finally, chemical passivation on planar and textured samples is compared in device simulation. Particularly, a two-dimensional approach is adopted for textured samples to evaluate chemical passivation. The intrinsic emitter saturation current density, which is only related to Auger and radiative recombination, is also simulated for both planar and textured samples. The differences between planar and textured samples are discussed

  13. A development of simulation and analytical program for through-diffusion experiments for a single layer of diffusion media

    International Nuclear Information System (INIS)

    Sato, Haruo

    2001-01-01

    A program (TDROCK1. FOR) for simulation and analysis of through-diffusion experiments for a single layer of diffusion media was developed. This program was made by Pro-Fortran language, which was suitable for scientific and technical calculations, and relatively easy explicit difference method was adopted for an analysis. In the analysis, solute concentration in the tracer cell as a function of time that we could not treat to date can be input and the decrease in the solute concentration as a function of time by diffusion from the tracer cell to the measurement cell, the solute concentration distribution in the porewater of diffusion media and the solute concentration in the measurement cell as a function of time can be calculated. In addition, solution volume in both cells and diameter and thickness of the diffusion media are also variable as an input condition. This simulation program could well explain measured result by simulating solute concentration in the measurement cell as a function of time for case which apparent and effective diffusion coefficients were already known. Based on this, the availability and applicability of this program to actual analysis and simulation were confirmed. This report describes the theoretical treatment for the through-diffusion experiments for a single layer of diffusion media, analytical model, an example of source program and the manual. (author)

  14. A discrete model to study reaction-diffusion-mechanics systems.

    Science.gov (United States)

    Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V

    2011-01-01

    This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.

  15. A discrete model to study reaction-diffusion-mechanics systems.

    Directory of Open Access Journals (Sweden)

    Louis D Weise

    Full Text Available This article introduces a discrete reaction-diffusion-mechanics (dRDM model to study the effects of deformation on reaction-diffusion (RD processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material. Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.

  16. Attractor of reaction-diffusion equations in Banach spaces

    Directory of Open Access Journals (Sweden)

    José Valero

    2001-04-01

    Full Text Available In this paper we prove first some abstract theorems on existence of global attractors for differential inclusions generated by w-dissipative operators. Then these results are applied to reaction-diffusion equations in which the Babach space Lp is used as phase space. Finally, new results concerning the fractal dimension of the global attractor in the space L2 are obtained.

  17. Laser Spot Detection Based on Reaction Diffusion

    OpenAIRE

    Alejandro Vázquez-Otero; Danila Khikhlukha; J. M. Solano-Altamirano; Raquel Dormido; Natividad Duro

    2016-01-01

    Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD) system as the main computational framework for robustly finding laser spot centers. The method presente...

  18. Molecular dynamics simulation of three plastic additives' diffusion in polyethylene terephthalate.

    Science.gov (United States)

    Li, Bo; Wang, Zhi-Wei; Lin, Qin-Bao; Hu, Chang-Ying

    2017-06-01

    Accurate diffusion coefficient data of additives in a polymer are of paramount importance for estimating the migration of the additives over time. This paper shows how this diffusion coefficient can be estimated for three plastic additives [2-(2'-hydroxy-5'-methylphenyl) (UV-P), 2,6-di-tert-butyl-4-methylphenol (BHT) and di-(2-ethylhexyl) phthalate (DEHP)] in polyethylene terephthalate (PET) using the molecular dynamics (MD) simulation method. MD simulations were performed at temperatures of 293-433 K. The diffusion coefficient was calculated through the Einstein relationship connecting the data of mean-square displacement at different times. Comparison of the diffusion coefficients simulated by the MD simulation technique, predicted by the Piringer model and experiments, showed that, except for a few samples, the MD-simulated values were in agreement with the experimental values within one order of magnitude. Furthermore, the diffusion process for additives is discussed in detail, and four factors - the interaction energy between additive molecules and PET, fractional free volume, molecular shape and size, and self-diffusion of the polymer - are proposed to illustrate the microscopic diffusion mechanism. The movement trajectories of additives in PET cell models suggested that the additive molecules oscillate slowly rather than hopping for a long time. Occasionally, when a sufficiently large hole was created adjacently, the molecule could undergo spatial motion by jumping into the free-volume hole and consequently start a continuous oscillation and hop. The results indicate that MD simulation is a useful approach for predicting the microstructure and diffusion coefficient of plastic additives, and help to estimate the migration level of additives from PET packaging.

  19. Mix and Inject: Reaction Initiation by Diffusion for Time-Resolved Macromolecular Crystallography

    Directory of Open Access Journals (Sweden)

    Marius Schmidt

    2013-01-01

    Full Text Available Time-resolved macromolecular crystallography unifies structure determination with chemical kinetics, since the structures of transient states and chemical and kinetic mechanisms can be determined simultaneously from the same data. To start a reaction in an enzyme, typically, an initially inactive substrate present in the crystal is activated. This has particular disadvantages that are circumvented when active substrate is directly provided by diffusion. However, then it is prohibitive to use macroscopic crystals because diffusion times become too long. With small micro- and nanocrystals diffusion times are adequately short for most enzymes and the reaction can be swiftly initiated. We demonstrate here that a time-resolved crystallographic experiment becomes feasible by mixing substrate with enzyme nanocrystals which are subsequently injected into the X-ray beam of a pulsed X-ray source.

  20. New complex variable meshless method for advection—diffusion problems

    International Nuclear Information System (INIS)

    Wang Jian-Fei; Cheng Yu-Min

    2013-01-01

    In this paper, an improved complex variable meshless method (ICVMM) for two-dimensional advection—diffusion problems is developed based on improved complex variable moving least-square (ICVMLS) approximation. The equivalent functional of two-dimensional advection—diffusion problems is formed, the variation method is used to obtain the equation system, and the penalty method is employed to impose the essential boundary conditions. The difference method for two-point boundary value problems is used to obtain the discrete equations. Then the corresponding formulas of the ICVMM for advection—diffusion problems are presented. Two numerical examples with different node distributions are used to validate and inestigate the accuracy and efficiency of the new method in this paper. It is shown that ICVMM is very effective for advection—diffusion problems, and has a good convergent character, accuracy, and computational efficiency

  1. Signatures of a quantum diffusion limited hydrogen atom tunneling reaction.

    Science.gov (United States)

    Balabanoff, Morgan E; Ruzi, Mahmut; Anderson, David T

    2017-12-20

    We are studying the details of hydrogen atom (H atom) quantum diffusion in highly enriched parahydrogen (pH 2 ) quantum solids doped with chemical species in an effort to better understand H atom transport and reactivity under these conditions. In this work we present kinetic studies of the 193 nm photo-induced chemistry of methanol (CH 3 OH) isolated in solid pH 2 . Short-term irradiation of CH 3 OH at 1.8 K readily produces CH 2 O and CO which we detect using FTIR spectroscopy. The in situ photochemistry also produces CH 3 O and H atoms which we can infer from the post-photolysis reaction kinetics that display significant CH 2 OH growth. The CH 2 OH growth kinetics indicate at least three separate tunneling reactions contribute; (i) reactions of photoproduced CH 3 O with the pH 2 host, (ii) H atom reactions with the CH 2 O photofragment, and (iii) long-range migration of H atoms and reaction with CH 3 OH. We assign the rapid CH 2 OH growth to the following CH 3 O + H 2 → CH 3 OH + H → CH 2 OH + H 2 two-step sequential tunneling mechanism by conducting analogous kinetic measurements using deuterated methanol (CD 3 OD). By performing photolysis experiments at 1.8 and 4.3 K, we show the post-photolysis reaction kinetics change qualitatively over this small temperature range. We use this qualitative change in the reaction kinetics with temperature to identify reactions that are quantum diffusion limited. While these results are specific to the conditions that exist in pH 2 quantum solids, they have direct implications on the analogous low temperature H atom tunneling reactions that occur on metal surfaces and on interstellar grains.

  2. Numerical simulation of compressible two-phase flow using a diffuse interface method

    International Nuclear Information System (INIS)

    Ansari, M.R.; Daramizadeh, A.

    2013-01-01

    Highlights: ► Compressible two-phase gas–gas and gas–liquid flows simulation are conducted. ► Interface conditions contain shock wave and cavitations. ► A high-resolution diffuse interface method is investigated. ► The numerical results exhibit very good agreement with experimental results. -- Abstract: In this article, a high-resolution diffuse interface method is investigated for simulation of compressible two-phase gas–gas and gas–liquid flows, both in the presence of shock wave and in flows with strong rarefaction waves similar to cavitations. A Godunov method and HLLC Riemann solver is used for discretization of the Kapila five-equation model and a modified Schmidt equation of state (EOS) is used to simulate the cavitation regions. This method is applied successfully to some one- and two-dimensional compressible two-phase flows with interface conditions that contain shock wave and cavitations. The numerical results obtained in this attempt exhibit very good agreement with experimental results, as well as previous numerical results presented by other researchers based on other numerical methods. In particular, the algorithm can capture the complex flow features of transient shocks, such as the material discontinuities and interfacial instabilities, without any oscillation and additional diffusion. Numerical examples show that the results of the method presented here compare well with other sophisticated modeling methods like adaptive mesh refinement (AMR) and local mesh refinement (LMR) for one- and two-dimensional problems

  3. Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds

    KAUST Repository

    Desvillettes, Laurent; Fellner, Klemens

    2008-01-01

    In the continuation of [Desvillettes, L., Fellner, K.: Exponential Decay toward Equilibrium via Entropy Methods for Reaction-Diffusion Equations. J. Math. Anal. Appl. 319 (2006), no. 1, 157-176], we study reversible reaction-diffusion equations via entropy methods (based on the free energy functional) for a 1D system of four species. We improve the existing theory by getting 1) almost exponential convergence in L1 to the steady state via a precise entropy-entropy dissipation estimate, 2) an explicit global L∞ bound via interpolation of a polynomially growing H1 bound with the almost exponential L1 convergence, and 3), finally, explicit exponential convergence to the steady state in all Sobolev norms.

  4. Reaction and diffusion in turbulent combustion

    Energy Technology Data Exchange (ETDEWEB)

    Pope, S.B. [Mechanical and Aerospace Engineering, Ithaca, NY (United States)

    1993-12-01

    The motivation for this project is the need to obtain a better quantitative understanding of the technologically-important phenomenon of turbulent combustion. In nearly all applications in which fuel is burned-for example, fossil-fuel power plants, furnaces, gas-turbines and internal-combustion engines-the combustion takes place in a turbulent flow. Designers continually demand more quantitative information about this phenomenon-in the form of turbulent combustion models-so that they can design equipment with increased efficiency and decreased environmental impact. For some time the PI has been developing a class of turbulent combustion models known as PDF methods. These methods have the important virtue that both convection and reaction can be treated without turbulence-modelling assumptions. However, a mixing model is required to account for the effects of molecular diffusion. Currently, the available mixing models are known to have some significant defects. The major motivation of the project is to seek a better understanding of molecular diffusion in turbulent reactive flows, and hence to develop a better mixing model.

  5. A Radiation Chemistry Code Based on the Greens Functions of the Diffusion Equation

    Science.gov (United States)

    Plante, Ianik; Wu, Honglu

    2014-01-01

    Ionizing radiation produces several radiolytic species such as.OH, e-aq, and H. when interacting with biological matter. Following their creation, radiolytic species diffuse and chemically react with biological molecules such as DNA. Despite years of research, many questions on the DNA damage by ionizing radiation remains, notably on the indirect effect, i.e. the damage resulting from the reactions of the radiolytic species with DNA. To simulate DNA damage by ionizing radiation, we are developing a step-by-step radiation chemistry code that is based on the Green's functions of the diffusion equation (GFDE), which is able to follow the trajectories of all particles and their reactions with time. In the recent years, simulations based on the GFDE have been used extensively in biochemistry, notably to simulate biochemical networks in time and space and are often used as the "gold standard" to validate diffusion-reaction theories. The exact GFDE for partially diffusion-controlled reactions is difficult to use because of its complex form. Therefore, the radial Green's function, which is much simpler, is often used. Hence, much effort has been devoted to the sampling of the radial Green's functions, for which we have developed a sampling algorithm This algorithm only yields the inter-particle distance vector length after a time step; the sampling of the deviation angle of the inter-particle vector is not taken into consideration. In this work, we show that the radial distribution is predicted by the exact radial Green's function. We also use a technique developed by Clifford et al. to generate the inter-particle vector deviation angles, knowing the inter-particle vector length before and after a time step. The results are compared with those predicted by the exact GFDE and by the analytical angular functions for free diffusion. This first step in the creation of the radiation chemistry code should help the understanding of the contribution of the indirect effect in the

  6. Large eddy simulation modeling of particle-laden flows in complex terrain

    Science.gov (United States)

    Salesky, S.; Giometto, M. G.; Chamecki, M.; Lehning, M.; Parlange, M. B.

    2017-12-01

    The transport, deposition, and erosion of heavy particles over complex terrain in the atmospheric boundary layer is an important process for hydrology, air quality forecasting, biology, and geomorphology. However, in situ observations can be challenging in complex terrain due to spatial heterogeneity. Furthermore, there is a need to develop numerical tools that can accurately represent the physics of these multiphase flows over complex surfaces. We present a new numerical approach to accurately model the transport and deposition of heavy particles in complex terrain using large eddy simulation (LES). Particle transport is represented through solution of the advection-diffusion equation including terms that represent gravitational settling and inertia. The particle conservation equation is discretized in a cut-cell finite volume framework in order to accurately enforce mass conservation. Simulation results will be validated with experimental data, and numerical considerations required to enforce boundary conditions at the surface will be discussed. Applications will be presented in the context of snow deposition and transport, as well as urban dispersion.

  7. Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case

    NARCIS (Netherlands)

    Bedeaux, D.; Ortiz de Zárate, J.M.; Pagonabarraga, I.; Sengers, J.V.; Kjelstrup, S.

    2011-01-01

    In this paper, we consider a simple reaction-diffusion system, namely, a binary fluid mixture with an association-dissociation reaction between two species. We study fluctuations at hydrodynamic spatiotemporal scales when this mixture is driven out of equilibrium by the presence of a temperature

  8. Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients

    Directory of Open Access Journals (Sweden)

    Nauman Raza

    2013-01-01

    Full Text Available Critical points related to the singular perturbed reaction diffusion models are calculated using weighted Sobolev gradient method in finite element setting. Performance of different Sobolev gradients has been discussed for varying diffusion coefficient values. A comparison is shown between the weighted and unweighted Sobolev gradients in two and three dimensions. The superiority of the method is also demonstrated by showing comparison with Newton's method.

  9. Stochastic analysis of complex reaction networks using binomial moment equations.

    Science.gov (United States)

    Barzel, Baruch; Biham, Ofer

    2012-09-01

    The stochastic analysis of complex reaction networks is a difficult problem because the number of microscopic states in such systems increases exponentially with the number of reactive species. Direct integration of the master equation is thus infeasible and is most often replaced by Monte Carlo simulations. While Monte Carlo simulations are a highly effective tool, equation-based formulations are more amenable to analytical treatment and may provide deeper insight into the dynamics of the network. Here, we present a highly efficient equation-based method for the analysis of stochastic reaction networks. The method is based on the recently introduced binomial moment equations [Barzel and Biham, Phys. Rev. Lett. 106, 150602 (2011)]. The binomial moments are linear combinations of the ordinary moments of the probability distribution function of the population sizes of the interacting species. They capture the essential combinatorics of the reaction processes reflecting their stoichiometric structure. This leads to a simple and transparent form of the equations, and allows a highly efficient and surprisingly simple truncation scheme. Unlike ordinary moment equations, in which the inclusion of high order moments is prohibitively complicated, the binomial moment equations can be easily constructed up to any desired order. The result is a set of equations that enables the stochastic analysis of complex reaction networks under a broad range of conditions. The number of equations is dramatically reduced from the exponential proliferation of the master equation to a polynomial (and often quadratic) dependence on the number of reactive species in the binomial moment equations. The aim of this paper is twofold: to present a complete derivation of the binomial moment equations; to demonstrate the applicability of the moment equations for a representative set of example networks, in which stochastic effects play an important role.

  10. WNT and DKK Determine Hair Follicle Spacing Through a Reaction-Diffusion Mechanism

    Science.gov (United States)

    Sick, Stefanie; Reinker, Stefan; Timmer, Jens; Schlake, Thomas

    2006-12-01

    Mathematical reaction-diffusion models have been suggested to describe formation of animal pigmentation patterns and distribution of epidermal appendages. However, the crucial signals and in vivo mechanisms are still elusive. Here we identify WNT and its inhibitor DKK as primary determinants of murine hair follicle spacing, using a combined experimental and computational modeling approach. Transgenic DKK overexpression reduces overall appendage density. Moderate suppression of endogenous WNT signaling forces follicles to form clusters during an otherwise normal morphogenetic program. These results confirm predictions of a WNT/DKK-specific mathematical model and provide in vivo corroboration of the reaction-diffusion mechanism for epidermal appendage formation.

  11. Hybrid Multilevel Monte Carlo Simulation of Stochastic Reaction Networks

    KAUST Repository

    Moraes, Alvaro

    2015-01-07

    Stochastic reaction networks (SRNs) is a class of continuous-time Markov chains intended to describe, from the kinetic point of view, the time-evolution of chemical systems in which molecules of different chemical species undergo a finite set of reaction channels. This talk is based on articles [4, 5, 6], where we are interested in the following problem: given a SRN, X, defined though its set of reaction channels, and its initial state, x0, estimate E (g(X(T))); that is, the expected value of a scalar observable, g, of the process, X, at a fixed time, T. This problem lead us to define a series of Monte Carlo estimators, M, such that, with high probability can produce values close to the quantity of interest, E (g(X(T))). More specifically, given a user-selected tolerance, TOL, and a small confidence level, η, find an estimator, M, based on approximate sampled paths of X, such that, P (|E (g(X(T))) − M| ≤ TOL) ≥ 1 − η; even more, we want to achieve this objective with near optimal computational work. We first introduce a hybrid path-simulation scheme based on the well-known stochastic simulation algorithm (SSA)[3] and the tau-leap method [2]. Then, we introduce a Multilevel Monte Carlo strategy that allows us to achieve a computational complexity of order O(T OL−2), this is the same computational complexity as in an exact method but with a smaller constant. We provide numerical examples to show our results.

  12. Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers.

    Science.gov (United States)

    Stamova, Ivanka; Stamov, Gani

    2017-12-01

    In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives. Copyright © 2017 Elsevier Ltd. All rights reserved.

  13. Emergent structures in reaction-advection-diffusion systems on a sphere

    Science.gov (United States)

    Krause, Andrew L.; Burton, Abigail M.; Fadai, Nabil T.; Van Gorder, Robert A.

    2018-04-01

    We demonstrate unusual effects due to the addition of advection into a two-species reaction-diffusion system on the sphere. We find that advection introduces emergent behavior due to an interplay of the traditional Turing patterning mechanisms with the compact geometry of the sphere. Unidirectional advection within the Turing space of the reaction-diffusion system causes patterns to be generated at one point of the sphere, and transported to the antipodal point where they are destroyed. We illustrate these effects numerically and deduce conditions for Turing instabilities on local projections to understand the mechanisms behind these behaviors. We compare this behavior to planar advection which is shown to only transport patterns across the domain. Analogous transport results seem to hold for the sphere under azimuthal transport or away from the antipodal points in unidirectional flow regimes.

  14. Optimal Design for the Diffusion Plate with Nanoparticles in a Diffusive Solar Cell Window by Mie Scattering Simulation

    Directory of Open Access Journals (Sweden)

    Ruei-Tang Chen

    2013-01-01

    Full Text Available A diffusive solar cell window comprises a diffusion plate with TiO2 nanoparticles sandwiched between two glass layers. It is a simple, inexpensive, easy-to-made, and highly reliable transparent solar energy module. To improve its power generation efficiency as well as maintain indoor natural lighting, we examined the scattering mechanism in the diffusion plate with TiO2 nanoparticles within a diffusive solar cell window by Mie scattering simulations. In this work, a multiwavelength ASAP ray tracing model for a diffusive solar cell window with acceptable accuracy was developed to investigate the influence of the diffusion plate design parameter, mainly concentration of a diffusion plate with determined particle size distribution, on power generation efficiency and color shift of transmitted sun light. A concept of “effective average radius” was proposed to account for the equivalent scattering effect of a size distribution of quasispherical particles. Simulation results demonstrated that both the transmitted light and its correlated color temperature decreased as the concentration increased for a large-size diffusive solar cell window. However, there existed a maximum power generation efficiency at around 160 ppm concentration. The optimal design for a large-size diffusion plate inside a diffusive solar cell window by taking indoor lighting into account was suggested based on the simulation results.

  15. Kinetics of CO2 diffusion in human carbonic anhydrase: a study using molecular dynamics simulations and the Markov-state model.

    Science.gov (United States)

    Chen, Gong; Kong, Xian; Lu, Diannan; Wu, Jianzhong; Liu, Zheng

    2017-05-10

    Molecular dynamics (MD) simulations, in combination with the Markov-state model (MSM), were applied to probe CO 2 diffusion from an aqueous solution into the active site of human carbonic anhydrase II (hCA-II), an enzyme useful for enhanced CO 2 capture and utilization. The diffusion process in the hydrophobic pocket of hCA-II was illustrated in terms of a two-dimensional free-energy landscape. We found that CO 2 diffusion in hCA-II is a rate-limiting step in the CO 2 diffusion-binding-reaction process. The equilibrium distribution of CO 2 shows its preferential accumulation within a hydrophobic domain in the protein core region. An analysis of the committors and reactive fluxes indicates that the main pathway for CO 2 diffusion into the active site of hCA-II is through a binding pocket where residue Gln 136 contributes to the maximal flux. The simulation results offer a new perspective on the CO 2 hydration kinetics and useful insights toward the development of novel biochemical processes for more efficient CO 2 sequestration and utilization.

  16. Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

    Science.gov (United States)

    Simpson, Matthew J

    2015-01-01

    Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).

  17. An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations

    KAUST Repository

    Burrage, Kevin

    2012-01-01

    Fractional differential equations are becoming increasingly used as a modelling tool for processes associated with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time fractional) or nonlocality (space fractional) issues that impose a number of computational constraints. In this paper we develop efficient, scalable techniques for solving fractional-in-space reaction diffusion equations using the finite element method on both structured and unstructured grids via robust techniques for computing the fractional power of a matrix times a vector. Our approach is show-cased by solving the fractional Fisher and fractional Allen-Cahn reaction-diffusion equations in two and three spatial dimensions, and analyzing the speed of the traveling wave and size of the interface in terms of the fractional power of the underlying Laplacian operator. © 2012 Society for Industrial and Applied Mathematics.

  18. Water vapor permeabilities through polymers: diffusivities from experiments and simulations

    International Nuclear Information System (INIS)

    Seethamraju, Sindhu; Ramamurthy, Praveen Chandrashekarapura; Madras, Giridhar

    2014-01-01

    This study experimentally determines water vapor permeabilities, which are subsequently correlated with the diffusivities obtained from simulations. Molecular dynamics (MD) simulations were used for determining the diffusion of water vapor in various polymeric systems such as polyethylene, polypropylene, poly (vinyl alcohol), poly (vinyl acetate), poly (vinyl butyral), poly (vinylidene chloride), poly (vinyl chloride) and poly (methyl methacrylate). Cavity ring down spectroscopy (CRDS) based methodology has been used to determine the water vapor transmission rates. These values were then used to calculate the diffusion coefficients for water vapor through these polymers. A comparative analysis is provided for diffusivities calculated from CRDS and MD based results by correlating the free volumes. (paper)

  19. Innovation Diffusion: Assessment of Strategies within the Diffusion Simulation Game

    Science.gov (United States)

    Enfield, Jacob; Myers, Rodney D.; Lara, Miguel; Frick, Theodore W.

    2012-01-01

    Educators increasingly view the high level of engagement and experiential learning offered by games as a means to promote learning. However, as with any designed learning experience, player experiences should provide an accurate representation of content to be learned. In this study, the authors investigated the DIFFUSION SIMULATION GAME (DSG) to…

  20. Adsorption and diffusion of H and NH{sub x} as key steps of the NH{sub x} dehydrogenation reaction at the V{sub 2}O{sub 5} (010) surface

    Energy Technology Data Exchange (ETDEWEB)

    Gruber, Mathis; Hermann, Klaus [Fritz-Haber-Institut der MPG, und Sfb 546, Berlin (Germany)

    2009-07-01

    Various selective oxidation reactions as the selective catalytic reduction (SCR) of NO{sub x} or the ammoxidation of propane/propene to acrylonitrile are processed on vanadium based metal-oxide catalysts in the presence of ammonia. In the reactions the intermediates NH{sub 2}, NH{sub 3}, and NH{sub 4} are involved indicating that the adsorption and dehydrogenation of NH{sub x}, x < 4, are important steps. We have performed theoretical studies of corresponding reaction steps where the catalyst is simulated by a finite section of the V{sub 2}O{sub 5} (010) surface. The calculations apply density-functional theory combined with clusters modeling the adsorbate system. The substrate lowers corresponding dehydrogenation energies considerably compared with values for the gas phase reaction. However, the lowering is too small to make dehydrogenation of NH{sub 3} likely to happen. Our results on the role of oxygen vacancies for the dehydrogenation indicate that such surface defects become important for the reaction. Besides the energetics also the diffusion at the surface influences the reaction. A nudged elastic band (NEB) routine has been implemented to evaluate diffusion paths and barriers. Hydrogen diffusion on the surface will be discussed and additional examples for NH{sub x} diffusion will be shown. Based on these results possible reaction scenarios for the dehydrogenation reaction will be presented.

  1. Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations

    Science.gov (United States)

    Zhang, Linghai

    2017-10-01

    The main purposes of this paper are to accomplish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations ut =uxx + α [ βH (u - θ) - u ] - w, wt = ε (u - γw) and to establish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ], under different conditions on the model constants. To establish the bifurcation for the system, we will study the existence and instability of a standing pulse solution if 0 1; the existence and instability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and 0 traveling wave front as well as the existence and instability of a standing pulse solution if 0 traveling wave front as well as the existence and instability of an upside down standing pulse solution if 0 traveling wave back of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ] -w0, where w0 = α (β - 2 θ) > 0 is a positive constant, if 0 motivation to study the existence, stability, instability and bifurcations of the nonlinear waves is to study the existence and stability/instability of infinitely many fast/slow multiple traveling pulse solutions of the nonlinear system of reaction diffusion equations. The existence and stability of infinitely many fast multiple traveling pulse solutions are of great interests in mathematical neuroscience.

  2. SCScore: Synthetic Complexity Learned from a Reaction Corpus.

    Science.gov (United States)

    Coley, Connor W; Rogers, Luke; Green, William H; Jensen, Klavs F

    2018-02-26

    Several definitions of molecular complexity exist to facilitate prioritization of lead compounds, to identify diversity-inducing and complexifying reactions, and to guide retrosynthetic searches. In this work, we focus on synthetic complexity and reformalize its definition to correlate with the expected number of reaction steps required to produce a target molecule, with implicit knowledge about what compounds are reasonable starting materials. We train a neural network model on 12 million reactions from the Reaxys database to impose a pairwise inequality constraint enforcing the premise of this definition: that on average, the products of published chemical reactions should be more synthetically complex than their corresponding reactants. The learned metric (SCScore) exhibits highly desirable nonlinear behavior, particularly in recognizing increases in synthetic complexity throughout a number of linear synthetic routes.

  3. Pattern formation and control of spatiotemporal chaos in a reaction diffusion prey–predator system supplying additional food

    International Nuclear Information System (INIS)

    Ghorai, Santu; Poria, Swarup

    2016-01-01

    Spatiotemporal dynamics of a predator–prey system in presence of spatial diffusion is investigated in presence of additional food exists for predators. Conditions for stability of Hopf as well as Turing patterns in a spatial domain are determined by making use of the linear stability analysis. Impact of additional food is clear from these conditions. Numerical simulation results are presented in order to validate the analytical findings. Finally numerical simulations are carried out around the steady state under zero flux boundary conditions. With the help of numerical simulations, the different types of spatial patterns (including stationary spatial pattern, oscillatory pattern, and spatiotemporal chaos) are identified in this diffusive predator–prey system in presence of additional food, depending on the quantity, quality of the additional food and the spatial domain and other parameters of the model. The key observation is that spatiotemporal chaos can be controlled supplying suitable additional food to predator. These investigations may be useful to understand complex spatiotemporal dynamics of population dynamical models in presence of additional food.

  4. Application of multicomponent diffusion theory for description of impurities distribution in complex diffusive doping of semiconductors

    International Nuclear Information System (INIS)

    Uskov, V.A.; Kondrachenko, O.E.; Kondrachenko, L.A.

    1977-01-01

    A phenomenological theory of multicomponent diffusion involving interaction between the components is employed to analyze how the interaction between two admixtures affects their simultaneous or consequent diffusion into a semiconductor. The theory uses the equations of multicomponent dissusion under common conditions (constant diffusion coefficients and equilibrium distribution of vacancies). The experiments are described on In and Sb simultaneous diffusion into Ge. The diffusion is performed according to the routine gas phase technology with the use of radioactive isotopes In 114 and Sb 124 . It is shown that the introduction of an additional diffusion coefficient D 12 makes it possible to simply and precisely describe the distribution of interacting admixtures in complex diffusion alloying of semiconductors

  5. Reaction mechanisms of metal complexes

    CERN Document Server

    Hay, R W

    2000-01-01

    This text provides a general background as a course module in the area of inorganic reaction mechanisms, suitable for advanced undergraduate and postgraduate study and/or research. The topic has important research applications in the metallurgical industry and is of interest in the science of biochemistry, biology, organic, inorganic and bioinorganic chemistry. In addition to coverage of substitution reactions in four-, five- and six-coordinate complexes, the book contains further chapters devoted to isomerization and racemization reactions, to the general field of redox reactions, and to the reactions of coordinated ligands. It is relevant in other fields such as organic, bioinorganic and biological chemistry, providing a bridge to organic reaction mechanisms. The book also contains a chapter on the kinetic background to the subject with many illustrative examples which should prove useful to those beginning research. Provides a general background as a course module in the area of inorganic reaction mechanis...

  6. Morphological inversion of complex diffusion

    Science.gov (United States)

    Nguyen, V. A. T.; Vural, D. C.

    2017-09-01

    Epidemics, neural cascades, power failures, and many other phenomena can be described by a diffusion process on a network. To identify the causal origins of a spread, it is often necessary to identify the triggering initial node. Here, we define a new morphological operator and use it to detect the origin of a diffusive front, given the final state of a complex network. Our method performs better than algorithms based on distance (closeness) and Jordan centrality. More importantly, our method is applicable regardless of the specifics of the forward model, and therefore can be applied to a wide range of systems such as identifying the patient zero in an epidemic, pinpointing the neuron that triggers a cascade, identifying the original malfunction that causes a catastrophic infrastructure failure, and inferring the ancestral species from which a heterogeneous population evolves.

  7. An electromechanical based deformable model for soft tissue simulation.

    Science.gov (United States)

    Zhong, Yongmin; Shirinzadeh, Bijan; Smith, Julian; Gu, Chengfan

    2009-11-01

    Soft tissue deformation is of great importance to surgery simulation. Although a significant amount of research efforts have been dedicated to simulating the behaviours of soft tissues, modelling of soft tissue deformation is still a challenging problem. This paper presents a new deformable model for simulation of soft tissue deformation from the electromechanical viewpoint of soft tissues. Soft tissue deformation is formulated as a reaction-diffusion process coupled with a mechanical load. The mechanical load applied to a soft tissue to cause a deformation is incorporated into the reaction-diffusion system, and consequently distributed among mass points of the soft tissue. Reaction-diffusion of mechanical load and non-rigid mechanics of motion are combined to govern the simulation dynamics of soft tissue deformation. An improved reaction-diffusion model is developed to describe the distribution of the mechanical load in soft tissues. A three-layer artificial cellular neural network is constructed to solve the reaction-diffusion model for real-time simulation of soft tissue deformation. A gradient based method is established to derive internal forces from the distribution of the mechanical load. Integration with a haptic device has also been achieved to simulate soft tissue deformation with haptic feedback. The proposed methodology does not only predict the typical behaviours of living tissues, but it also accepts both local and large-range deformations. It also accommodates isotropic, anisotropic and inhomogeneous deformations by simple modification of diffusion coefficients.

  8. Molecular dynamics simulation of metallic impurity diffusion in liquid lead-bismuth eutectic (LBE)

    Science.gov (United States)

    Gao, Yun; Takahashi, Minoru; Cavallotti, Carlo; Raos, Guido

    2018-04-01

    Corrosion of stainless steels by lead-bismuth eutectic (LBE) is an important problem which depends, amongst other things, on the diffusion of the steel components inside this liquid alloy. Here we present the results of classical molecular dynamics simulations of the diffusion of Fe and Ni within LBE. The simulations complement experimental studies of impurity diffusion by our group and provide an atomic-level understanding of the relevant diffusion phenomena. They are based on the embedded atom method (EAM) to represent many-body interactions among atoms. The EAM potentials employed in our simulations have been validated against ab initio density functional calculations. We show that the experimental and simulation results for the temperature-dependent viscosity of LBE and the impurity diffusion coefficients can be reconciled by assuming that the Ni and Fe diffuse mainly as nanoscopic clusters below 1300 K. The average Fe and Ni cluster sizes decrease with increasing the temperature and there is essentially single-atom diffusion at higher temperatures.

  9. A fully coupled diffusion-reaction scheme for moisture sorption-desorption in an anhydride-cured epoxy resin

    KAUST Repository

    El Yagoubi, Jalal; Lubineau, Gilles; Roger, Frederic; Verdu, Jacques

    2012-01-01

    Thermoset materials frequently display non-classical moisture sorption behaviors. In this paper, we investigated this issue from an experimental point of view as well as in terms of modeling the water transport. We used the gravimetric technique to monitor water uptake by epoxy samples, with several thicknesses exposed to different levels of humidity during absorption and desorption tests. Our results revealed that the polymer displays a two-stage behavior with a residual amount of water that is desorbed progressively. We proposed a phenomenological reaction-diffusion scheme to describe this behavior. The model describes water transport as a competition between diffusion and the reaction, during which the local diffusivity and solubility depend on the local advancement of the reaction. We then implemented our model using COMSOL Multiphysics and identified it using a MATLAB-COMSOL optimization tool and the experimental data. We discussed the relation between the hydrophilicity of the product of the reaction and the diffusion behavior. We examined the reaction-induced modification of the water concentration field. It is worth noting that part of the phenomenology can be explained by the presence of hydrolyzable groups. © 2012 Elsevier Ltd. All rights reserved.

  10. Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

    Directory of Open Access Journals (Sweden)

    Matthew J Simpson

    Full Text Available Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0diffusivity associated with the spreading density profile, (iii the reaction rate, and (iv the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t.

  11. A fully coupled diffusion-reaction scheme for moisture sorption-desorption in an anhydride-cured epoxy resin

    KAUST Repository

    El Yagoubi, Jalal

    2012-11-01

    Thermoset materials frequently display non-classical moisture sorption behaviors. In this paper, we investigated this issue from an experimental point of view as well as in terms of modeling the water transport. We used the gravimetric technique to monitor water uptake by epoxy samples, with several thicknesses exposed to different levels of humidity during absorption and desorption tests. Our results revealed that the polymer displays a two-stage behavior with a residual amount of water that is desorbed progressively. We proposed a phenomenological reaction-diffusion scheme to describe this behavior. The model describes water transport as a competition between diffusion and the reaction, during which the local diffusivity and solubility depend on the local advancement of the reaction. We then implemented our model using COMSOL Multiphysics and identified it using a MATLAB-COMSOL optimization tool and the experimental data. We discussed the relation between the hydrophilicity of the product of the reaction and the diffusion behavior. We examined the reaction-induced modification of the water concentration field. It is worth noting that part of the phenomenology can be explained by the presence of hydrolyzable groups. © 2012 Elsevier Ltd. All rights reserved.

  12. Global dynamics of a reaction-diffusion system

    Directory of Open Access Journals (Sweden)

    Yuncheng You

    2011-02-01

    Full Text Available In this work the existence of a global attractor for the semiflow of weak solutions of a two-cell Brusselator system is proved. The method of grouping estimation is exploited to deal with the challenge in proving the absorbing property and the asymptotic compactness of this type of coupled reaction-diffusion systems with cubic autocatalytic nonlinearity and linear coupling. It is proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite. Moreover, the existence of an exponential attractor for this solution semiflow is shown.

  13. Diffuse Urticarial Reaction Associated with Titanium Dioxide Following Laser Tattoo Removal Treatments.

    Science.gov (United States)

    Willardson, Hal Bret; Kobayashi, Todd T; Arnold, Jason G; Hivnor, Chad M; Bowen, Casey D

    2017-03-01

    Local and generalized allergic reactions following laser tattoo removal have been documented, but are rare. To our knowledge, this is the fourth documented case of widespread urticarial eruptions following laser tattoo removal treatment. Unlike previously documented cases, this patient's reaction was found to be associated with titanium dioxide within the tattoo and her symptoms were recalcitrant to medical therapy. A 46-year-old female experienced diffuse urticarial plaques, erythema, and pruritis following multiple laser tattoo removal treatments with an Nd:YAG laser. The systemic allergic reaction was recalcitrant to increasing doses of antihistamines and corticosteroids. The tattoo was finally surgically excised. The excised tissue was analyzed by scanning electron microscopy and energy-dispersive X-ray analysis and contained high levels of titanium dioxide. Two weeks following the excision, and without the use of medical therapy, the patient had complete resolution of her generalized urticaria. Ours is the first documented case of a diffuse urticarial reaction following laser tattoo removal treatments that shows a strong association to titanium dioxide within the tattoo pigment. Herein, we describe a novel surgical approach to treat recalcitrant generalized allergic reaction to tattoo pigment.

  14. Diffusion of Telecommunications Services in a Complex Socio-Economic Context

    DEFF Research Database (Denmark)

    Ismail, Abdullah

    This research aims at creating a detailed account on the diffusion of telecommunications services in a complex socio-economic context, taking Pakistan as a case study. The core research question of this thesis is to investigate why the successful experience of the rapid and an effective diffusion...... of mobile communications services in case of Pakistan couldn’t be replicated in the cases of fixed telephony and internet services. The book investigates those major attributes which play a significant role in the diffusion of telecommunications services in a complex socio-economic and political context...... of telecom services within a complex unit of adoption. The empirical part of the research includes a significantly high number of interviews that were conducted from the key players of the local telecom market, and they essentially represented all the five major domains i.e. the supplier, policy, regulatory...

  15. Molecular Dynamics Simulations of Grain Boundary and Bulk Diffusion in Metals.

    Science.gov (United States)

    Plimpton, Steven James

    Diffusion is a microscopic mass transport mechanism that underlies many important macroscopic phenomena affecting the structural, electrical, and mechanical properties of metals. This thesis presents results from atomistic simulation studies of diffusion both in bulk and in the fast diffusion paths known as grain boundaries. Using the principles of molecular dynamics single boundaries are studied and their structure and dynamic properties characterized. In particular, tilt boundary bicrystal and bulk models of fcc Al and bcc alpha-Fe are simulated. Diffusion coefficients and activation energies for atomic motion are calculated for both models and compared to experimental data. The influence of the interatomic pair potential on the diffusion is studied in detail. A universal relation between the melting temperature that a pair potential induces in a simulated bulk model and the potential energy barrier height for atomic hopping is derived and used to correlate results for a wide variety of pair potentials. Using these techniques grain boundary and bulk diffusion coefficients for any fcc material can be estimated from simple static calculations without the need to perform more time-consuming dynamic simulations. The influences of two other factors on grain boundary diffusion are also studied because of the interest of the microelectronics industry in the diffusion related reliability problem known as electromigration. The first factor, known to affect the self diffusion rate of Al, is the presence of Cu impurity atoms in Al tilt boundaries. The bicrystal model for Al is seeded randomly with Cu atoms and a simple hybrid Morse potential used to model the Al-Cu interaction. While some effect due to the Cu is noted, it is concluded that pair potentials are likely an inadequate approximation for the alloy system. The second factor studied is the effect of the boundary orientation angle on the diffusion rate. Symmetric bcc Fe boundaries are relaxed to find optimal

  16. Photoinitiated reactions in weakly bonded complexes

    International Nuclear Information System (INIS)

    Wittig, C.

    1993-01-01

    This paper discusses photoinitiated reactions in weakly bonded binary complexes in which the constituents are only mildly perturbed by the intermolecular bond. Such complexes, with their large zero point excursions, set the stage for events that occur following electronic excitation of one of the constituents. This can take several forms, but in all cases, entrance channel specificity is imposed by the character of the complex as well as the nature of the photoinitiation process. This has enabled us to examine aspects of bimolecular processes: steric effects, chemical branching ratios, and inelastic scattering. Furthermore, monitoring reactions directly in the time domain can reveal mechanisms that cannot be inferred from measurements of nascent product excitations. Consequently, we examined several systems that had been studied previously by our group with product state resolution. With CO 2 /HI, in which reaction occurs via a HOCO intermediate, the rates agree with RRKM predictions. With N 2 O/HI, the gas phase single collision reaction yielding OH + N 2 has been shown to proceed mainly via an HNNO intermediate that undergoes a 1,3-hydrogen shift to the OH + N 2 channel. With complexes, ab initio calculations and high resolution spectroscopic studies of analogous systems suggest that the hydrogen, while highly delocalized, prefers the oxygen to the nitrogen. We observe that OH is produced with a fast risetime (< 250 fs) which can be attributed to either direct oxygen-side attack or rapid HNNO decomposition and/or a termolecular contribution involving the nearby iodine

  17. Dynamic phase transition in diffusion-limited reactions

    International Nuclear Information System (INIS)

    Tauber, U.C.

    2002-01-01

    Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means of the renormalization group. The resulting universality classes for single-species systems are reviewed here. Generically, the critical exponents are those of directed percolation (Reggeon field theory), with critical dimension d c = 4. Yet local particle number parity conservation in even-offspring branching and annihilating random walks implies an inactive phase (emerging below d c = 4/3) that is characterized by the power laws of the pair annihilation reaction, and leads to different critical exponents at the transition. For local processes without memory, the pair contact process with diffusion represents the only other non-trivial universality class. The consistent treatment of restricted site occupations and quenched random reaction rates are important open issues (Author)

  18. Diffusion-controlled reactions modeling in Geant4-DNA

    Czech Academy of Sciences Publication Activity Database

    Karamitros, M.; Luan, S.; Bernal, M. A.; Allison, J.; Baldacchino, G.; Davídková, Marie; Francis, Z.; Friedland, W.; Ivanchenko, A.; Ivanchenko, V.; Mantero, A.; Nieminen, P.; Santin, G.; Tran, H. N.; Stepan, V.; Incerti, S.

    2014-01-01

    Roč. 274, OCT (2014), s. 841-882 ISSN 0021-9991 Institutional support: RVO:61389005 Keywords : chemical kinetics simulation * radiation chemistry * Fokker-Planck equation * Smoluchowski diffusion equation * Brownian bridge * dynamical time steps * k-d tree * radiolysis * radiobiology * Geant4-DNA * Brownian dynamics Subject RIV: BO - Biophysics Impact factor: 2.434, year: 2014

  19. Generalized random walk algorithm for the numerical modeling of complex diffusion processes

    CERN Document Server

    Vamos, C; Vereecken, H

    2003-01-01

    A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested.

  20. Generalized random walk algorithm for the numerical modeling of complex diffusion processes

    International Nuclear Information System (INIS)

    Vamos, Calin; Suciu, Nicolae; Vereecken, Harry

    2003-01-01

    A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested

  1. Simulation in Complex Modelling

    DEFF Research Database (Denmark)

    Nicholas, Paul; Ramsgaard Thomsen, Mette; Tamke, Martin

    2017-01-01

    This paper will discuss the role of simulation in extended architectural design modelling. As a framing paper, the aim is to present and discuss the role of integrated design simulation and feedback between design and simulation in a series of projects under the Complex Modelling framework. Complex...... performance, engage with high degrees of interdependency and allow the emergence of design agency and feedback between the multiple scales of architectural construction. This paper presents examples for integrated design simulation from a series of projects including Lace Wall, A Bridge Too Far and Inflated...... Restraint developed for the research exhibition Complex Modelling, Meldahls Smedie Gallery, Copenhagen in 2016. Where the direct project aims and outcomes have been reported elsewhere, the aim for this paper is to discuss overarching strategies for working with design integrated simulation....

  2. Reaction diffusion voronoi diagrams: from sensors data to computing

    Czech Academy of Sciences Publication Activity Database

    Vázquez-Otero, Alejandro (ed.); Faigl, J.; Dormido, R.; Duro, N.

    2015-01-01

    Roč. 15, č. 6 (2015), s. 12736-12764 ISSN 1424-8220 R&D Projects: GA MŠk ED1.1.00/02.0061 Grant - others:ELI Beamlines(XE) CZ.1.05/1.1.00/02.0061 Institutional support: RVO:68378271 Keywords : reaction diffusion * FitzHugh–Nagumo * path planning * navigation * exploration Subject RIV: BD - Theory of Information Impact factor: 2.033, year: 2015

  3. Simulation of the proton implantation process in silicon

    Energy Technology Data Exchange (ETDEWEB)

    Faccinelli, Martin; Hadley, Peter [Graz University of Technology, Institute of Solid State Physics (Austria); Jelinek, Moriz; Wuebben, Thomas [Infineon Technologies Austria AG, Villach (Austria); Laven, Johannes G.; Schulze, Hans-Joachim [Infineon Technologies AG, Neubiberg (Germany)

    2016-12-15

    Proton implantation is one of many processes used to ad-just the electronic and mechanical properties of silicon. Though the process has been extensively studied, it is still not clear which exact defects are formed and what their concentration profiles are. In this article, a simulation method is presented, which provides a better understanding of the implantation process. The simulation takes into account the diffusion of mobile point defects and their reactions to defect complexes, as well as the dissociation of defect complexes. Concentration profiles for a set of defect complexes after an implantation at 400 keV and a dose of 5 x 10{sup 14} H{sup +}cm{sup -2} are presented. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  4. Nox diffusion-simulation in an urban area in using the vertical diffusion diagram including a surface roughness parameter

    Energy Technology Data Exchange (ETDEWEB)

    Kono, Hitoshi; Fujimoto, Akira; Nakano, Hiroshi

    1988-03-31

    In recent years, in order to attain a total quantity regulation of air pollution and to prepare a local air-control program, a diffusion simulation is often made using a Gaussian plume model. NOx diffusion simulation of the urban area was carried out using a vertical diffusion width by taking a parameter of ground-surface roughness using Smith's correction to the Gaussian model. For the diffusion of car exhaust gas, comparison was made for the estimate and the measurement by jointly using the values of ground-surface roughness and the initial diffusion width. As a result, change in the diffusion width of the car exhaust gas due to the urban buildings was expressed at a necessary practical level by giving the height of the point of calculation, 1 - 3 m in the central part and 30 cm at the peripheral part, and giving the initial diffusion width of roughly half to equal size of initial diffusion width to the average height of the buildings. (2 figs, 8 tabs, 20 refs)

  5. Methods for forming complex oxidation reaction products including superconducting articles

    International Nuclear Information System (INIS)

    Rapp, R.A.; Urquhart, A.W.; Nagelberg, A.S.; Newkirk, M.S.

    1992-01-01

    This patent describes a method for producing a superconducting complex oxidation reaction product of two or more metals in an oxidized state. It comprises positioning at least one parent metal source comprising one of the metals adjacent to a permeable mass comprising at least one metal-containing compound capable of reaction to form the complex oxidation reaction product in step below, the metal component of the at least one metal-containing compound comprising at least a second of the two or more metals, and orienting the parent metal source and the permeable mass relative to each other so that formation of the complex oxidation reaction product will occur in a direction towards and into the permeable mass; and heating the parent metal source in the presence of an oxidant to a temperature region above its melting point to form a body of molten parent metal to permit infiltration and reaction of the molten parent metal into the permeable mass and with the oxidant and the at least one metal-containing compound to form the complex oxidation reaction product, and progressively drawing the molten parent metal source through the complex oxidation reaction product towards the oxidant and towards and into the adjacent permeable mass so that fresh complex oxidation reaction product continues to form within the permeable mass; and recovering the resulting complex oxidation reaction product

  6. Stochastic Simulation of Soot Formation Evolution in Counterflow Diffusion Flames

    Directory of Open Access Journals (Sweden)

    Xiao Jiang

    2018-01-01

    Full Text Available Soot generally refers to carbonaceous particles formed during incomplete combustion of hydrocarbon fuels. A typical simulation of soot formation and evolution contains two parts: gas chemical kinetics, which models the chemical reaction from hydrocarbon fuels to soot precursors, that is, polycyclic aromatic hydrocarbons or PAHs, and soot dynamics, which models the soot formation from PAHs and evolution due to gas-soot and soot-soot interactions. In this study, two detailed gas kinetic mechanisms (ABF and KM2 have been compared during the simulation (using the solver Chemkin II of ethylene combustion in counterflow diffusion flames. Subsequently, the operator splitting Monte Carlo method is used to simulate the soot dynamics. Both the simulated data from the two mechanisms for gas and soot particles are compared with experimental data available in the literature. It is found that both mechanisms predict similar profiles for the gas temperature and velocity, agreeing well with measurements. However, KM2 mechanism provides much closer prediction compared to measurements for soot gas precursors. Furthermore, KM2 also shows much better predictions for soot number density and volume fraction than ABF. The effect of nozzle exit velocity on soot dynamics has also been investigated. Higher nozzle exit velocity renders shorter residence time for soot particles, which reduces the soot number density and volume fraction accordingly.

  7. Localization of (photorespiration and CO2 re-assimilation in tomato leaves investigated with a reaction-diffusion model.

    Directory of Open Access Journals (Sweden)

    Herman N C Berghuijs

    Full Text Available The rate of photosynthesis depends on the CO2 partial pressure near Rubisco, Cc, which is commonly calculated by models using the overall mesophyll resistance. Such models do not explain the difference between the CO2 level in the intercellular air space and Cc mechanistically. This problem can be overcome by reaction-diffusion models for CO2 transport, production and fixation in leaves. However, most reaction-diffusion models are complex and unattractive for procedures that require a large number of runs, like parameter optimisation. This study provides a simpler reaction-diffusion model. It is parameterized by both leaf physiological and leaf anatomical data. The anatomical data consisted of the thickness of the cell wall, cytosol and stroma, and the area ratios of mesophyll exposed to the intercellular air space to leaf surfaces and exposed chloroplast to exposed mesophyll surfaces. The model was used directly to estimate photosynthetic parameters from a subset of the measured light and CO2 response curves; the remaining data were used for validation. The model predicted light and CO2 response curves reasonably well for 15 days old tomato (cv. Admiro leaves, if (photorespiratory CO2 release was assumed to take place in the inner cytosol or in the gaps between the chloroplasts. The model was also used to calculate the fraction of CO2 produced by (photorespiration that is re-assimilated in the stroma, and this fraction ranged from 56 to 76%. In future research, the model should be further validated to better understand how the re-assimilation of (photorespired CO2 is affected by environmental conditions and physiological parameters.

  8. Evolution of density profiles for reaction-diffusion processes

    International Nuclear Information System (INIS)

    Ondarza-Rovira, R.

    1990-01-01

    The purpose of this work is to study the reaction diffusion equations for the concentration of one species in one spatial dimension. Nonlinear diffusion equations paly an important role in several fields: Physics, Kinetic Chemistry, Poblational Biology, Neurophysics, etc. The study of the behavior of solutions, with nonlinear diffusion coefficient, and monomial creation and annihilation terms, is considered. It is found, that when the exponent of the annihilation term is smaller than the one of the creation term, unstable equilibrium solutions may exist, for which solutions above it explode in finite time, but solutions below it decay exponentially. By means of the reduction to quadratures technique, it is found that is possible to obtain travelling wave solution in those cases when the annihilation term is greater than the creation term. This method of solution always permits to know the propagation velocity of the front, even if the concentration cannot be written in closed form. The portraits of the solutions in phase space show the existence of solutions which velocities may be smaller or greater than the ones found analytically. Linear and nonlinear diffusion equations, differ significantly in that the former are of change of solutions are considered. This is reminiscent of the fact that linear diffusion yields infinite propagation speed, even though the speed of the front is finite. When the strength of the annihilation term increases, as compared with that of the creation term, arbitrary initial conditions (studied numerically) relax to stable platforms that move indefinitly with constant speed. (Author)

  9. Electron transfer reactions of metal complexes in solution

    International Nuclear Information System (INIS)

    Sutin, N.

    1977-01-01

    A few representative electron-transfer reactions are selected and their kinetic parameters compared with the predictions of activated complex models. Since Taube has presented an elegant treatment of intramolecular electron-transfer reactions, emphasis is on bimolecular reactions. The latter electron-transfer reactions are more complicated to treat theoretically since the geometries of their activated complexes are not as well known as for the intramolecular case. In addition in biomolecular reactions, the work required to bring the two reactants together needs to be calculated. Since both reactants generally carry charges this presents a non-trivial problem at the ionic strengths usually used to study bimolecular electron transfer

  10. Data of NODDI diffusion metrics in the brain and computer simulation of hybrid diffusion imaging (HYDI acquisition scheme

    Directory of Open Access Journals (Sweden)

    Chandana Kodiweera

    2016-06-01

    Full Text Available This article provides NODDI diffusion metrics in the brains of 52 healthy participants and computer simulation data to support compatibility of hybrid diffusion imaging (HYDI, “Hybrid diffusion imaging” [1] acquisition scheme in fitting neurite orientation dispersion and density imaging (NODDI model, “NODDI: practical in vivo neurite orientation dispersion and density imaging of the human brain” [2]. HYDI is an extremely versatile diffusion magnetic resonance imaging (dMRI technique that enables various analyzes methods using a single diffusion dataset. One of the diffusion data analysis methods is the NODDI computation, which models the brain tissue with three compartments: fast isotropic diffusion (e.g., cerebrospinal fluid, anisotropic hindered diffusion (e.g., extracellular space, and anisotropic restricted diffusion (e.g., intracellular space. The NODDI model produces microstructural metrics in the developing brain, aging brain or human brain with neurologic disorders. The first dataset provided here are the means and standard deviations of NODDI metrics in 48 white matter region-of-interest (ROI averaging across 52 healthy participants. The second dataset provided here is the computer simulation with initial conditions guided by the first dataset as inputs and gold standard for model fitting. The computer simulation data provide a direct comparison of NODDI indices computed from the HYDI acquisition [1] to the NODDI indices computed from the originally proposed acquisition [2]. These data are related to the accompanying research article “Age Effects and Sex Differences in Human Brain White Matter of Young to Middle-Aged Adults: A DTI, NODDI, and q-Space Study” [3].

  11. Automatic simplification of systems of reaction-diffusion equations by a posteriori analysis.

    Science.gov (United States)

    Maybank, Philip J; Whiteley, Jonathan P

    2014-02-01

    Many mathematical models in biology and physiology are represented by systems of nonlinear differential equations. In recent years these models have become increasingly complex in order to explain the enormous volume of data now available. A key role of modellers is to determine which components of the model have the greatest effect on a given observed behaviour. An approach for automatically fulfilling this role, based on a posteriori analysis, has recently been developed for nonlinear initial value ordinary differential equations [J.P. Whiteley, Model reduction using a posteriori analysis, Math. Biosci. 225 (2010) 44-52]. In this paper we extend this model reduction technique for application to both steady-state and time-dependent nonlinear reaction-diffusion systems. Exemplar problems drawn from biology are used to demonstrate the applicability of the technique. Copyright © 2014 Elsevier Inc. All rights reserved.

  12. Development of a 3D-Multigroup program to simulate anomalous diffusion phenomena in the nuclear reactors

    International Nuclear Information System (INIS)

    Maleki Moghaddam, Nader; Afarideh, Hossein; Espinosa-Paredes, Gilberto

    2015-01-01

    Highlights: • The new version of neutron diffusion equation for simulating anomalous diffusion is presented. • Application of fractional calculus in the nuclear reactor is revealed. • A 3D-Multigroup program is developed based on the fractional operators. • The super-diffusion and sub-diffusion phenomena are modeled in the nuclear reactors core. - Abstract: The diffusion process is categorized in three parts, normal diffusion, super-diffusion and sub-diffusion. The classical neutron diffusion equation is used to model normal diffusion. A new scheme of derivatives is required to model anomalous diffusion phenomena. The fractional space derivatives are employed to model anomalous diffusion processes where a plume of particles spreads at an inconsistent rate with the classical Brownian motion model. In the fractional diffusion equation, the fractional Laplacians are used; therefore the statistical jump length of neutrons is unrestricted. It is clear that the fractional Laplacians are capable to model the anomalous phenomena in nuclear reactors. We have developed a NFDE-3D (neutron fractional diffusion equation) as a core calculation code to model normal and anomalous diffusion phenomena. The NFDE-3D is validated against the LMW-LWR reactor. The results demonstrate that reactors exhibit complex behavior versus order of the fractional derivatives which depends on the competition between neutron absorption and super-diffusion phenomenon

  13. Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection at large Rayleigh numbers

    Science.gov (United States)

    Kozitskiy, Sergey

    2018-05-01

    Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection has been performed by using the previously derived system of complex Ginzburg-Landau type amplitude equations, valid in a neighborhood of Hopf bifurcation points. Simulation has shown that the state of spatiotemporal chaos develops in the system. It has the form of nonstationary structures that depend on the parameters of the system. The shape of structures does not depend on the initial conditions, and a limited number of spectral components participate in their formation.

  14. Simulation of Weak Signals of Nanotechnology Innovation in Complex System

    Directory of Open Access Journals (Sweden)

    Sun Hi Yoo

    2018-02-01

    Full Text Available It is especially indispensable for new businesses or industries to predict the innovation of new technologies. This requires an understanding of how the complex process of innovation, which is accomplished through more efficient products, processes, services, technologies, or ideas, is adopted and diffused in the market, government, and society. Furthermore, detecting “weak signals” (signs of change in science and technology (S&T is also important to foretell events associated with innovations in technology. Thus, we explore the dynamic behavior of weak signals of a specific technological innovation using the agent-based simulating tool NetLogo. This study provides a deeper understanding of the early stages of complex technology innovation, and the models are capable of analyzing initial complex interaction structures between components of technologies and between agents engaged in collective invention.

  15. Existence of global solutions to reaction-diffusion systems via a Lyapunov functional

    Directory of Open Access Journals (Sweden)

    Said Kouachi

    2001-10-01

    Full Text Available The purpose of this paper is to construct polynomial functionals (according to solutions of the coupled reaction-diffusion equations which give $L^{p}$-bounds for solutions. When the reaction terms are sufficiently regular, using the well known regularizing effect, we deduce the existence of global solutions. These functionals are obtained independently of work done by Malham and Xin [11].

  16. A model for self-diffusion of guanidinium-based ionic liquids: a molecular simulation study.

    Science.gov (United States)

    Klähn, Marco; Seduraman, Abirami; Wu, Ping

    2008-11-06

    We propose a novel self-diffusion model for ionic liquids on an atomic level of detail. The model is derived from molecular dynamics simulations of guanidinium-based ionic liquids (GILs) as a model case. The simulations are based on an empirical molecular mechanical force field, which has been developed in our preceding work, and it relies on the charge distribution in the actual liquid. The simulated GILs consist of acyclic and cyclic cations that were paired with nitrate and perchlorate anions. Self-diffusion coefficients are calculated at different temperatures from which diffusive activation energies between 32-40 kJ/mol are derived. Vaporization enthalpies between 174-212 kJ/mol are calculated, and their strong connection with diffusive activation energies is demonstrated. An observed formation of cavities in GILs of up to 6.5% of the total volume does not facilitate self-diffusion. Instead, the diffusion of ions is found to be determined primarily by interactions with their immediate environment via electrostatic attraction between cation hydrogen and anion oxygen atoms. The calculated average time between single diffusive transitions varies between 58-107 ps and determines the speed of diffusion, in contrast to diffusive displacement distances, which were found to be similar in all simulated GILs. All simulations indicate that ions diffuse by using a brachiation type of movement: a diffusive transition is initiated by cleaving close contacts to a coordinated counterion, after which the ion diffuses only about 2 A until new close contacts are formed with another counterion in its vicinity. The proposed diffusion model links all calculated energetic and dynamic properties of GILs consistently and explains their molecular origin. The validity of the model is confirmed by providing an explanation for the variation of measured ratios of self-diffusion coefficients of cations and paired anions over a wide range of values, encompassing various ionic liquid classes

  17. Mass transfer rate through liquid membranes: interfacial chemical reactions and diffusion as simultaneous permeability controlling factors

    International Nuclear Information System (INIS)

    Danesi, P.R.; Horwitz, E.P.; Vandegrift, G.F.; Chiarizia, R.

    1981-01-01

    Equations describing the permeability of a liquid membrane to metal cations have been derived taking into account aqueous diffusion, membrane diffusion, and interfacial chemical reactions as simultaneous permeability controlling factors. Diffusion and chemical reactions have been coupled by a simple model analogous to the one previously described by us to represent liquid-liquid extraction kinetics. The derived equations, which make use of experimentally determined interfacial reaction mechanisms, qualitatively fit unexplained literature data regarding Cu 2+ transfer through liquid membranes. Their use to predict and optimize membrane permeability in practical separation processes by setting the appropriate concentration of the membrane carrier [LIX 64 (General Mills), a commercial β-hydroxy-oxime] and the pH of the aqueous copper feed solution is briefly discussed. 4 figures

  18. Continuous Dependence in Front Propagation for Convective Reaction-Diffusion Models with Aggregative Movements

    Directory of Open Access Journals (Sweden)

    Luisa Malaguti

    2011-01-01

    Full Text Available The paper deals with a degenerate reaction-diffusion equation, including aggregative movements and convective terms. The model also incorporates a real parameter causing the change from a purely diffusive to a diffusive-aggregative and to a purely aggregative regime. Existence and qualitative properties of traveling wave solutions are investigated, and estimates of their threshold speeds are furnished. Further, the continuous dependence of the threshold wave speed and of the wave profiles on a real parameter is studied, both when the process maintains its diffusion-aggregation nature and when it switches from it to another regime.

  19. From conservative to reactive transport under diffusion-controlled conditions

    Science.gov (United States)

    Babey, Tristan; de Dreuzy, Jean-Raynald; Ginn, Timothy R.

    2016-05-01

    We assess the possibility to use conservative transport information, such as that contained in transit time distributions, breakthrough curves and tracer tests, to predict nonlinear fluid-rock interactions in fracture/matrix or mobile/immobile conditions. Reference simulated data are given by conservative and reactive transport simulations in several diffusive porosity structures differing by their topological organization. Reactions includes nonlinear kinetically controlled dissolution and desorption. Effective Multi-Rate Mass Transfer models (MRMT) are calibrated solely on conservative transport information without pore topology information and provide concentration distributions on which effective reaction rates are estimated. Reference simulated reaction rates and effective reaction rates evaluated by MRMT are compared, as well as characteristic desorption and dissolution times. Although not exactly equal, these indicators remain very close whatever the porous structure, differing at most by 0.6% and 10% for desorption and dissolution. At early times, this close agreement arises from the fine characterization of the diffusive porosity close to the mobile zone that controls fast mobile-diffusive exchanges. At intermediate to late times, concentration gradients are strongly reduced by diffusion, and reactivity can be captured by a very limited number of rates. We conclude that effective models calibrated solely on conservative transport information like MRMT can accurately estimate monocomponent kinetically controlled nonlinear fluid-rock interactions. Their relevance might extend to more advanced biogeochemical reactions because of the good characterization of conservative concentration distributions, even by parsimonious models (e.g., MRMT with 3-5 rates). We propose a methodology to estimate reactive transport from conservative transport in mobile-immobile conditions.

  20. Study and simulations of quick diffusion in Zr-based alloys

    Energy Technology Data Exchange (ETDEWEB)

    Corvalán, C., E-mail: corvalan@cnea.gov.ar [UNTREF (Universidad Nacional de Tres de Febrero), General Enrique Mosconi 2736, B1674AHF, Buenos Aires (Argentina); Gerencia de Materiales, CAC, Comisión de Energía Atómica, Av. del Libertador 8250, C1429BNP Buenos Aires (Argentina); Consejo Nacional de Investigaciones Científicas y Técnicas (Argentina); Lucía, A. [UNTREF (Universidad Nacional de Tres de Febrero), General Enrique Mosconi 2736, B1674AHF, Buenos Aires (Argentina); Instituto Sabato, Comisión Nacional de Energía Atómica, Universidad Nacional de San Martín, Buenos Aires (Argentina); Iribarren, M. [Gerencia de Materiales, CAC, Comisión de Energía Atómica, Av. del Libertador 8250, C1429BNP Buenos Aires (Argentina); Instituto Sabato, Comisión Nacional de Energía Atómica, Universidad Nacional de San Martín, Buenos Aires (Argentina); Servant, C. [Laboratoire de Physicochimie de l' Etat Solide, UMR 8182, ICMMO, Université de Paris-Sud XI, 91405 Orsay Cedex (France); Costa e Silva, A. [Universidade Federal Fluminense, Volta Redonda, RJ (Brazil)

    2015-11-15

    Zirconium and its alloys are widely used in the nuclear industry. Under normal conditions, Zr-alloys are polycrystalline and contain a high density of grain and interphase boundaries. These boundaries function as paths for accelerated matter movement. The movement of fast diffusing elements (Co, Fe, Cr, Ni) in Zr alloys along boundaries produces technologically important changes in the materials in nuclear reactors at normal temperatures (∼550 K) e.g.: segregation, phase precipitation, hydrogen absorption, etc. In this work, diffusion parameters for fast diffusion in Zr at low temperature were assessed for Co and Cr. An improved database for DICTRA (DIffusion-Controlled-TRAnsformation) software for fast diffusion was obtained. The diffusion parameters in grain boundaries of α-Zr for Cr and Co were used from a particular kinetic diffusion model [1]. Simulated profiles were compared with previous experimental work [2]. The results of the comparison and the adequacy of the improved database are discussed. Diffusion profiles on grain boundaries in α-Zr for Cr and Co are presented in the temperature range of 380–460 K. - Highlights: • An improved database for fast diffusion paths was obtained. • The diffusion parameters in type C kinetic on fast paths in α-Zr for Cr and Co were used. • Simulated diffusion profiles were compared with previous experimental results. This comparison and the adequacy of the improved database are discussed. • Diffusion parameters for fast diffusion paths in Zr at low temperature were assessed for Co and Cr. • Diffusion profiles on grain boundaries in α-Zr for Cr and Co are presented in the temperature range of 380–460 K.

  1. Study and simulations of quick diffusion in Zr-based alloys

    International Nuclear Information System (INIS)

    Corvalán, C.; Lucía, A.; Iribarren, M.; Servant, C.; Costa e Silva, A.

    2015-01-01

    Zirconium and its alloys are widely used in the nuclear industry. Under normal conditions, Zr-alloys are polycrystalline and contain a high density of grain and interphase boundaries. These boundaries function as paths for accelerated matter movement. The movement of fast diffusing elements (Co, Fe, Cr, Ni) in Zr alloys along boundaries produces technologically important changes in the materials in nuclear reactors at normal temperatures (∼550 K) e.g.: segregation, phase precipitation, hydrogen absorption, etc. In this work, diffusion parameters for fast diffusion in Zr at low temperature were assessed for Co and Cr. An improved database for DICTRA (DIffusion-Controlled-TRAnsformation) software for fast diffusion was obtained. The diffusion parameters in grain boundaries of α-Zr for Cr and Co were used from a particular kinetic diffusion model [1]. Simulated profiles were compared with previous experimental work [2]. The results of the comparison and the adequacy of the improved database are discussed. Diffusion profiles on grain boundaries in α-Zr for Cr and Co are presented in the temperature range of 380–460 K. - Highlights: • An improved database for fast diffusion paths was obtained. • The diffusion parameters in type C kinetic on fast paths in α-Zr for Cr and Co were used. • Simulated diffusion profiles were compared with previous experimental results. This comparison and the adequacy of the improved database are discussed. • Diffusion parameters for fast diffusion paths in Zr at low temperature were assessed for Co and Cr. • Diffusion profiles on grain boundaries in α-Zr for Cr and Co are presented in the temperature range of 380–460 K.

  2. Stability and Hopf Bifurcation of a Reaction-Diffusion Neutral Neuron System with Time Delay

    Science.gov (United States)

    Dong, Tao; Xia, Linmao

    2017-12-01

    In this paper, a type of reaction-diffusion neutral neuron system with time delay under homogeneous Neumann boundary conditions is considered. By constructing a basis of phase space based on the eigenvectors of the corresponding Laplace operator, the characteristic equation of this system is obtained. Then, by selecting time delay and self-feedback strength as the bifurcating parameters respectively, the dynamic behaviors including local stability and Hopf bifurcation near the zero equilibrium point are investigated when the time delay and self-feedback strength vary. Furthermore, the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are obtained by using the normal form and the center manifold theorem for the corresponding partial differential equation. Finally, two simulation examples are given to verify the theory.

  3. Open complex-balanced mass action chemical reaction networks

    NARCIS (Netherlands)

    Rao, Shodhan; van der Schaft, Arjan; Jayawardhana, Bayu

    We consider open chemical reaction networks, i.e. ones with inflows and outflows. We assume that all the inflows to the network are constant and all outflows obey the mass action kinetics rate law. We define a complex-balanced open reaction network as one that admits a complex-balanced steady state.

  4. On the solutions of fractional reaction-diffusion equations

    Directory of Open Access Journals (Sweden)

    Jagdev Singh

    2013-05-01

    Full Text Available In this paper, we obtain the solution of a fractional reaction-diffusion equation associated with the generalized Riemann-Liouville fractional derivative as the time derivative and Riesz-Feller fractional derivative as the space-derivative. The results are derived by the application of the Laplace and Fourier transforms in compact and elegant form in terms of Mittag-Leffler function and H-function. The results obtained here are of general nature and include the results investigated earlier by many authors.

  5. Exact substitute processes for diffusion-reaction systems with local complete exclusion rules

    International Nuclear Information System (INIS)

    Schulz, Michael; Reineker, Peter

    2005-01-01

    Lattice systems with one species diffusion-reaction processes under local complete exclusion rules are studied analytically starting from the usual master equations with discrete variables and their corresponding representation in a Fock space. On this basis, a formulation of the transition probability as a Grassmann path integral is derived in a straightforward manner. It will be demonstrated that this Grassmann path integral is equivalent to a set of Ito stochastic differential equations. Averages of arbitrary variables and correlation functions of the underlying diffusion-reaction system can be expressed as weighted averages over all solutions of the system of stochastic differential equations. Furthermore, these differential equations are equivalent to a Fokker-Planck equation describing the probability distribution of the actual Ito solutions. This probability distribution depends on continuous variables in contrast to the original master equation, and their stochastic dynamics may be interpreted as a substitute process which is completely equivalent to the original lattice dynamics. Especially, averages and correlation functions of the continuous variables are connected to the corresponding lattice quantities by simple relations. Although the substitute process for diffusion-reaction systems with exclusion rules has some similarities to the well-known substitute process for the same system without exclusion rules, there exists a set of remarkable differences. The given approach is not only valid for the discussed single-species processes. We give sufficient arguments to show that arbitrary combinations of unimolecular and bimolecular lattice reactions under complete local exclusions may be described in terms of our approach

  6. Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

    Science.gov (United States)

    Indekeu, Joseph O.; Smets, Ruben

    2017-08-01

    Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

  7. Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

    International Nuclear Information System (INIS)

    Indekeu, Joseph O; Smets, Ruben

    2017-01-01

    Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically. (paper)

  8. On some limitations of reaction-diffusion chemical computers in relation to Voronoi diagram and its inversion

    International Nuclear Information System (INIS)

    Adamatzky, Andrew; Lacy Costello, Benjamin de

    2003-01-01

    A reaction-diffusion chemical computer in this context is a planar uniform chemical reactor, where data and results of a computation are represented by concentration profiles of reactants and the computation itself is implemented via the spreading and interaction of diffusive and phase waves. This class of chemical computers are efficient at solving problems with a 'natural' parallelism where data sets are decomposable onto a large number of geographically neighboring domains which are then processed in parallel. Typical problems of this type include image processing, geometrical transformations and optimisation. When chemical based devices are used to solve such problems questions regarding their reproducible, efficiency and the accuracy of their computations arise. In addition to these questions what are the limitations of reaction-diffusion chemical processors--what type of problems cannot currently and are unlikely ever to be solved? To answer the questions we study how a Voronoi diagram is constructed and how it is inverted in a planar chemical processor. We demonstrate that a Voronoi diagram is computed only partially in the chemical processor. We also prove that given a specific Voronoi diagram it is impossible to reconstruct the planar set (from which diagram was computed) in the reaction-diffusion chemical processor. In the Letter we open the first ever line of enquiry into the computational inability of reaction-diffusion chemical computers

  9. Possible self-complexity and affective reactions to goal-relevant evaluation.

    Science.gov (United States)

    Niedenthal, P M; Setterlund, M B; Wherry, M B

    1992-07-01

    The complexity of people's self-concept appears to be inversely related to the intensity of their reactions to evaluative feedback about present goals and abilities (Linville, 1985, 1987). The idea that the complexity of individuals' possible self-concept similarly mediates reactions to feedback regarding future goals was investigated. Two preliminary studies suggested that complexity of the actual self only explains 20% to 30% of the variance in possible self-complexity. Three studies were conducted. Support was found for the idea that possible self-complexity mediates affective reactions to evaluative feedback about future goals and actual self-complexity mediates affective reactions to evaluative feedback about present goals. The findings underscore the independent roles of the organization of actual and possible self-concepts in affective processes.

  10. The Induced Dimension Reduction method applied to convection-diffusion-reaction problems

    NARCIS (Netherlands)

    Astudillo, R.; Van Gijzen, M.B.

    2016-01-01

    Discretization of (linearized) convection-diffusion-reaction problems yields a large and sparse non symmetric linear system of equations, Ax = b. (1) In this work, we compare the computational behavior of the Induced Dimension Reduction method (IDR(s)) [10], with other short-recurrences Krylov

  11. Self-learning kinetic Monte Carlo simulations of Al diffusion in Mg

    International Nuclear Information System (INIS)

    Nandipati, Giridhar; Govind, Niranjan; Andersen, Amity; Rohatgi, Aashish

    2016-01-01

    Vacancy-mediated diffusion of an Al atom in the pure Mg matrix is studied using the atomistic, on-lattice self-learning kinetic Monte Carlo (SLKMC) method. Activation barriers for vacancy-Mg and vacancy-Al atom exchange processes are calculated on the fly using the climbing image nudged-elastic-band method and binary Mg–Al modified embedded-atom method interatomic potential. Diffusivities of an Al atom obtained from SLKMC simulations show the same behavior as observed in experimental and theoretical studies available in the literature; that is, an Al atom diffuses faster within the basal plane than along the c-axis. Although the effective activation barriers for an Al atom diffusion from SLKMC simulations are close to experimental and theoretical values, the effective prefactors are lower than those obtained from experiments. We present all the possible vacancy-Mg and vacancy-Al atom exchange processes and their activation barriers identified in SLKMC simulations. A simple mapping scheme to map an HCP lattice onto a simple cubic lattice is described, which enables simulation of the HCP lattice using the on-lattice framework. We also present the pattern recognition scheme which is used in SLKMC simulations to identify the local Al atom configuration around a vacancy. (paper)

  12. Direct interaction in nuclear reactions: a theory; L'interaction directe dans les reactions nucleaires: theorie

    Energy Technology Data Exchange (ETDEWEB)

    Dominicis, C.T. de [Commissariat a l' Energie Atomique, Saclay (France).Centre d' Etudes Nucleaires

    1959-07-01

    General treatment of the foundations of direct interaction in nuclear reactions; representation of the instantaneous elastic scattering amplitude by the scattering amplitude due to a complex potential; expansion of the instantaneous inelastic scattering amplitude and discussion of the 1. Bohr approximation (distorted waves) contribution to individual and collective states of excitation. (author) [French] Expose general sur les fondements de l'interaction directe dans les reactions nucleaires; representation de l'amplitude de diffusion instantanee elastique par celle due a un potentiel complexe; developpement de l'amplitude de diffusion instantanee inelastique et discussion de la contribution de la premiere approximation de Bohr (sur des distendues) a l'excitation d'etats individuels et collectifs. (auteur)

  13. Diffusion, sorption and stability of radionuclide-organic complexes in clays and clay-organic complexes

    International Nuclear Information System (INIS)

    Staunton, S.; Rees, L.V.C.

    1991-01-01

    The dependence on various parameters of the diffusion coefficient of neptunium (V) in clay systems has been studied. The effect of the clay mineralogy, the charge compensating cation in the clay, the ionic strength of a background perchlorate solution and the presence of three organic ligands have been investigated. The diffusion coefficients were compared to those predicted if diffusion occurred only in the liquid phase and adsorption was reversible; agreement was fairly good. An approximation to the diffusion coefficient can thus be obtained from readily measured experimental parameters. There is no evidence of surface phase diffusion. The most significant factor in determining the diffusion coefficient is the magnitude of the distribution ratio, itself highly dependent on the nature of the clay. Neither EDTA nor citrate modified the diffusion coefficient. Although the presence of 1 or 100 mg dm -3 of Aldrich humic acid had little effect on the distribution ratio of neptunium, it caused a lowering of the measured diffusion coefficient. This is interpreted in terms of the limiting liquid phase diffusion coefficient and the true liquid phase impedance factor of neptunium-humic acid complexes. 21 figs; 3 tabs; 20 refs

  14. Estimating the Diffusion Coefficients of Sugars Using Diffusion Experiments in Agar-Gel and Computer Simulations.

    Science.gov (United States)

    Miyamoto, Shuichi; Atsuyama, Kenji; Ekino, Keisuke; Shin, Takashi

    2018-01-01

    The isolation of useful microbes is one of the traditional approaches for the lead generation in drug discovery. As an effective technique for microbe isolation, we recently developed a multidimensional diffusion-based gradient culture system of microbes. In order to enhance the utility of the system, it is favorable to have diffusion coefficients of nutrients such as sugars in the culture medium beforehand. We have, therefore, built a simple and convenient experimental system that uses agar-gel to observe diffusion. Next, we performed computer simulations-based on random-walk concepts-of the experimental diffusion system and derived correlation formulas that relate observable diffusion data to diffusion coefficients. Finally, we applied these correlation formulas to our experimentally-determined diffusion data to estimate the diffusion coefficients of sugars. Our values for these coefficients agree reasonably well with values published in the literature. The effectiveness of our simple technique, which has elucidated the diffusion coefficients of some molecules which are rarely reported (e.g., galactose, trehalose, and glycerol) is demonstrated by the strong correspondence between the literature values and those obtained in our experiments.

  15. Particle Simulation of Fractional Diffusion Equations

    KAUST Repository

    Allouch, Samer

    2017-07-12

    This work explores different particle-based approaches to the simulation of one-dimensional fractional subdiffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the fractional diffusion term. The first method is based on direct differentiation of the particle representation, it follows the Riesz definition of the fractional derivative and results in a non-conservative scheme. The other three methods follow the particle strength exchange (PSE) methodology and are by construction conservative, in the sense that the total particle strength is time invariant. The first PSE algorithm is based on using direct differentiation to estimate the fractional diffusion flux, and exploiting the resulting estimates in an integral representation of the divergence operator. Meanwhile, the second one relies on the regularized Riesz representation of the fractional diffusion term to derive a suitable interaction formula acting directly on the particle representation of the diffusing field. A third PSE construction is considered that exploits the Green\\'s function of the fractional diffusion equation. The performance of all four approaches is assessed for the case of a one-dimensional diffusion equation with constant diffusivity. This enables us to take advantage of known analytical solutions, and consequently conduct a detailed analysis of the performance of the methods. This includes a quantitative study of the various sources of error, namely filtering, quadrature, domain truncation, and time integration, as well as a space and time self-convergence analysis. These analyses are conducted for different values of the order of the fractional derivatives, and computational experiences are used to gain insight that can be used for generalization of the present constructions.

  16. Particle Simulation of Fractional Diffusion Equations

    KAUST Repository

    Allouch, Samer; Lucchesi, Marco; Maî tre, O. P. Le; Mustapha, K. A.; Knio, Omar

    2017-01-01

    This work explores different particle-based approaches to the simulation of one-dimensional fractional subdiffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the fractional diffusion term. The first method is based on direct differentiation of the particle representation, it follows the Riesz definition of the fractional derivative and results in a non-conservative scheme. The other three methods follow the particle strength exchange (PSE) methodology and are by construction conservative, in the sense that the total particle strength is time invariant. The first PSE algorithm is based on using direct differentiation to estimate the fractional diffusion flux, and exploiting the resulting estimates in an integral representation of the divergence operator. Meanwhile, the second one relies on the regularized Riesz representation of the fractional diffusion term to derive a suitable interaction formula acting directly on the particle representation of the diffusing field. A third PSE construction is considered that exploits the Green's function of the fractional diffusion equation. The performance of all four approaches is assessed for the case of a one-dimensional diffusion equation with constant diffusivity. This enables us to take advantage of known analytical solutions, and consequently conduct a detailed analysis of the performance of the methods. This includes a quantitative study of the various sources of error, namely filtering, quadrature, domain truncation, and time integration, as well as a space and time self-convergence analysis. These analyses are conducted for different values of the order of the fractional derivatives, and computational experiences are used to gain insight that can be used for generalization of the present constructions.

  17. An Application of Equivalence Transformations to Reaction Diffusion Equations

    Directory of Open Access Journals (Sweden)

    Mariano Torrisi

    2015-10-01

    Full Text Available In this paper, we consider a quite general class of advection reaction diffusion systems. By using an equivalence generator, derived in a previous paper, the authors apply a projection theorem to determine some special forms of the constitutive functions that allow the extension by one of the two-dimensional principal Lie algebra. As an example, a special case is discussed at the end of the paper.

  18. Multiple Scale Reaction-Diffusion-Advection Problems with Moving Fronts

    Science.gov (United States)

    Nefedov, Nikolay

    2016-06-01

    In this work we discuss the further development of the general scheme of the asymptotic method of differential inequalities to investigate stability and motion of sharp internal layers (fronts) for nonlinear singularly perturbed parabolic equations, which are called in applications reaction-diffusion-advection equations. Our approach is illustrated for some new important cases of initial boundary value problems. We present results on stability and on the motion of the fronts.

  19. FERN - a Java framework for stochastic simulation and evaluation of reaction networks.

    Science.gov (United States)

    Erhard, Florian; Friedel, Caroline C; Zimmer, Ralf

    2008-08-29

    Stochastic simulation can be used to illustrate the development of biological systems over time and the stochastic nature of these processes. Currently available programs for stochastic simulation, however, are limited in that they either a) do not provide the most efficient simulation algorithms and are difficult to extend, b) cannot be easily integrated into other applications or c) do not allow to monitor and intervene during the simulation process in an easy and intuitive way. Thus, in order to use stochastic simulation in innovative high-level modeling and analysis approaches more flexible tools are necessary. In this article, we present FERN (Framework for Evaluation of Reaction Networks), a Java framework for the efficient simulation of chemical reaction networks. FERN is subdivided into three layers for network representation, simulation and visualization of the simulation results each of which can be easily extended. It provides efficient and accurate state-of-the-art stochastic simulation algorithms for well-mixed chemical systems and a powerful observer system, which makes it possible to track and control the simulation progress on every level. To illustrate how FERN can be easily integrated into other systems biology applications, plugins to Cytoscape and CellDesigner are included. These plugins make it possible to run simulations and to observe the simulation progress in a reaction network in real-time from within the Cytoscape or CellDesigner environment. FERN addresses shortcomings of currently available stochastic simulation programs in several ways. First, it provides a broad range of efficient and accurate algorithms both for exact and approximate stochastic simulation and a simple interface for extending to new algorithms. FERN's implementations are considerably faster than the C implementations of gillespie2 or the Java implementations of ISBJava. Second, it can be used in a straightforward way both as a stand-alone program and within new

  20. Reaction layer in U-7WT%MO/Al diffusion couples

    International Nuclear Information System (INIS)

    Mirandou, M.I.; Balart, S.N.; Ortiz, M.; Granovsky, M.S.

    2003-01-01

    New results of the reaction layer characterization between γ (U-7wt%Mo) alloy and Al, in chemical diffusion couples, are presented. The analysis was performed using optical and scanning electron microscopy with EDAX and X-ray diffraction techniques. Besides the main components (U, Mo)Al 3 and (U, Mo)Al 4 , already reported, two ternary compounds of high Al content have been identified in the reaction layer when it grew in retained or decomposed γ (U, Mo) phase, respectively. The drastic consequence on the interdiffusion behavior due to the thermal instability of the retained γ (U, Mo) phase is discussed. (author)

  1. Interface conditions for fast-reaction fronts in wet porous mineral materials: the case of concrete carbonation

    NARCIS (Netherlands)

    Muntean, A.; Böhm, M.

    2009-01-01

    Reaction–diffusion processes, where slow diffusion balances fast reaction, usually exhibit internal loci where the reactions are concentrated. Some modeling and simulation aspects of using kinetic free-boundary conditions to drive fast carbonation reaction fronts into unsaturated porous cement-based

  2. A Green's function method for simulation of time-dependent solute transport and reaction in realistic microvascular geometries.

    Science.gov (United States)

    Secomb, Timothy W

    2016-12-01

    A novel theoretical method is presented for simulating the spatially resolved convective and diffusive transport of reacting solutes between microvascular networks and the surrounding tissues. The method allows for efficient computational solution of problems involving convection and non-linear binding of solutes in blood flowing through microvascular networks with realistic 3D geometries, coupled with transvascular exchange and diffusion and reaction in the surrounding tissue space. The method is based on a Green's function approach, in which the solute concentration distribution in the tissue is expressed as a sum of fields generated by time-varying distributions of discrete sources and sinks. As an example of the application of the method, the washout of an inert diffusible tracer substance from a tissue region perfused by a network of microvessels is simulated, showing its dependence on the solute's transvascular permeability and tissue diffusivity. Exponential decay of the washout concentration is predicted, with rate constants that are about 10-30% lower than the rate constants for a tissue cylinder model with the same vessel length, vessel surface area and blood flow rate per tissue volume. © The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

  3. Competitive autocatalytic reactions in chaotic flows with diffusion: Prediction using finite-time Lyapunov exponents

    International Nuclear Information System (INIS)

    Schlick, Conor P.; Umbanhowar, Paul B.; Ottino, Julio M.; Lueptow, Richard M.

    2014-01-01

    We investigate chaotic advection and diffusion in autocatalytic reactions for time-periodic sine flow computationally using a mapping method with operator splitting. We specifically consider three different autocatalytic reaction schemes: a single autocatalytic reaction, competitive autocatalytic reactions, which can provide insight into problems of chiral symmetry breaking and homochirality, and competitive autocatalytic reactions with recycling. In competitive autocatalytic reactions, species B and C both undergo an autocatalytic reaction with species A such that A+B→2B and A+C→2C. Small amounts of initially spatially localized B and C and a large amount of spatially homogeneous A are advected by the velocity field, diffuse, and react until A is completely consumed and only B and C remain. We find that local finite-time Lyapunov exponents (FTLEs) can accurately predict the final average concentrations of B and C after the reaction completes. The species that starts in the region with the larger FTLE has, with high probability, the larger average concentration at the end of the reaction. If B and C start in regions with similar FTLEs, their average concentrations at the end of the reaction will also be similar. When a recycling reaction is added, the system evolves towards a single species state, with the FTLE often being useful in predicting which species fills the entire domain and which is depleted. The FTLE approach is also demonstrated for competitive autocatalytic reactions in journal bearing flow, an experimentally realizable flow that generates chaotic dynamics

  4. Interplay between inhibited transport and reaction in nanoporous materials

    Energy Technology Data Exchange (ETDEWEB)

    Ackerman, David Michael [Iowa State Univ., Ames, IA (United States)

    2013-01-01

    This work presents a detailed formulation of reaction and diffusion dynamics of molecules in confined pores such as mesoporous silica and zeolites. A general reaction-diffusion model and discrete Monte Carlo simulations are presented. Both transient and steady state behavior is covered. Failure of previous mean-field models for these systems is explained and discussed. A coarse-grained, generalized hydrodynamic model is developed that accurately captures the interplay between reaction and restricted transport in these systems. This method incorporates the non-uniform chemical diffusion behavior present in finite pores with multi-component diffusion. Two methods of calculating these diffusion values are developed: a random walk based approach and a driven diffusion model based on an extension of Fick's law. The effects of reaction, diffusion, pore length, and catalytic site distribution are investigated. In addition to strictly single file motion, quasi-single file diffusion is incorporated into the model to match a range of experimental systems. The connection between these experimental systems and model parameters is made through Langevin dynamics modeling of particles in confined pores.

  5. Near wall combustion modeling in spark ignition engines. Part B: Post-flame reactions

    International Nuclear Information System (INIS)

    Demesoukas, Sokratis; Caillol, Christian; Higelin, Pascal; Boiarciuc, Andrei; Floch, Alain

    2015-01-01

    Highlights: • Models for the post flame reactions (CO and hydrocarbons) and heat release rate are proposed. • ‘Freezing’ effect of CO kinetics is captured but equilibrium CO concentrations are low. • Reactive–diffusive processes are modeled for hydrocarbons and the last stage of combustion is captured. - Abstract: Reduced fuel consumption, low pollutant emissions and adequate output performance are key features in the contemporary design of spark ignition engines. Zero-dimensional numerical simulation is an attractive alternative to engine experiments for the evaluation of various engine configurations. Both flame front reaction and post-flame processes contribute to the heat release rate. The contribution of this work is to highlight and model the role of post-flame reactions (CO and hydrocarbons) in the heat release rate. The modeling approach to CO kinetics used two reactions considered to be dominant and thus more suitable for the description of CO chemical mechanism. Equilibrium concentrations of all the species involved were calculated by a two-zone thermodynamic model. The computed characteristic time of CO kinetics was found to be of a similar order to the results of complex chemistry simulations. The proposed model captured the ‘freezing’ effect (reaction rate is almost zero) for temperatures lower than 1800 K and followed the trends of the measured values at exhaust. However, a consistent underestimation of CO levels at the exhaust was observed. The impact of the remaining CO on the combustion efficiency is considerable especially for rich mixtures. For a remaining 0.4% CO mass fraction, the impact on combustion inefficiency is 0.1%. Unburnt hydrocarbon, which have not reacted within the flame front before quenching, diffuse in the burnt gas and react. In this work, a global reaction rate models the kinetic behavior of hydrocarbon. The diffusion process was modeled by a relaxation equation applied on the calculated kinetic concentration

  6. Global exponential stability of fuzzy cellular neural networks with delays and reaction-diffusion terms

    International Nuclear Information System (INIS)

    Wang Jian; Lu Junguo

    2008-01-01

    In this paper, we study the global exponential stability of fuzzy cellular neural networks with delays and reaction-diffusion terms. By constructing a suitable Lyapunov functional and utilizing some inequality techniques, we obtain a sufficient condition for the uniqueness and global exponential stability of the equilibrium solution for a class of fuzzy cellular neural networks with delays and reaction-diffusion terms. The result imposes constraint conditions on the network parameters independently of the delay parameter. The result is also easy to check and plays an important role in the design and application of globally exponentially stable fuzzy neural circuits

  7. A hybrid transport-diffusion method for Monte Carlo radiative-transfer simulations

    International Nuclear Information System (INIS)

    Densmore, Jeffery D.; Urbatsch, Todd J.; Evans, Thomas M.; Buksas, Michael W.

    2007-01-01

    Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Monte Carlo particle-transport simulations in diffusive media. If standard Monte Carlo is used in such media, particle histories will consist of many small steps, resulting in a computationally expensive calculation. In DDMC, particles take discrete steps between spatial cells according to a discretized diffusion equation. Each discrete step replaces many small Monte Carlo steps, thus increasing the efficiency of the simulation. In addition, given that DDMC is based on a diffusion equation, it should produce accurate solutions if used judiciously. In practice, DDMC is combined with standard Monte Carlo to form a hybrid transport-diffusion method that can accurately simulate problems with both diffusive and non-diffusive regions. In this paper, we extend previously developed DDMC techniques in several ways that improve the accuracy and utility of DDMC for nonlinear, time-dependent, radiative-transfer calculations. The use of DDMC in these types of problems is advantageous since, due to the underlying linearizations, optically thick regions appear to be diffusive. First, we employ a diffusion equation that is discretized in space but is continuous in time. Not only is this methodology theoretically more accurate than temporally discretized DDMC techniques, but it also has the benefit that a particle's time is always known. Thus, there is no ambiguity regarding what time to assign a particle that leaves an optically thick region (where DDMC is used) and begins transporting by standard Monte Carlo in an optically thin region. Also, we treat the interface between optically thick and optically thin regions with an improved method, based on the asymptotic diffusion-limit boundary condition, that can produce accurate results regardless of the angular distribution of the incident Monte Carlo particles. Finally, we develop a technique for estimating radiation momentum deposition during the

  8. Exploring the Dynamics of Cell Processes through Simulations of Fluorescence Microscopy Experiments

    Science.gov (United States)

    Angiolini, Juan; Plachta, Nicolas; Mocskos, Esteban; Levi, Valeria

    2015-01-01

    Fluorescence correlation spectroscopy (FCS) methods are powerful tools for unveiling the dynamical organization of cells. For simple cases, such as molecules passively moving in a homogeneous media, FCS analysis yields analytical functions that can be fitted to the experimental data to recover the phenomenological rate parameters. Unfortunately, many dynamical processes in cells do not follow these simple models, and in many instances it is not possible to obtain an analytical function through a theoretical analysis of a more complex model. In such cases, experimental analysis can be combined with Monte Carlo simulations to aid in interpretation of the data. In response to this need, we developed a method called FERNET (Fluorescence Emission Recipes and Numerical routines Toolkit) based on Monte Carlo simulations and the MCell-Blender platform, which was designed to treat the reaction-diffusion problem under realistic scenarios. This method enables us to set complex geometries of the simulation space, distribute molecules among different compartments, and define interspecies reactions with selected kinetic constants, diffusion coefficients, and species brightness. We apply this method to simulate single- and multiple-point FCS, photon-counting histogram analysis, raster image correlation spectroscopy, and two-color fluorescence cross-correlation spectroscopy. We believe that this new program could be very useful for predicting and understanding the output of fluorescence microscopy experiments. PMID:26039162

  9. Global asymptotic stability of bistable traveling fronts in reaction-diffusion systems and their applications to biological models

    International Nuclear Information System (INIS)

    Wu Shiliang; Li Wantong

    2009-01-01

    This paper deals with the global asymptotic stability and uniqueness (up to translation) of bistable traveling fronts in a class of reaction-diffusion systems. The known results do not apply in solving these problems because the reaction terms do not satisfy the required monotone condition. To overcome the difficulty, a weak monotone condition is proposed for the reaction terms, which is called interval monotone condition. Under such a weak monotone condition, the existence and comparison theorem of solutions is first established for reaction-diffusion systems on R by appealing to the theory of abstract differential equations. The global asymptotic stability and uniqueness (up to translation) of bistable traveling fronts are then proved by the elementary super- and sub-solution comparison and squeezing methods for nonlinear evolution equations. Finally, these abstract results are applied to a two species competition-diffusion model and a system modeling man-environment-man epidemics.

  10. Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

    Science.gov (United States)

    Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

    2017-07-01

    This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

  11. Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

    Directory of Open Access Journals (Sweden)

    Shahid Hasnain

    2017-07-01

    Full Text Available This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

  12. Measuring cognitive load: performance, mental effort and simulation task complexity.

    Science.gov (United States)

    Haji, Faizal A; Rojas, David; Childs, Ruth; de Ribaupierre, Sandrine; Dubrowski, Adam

    2015-08-01

    Interest in applying cognitive load theory in health care simulation is growing. This line of inquiry requires measures that are sensitive to changes in cognitive load arising from different instructional designs. Recently, mental effort ratings and secondary task performance have shown promise as measures of cognitive load in health care simulation. We investigate the sensitivity of these measures to predicted differences in intrinsic load arising from variations in task complexity and learner expertise during simulation-based surgical skills training. We randomly assigned 28 novice medical students to simulation training on a simple or complex surgical knot-tying task. Participants completed 13 practice trials, interspersed with computer-based video instruction. On trials 1, 5, 9 and 13, knot-tying performance was assessed using time and movement efficiency measures, and cognitive load was assessed using subjective rating of mental effort (SRME) and simple reaction time (SRT) on a vibrotactile stimulus-monitoring secondary task. Significant improvements in knot-tying performance (F(1.04,24.95)  = 41.1, p cognitive load (F(2.3,58.5)  = 57.7, p load among novices engaged in simulation-based learning. These measures can be used to track cognitive load during skills training. Mental effort ratings are also sensitive to small differences in intrinsic load arising from variations in the physical complexity of a simulation task. The complementary nature of these subjective and objective measures suggests their combined use is advantageous in simulation instructional design research. © 2015 John Wiley & Sons Ltd.

  13. Reactions of sigma-bonded organochromium(III)complexes

    International Nuclear Information System (INIS)

    Leslie, J.P. II.

    1975-12-01

    Three projects were carried out, each dealing with the kinetics and mechanism of reactions of sigma-bonded organochromium(III) complexes of the form (H 2 O) 5 CrR 2+ . Part I describes the kinetics of the reaction of dichloromethylchromium(III) ion with chromium(II) ion in aqueous acid. Part II deals with the radioexchange of 4-pyridinomethylchromium(III) ion with 51 Cr 2+ and the kinetics of formation of the organochromium species at 55 0 in 1 M H + . Part III deals with the reactions of Hg 2+ and CH 3 Hg + with a series of (H 2 O) 5 CrR 2+ complexes, in which R is an aliphatic alkyl group, a haloalkyl group, or an aralkyl group

  14. An Ab Initio and Kinetic Monte Carlo Simulation Study of Lithium Ion Diffusion on Graphene

    Directory of Open Access Journals (Sweden)

    Kehua Zhong

    2017-07-01

    Full Text Available The Li+ diffusion coefficients in Li+-adsorbed graphene systems were determined by combining first-principle calculations based on density functional theory with Kinetic Monte Carlo simulations. The calculated results indicate that the interactions between Li ions have a very important influence on lithium diffusion. Based on energy barriers directly obtained from first-principle calculations for single-Li+ and two-Li+ adsorbed systems, a new equation predicting energy barriers with more than two Li ions was deduced. Furthermore, it is found that the temperature dependence of Li+ diffusion coefficients fits well to the Arrhenius equation, rather than meeting the equation from electrochemical impedance spectroscopy applied to estimate experimental diffusion coefficients. Moreover, the calculated results also reveal that Li+ concentration dependence of diffusion coefficients roughly fits to the equation from electrochemical impedance spectroscopy in a low concentration region; however, it seriously deviates from the equation in a high concentration region. So, the equation from electrochemical impedance spectroscopy technique could not be simply used to estimate the Li+ diffusion coefficient for all Li+-adsorbed graphene systems with various Li+ concentrations. Our work suggests that interactions between Li ions, and among Li ion and host atoms will influence the Li+ diffusion, which determines that the Li+ intercalation dependence of Li+ diffusion coefficient should be changed and complex.

  15. HSimulator: Hybrid Stochastic/Deterministic Simulation of Biochemical Reaction Networks

    Directory of Open Access Journals (Sweden)

    Luca Marchetti

    2017-01-01

    Full Text Available HSimulator is a multithread simulator for mass-action biochemical reaction systems placed in a well-mixed environment. HSimulator provides optimized implementation of a set of widespread state-of-the-art stochastic, deterministic, and hybrid simulation strategies including the first publicly available implementation of the Hybrid Rejection-based Stochastic Simulation Algorithm (HRSSA. HRSSA, the fastest hybrid algorithm to date, allows for an efficient simulation of the models while ensuring the exact simulation of a subset of the reaction network modeling slow reactions. Benchmarks show that HSimulator is often considerably faster than the other considered simulators. The software, running on Java v6.0 or higher, offers a simulation GUI for modeling and visually exploring biological processes and a Javadoc-documented Java library to support the development of custom applications. HSimulator is released under the COSBI Shared Source license agreement (COSBI-SSLA.

  16. On Medium Chemical Reaction in Diffusion-Based Molecular Communication: a Two-Way Relaying Example

    OpenAIRE

    Farahnak-Ghazani, Maryam; Aminian, Gholamali; Mirmohseni, Mahtab; Gohari, Amin; Nasiri-Kenari, Masoumeh

    2016-01-01

    Chemical reactions are a prominent feature of molecular communication (MC) systems, with no direct parallels in wireless communications. While chemical reactions may be used inside the transmitter nodes, receiver nodes or the communication medium, we focus on its utility in the medium in this paper. Such chemical reactions can be used to perform computation over the medium as molecules diffuse and react with each other (physical-layer computation). We propose the use of chemical reactions for...

  17. Rigorous Derivation of a Nonlinear Diffusion Equation as Fast-Reaction Limit of a Continuous Coagulation-Fragmentation Model with Diffusion

    KAUST Repository

    Carrillo, J. A.; Desvillettes, L.; Fellner, K.

    2009-01-01

    Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [5], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters. © Taylor & Francis Group, LLC.

  18. Rigorous Derivation of a Nonlinear Diffusion Equation as Fast-Reaction Limit of a Continuous Coagulation-Fragmentation Model with Diffusion

    KAUST Repository

    Carrillo, J. A.

    2009-10-30

    Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [5], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters. © Taylor & Francis Group, LLC.

  19. Global dynamics of a nonlocal delayed reaction-diffusion equation on a half plane

    Science.gov (United States)

    Hu, Wenjie; Duan, Yueliang

    2018-04-01

    We consider a delayed reaction-diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson's blowfly equation and the diffusive Mackey-Glass equation.

  20. Critical regimes driven by recurrent mobility patterns of reaction-diffusion processes in networks

    Science.gov (United States)

    Gómez-Gardeñes, J.; Soriano-Paños, D.; Arenas, A.

    2018-04-01

    Reaction-diffusion processes1 have been widely used to study dynamical processes in epidemics2-4 and ecology5 in networked metapopulations. In the context of epidemics6, reaction processes are understood as contagions within each subpopulation (patch), while diffusion represents the mobility of individuals between patches. Recently, the characteristics of human mobility7, such as its recurrent nature, have been proven crucial to understand the phase transition to endemic epidemic states8,9. Here, by developing a framework able to cope with the elementary epidemic processes, the spatial distribution of populations and the commuting mobility patterns, we discover three different critical regimes of the epidemic incidence as a function of these parameters. Interestingly, we reveal a regime of the reaction-diffussion process in which, counter-intuitively, mobility is detrimental to the spread of disease. We analytically determine the precise conditions for the emergence of any of the three possible critical regimes in real and synthetic networks.

  1. Molecular dynamics simulation of self-diffusion coefficients for liquid metals

    International Nuclear Information System (INIS)

    Ju Yuan-Yuan; Zhang Qing-Ming; Gong Zi-Zheng; Ji Guang-Fu

    2013-01-01

    The temperature-dependent coefficients of self-diffusion for liquid metals are simulated by molecular dynamics methods based on the embedded-atom-method (EAM) potential function. The simulated results show that a good inverse linear relation exists between the natural logarithm of self-diffusion coefficients and temperature, though the results in the literature vary somewhat, due to the employment of different potential functions. The estimated activation energy of liquid metals obtained by fitting the Arrhenius formula is close to the experimental data. The temperature-dependent shear-viscosities obtained from the Stokes—Einstein relation in conjunction with the results of molecular dynamics simulation are generally consistent with other values in the literature. (atomic and molecular physics)

  2. Reduced Graphene Oxide-Immobilized Tris(bipyridine)ruthenium(II) Complex for Efficient Visible-Light-Driven Reductive Dehalogenation Reaction.

    Science.gov (United States)

    Li, Xiaoyan; Hao, Zhongkai; Zhang, Fang; Li, Hexing

    2016-05-18

    A sodium benzenesulfonate (PhSO3Na)-functionalized reduced graphene oxide was synthesized via a two-step aryl diazonium coupling and subsequent NaCl ion-exchange procedure, which was used as a support to immobilize tris(bipyridine)ruthenium(II) complex (Ru(bpy)3Cl2) by coordination reaction. This elaborated Ru(bpy)3-rGO catalyst exhibited excellent catalytic efficiency in visible-light-driven reductive dehalogenation reactions under mild conditions, even for ary chloride. Meanwhile, it showed the comparable reactivity with the corresponding homogeneous Ru(bpy)3Cl2 catalyst. This high catalytic performance could be attributed to the unique two-dimensional sheet-like structure of Ru(bpy)3-rGO, which efficiently diminished diffusion resistance of the reactants. Meanwhile, the nonconjugated PhSO3Na-linkage between Ru(II) complex and the support and the very low electrical conductivity of the catalyst inhibited energy/electron transfer from Ru(II) complex to rGO support, resulting in the decreased support-induced quenching effect. Furthermore, it could be easily recycled at least five times without significant loss of catalytic reactivity.

  3. Stability analysis of impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms

    International Nuclear Information System (INIS)

    Li Zuoan; Li Kelin

    2009-01-01

    In this paper, we investigate a class of impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms. By employing the delay differential inequality with impulsive initial conditions and M-matrix theory, we find some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms. In particular, the estimate of the exponential converging index is also provided, which depends on the system parameters. An example is given to show the effectiveness of the results obtained here.

  4. Nonequilibrium transition and pattern formation in a linear reaction-diffusion system with self-regulated kinetics

    Science.gov (United States)

    Paul, Shibashis; Ghosh, Shyamolina; Ray, Deb Shankar

    2018-02-01

    We consider a reaction-diffusion system with linear, stochastic activator-inhibitor kinetics where the time evolution of concentration of a species at any spatial location depends on the relative average concentration of its neighbors. This self-regulating nature of kinetics brings in spatial correlation between the activator and the inhibitor. An interplay of this correlation in kinetics and disparity of diffusivities of the two species leads to symmetry breaking non-equilibrium transition resulting in stationary pattern formation. The role of initial noise strength and the linear reaction terms has been analyzed for pattern selection.

  5. Statistical error in simulations of Poisson processes: Example of diffusion in solids

    Science.gov (United States)

    Nilsson, Johan O.; Leetmaa, Mikael; Vekilova, Olga Yu.; Simak, Sergei I.; Skorodumova, Natalia V.

    2016-08-01

    Simulations of diffusion in solids often produce poor statistics of diffusion events. We present an analytical expression for the statistical error in ion conductivity obtained in such simulations. The error expression is not restricted to any computational method in particular, but valid in the context of simulation of Poisson processes in general. This analytical error expression is verified numerically for the case of Gd-doped ceria by running a large number of kinetic Monte Carlo calculations.

  6. Exploring dynamical complexity in diffusion driven predator-prey systems: Effect of toxin producing phytoplankton and spatial heterogeneities

    International Nuclear Information System (INIS)

    Upadhyay, Ranjit Kumar; Kumari, Nitu; Rai, Vikas

    2009-01-01

    In this paper, dynamical complexities in two reaction-diffusion (RD) model systems are explored. A spatial heterogeneity in the form of linear spatial gradient in the reproductive growth rate of the phytoplankton is incorporated in both the model systems. Extra mortality of the zooplankton due to toxin production by the phytoplankton is included in the second reaction diffusion model system. Effect of toxin production and spatial heterogeneity in the model systems are studied. Toxin production does not seem to have an appreciable effect on the asymptotic dynamics of the model systems. On the other hand, spatial heterogeneity does influence the dynamics. In particular, it increases the frequency of occurrence of chaos as evident from two dimensional parameter scans. Both these model systems display short term recurrent chaos [Rai V. Chaos in natural populations: edge or wedge? Ecol Complex 2004;1: 127-38] as they reside on 'edges of chaos' (EOC) [Rai V, Upadhyay RK. Evolving to the edge of chaos: chance or necessity? Chaos, Solitons and Fractals 2006;30:1074-87]. This suggests that the ecological systems have a tendency to evolve to EOC. The study corroborates the inferences drawn from an earlier study by Rai and Upadhyay [Rai V, Upadhyay RK. Evolving to the edge of chaos: chance or necessity? Chaos, Solitons and Fractals 2006;30:1074-87]. The system's dynamics is largely unpredictable and admits bursts of short-term predictability.

  7. Self-diffusion in monodisperse three-dimensional magnetic fluids by molecular dynamics simulations

    Energy Technology Data Exchange (ETDEWEB)

    Dobroserdova, A.B. [Ural Federal University, Lenin Av. 51, Ekaterinburg (Russian Federation); Kantorovich, S.S., E-mail: alla.dobroserdova@urfu.ru [Ural Federal University, Lenin Av. 51, Ekaterinburg (Russian Federation); University of Vienna, Sensengasse 8, Vienna (Austria)

    2017-06-01

    In the present work we study the self-diffusion behaviour in the three-dimensional monodisperse magnetic fluids using the Molecular Dynamics Simulation and Density Functional Theory. The peculiarity of computer simulation is to study two different systems: dipolar and soft sphere ones. In the theoretical method, it is important to choose the approximation for the main structures, which are chains. We compare the theoretical results and the computer simulation data for the self-diffusion coefficient as a function of the particle volume fraction and magnetic dipole-dipole interaction parameter and find the qualitative and quantitative agreement to be good. - Highlights: • The paper deals with the study of the self-diffusion in monodisperse three-dimensional magnetic fluids. • The theoretical approach contains the free energy density functional minimization. • Computer simulations are performed by the molecular dynamics method. • We have a good qualitative and quantitative agreement between the theoretical results and computer simulation data.

  8. Nonlinear reaction-diffusion equations with delay: some theorems, test problems, exact and numerical solutions

    Science.gov (United States)

    Polyanin, A. D.; Sorokin, V. G.

    2017-12-01

    The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.

  9. Development of regional meteorological and atmospheric diffusion simulation system

    International Nuclear Information System (INIS)

    Kubota, Ryuji; Iwashige, Kengo; Kasano, Toshio

    2002-01-01

    Regional atmospheric diffusion online network (RADON) with atmospheric diffusion analysis code (ADAC) : a simulation program of diffusion of radioactive materials, volcanic ash, pollen, NOx and SOx was developed. This system can be executed in personal computer (PC) and note PC on Windows. Emission data consists of online, offline and default data. It uses the meteorology data sources such as meteorological forecasting mesh data, automated meteorological data acquisition system (AMeDAS) data, meteorological observation data in site and municipality observation data. The meteorological forecasting mesh data shows forecasting value of temperature, wind speed, wind direction and humidity in about two days. The nuclear environmental monitoring center retains the online data (meteorological data, emission source data, monitoring station data) in its PC server and can run forecasting or repeating calculation using these data and store and print out the calculation results. About 30 emission materials can be calculated simultaneously. This system can simulate a series of weather from the past and real time to the future. (S.Y.)

  10. Modeling and Simulation of Claus Unit Reaction Furnace

    Directory of Open Access Journals (Sweden)

    Maryam Pahlavan

    2016-01-01

    Full Text Available Reaction furnace is the most important part of the Claus sulfur recovery unit and its performance has a significant impact on the process efficiency. Too many reactions happen in the furnace and their kinetics and mechanisms are not completely understood; therefore, modeling reaction furnace is difficult and several works have been carried out on in this regard so far. Equilibrium models are commonly used to simulate the furnace, but the related literature states that the outlet of furnace is not in equilibrium and the furnace reactions are controlled by kinetic laws; therefore, in this study, the reaction furnace is simulated by a kinetic model. The predicted outlet temperature and concentrations by this model are compared with experimental data published in the literature and the data obtained by PROMAX V2.0 simulator. The results show that the accuracy of the proposed kinetic model and PROMAX simulator is almost similar, but the kinetic model used in this paper has two importance abilities. Firstly, it is a distributed model and can be used to obtain the temperature and concentration profiles along the furnace. Secondly, it is a dynamic model and can be used for analyzing the transient behavior and designing the control system.

  11. Existence and Asymptotic Stability of Periodic Solutions of the Reaction-Diffusion Equations in the Case of a Rapid Reaction

    Science.gov (United States)

    Nefedov, N. N.; Nikulin, E. I.

    2018-01-01

    A singularly perturbed periodic in time problem for a parabolic reaction-diffusion equation in a two-dimensional domain is studied. The case of existence of an internal transition layer under the conditions of balanced and unbalanced rapid reaction is considered. An asymptotic expansion of a solution is constructed. To justify the asymptotic expansion thus constructed, the asymptotic method of differential inequalities is used. The Lyapunov asymptotic stability of a periodic solution is investigated.

  12. Simulating watercolor by modeling diffusion, pigment, and paper fibers

    Science.gov (United States)

    Small, David

    1991-08-01

    This paper explores a parallel approach to the problem of predicting the actions of pigment and water when applied to paper fibers. This work was done on the Connection Machine II, whose parallel architecture allows one to cast the problem as that of a complex cellular automata. One defines simple rules for the behavior of each cell based on the state of that cell and its immediate neighbors. By repeating the computation for each cell in the paper over many time steps, elaborate and realistic behaviors can be achieved. The simulation takes into account diffusion, surface tension, gravity, humidity, paper absorbency and the molecular weight of each pigment. At each time step a processor associated with each fiber in the paper computes water and pigment gradients, surface tension and gravitational forces, and decides if there should be any movement of material. Pigment and water can be applied and removed (blotting) with masks created from type or scanned images. Use of a parallel processor simplifies the creation and testing of software, and variables can be stored and manipulated at highprecision. The resulting simulation runs at approximately one-tenth real time.

  13. Molecular dynamics simulation of diffusion bonding of Al–Cu interface

    International Nuclear Information System (INIS)

    Li, Chang; Li, Dongxu; Tao, Xiaoma; Chen, Hongmei; Ouyang, Yifang

    2014-01-01

    The effects of temperature on diffusion bonding of Al–Cu interface have been investigated by using molecular dynamics (MD) technique with the embedded atomic method (EAM) potentials. The simulated results indicate that the Cu atoms predominantly diffuse into the Al side in the process of diffusion bonding, and the thickness of the interfacial region depends on temperature, with higher temperatures resulting in larger thickness. In the course of diffusion bonding, the interfacial region became disordered. In addition, the Cu atoms diffuse at low ratios but can deeply diffuse into the interior of Al, and the Al atoms diffuse at high ratios but hardly diffuse into the interior of Cu. The results show that the appropriate temperature range for diffusion bonding of Al–Cu interface is 750–800 K, and the diffusion activation energies of Al and Cu are 0.77 eV and 0.50 eV, respectively. Finally, in this work, three diffusion mechanisms of Cu atoms in Al lattice have been found and the main diffusion mechanism is the nearest neighbor hopping mechanism. (paper)

  14. Simulating Isotope Enrichment by Gaseous Diffusion

    Science.gov (United States)

    Reed, Cameron

    2015-04-01

    A desktop-computer simulation of isotope enrichment by gaseous diffusion has been developed. The simulation incorporates two non-interacting point-mass species whose members pass through a cascade of cells containing porous membranes and retain constant speeds as they reflect off the walls of the cells and the spaces between holes in the membranes. A particular feature is periodic forward recycling of enriched material to cells further along the cascade along with simultaneous return of depleted material to preceding cells. The number of particles, the mass ratio, the initial fractional abundance of the lighter species, and the time between recycling operations can be chosen by the user. The simulation is simple enough to be understood on the basis of two-dimensional kinematics, and demonstrates that the fractional abundance of the lighter-isotope species increases along the cascade. The logic of the simulation will be described and results of some typical runs will be presented and discussed.

  15. Ionic diffusion in quartz studied by transport measurements, SIMS and atomistic simulations

    International Nuclear Information System (INIS)

    Sartbaeva, Asel; Wells, Stephen A; Redfern, Simon A T; Hinton, Richard W; Reed, Stephen J B

    2005-01-01

    Ionic diffusion in the quartz-β-eucryptite system is studied by DC transport measurements, SIMS and atomistic simulations. Transport data show a large transient increase in ionic current at the α-β phase transition of quartz (the Hedvall effect). The SIMS data indicate two diffusion processes, one involving rapid Li + motion and the other involving penetration of Al and Li atoms into quartz at the phase transition. Atomistic simulations explain why the fine microstructure of twin domain walls in quartz near the transition does not hinder Li + diffusion

  16. Terrestrial Fe-oxide Concretions and Mars Blueberries: Comparisons of Similar Advective and Diffusive Chemical Infiltration Reaction Mechanisms

    Science.gov (United States)

    Park, A. J.; Chan, M. A.

    2006-12-01

    Abundant iron oxide concretions occurring in Navajo Sandstone of southern Utah and those discovered at Meridiani Planum, Mars share many common observable physical traits such as their spheriodal shapes, occurrence, and distribution patterns in sediments. Terrestrial concretions are products of interaction between oxygen-rich aquifer water and basin-derived reducing (iron-rich) water. Water-rock interaction simulations show that diffusion of oxygen and iron supplied by slow-moving water is a reasonable mechanism for producing observed concretion patterns. In short, southern Utah iron oxide concretions are results of Liesegang-type diffusive infiltration reactions in sediments. We propose that the formation of blueberry hematite concretions in Mars sediments followed a similar diagenetic mechanism where iron was derived from the alteration of volcanic substrate and oxygen was provided by the early Martian atmosphere. Although the terrestrial analog differs in the original host rock composition, both the terrestrial and Mars iron-oxide precipitation mechanisms utilize iron and oxygen interactions in sedimentary host rock with diffusive infiltration of solutes from two opposite sources. For the terrestrial model, slow advection of iron-rich water is an important factor that allowed pervasive and in places massive precipitation of iron-oxide concretions. In Mars, evaporative flux of water at the top of the sediment column may have produced a slow advective mass-transfer mechanism that provided a steady source and the right quantity of iron. The similarities of the terrestrial and Martian systems are demonstrated using a water-rock interaction simulator Sym.8, initially in one-dimensional systems. Boundary conditions such as oxygen content of water, partial pressure of oxygen, and supply rate of iron were varied. The results demonstrate the importance of slow advection of water and diffusive processes for producing diagenetic iron oxide concretions.

  17. Simulation of tracer dispersion from elevated and surface releases in complex terrain

    Science.gov (United States)

    Hernández, J. F.; Cremades, L.; Baldasano, J. M.

    A new version of an advanced mesoscale dispersion modeling system for simulating passive air pollutant dispersion in the real atmospheric planetary boundary layer (PBL), is presented. The system comprises a diagnostic mass-consistent meteorological model and a Lagrangian particle dispersion model (LADISMO). The former version of LADISMO, developed according to Zannetti (Air pollution modelling, 1990), was based on the Monte Carlo technique and included calculation of higher-order moments of vertical random forcing for convective conditions. Its ability to simulate complex flow dispersion has been stated in a previous paper (Hernández et al. 1995, Atmospheric Environment, 29A, 1331-1341). The new version follows Thomson's scheme (1984, Q. Jl Roy. Met. Soc.110, 1107-1120). It is also based on Langevin equation and follows the ideas given by Brusasca et al. (1992, Atmospheric Environment26A, 707-723) and Anfossi et al. (1992, Nuovo Cemento 15c, 139-158). The model is used to simulate the dispersion and predict the ground level concentration (g.l.c.) of a tracer (SF 6) released from both an elevated source ( case a) and a ground level source ( case b) in a highly complex mountainous terrain during neutral and synoptically dominated conditions ( case a) and light and apparently stable conditions ( case b). The last case is considered as being a specially difficult task to simulate. In fact, few works have reported situations with valley drainage flows in complex terrains and real stable atmospheric conditions with weak winds. The model assumes that nearly calm situations associated to strong stability and air stagnation, make the lowest layers of PBL poorly diffusive (Brusasca et al., 1992, Atmospheric Environment26A, 707-723). Model results are verified against experimental data from Guardo-90 tracer experiments, an intensive field campaign conducted in the Carrion river valley (Northern Spain) to study atmospheric diffusion within a steep walled valley in mountainous

  18. A hybrid multiscale kinetic Monte Carlo method for simulation of copper electrodeposition

    International Nuclear Information System (INIS)

    Zheng Zheming; Stephens, Ryan M.; Braatz, Richard D.; Alkire, Richard C.; Petzold, Linda R.

    2008-01-01

    A hybrid multiscale kinetic Monte Carlo (HMKMC) method for speeding up the simulation of copper electrodeposition is presented. The fast diffusion events are simulated deterministically with a heterogeneous diffusion model which considers site-blocking effects of additives. Chemical reactions are simulated by an accelerated (tau-leaping) method for discrete stochastic simulation which adaptively selects exact discrete stochastic simulation for the appropriate reaction whenever that is necessary. The HMKMC method is seen to be accurate and highly efficient

  19. Emergency Evacuation of Hazardous Chemical Accidents Based on Diffusion Simulation

    Directory of Open Access Journals (Sweden)

    Jiang-Hua Zhang

    2017-01-01

    Full Text Available The recent rapid development of information technology, such as sensing technology, communications technology, and database, allows us to use simulation experiments for analyzing serious accidents caused by hazardous chemicals. Due to the toxicity and diffusion of hazardous chemicals, these accidents often lead to not only severe consequences and economic losses, but also traffic jams at the same time. Emergency evacuation after hazardous chemical accidents is an effective means to reduce the loss of life and property and to smoothly resume the transport network as soon as possible. This paper considers the dynamic changes of the hazardous chemicals’ concentration after their leakage and simulates the diffusion process. Based on the characteristics of emergency evacuation of hazardous chemical accidents, we build a mixed-integer programming model and design a heuristic algorithm using network optimization and diffusion simulation (hereafter NODS. We then verify the validity and feasibility of the algorithm using Jinan, China, as a computational example. In the end, we compare the results from different scenarios to explore the key factors affecting the effectiveness of the evacuation process.

  20. Atomistic simulations of diffusion mechanisms in off-stoichiometric Al-rich Ni3Al

    International Nuclear Information System (INIS)

    Duan, Jinsong

    2007-01-01

    This paper presents dynamics simulation results of diffusion in off-stoichiometric Al-rich Ni 3 Al (Ni 73 Al 27 ) at temperature ranging from 1300 to 1550 K. The interatomic forces are described by the Finnis-Sinclair type N-body potentials. Particular attention is devoted to the effect of the extra 2% of Al atoms sitting on the Ni sublattice as antisite point defects (Al Ni ) on diffusion. Simulation results show that Ni atoms mainly diffuse through the Ni sublattice at the temperatures investigated. Al atoms diffuse via both the intrasublattice and antistructure bridge (ASB) mechanisms. The contribution to Al diffusion from the ASB mechanism decreases at the lower temperature (T Ni ) enhances both Al and Ni diffusion in Ni 73 Al 27 . The Ni-Al coupled diffusion effect is observed and understood at the atomic level for the first time

  1. EXAFS studies on the reaction of gold (III) chloride complex ions with sodium hydroxide and glucose.

    Science.gov (United States)

    Pacławski, K; Zajac, D A; Borowiec, M; Kapusta, Cz; Fitzner, K

    2010-11-11

    EXAFS and QEXAFS experiments were carried out at Hasylab laboratory in DESY center (X1 beamline, Hamburg, Germany) to monitor the course of the hydrolysis reactions of [AuCl(4)](-) complex ions as well as their reduction using glucose. As a result, changes in the spectra of [AuCl(4)](-) ions and disappearance of absorption Au-L(3) edge were registered. From the results of the experiments we have carried out, the changes in bond lengths between Au(3+) central ion and Cl(-) ligands as well as the reduction of Au(3+) to metallic form (colloidal gold was formed in the system) are evident. Good quality spectra obtained before and after the reactions gave a chance to determine the bond length characteristic of Au-Cl, Au-OH and Au-Au pairs. Additionally, the obtained results were compared with the simulated spectra of different gold (III) complex ions, possibly present in the solution. Finally, the mechanism of these reactions was suggested. Unfortunately, it was not possible to detect the changes in the structure of gold (III) complex ions within the time of reaction, because of too high rates of both processes (hydrolysis and reduction) as compared with the detection time.

  2. Reaction-assisted diffusion bonding of TiAl alloy to steel

    Energy Technology Data Exchange (ETDEWEB)

    Simões, S., E-mail: ssimoes@fe.up.pt [CEMUC, Department of Metallurgical and Materials Engineering, University of Porto, R. Dr. Roberto Frias, 4200-465 Porto (Portugal); Viana, F. [CEMUC, Department of Metallurgical and Materials Engineering, University of Porto, R. Dr. Roberto Frias, 4200-465 Porto (Portugal); Ramos, A.S.; Vieira, M.T. [CEMUC, Department of Mechanical Engineering, University of Coimbra, R. Luís Reis Santos, 3030-788 Coimbra (Portugal); Vieira, M.F. [CEMUC, Department of Metallurgical and Materials Engineering, University of Porto, R. Dr. Roberto Frias, 4200-465 Porto (Portugal)

    2016-03-01

    The dissimilar joining of TiAl to AISI 310 stainless steel by a reaction-assisted diffusion bonding process, using Ni/Al nanolayers as an interlayer, was investigated in the present work. The Ni and Al alternated nanolayers were deposited by d.c. magnetron sputtering onto the base materials, with a bilayer thickness of 14 nm. Joining experiments were performed at 800 °C for 60 min with compressive stress of 25 and 50 MPa. The effectiveness of the interlayer on the bonding process was assessed by microstructural characterization of the interface and by mechanical tests. Diffusion bonded joints were characterized by scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), transmission electron microscopy (TEM), high resolution transmission electron microscopy (HRTEM), scanning transmission electron microscopy (STEM) and analyzed by energy dispersive X-ray spectroscopy (EDS) in SEM and TEM and Fast Fourier Transform (FFT). The thickness of the interface region, together with its microstructural and mechanical characteristics, is affected by the use of Ni/Al multilayers; which promote joints with lower hardness values, closer to the values of the base materials, and exhibit higher shear strength. - Highlights: • Dissimilar joining by a reaction-assisted diffusion bonding were studied. • Ni/Al nanolayers allows join TiAl to steel in less demanding processing conditions. • The microstructural and mechanical characterization of the joints were investigated. • The fracture occurring in the TiAl base material attests to the sound joining. • Shear strength value decreases for joints with base materials without nanolayers.

  3. Parabolic equations in biology growth, reaction, movement and diffusion

    CERN Document Server

    Perthame, Benoît

    2015-01-01

    This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.

  4. Complex Chemical Reaction Networks from Heuristics-Aided Quantum Chemistry.

    Science.gov (United States)

    Rappoport, Dmitrij; Galvin, Cooper J; Zubarev, Dmitry Yu; Aspuru-Guzik, Alán

    2014-03-11

    While structures and reactivities of many small molecules can be computed efficiently and accurately using quantum chemical methods, heuristic approaches remain essential for modeling complex structures and large-scale chemical systems. Here, we present a heuristics-aided quantum chemical methodology applicable to complex chemical reaction networks such as those arising in cell metabolism and prebiotic chemistry. Chemical heuristics offer an expedient way of traversing high-dimensional reactive potential energy surfaces and are combined here with quantum chemical structure optimizations, which yield the structures and energies of the reaction intermediates and products. Application of heuristics-aided quantum chemical methodology to the formose reaction reproduces the experimentally observed reaction products, major reaction pathways, and autocatalytic cycles.

  5. Monte Carlo simulations of flexible polyanions complexing with whey proteins at their isoelectric point.

    Science.gov (United States)

    de Vries, R

    2004-02-15

    Electrostatic complexation of flexible polyanions with the whey proteins alpha-lactalbumin and beta-lactoglobulin is studied using Monte Carlo simulations. The proteins are considered at their respective isoelectric points. Discrete charges on the model polyelectrolytes and proteins interact through Debye-Huckel potentials. Protein excluded volume is taken into account through a coarse-grained model of the protein shape. Consistent with experimental results, it is found that alpha-lactalbumin complexes much more strongly than beta-lactoglobulin. For alpha-lactalbumin, strong complexation is due to localized binding to a single large positive "charge patch," whereas for beta-lactoglobulin, weak complexation is due to diffuse binding to multiple smaller charge patches. Copyright 2004 American Institute of Physics

  6. Stability of reaction fronts in random walk simulations

    NARCIS (Netherlands)

    Nagy, Noemi; Izsak, F.

    A model of propagating reaction fronts is given for simple autocatalytic reactions and the stability of the propagating reaction fronts are studied in several numerical experiments. The corresponding random walk simulations - extending of a recent algorithm - make possible the simultaneous treatment

  7. Communication: A method to compute the transport coefficient of pure fluids diffusing through planar interfaces from equilibrium molecular dynamics simulations.

    Science.gov (United States)

    Vermorel, Romain; Oulebsir, Fouad; Galliero, Guillaume

    2017-09-14

    The computation of diffusion coefficients in molecular systems ranks among the most useful applications of equilibrium molecular dynamics simulations. However, when dealing with the problem of fluid diffusion through vanishingly thin interfaces, classical techniques are not applicable. This is because the volume of space in which molecules diffuse is ill-defined. In such conditions, non-equilibrium techniques allow for the computation of transport coefficients per unit interface width, but their weak point lies in their inability to isolate the contribution of the different physical mechanisms prone to impact the flux of permeating molecules. In this work, we propose a simple and accurate method to compute the diffusional transport coefficient of a pure fluid through a planar interface from equilibrium molecular dynamics simulations, in the form of a diffusion coefficient per unit interface width. In order to demonstrate its validity and accuracy, we apply our method to the case study of a dilute gas diffusing through a smoothly repulsive single-layer porous solid. We believe this complementary technique can benefit to the interpretation of the results obtained on single-layer membranes by means of complex non-equilibrium methods.

  8. Impulsive Synchronization of Reaction-Diffusion Neural Networks With Mixed Delays and Its Application to Image Encryption.

    Science.gov (United States)

    Chen, Wu-Hua; Luo, Shixian; Zheng, Wei Xing

    2016-12-01

    This paper presents a new impulsive synchronization criterion of two identical reaction-diffusion neural networks with discrete and unbounded distributed delays. The new criterion is established by applying an impulse-time-dependent Lyapunov functional combined with the use of a new type of integral inequality for treating the reaction-diffusion terms. The impulse-time-dependent feature of the proposed Lyapunov functional can capture more hybrid dynamical behaviors of the impulsive reaction-diffusion neural networks than the conventional impulse-time-independent Lyapunov functions/functionals, while the new integral inequality, which is derived from Wirtinger's inequality, overcomes the conservatism introduced by the integral inequality used in the previous results. Numerical examples demonstrate the effectiveness of the proposed method. Later, the developed impulsive synchronization method is applied to build a spatiotemporal chaotic cryptosystem that can transmit an encrypted image. The experimental results verify that the proposed image-encrypting cryptosystem has the advantages of large key space and high security against some traditional attacks.

  9. Interpretation of diffusion coefficients in nanostructured materials from random walk numerical simulation.

    Science.gov (United States)

    Anta, Juan A; Mora-Seró, Iván; Dittrich, Thomas; Bisquert, Juan

    2008-08-14

    We make use of the numerical simulation random walk (RWNS) method to compute the "jump" diffusion coefficient of electrons in nanostructured materials via mean-square displacement. First, a summary of analytical results is given that relates the diffusion coefficient obtained from RWNS to those in the multiple-trapping (MT) and hopping models. Simulations are performed in a three-dimensional lattice of trap sites with energies distributed according to an exponential distribution and with a step-function distribution centered at the Fermi level. It is observed that once the stationary state is reached, the ensemble of particles follow Fermi-Dirac statistics with a well-defined Fermi level. In this stationary situation the diffusion coefficient obeys the theoretical predictions so that RWNS effectively reproduces the MT model. Mobilities can be also computed when an electrical bias is applied and they are observed to comply with the Einstein relation when compared with steady-state diffusion coefficients. The evolution of the system towards the stationary situation is also studied. When the diffusion coefficients are monitored along simulation time a transition from anomalous to trap-limited transport is observed. The nature of this transition is discussed in terms of the evolution of electron distribution and the Fermi level. All these results will facilitate the use of RW simulation and related methods to interpret steady-state as well as transient experimental techniques.

  10. Effects of chemical reaction on moving isothermal vertical plate with variable mass diffusion

    Directory of Open Access Journals (Sweden)

    Muthucumaraswamy R.

    2003-01-01

    Full Text Available An exact solution to the problem of flow past an impulsively started infinite vertical isothermal plate with variable mass diffusion is presented here, taking into account of the homogeneous chemical reaction of first-order. The dimensionless governing equations are solved by using the Laplace - transform technique. The velocity and skin-friction are studied for different parameters like chemical reaction parameter, Schmidt number and buoyancy ratio parameter. It is observed that the veloc­ity increases with decreasing chemical reaction parameter and increases with increasing buoyancy ratio parameter.

  11. Random-walk simulation of diffusion-controlled processes among static traps

    International Nuclear Information System (INIS)

    Lee, S.B.; Kim, I.C.; Miller, C.A.; Torquato, S.; Department of Mechanical and Aerospace Engineering and Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910)

    1989-01-01

    We present computer-simulation results for the trapping rate (rate constant) k associated with diffusion-controlled reactions among identical, static spherical traps distributed with an arbitrary degree of impenetrability using a Pearson random-walk algorithm. We specifically consider the penetrable-concentric-shell model in which each trap of diameter σ is composed of a mutually impenetrable core of diameter λσ, encompassed by a perfectly penetrable shell of thickness (1-λ)σ/2: λ=0 corresponding to randomly centered or ''fully penetrable'' traps and λ=1 corresponding to totally impenetrable traps. Trapping rates are calculated accurately from the random-walk algorithm at the extreme limits of λ (λ=0 and 1) and at an intermediate value (λ=0.8), for a wide range of trap densities. Our simulation procedure has a relatively fast execution time. It is found that k increases with increasing impenetrability at fixed trap concentration. These ''exact'' data are compared with previous theories for the trapping rate. Although a good approximate theory exists for the fully-penetrable-trap case, there are no currently available theories that can provide good estimates of the trapping rate for a moderate to high density of traps with nonzero hard cores (λ>0)

  12. Determination of transport and reaction swarm coefficients from the analysis of complex transient pulses from the pulsed Townsend experiment

    International Nuclear Information System (INIS)

    Bekstein, A; De Urquijo, J; Rodríguez-Luna, J C; Juárez, A M; Ducasse, O

    2012-01-01

    We present in this paper the interpretation and analysis of transient pulses from a pulsed Townsend experiment by solving the continuity equations of the charged carriers (electrons and ions) involved in the avalanche. The set of second order partial differential equations is solved by SIMAV, a simulator designed specifically for the pulsed Townsend avalanche. Complex situations involving processes such as electron detachment, ion-molecule reactions, Penning ionization and secondary electron emission from ion impact at the cathode, virtually impossible to solve analytically, are discussed here to illustrate the capability of the simulator to help explain the various reaction processes involved in the avalanche, and also to derive some of the transport and reaction coefficients.

  13. Laser Spot Detection Based on Reaction Diffusion.

    Science.gov (United States)

    Vázquez-Otero, Alejandro; Khikhlukha, Danila; Solano-Altamirano, J M; Dormido, Raquel; Duro, Natividad

    2016-03-01

    Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD) system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations.

  14. Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations

    Directory of Open Access Journals (Sweden)

    Guichen Lu

    2016-01-01

    Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.

  15. Modeling Studies of Inhomogeneity Effects during Laser Flash Photolysis Experiments: A Reaction-Diffusion Approach.

    Science.gov (United States)

    Dóka, Éva; Lente, Gábor

    2017-04-13

    This work presents a rigorous mathematical study of the effect of unavoidable inhomogeneities in laser flash photolysis experiments. There are two different kinds of inhomegenities: the first arises from diffusion, whereas the second one has geometric origins (the shapes of the excitation and detection light beams). Both of these are taken into account in our reported model, which gives rise to a set of reaction-diffusion type partial differential equations. These equations are solved by a specially developed finite volume method. As an example, the aqueous reaction between the sulfate ion radical and iodide ion is used, for which sufficiently detailed experimental data are available from an earlier publication. The results showed that diffusion itself is in general too slow to influence the kinetic curves on the usual time scales of laser flash photolysis experiments. However, the use of the absorbances measured (e.g., to calculate the molar absorption coefficients of transient species) requires very detailed mathematical consideration and full knowledge of the geometrical shapes of the excitation laser beam and the separate detection light beam. It is also noted that the usual pseudo-first-order approach to evaluating the kinetic traces can be used successfully even if the usual large excess condition is not rigorously met in the reaction cell locally.

  16. NMTC/JAM, Simulates High Energy Nuclear Reactions and Nuclear-Meson Transport Processes

    International Nuclear Information System (INIS)

    Furihata, Shiori

    2002-01-01

    and the pre-equilibrium calculation model based on the exciton one are also implemented for simulating the nuclear reactions. Inter-nuclear transport processes of the incident and secondary nucleons in macroscopic material regions are simulated with the Monte Carlo method based on the O5R algorithm and a continuous slowing down model for charged particles using the nucleon-nucleus cross sections based on the systematics of Pearlstein. 3 - Restrictions on the complexity of the problem: Upper energy of an incident particle is limited to 200 GeV. When ISOBAR code is selected for intra-nuclear cascade calculation, the upper energy is limited to 1 GeV

  17. Multi-scale modeling of diffusion-controlled reactions in polymers: renormalisation of reactivity parameters.

    Science.gov (United States)

    Everaers, Ralf; Rosa, Angelo

    2012-01-07

    The quantitative description of polymeric systems requires hierarchical modeling schemes, which bridge the gap between the atomic scale, relevant to chemical or biomolecular reactions, and the macromolecular scale, where the longest relaxation modes occur. Here, we use the formalism for diffusion-controlled reactions in polymers developed by Wilemski, Fixman, and Doi to discuss the renormalisation of the reactivity parameters in polymer models with varying spatial resolution. In particular, we show that the adjustments are independent of chain length. As a consequence, it is possible to match reactions times between descriptions with different resolution for relatively short reference chains and to use the coarse-grained model to make quantitative predictions for longer chains. We illustrate our results by a detailed discussion of the classical problem of chain cyclization in the Rouse model, which offers the simplest example of a multi-scale descriptions, if we consider differently discretized Rouse models for the same physical system. Moreover, we are able to explore different combinations of compact and non-compact diffusion in the local and large-scale dynamics by varying the embedding dimension.

  18. Accelerating rejection-based simulation of biochemical reactions with bounded acceptance probability

    Energy Technology Data Exchange (ETDEWEB)

    Thanh, Vo Hong, E-mail: vo@cosbi.eu [The Microsoft Research - University of Trento Centre for Computational and Systems Biology, Piazza Manifattura 1, Rovereto 38068 (Italy); Priami, Corrado, E-mail: priami@cosbi.eu [The Microsoft Research - University of Trento Centre for Computational and Systems Biology, Piazza Manifattura 1, Rovereto 38068 (Italy); Department of Mathematics, University of Trento, Trento (Italy); Zunino, Roberto, E-mail: roberto.zunino@unitn.it [Department of Mathematics, University of Trento, Trento (Italy)

    2016-06-14

    Stochastic simulation of large biochemical reaction networks is often computationally expensive due to the disparate reaction rates and high variability of population of chemical species. An approach to accelerate the simulation is to allow multiple reaction firings before performing update by assuming that reaction propensities are changing of a negligible amount during a time interval. Species with small population in the firings of fast reactions significantly affect both performance and accuracy of this simulation approach. It is even worse when these small population species are involved in a large number of reactions. We present in this paper a new approximate algorithm to cope with this problem. It is based on bounding the acceptance probability of a reaction selected by the exact rejection-based simulation algorithm, which employs propensity bounds of reactions and the rejection-based mechanism to select next reaction firings. The reaction is ensured to be selected to fire with an acceptance rate greater than a predefined probability in which the selection becomes exact if the probability is set to one. Our new algorithm improves the computational cost for selecting the next reaction firing and reduces the updating the propensities of reactions.

  19. Extracting the diffusion tensor from molecular dynamics simulation with Milestoning

    International Nuclear Information System (INIS)

    Mugnai, Mauro L.; Elber, Ron

    2015-01-01

    We propose an algorithm to extract the diffusion tensor from Molecular Dynamics simulations with Milestoning. A Kramers-Moyal expansion of a discrete master equation, which is the Markovian limit of the Milestoning theory, determines the diffusion tensor. To test the algorithm, we analyze overdamped Langevin trajectories and recover a multidimensional Fokker-Planck equation. The recovery process determines the flux through a mesh and estimates local kinetic parameters. Rate coefficients are converted to the derivatives of the potential of mean force and to coordinate dependent diffusion tensor. We illustrate the computation on simple models and on an atomically detailed system—the diffusion along the backbone torsions of a solvated alanine dipeptide

  20. Global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms

    International Nuclear Information System (INIS)

    Wang Xiaohu; Xu Daoyi

    2009-01-01

    In this paper, the global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms is considered. By establishing an integro-differential inequality with impulsive initial condition and using the properties of M-cone and eigenspace of the spectral radius of nonnegative matrices, several new sufficient conditions are obtained to ensure the global exponential stability of the equilibrium point for fuzzy cellular neural networks with delays and reaction-diffusion terms. These results extend and improve the earlier publications. Two examples are given to illustrate the efficiency of the obtained results.

  1. Molecular dynamics simulation of sodium aluminosilicate glass structures and glass surface-water reactions using the reactive force field (ReaxFF)

    Science.gov (United States)

    Dongol, R.; Wang, L.; Cormack, A. N.; Sundaram, S. K.

    2018-05-01

    Reactive potentials are increasingly used to study the properties of glasses and glass water reactions in a reactive molecular dynamics (MD) framework. In this study, we have simulated a ternary sodium aluminosilicate glass and investigated the initial stages of the glass surface-water reactions at 300 K using reactive force field (ReaxFF). On comparison of the simulated glass structures generated using ReaxFF and classical Buckingham potentials, our results show that the atomic density profiles calculated for the surface glass structures indicate a bond-angle distribution dependency. The atomic density profiles also show higher concentrations of non-bridging oxygens (NBOs) and sodium ions at the glass surface. Additionally, we present our results of formation of silanol species and the diffusion of water molecules at the glass surface using ReaxFF.

  2. Reaction diffusion and solid state chemical kinetics handbook

    CERN Document Server

    Dybkov, V I

    2010-01-01

    This monograph deals with a physico-chemical approach to the problem of the solid-state growth of chemical compound layers and reaction-diffusion in binary heterogeneous systems formed by two solids; as well as a solid with a liquid or a gas. It is explained why the number of compound layers growing at the interface between the original phases is usually much lower than the number of chemical compounds in the phase diagram of a given binary system. For example, of the eight intermetallic compounds which exist in the aluminium-zirconium binary system, only ZrAl3 was found to grow as a separate

  3. Wang-Landau Reaction Ensemble Method: Simulation of Weak Polyelectrolytes and General Acid-Base Reactions.

    Science.gov (United States)

    Landsgesell, Jonas; Holm, Christian; Smiatek, Jens

    2017-02-14

    We present a novel method for the study of weak polyelectrolytes and general acid-base reactions in molecular dynamics and Monte Carlo simulations. The approach combines the advantages of the reaction ensemble and the Wang-Landau sampling method. Deprotonation and protonation reactions are simulated explicitly with the help of the reaction ensemble method, while the accurate sampling of the corresponding phase space is achieved by the Wang-Landau approach. The combination of both techniques provides a sufficient statistical accuracy such that meaningful estimates for the density of states and the partition sum can be obtained. With regard to these estimates, several thermodynamic observables like the heat capacity or reaction free energies can be calculated. We demonstrate that the computation times for the calculation of titration curves with a high statistical accuracy can be significantly decreased when compared to the original reaction ensemble method. The applicability of our approach is validated by the study of weak polyelectrolytes and their thermodynamic properties.

  4. Complexant Identification in Hanford Waste Simulant Sr/TRU Filtrate

    International Nuclear Information System (INIS)

    Bannochie, C.J.

    2003-01-01

    This project was designed to characterize the available multidentate ligand species and metal ion complexes of iron, strontium and manganese formed with the parent chelators, complexing agents and their fragment products. Complex identification was applied to AN-102 and AN-107 filtrate simulants for Hanford waste after an oxidation reaction with sodium permanganate to create a freshly precipitated manganese dioxide solid for adsorption of transuranic elements. Separation efficiency of different ligands was investigated based on the exchange capability of different ion exchange and ion exclusion analytical columns including Dionex IonPac AS-5A, AS-10, AS-11 and AS-6. The elution programs developed with different mobile phase concentrations were based on the change in the effective charge of the anionic species and therefore the retention on the stationary phase. In the present work, qualitative and quantitative assessments of multidentate ligands were investigated. Identification methods for the metal ion complexes responsible for solubilizing Fe, Mn and Sr were applied to aged and fresh simulant waste filtrates. Although concentration measurements of both fresh and 3-week aged filtrates showed that the degradation process occurs mainly due to the harsh chemical environment, it was found that the concentration of iron and manganese did not increase, within the error of the analytical measurements, after three weeks when compared with fresh filtrate

  5. Complex diffusion process for noise reduction

    DEFF Research Database (Denmark)

    Nadernejad, Ehsan; Barari, A.

    2014-01-01

    equations (PDEs) in image restoration and de-noising prompted many researchers to search for an improvement in the technique. In this paper, a new method is presented for signal de-noising, based on PDEs and Schrodinger equations, named as complex diffusion process (CDP). This method assumes that variations...... for signal de-noising. To evaluate the performance of the proposed method, a number of experiments have been performed using Sinusoid, multi-component and FM signals cluttered with noise. The results indicate that the proposed method outperforms the approaches for signal de-noising known in prior art....

  6. Effect of electrostatic interactions on electron-transfer reactions

    International Nuclear Information System (INIS)

    Hickel, B.

    1987-01-01

    Fast reactions of electron transfer are studied by pulsed radiolysis. By this technique radicals and ionic radicals with high redox potentials are created homogeneously in the solution in about 10 -8 second. For solvated electron effect of electrostatic interaction on kinetics of reactions limited by diffusion is obtained with a good approximation by the Debye equation when ion mobility is known. Deviation from the theory occurs in ion pair formation, which is evidenced experimentally in reactions between anions when cations are complexed by a cryptate. Slow reactions k 8 M -1 s -1 are more sensitive to electrostatic interactions than reactions limited by diffusion. When there is no ion pair formation the velocity constant depends upon dielectric constant of the solvent and reaction distance. 17 refs

  7. Molecular Dynamics Simulation of Salt Diffusion in Polyelectrolyte Assemblies.

    Science.gov (United States)

    Zhang, Ran; Duan, Xiaozheng; Ding, Mingming; Shi, Tongfei

    2018-06-05

    The diffusion of salt ions and charged probe molecules in polyelectrolyte assemblies is often assumed to follow a theoretical hopping model, in which the diffusing ion is hopping between charged sites of chains based on electroneutrality. However, experimental verification of diffusing pathway at such microscales is difficult, and the corresponding molecular mechanisms remain elusive. In this study, we perform all-atom molecular dynamics (MD) simulations of salt diffusion in polyelectrolyte (PE) assembly of poly (sodium 4-styrenesulfonate) (PSS) and poly (diallyldimethylammonium chloride) (PDAC). Besides the ion hopping mode, the diffusing trajectories are found presenting common features of a jump process, i.e., subjecting to PE relaxation, water pockets in the structure open and close, thus the ion can move from one pocket to another. Anomalous subdiffusion of ions and water is observed due to the trapping scenarios in these water pockets. The jump events are much rarer compared with ion hopping but significantly increases salt diffusion with increasing temperature. Our result strongly indicates that salt diffusion in hydrated PDAC/PSS is a combined process of ion hopping and jump motion. This provides new molecular explanation for the coupling of salt motion with chain motion and the nonlinear increase of salt diffusion at glass transition temperature.

  8. Two dimensional dopant diffusion study by scanning capacitance microscopy and TSUPREM IV process simulation

    International Nuclear Information System (INIS)

    Kim, J.; McMurray, J. S.; Williams, C. C.; Slinkman, J.

    1998-01-01

    We report the results of a 2-step two-dimensional (2D) diffusion study by Scanning Capacitance Microscopy (SCM) and 2D TSUPREM IV process simulation. A quantitative 2D dopant profile of gate-like structures consisting heavily implanted n+ regions separated by a lighter doped n-type region underneath 0.56 μm gates is measured with the SCM. The SCM is operated in the constant-change-in-capacitance mode. The 2-D SCM data is converted to dopant density through a physical model of the SCM/silicon interaction. This profile has been directly compared with 2D TSUPREM IV process simulation and used to calibrate the simulation parameters. The sample is then further subjected to an additional diffusion in a furnace for 80 minutes at 1000C. The SCM measurement is repeated on the diffused sample. This final 2D dopant profile is compared with a TSUPREM IV process simulation tuned to fit the earlier profile with no change in the parameters except the temperature and time for the additional diffusion. Our results indicate that there is still a significant disagreement between the two profiles in the lateral direction. TSUPREM IV simulation considerably underestimates the diffusion under the gate region

  9. Numerical simulation of swirling flow in complex hydroturbine draft tube using unsteady statistical turbulence models

    Energy Technology Data Exchange (ETDEWEB)

    Paik, Joongcheol [University of Minnesota; Sotiropoulos, Fotis [University of Minnesota; Sale, Michael J [ORNL

    2005-06-01

    A numerical method is developed for carrying out unsteady Reynolds-averaged Navier-Stokes (URANS) simulations and detached-eddy simulations (DESs) in complex 3D geometries. The method is applied to simulate incompressible swirling flow in a typical hydroturbine draft tube, which consists of a strongly curved 90 degree elbow and two piers. The governing equations are solved with a second-order-accurate, finite-volume, dual-time-stepping artificial compressibility approach for a Reynolds number of 1.1 million on a mesh with 1.8 million nodes. The geometrical complexities of the draft tube are handled using domain decomposition with overset (chimera) grids. Numerical simulations show that unsteady statistical turbulence models can capture very complex 3D flow phenomena dominated by geometry-induced, large-scale instabilities and unsteady coherent structures such as the onset of vortex breakdown and the formation of the unsteady rope vortex downstream of the turbine runner. Both URANS and DES appear to yield the general shape and magnitude of mean velocity profiles in reasonable agreement with measurements. Significant discrepancies among the DES and URANS predictions of the turbulence statistics are also observed in the straight downstream diffuser.

  10. Laser Spot Detection Based on Reaction Diffusion

    Directory of Open Access Journals (Sweden)

    Alejandro Vázquez-Otero

    2016-03-01

    Full Text Available Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations.

  11. Diffusion in flexible pipes

    Energy Technology Data Exchange (ETDEWEB)

    Brogaard Kristensen, S

    2000-06-01

    This report describes the work done on modelling and simulation of the complex diffusion of gas through the wall of a flexible pipe. The diffusion and thus the pressure in annulus depends strongly on the diffusion and solubility parameters of the gas-polymer system and on the degree of blocking of the outer surface of the inner liner due to pressure reinforcements. The report evaluates the basis modelling required to describe the complex geometries and flow patterns. Qualitatively results of temperature and concentration profiles are shown in the report. For the program to serve any modelling purpose in 'real life' the results need to be validated and possibly the model needs corrections. Hopefully, a full-scale test of a flexible pipe will provide the required temperatures and pressures in annulus to validate the models. (EHS)

  12. Defects and diffusion, theory and simulation an annual retrospective I

    CERN Document Server

    Fisher, David J

    2009-01-01

    This first volume, in a new series covering entirely general results in the fields of defects and diffusion, includes abstracts of papers which appeared between the beginning of 2008 and the end of October 2009 (journal availability permitting).This new series replaces the 'general' section which was previously part of each issue of the Metals, Ceramics and Semiconductor retrospective series. As well as 356 abstracts, the volume includes original papers on all of the usual material groups: ""Predicting Diffusion Coefficients from First Principles via Eyring's Reaction Rate Theory"" (Mantina, C

  13. Reactive diffusion and stresses in nanowires or nanorods

    International Nuclear Information System (INIS)

    Roussel, Manuel; Erdélyi, Zoltán; Schmitz, Guido

    2017-01-01

    Heterostructured nanowires are of prime interest in nowadays technology such as field-effect transistors, field emitters, batteries and solar cells. We consider their aging behavior and developed a model focusing on reactive diffusion in core-shell nanowires. A complete set of analytical equations is presented that takes into account thermodynamic driving forces, vacancy distribution, elastic stress and its plastic relaxation. This complete description of the reactive diffusion can be used in finite element simulations to investigate diffusion processes in various geometries. In order to show clearly the interplay between the cylindrical geometry, the reactive diffusion and the stresses developing in the nanowire, we investigate the formation of an intermetallic reaction product in various core-shell geometries. Emphasis is placed on showing how it is possible to control the kinetics of the reaction by applying an axial stress to the nanowires.

  14. Mode-locking in advection-reaction-diffusion systems: An invariant manifold perspective

    Science.gov (United States)

    Locke, Rory A.; Mahoney, John R.; Mitchell, Kevin A.

    2018-01-01

    Fronts propagating in two-dimensional advection-reaction-diffusion systems exhibit a rich topological structure. When the underlying fluid flow is periodic in space and time, the reaction front can lock to the driving frequency. We explain this mode-locking phenomenon using the so-called burning invariant manifolds (BIMs). In fact, the mode-locked profile is delineated by a BIM attached to a relative periodic orbit (RPO) of the front element dynamics. Changes in the type (and loss) of mode-locking can be understood in terms of local and global bifurcations of the RPOs and their BIMs. We illustrate these concepts numerically using a chain of alternating vortices in a channel geometry.

  15. Quantitative modeling of the reaction/diffusion kinetics of two-chemistry photopolymers

    Science.gov (United States)

    Kowalski, Benjamin Andrew

    Optically driven diffusion in photopolymers is an appealing material platform for a broad range of applications, in which the recorded refractive index patterns serve either as images (e.g. data storage, display holography) or as optical elements (e.g. custom GRIN components, integrated optical devices). A quantitative understanding of the reaction/diffusion kinetics is difficult to obtain directly, but is nevertheless necessary in order to fully exploit the wide array of design freedoms in these materials. A general strategy for characterizing these kinetics is proposed, in which key processes are decoupled and independently measured. This strategy enables prediction of a material's potential refractive index change, solely on the basis of its chemical components. The degree to which a material does not reach this potential reveals the fraction of monomer that has participated in unwanted reactions, reducing spatial resolution and dynamic range. This approach is demonstrated for a model material similar to commercial media, achieving quantitative predictions of index response over three orders of exposure dose (~1 to ~103 mJ cm-2) and three orders of feature size (0.35 to 500 microns). The resulting insights enable guided, rational design of new material formulations with demonstrated performance improvement.

  16. Modelling and simulation of diffusive processes methods and applications

    CERN Document Server

    Basu, SK

    2014-01-01

    This book addresses the key issues in the modeling and simulation of diffusive processes from a wide spectrum of different applications across a broad range of disciplines. Features: discusses diffusion and molecular transport in living cells and suspended sediment in open channels; examines the modeling of peristaltic transport of nanofluids, and isotachophoretic separation of ionic samples in microfluidics; reviews thermal characterization of non-homogeneous media and scale-dependent porous dispersion resulting from velocity fluctuations; describes the modeling of nitrogen fate and transport

  17. Program BETA for simulation of particle decays and reactions

    International Nuclear Information System (INIS)

    Takhtamyshev, G.G.; Merkulova, T.A.

    1997-01-01

    Program BETA is designed for simulation of particle decays and reactions. The program also produces integration over the phase space and decay rate or the reaction cross section are calculated as a result of such integration. At the simulation process the adaptive random number generator SMART may be used, what is found to be useful for some difficult cases

  18. Redox reactions of Cu(II)-amine complexes in aqueous solutions

    International Nuclear Information System (INIS)

    Kumbhar, A.G.; Kishore, Kamal

    2003-01-01

    A number of amines can be employed for all volatile treatment (AVT) of steam generator (SG) systems of nuclear power reactors. These amines form complexes with Cu 2+ and Ni 2+ ions which come into water due to corrosion. The redox reactions of a number of Cu(II)-AVT amine complexes and the stability of the transient species formed have been studied by pulse radiolysis technique. Rate constants for the reaction of e aq - with a number of Cu(II)-amine complexes have been determined by following the decay of e aq - absorption. Stability of Cu(I)-amine complexes was studied by following the kinetics of the bleaching signal formed at the λ max of the Cu(II) amine complex. Except for Cu(I)-triethanolamine complex all other Cu(I)-amine complexes were found to be stable. One-electron oxidation of Cu(II) amine complexes was studied using azidyl radicals for the oxidation reaction as OH radicals react with the alcohol groups present in the amines used in this study. Cu(III)-amine complexes were found to be unstable and decayed by second-order kinetics

  19. Catching gas with droplets : modelling and simulation of a diffusion-reaction process

    NARCIS (Netherlands)

    Mourik, van S.; Gennip, van Y.; Peletier, M.A.; Hlod, A.V.; Shcherbakov, V.; Panhuis, in 't P.H.M.W.; Vondenhoff, E.; Eendebak, P.; Berg, van den J.B.; Fledderus, E.R.; Hofstad, van der R.W.; Jochemsz, E.; Molenaar, J.; Mussche, T.J.J.; Peletier, M.A.; Prokert, G.

    2006-01-01

    The packaging industry wants to produce a foil for food packaging purposes, which is transparent and lets very little oxygen pass. To accomplish this they add a scavenger material to the foil which reacts with the oxygen that diffuses through the foil. We model this process by a system of partial

  20. Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models

    Directory of Open Access Journals (Sweden)

    Narcisa Apreutesei

    2014-05-01

    Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.

  1. Solid state reaction studies in Fe3O4–TiO2 system by diffusion couple method

    International Nuclear Information System (INIS)

    Ren, Zhongshan; Hu, Xiaojun; Xue, Xiangxin; Chou, Kuochih

    2013-01-01

    Highlights: •The solid state reactions of Fe2O3-TiO2 system was studied by the diffusion couple method. •Different products were formed by diffusion, and the FeTiO3 was more stable phase. •The inter-diffusion coefficients and diffusion activation energy were estimated. -- Abstract: The solid state reactions in Fe 3 O 4 –TiO 2 system has been studied by diffusion couple experiments at 1323–1473 K, in which the oxygen partial pressure was controlled by the CO–CO 2 gas mixture. The XRD analysis was used to confirm the phases of the inter-compound, and the concentration profiles were determined by electron probe microanalysis (EPMA). Based on the concentration profile of Ti, the inter-diffusion coefficients in Fe 3 O 4 phase, which were both temperature and concentration of Ti ions dependent, were calculated by the modified Boltzmann–Matano method. According to the relation between the thickness of diffusion layer and temperature, the diffusion coefficient of the Fe 3 O 4 –TiO 2 system was obtained. According to the Arrhenius equation, the estimated diffusion activation energy was about 282.1 ± 18.8 kJ mol −1

  2. Hopf bifurcation in a reaction-diffusive two-species model with nonlocal delay effect and general functional response

    International Nuclear Information System (INIS)

    Han, Renji; Dai, Binxiang

    2017-01-01

    Highlights: • We model general two-dimensional reaction-diffusion with nonlocal delay. • The existence of unique positive steady state is studied. • The bilinear form for the proposed system is given. • The existence, direction of Hopf bifurcation are given by symmetry method. - Abstract: A nonlocal delayed reaction-diffusive two-species model with Dirichlet boundary condition and general functional response is investigated in this paper. Based on the Lyapunov–Schmidt reduction, the existence, bifurcation direction and stability of Hopf bifurcating periodic orbits near the positive spatially nonhomogeneous steady-state solution are obtained, where the time delay is taken as the bifurcation parameter. Moreover, the general results are applied to a diffusive Lotka–Volterra type food-limited population model with nonlocal delay effect, and it is found that diffusion and nonlocal delay can also affect the other dynamic behavior of the system by numerical experiments.

  3. HRSSA – Efficient hybrid stochastic simulation for spatially homogeneous biochemical reaction networks

    International Nuclear Information System (INIS)

    Marchetti, Luca; Priami, Corrado; Thanh, Vo Hong

    2016-01-01

    This paper introduces HRSSA (Hybrid Rejection-based Stochastic Simulation Algorithm), a new efficient hybrid stochastic simulation algorithm for spatially homogeneous biochemical reaction networks. HRSSA is built on top of RSSA, an exact stochastic simulation algorithm which relies on propensity bounds to select next reaction firings and to reduce the average number of reaction propensity updates needed during the simulation. HRSSA exploits the computational advantage of propensity bounds to manage time-varying transition propensities and to apply dynamic partitioning of reactions, which constitute the two most significant bottlenecks of hybrid simulation. A comprehensive set of simulation benchmarks is provided for evaluating performance and accuracy of HRSSA against other state of the art algorithms.

  4. HRSSA – Efficient hybrid stochastic simulation for spatially homogeneous biochemical reaction networks

    Energy Technology Data Exchange (ETDEWEB)

    Marchetti, Luca, E-mail: marchetti@cosbi.eu [The Microsoft Research – University of Trento Centre for Computational and Systems Biology (COSBI), Piazza Manifattura, 1, 38068 Rovereto (Italy); Priami, Corrado, E-mail: priami@cosbi.eu [The Microsoft Research – University of Trento Centre for Computational and Systems Biology (COSBI), Piazza Manifattura, 1, 38068 Rovereto (Italy); University of Trento, Department of Mathematics (Italy); Thanh, Vo Hong, E-mail: vo@cosbi.eu [The Microsoft Research – University of Trento Centre for Computational and Systems Biology (COSBI), Piazza Manifattura, 1, 38068 Rovereto (Italy)

    2016-07-15

    This paper introduces HRSSA (Hybrid Rejection-based Stochastic Simulation Algorithm), a new efficient hybrid stochastic simulation algorithm for spatially homogeneous biochemical reaction networks. HRSSA is built on top of RSSA, an exact stochastic simulation algorithm which relies on propensity bounds to select next reaction firings and to reduce the average number of reaction propensity updates needed during the simulation. HRSSA exploits the computational advantage of propensity bounds to manage time-varying transition propensities and to apply dynamic partitioning of reactions, which constitute the two most significant bottlenecks of hybrid simulation. A comprehensive set of simulation benchmarks is provided for evaluating performance and accuracy of HRSSA against other state of the art algorithms.

  5. Kinetic Monte Carlo Simulation of Oxygen and Cation Diffusion in Yttria-Stabilized Zirconia

    Science.gov (United States)

    Good, Brian

    2011-01-01

    Yttria-stabilized zirconia (YSZ) is of interest to the aerospace community, notably for its application as a thermal barrier coating for turbine engine components. In such an application, diffusion of both oxygen ions and cations is of concern. Oxygen diffusion can lead to deterioration of a coated part, and often necessitates an environmental barrier coating. Cation diffusion in YSZ is much slower than oxygen diffusion. However, such diffusion is a mechanism by which creep takes place, potentially affecting the mechanical integrity and phase stability of the coating. In other applications, the high oxygen diffusivity of YSZ is useful, and makes the material of interest for use as a solid-state electrolyte in fuel cells. The kinetic Monte Carlo (kMC) method offers a number of advantages compared with the more widely known molecular dynamics simulation method. In particular, kMC is much more efficient for the study of processes, such as diffusion, that involve infrequent events. We describe the results of kinetic Monte Carlo computer simulations of oxygen and cation diffusion in YSZ. Using diffusive energy barriers from ab initio calculations and from the literature, we present results on the temperature dependence of oxygen and cation diffusivity, and on the dependence of the diffusivities on yttria concentration and oxygen sublattice vacancy concentration. We also present results of the effect on diffusivity of oxygen vacancies in the vicinity of the barrier cations that determine the oxygen diffusion energy barriers.

  6. Real-time nonlinear feedback control of pattern formation in (bio)chemical reaction-diffusion processes: a model study.

    Science.gov (United States)

    Brandt-Pollmann, U; Lebiedz, D; Diehl, M; Sager, S; Schlöder, J

    2005-09-01

    Theoretical and experimental studies related to manipulation of pattern formation in self-organizing reaction-diffusion processes by appropriate control stimuli become increasingly important both in chemical engineering and cellular biochemistry. In a model study, we demonstrate here exemplarily the application of an efficient nonlinear model predictive control (NMPC) algorithm to real-time optimal feedback control of pattern formation in a bacterial chemotaxis system modeled by nonlinear partial differential equations. The corresponding drift-diffusion model type is representative for many (bio)chemical systems involving nonlinear reaction dynamics and nonlinear diffusion. We show how the computed optimal feedback control strategy exploits the system inherent physical property of wave propagation to achieve desired control aims. We discuss various applications of our approach to optimal control of spatiotemporal dynamics.

  7. Investigation of the extraction of short diffusion lengths from simulated electron-beam induced current

    Energy Technology Data Exchange (ETDEWEB)

    Wee, D.; Parish, G.; Nener, B. [Microelectronics Research Group, The University of Western Australia, 35 Stirling Highway, 6009 Crawley (Perth) (Australia)

    2010-10-15

    This paper reports on the investigations via 2-D simulation into the accuracy of diffusion length extraction from scanning electron-beam induced current measurements when the diffusion length, L is very short. L is extracted by using the direct method proposed by Chan et al.[1] and later refined by Kurniawan and Ong[2] to take finite junction depth into account. The 2-D simulations were undertaken using Synopsys {sup registered} Sentaurus TCAD and a realistic electron-hole pair generation volume was created using CASINO v2.42[3], a Monte Carlo Scanning Electron Microscope interaction simulation software, and imported into Sentaurus. The voltage and diameter of the electron beam and diffusion length and surface recombination velocity of the semiconductor materials were varied in the simulations to determine the errors in the diffusion length extracted from the EBIC signals as a function of these parameters. The results of the simulation show that the accuracy of the method proposed in[1] is reasonably accurate and that the beam voltage and spot size do not have significant effects on the accuracy (copyright 2010 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

  8. Investigation of the extraction of short diffusion lengths from simulated electron-beam induced current

    International Nuclear Information System (INIS)

    Wee, D.; Parish, G.; Nener, B.

    2010-01-01

    This paper reports on the investigations via 2-D simulation into the accuracy of diffusion length extraction from scanning electron-beam induced current measurements when the diffusion length, L is very short. L is extracted by using the direct method proposed by Chan et al.[1] and later refined by Kurniawan and Ong[2] to take finite junction depth into account. The 2-D simulations were undertaken using Synopsys registered Sentaurus TCAD and a realistic electron-hole pair generation volume was created using CASINO v2.42[3], a Monte Carlo Scanning Electron Microscope interaction simulation software, and imported into Sentaurus. The voltage and diameter of the electron beam and diffusion length and surface recombination velocity of the semiconductor materials were varied in the simulations to determine the errors in the diffusion length extracted from the EBIC signals as a function of these parameters. The results of the simulation show that the accuracy of the method proposed in[1] is reasonably accurate and that the beam voltage and spot size do not have significant effects on the accuracy (copyright 2010 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

  9. Tutorial Review: Simulation of Oscillating Chemical Reactions Using Microsoft Excel Macros

    Directory of Open Access Journals (Sweden)

    Abdolhossein Naseri

    2016-12-01

    Full Text Available Oscillating reactions are one of the most interesting topics in chemistry and analytical chemistry. Fluctuations in concentrations of one the reacting species (usually a reaction intermediate create an oscillating chemical reaction. In oscillating systems, the reaction is far from thermodynamic equilibrium. In these systems, at least one autocatalytic step is required. Developing an instinctive feeling for how oscillating reactions work will be invaluable to future generations of chemists. Some software programs have been released for simulating oscillating systems; however, the algorithm details of such software are not transparent to chemists. In contrast, function of spreadsheet tools, like Microsoft Excel, is well understood, and the software is nearly universally available. In this work, the simulation and visualization of different oscillating systems are performed using Microsoft excel. The simple repetitive solving of the ordinary differential equation of an autocatalytic reaction (a spreadsheet row followed by time, easily automated by a subroutine (a “Macro” in Excel, readily simulates an oscillating reaction. This permits the simulation of some oscillating systems such asBelousov-Zhabotinsky. The versatility of an easily understandable computational platform further enables the simulation of the effects of linear and nonlinear parameters such as concentrations of reactants and catalyst, and kinetic constants. These parameters are readily changed to examine their effects.

  10. Transport and reaction processes affecting the attenuation of landfill gas in cover soils

    DEFF Research Database (Denmark)

    Molins, S.; Mayer, K.U.; Scheutz, Charlotte

    2008-01-01

    of methane, chlorofluorocarbons, and hydrochlorofluorocarbons to the atmosphere. This study was conducted to investigate the effect of oxidation reactions on the overall gas transport regime and to evaluate, the contributions of various gas transport processes on methane attenuation in landfill cover soils....... For this purpose, a reactive transport model that includes advection and the Dusty Gas Model for simulation of multicomponent gas diffusion was used. The simulations are constrained by data from a series of counter-gradient laboratory experiments. Diffusion typically accounts for over 99% of methane emission...... to the atmosphere. Oxygen supply into the soil column is driven exclusively by diffusion, whereas advection outward offsets part of the diffusive contribution. In the reaction zone, methane consumption reduces the pressure gradient, further decreasing the significance of advection near the top of the column...

  11. Three dimensional simulated modelling of diffusion capacitance of ...

    African Journals Online (AJOL)

    A three dimensional (3-D) simulated modelling was developed to analyse the excess minority carrier density in the base of a polycrystalline bifacial silicon solar cell. The concept of junction recombination velocity was ado-pted to quantify carrier flow through the junction, and to examine the solar cell diffusion capacitance for ...

  12. Numerical simulation of dynamic flow characteristics in a centrifugal water pump with three-vaned diffuser

    Directory of Open Access Journals (Sweden)

    Zhi-Jun Shuai

    2015-08-01

    Full Text Available The complex three-dimensional turbulent flow field in a centrifugal water pump with three asymmetrical diffusers was numerically simulated. The characteristics of pressure and force fluctuations inside the model pump were investigated. Fast Fourier transformation was performed to obtain the spectra of pressure and force fluctuations. It indicates that the dominant frequency of pressure fluctuations is the blade passing frequency in all the sub-domains inside the pump and the first blade passing frequency energy (first order of blade passing frequency is the most significant. The dominant frequency of pressure fluctuations at the location of diffuser outlet is featured by low frequency (less than 1 Hz, which may be due to the locally generated eddy structures. Besides, the dominant frequency force fluctuations on the impeller blades are also the blade passing frequency. The existence of the three asymmetrical diffusers has damping effect on the pressure fluctuation amplitude and energy amplitude of pressure fluctuations in the diffuser domain dramatically, which indicates that the diffusers can effectively control the hydraulically excited vibration in the pump. Besides, the prediction of the dominant frequency of pressure fluctuations inside the pump can help to utilize the pump effectively and to extend the pump life. The main findings of this work can provide prediction of the pump performance and information for further optimal design of centrifugal pumps as well.

  13. Justification of a Monte Carlo Algorithm for the Diffusion-Growth Simulation of Helium Clusters in Materials

    International Nuclear Information System (INIS)

    Yu-Lu, Zhou; Ai-Hong, Deng; Qing, Hou; Jun, Wang

    2009-01-01

    A theoretical analysis of a Monte Carlo (MC) method for the simulation of the diffusion-growth of helium clusters in materials is presented. This analysis is based on an assumption that the diffusion-growth process consists of first stage, during which the clusters diffuse freely, and second stage in which the coalescence occurs with certain probability. Since the accuracy of MC simulation results is sensitive to the coalescence probability, the MC calculations in the second stage is studied in detail. Firstly, the coalescence probability is analytically formulated for the one-dimensional diffusion-growth case. Thereafter, the one-dimensional results are employed to justify the MC simulation. The choice of time step and the random number generator used in the MC simulation are discussed

  14. Production of complex particles in low energy spallation and in fragmentation reactions by in-medium random clusterization

    International Nuclear Information System (INIS)

    Lacroix, D.; Durand, D.

    2005-09-01

    Rules for in-medium complex particle production in nuclear reactions are proposed. These rules have been implemented in two models to simulate nucleon-nucleus and nucleus-nucleus reactions around the Fermi energy. Our work emphasizes the effect of randomness in cluster formation, the importance of the nucleonic Fermi motion as well as the role of conservation laws. The concepts of total available phase-space and explored phase-space under constraint imposed by the reaction are clarified. The compatibility of experimental observations with a random clusterization is illustrated in a schematic scenario of a proton-nucleus collision. The role of randomness under constraint is also illustrated in the nucleus-nucleus case. (authors)

  15. Light induced electron transfer reactions of metal complexes

    International Nuclear Information System (INIS)

    Sutin, N.; Creutz, C.

    1980-01-01

    Properties of the excited states of tris(2,2'-bipyridine) and tris(1,10-phenanthroline) complexes of chromium(III), iron(II), ruthenium(II), osmium(II), rhodium(III), and iridium(III) are described. The electron transfer reactions of the ground and excited states are discussed and interpreted in terms of the driving force for the reaction and the distortions of the excited states relative to the corresponding ground states. General considerations relevant to the conversion of light into chemical energy are presented and progress in the use of polypyridine complexes to effect the light decomposition of water into hydrogen and oxygen is reviewed

  16. Diffusion in flexible pipes

    Energy Technology Data Exchange (ETDEWEB)

    Brogaard Kristensen, S.

    2000-06-01

    This report describes the work done on modelling and simulation of the complex diffusion of gas through the wall of a flexible pipe. The diffusion and thus the pressure in annulus depends strongly on the diffusion and solubility parameters of the gas-polymer system and on the degree of blocking of the outer surface of the inner liner due to pressure reinforcements. The report evaluates the basis modelling required to describe the complex geometries and flow patterns. Qualitatively results of temperature and concentration profiles are shown in the report. For the program to serve any modelling purpose in 'real life' the results need to be validated and possibly the model needs corrections. Hopefully, a full-scale test of a flexible pipe will provide the required temperatures and pressures in annulus to validate the models. (EHS)

  17. Influence of cold work on the diffusion of ion-implanted nitrogen in D9 steel using nuclear reaction analysis

    International Nuclear Information System (INIS)

    Arunkumar, J.; David, C.; Panigrahi, B.K.; Nair, K.G.M.

    2014-01-01

    D9 steels and their modified versions are envisaged for use as fuel cladding and wrapper materials in the Indian fast breeder reactor (FBR) programme. The role played by interstitially dissolved nitrogen in steel matrices for the stabilization of austenitic phase, increase of strength and corrosion resistance is well known. Various factors: the role of grain boundaries and the their orientation, stress mediation, grain fragmentation and production of short circuit paths as a result of compressive stress are known to affect the diffusion of nitrogen. Basically, cold working produces plethora of defects throughout the sample as compared to its solution annealed state. Our earlier studies on 1 x10"1"5 and 5x10"1"5 N"1"5 implanted Solution Annealed D9 (SAD9) showed significant vacancy-nitrogen complexes for higher fluence. Hence, thermal diffusion behaviour of nitrogen was studied in 5 x10"1"5 -N"1"5 implanted samples in solution annealed state. In the present study, to understand the influence of cold work, similar thermal diffusion behaviour of nitrogen has been studied in Cold Worked D9 steel (CWD9) using nuclear reaction analysis

  18. Dynamical Behaviors of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays

    Directory of Open Access Journals (Sweden)

    Li Wan

    2012-01-01

    Full Text Available This paper investigates dynamical behaviors of stochastic Cohen-Grossberg neural network with delays and reaction diffusion. By employing Lyapunov method, Poincaré inequality and matrix technique, some sufficient criteria on ultimate boundedness, weak attractor, and asymptotic stability are obtained. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.

  19. Degree, instability and bifurcation of reaction-diffusion systems with obstacles near certain hyperbolas

    Czech Academy of Sciences Publication Activity Database

    Eisner, J.; Väth, Martin

    2016-01-01

    Roč. 135, April (2016), s. 158-193 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : reaction-diffusion system * turing instability * global bifurcation Subject RIV: BA - General Mathematics Impact factor: 1.192, year: 2016 http://www.sciencedirect.com/science/article/pii/S0362546X16000146

  20. Theoretical description of spin-selective reactions of radical pairs diffusing in spherical 2D and 3D microreactors

    International Nuclear Information System (INIS)

    Ivanov, Konstantin L.; Lukzen, Nikita N.; Sadovsky, Vladimir M.

    2015-01-01

    In this work, we treat spin-selective recombination of a geminate radical pair (RP) in a spherical “microreactor,” i.e., of a RP confined in a micelle, vesicle, or liposome. We consider the microreactor model proposed earlier, in which one of the radicals is located at the center of the micelle and the other one undergoes three-dimensional diffusion inside the micelle. In addition, we suggest a two-dimensional model, in which one of the radicals is located at the “pole” of the sphere, while the other one diffuses on the spherical surface. For this model, we have obtained a general analytical expression for the RP recombination yield in terms of the free Green function of two-dimensional diffusion motion. In turn, this Green function is expressed via the Legendre functions and thus takes account of diffusion over a restricted spherical surface and its curvature. The obtained expression allows one to calculate the RP recombination efficiency at an arbitrary magnetic field strength. We performed a comparison of the two models taking the same geometric parameters (i.e., the microreactor radius and the closest approach distance of the radicals), chemical reactivity, magnetic interactions in the RP and diffusion coefficient. Significant difference between the predictions of the two models is found, which is thus originating solely from the dimensionality effect: for different dimensionality of space, the statistics of diffusional contacts of radicals becomes different altering the reaction yield. We have calculated the magnetic field dependence of the RP reaction yield and chemically induced dynamic nuclear polarization of the reaction products at different sizes of the microreactor, exchange interaction, and spin relaxation rates. Interestingly, due to the intricate interplay of diffusional contacts of reactants and spin dynamics, the dependence of the reaction yield on the microreactor radius is non-monotonous. Our results are of importance for (i) interpreting

  1. Characterization of the reaction layer in U-7wt%Mo/Al diffusion couples

    Energy Technology Data Exchange (ETDEWEB)

    Mirandou, M.I.; Balart, S.N.; Ortiz, M.; Granovsky, M.S. E-mail: granovsk@cnea.gov.ar

    2003-11-15

    The reaction layer in chemical diffusion couples U-7wt%Mo/Al was investigated using optical and scanning electron microscopy, electron probe microanalysis and X-ray diffraction (XRD) techniques. When the U-7wt%Mo alloy was previously homogenized and the {gamma}(U, Mo) phase was retained, the formation of (U, Mo)Al{sub 3} and (U, Mo)Al{sub 4} was observed at 580 deg. C. Also a very thin band was detected close to the Al side, the structure of the ternary compound Al{sub 20}UMo{sub 2} might be assigned to it. When the decomposition of the {gamma}(U, Mo) took place, a drastic change in the diffusion behavior was observed. In this case, XRD indicated the presence of phases with the structures of (U, Mo)Al{sub 3}, Al{sub 43}U{sub 6}Mo{sub 4}, {gamma}(U, Mo) and {alpha}(U) in the reaction layer.

  2. MEDYAN: Mechanochemical Simulations of Contraction and Polarity Alignment in Actomyosin Networks.

    Directory of Open Access Journals (Sweden)

    Konstantin Popov

    2016-04-01

    Full Text Available Active matter systems, and in particular the cell cytoskeleton, exhibit complex mechanochemical dynamics that are still not well understood. While prior computational models of cytoskeletal dynamics have lead to many conceptual insights, an important niche still needs to be filled with a high-resolution structural modeling framework, which includes a minimally-complete set of cytoskeletal chemistries, stochastically treats reaction and diffusion processes in three spatial dimensions, accurately and efficiently describes mechanical deformations of the filamentous network under stresses generated by molecular motors, and deeply couples mechanics and chemistry at high spatial resolution. To address this need, we propose a novel reactive coarse-grained force field, as well as a publicly available software package, named the Mechanochemical Dynamics of Active Networks (MEDYAN, for simulating active network evolution and dynamics (available at www.medyan.org. This model can be used to study the non-linear, far from equilibrium processes in active matter systems, in particular, comprised of interacting semi-flexible polymers embedded in a solution with complex reaction-diffusion processes. In this work, we applied MEDYAN to investigate a contractile actomyosin network consisting of actin filaments, alpha-actinin cross-linking proteins, and non-muscle myosin IIA mini-filaments. We found that these systems undergo a switch-like transition in simulations from a random network to ordered, bundled structures when cross-linker concentration is increased above a threshold value, inducing contraction driven by myosin II mini-filaments. Our simulations also show how myosin II mini-filaments, in tandem with cross-linkers, can produce a range of actin filament polarity distributions and alignment, which is crucially dependent on the rate of actin filament turnover and the actin filament's resulting super-diffusive behavior in the actomyosin-cross-linker system

  3. A hybrid transport-diffusion Monte Carlo method for frequency-dependent radiative-transfer simulations

    International Nuclear Information System (INIS)

    Densmore, Jeffery D.; Thompson, Kelly G.; Urbatsch, Todd J.

    2012-01-01

    Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Implicit Monte Carlo radiative-transfer simulations in optically thick media. In DDMC, particles take discrete steps between spatial cells according to a discretized diffusion equation. Each discrete step replaces many smaller Monte Carlo steps, thus improving the efficiency of the simulation. In this paper, we present an extension of DDMC for frequency-dependent radiative transfer. We base our new DDMC method on a frequency-integrated diffusion equation for frequencies below a specified threshold, as optical thickness is typically a decreasing function of frequency. Above this threshold we employ standard Monte Carlo, which results in a hybrid transport-diffusion scheme. With a set of frequency-dependent test problems, we confirm the accuracy and increased efficiency of our new DDMC method.

  4. Thermal and non-thermal lattice gas models for a dimer-trimer surface catalytic reaction: a Monte-Carlo simulation study

    International Nuclear Information System (INIS)

    Iqbal, K.; Khand, P.A.

    2012-01-01

    The kinetics of an irreversible dimer-trimer reaction of the type 2 A/sub 3/ +3 B/sub 2/ -- 6 AB by considering the precursor motion of the dimer (B/sub 2) on a square, as well as on a hexagonal surface, by using a Monte Carlo simulation have been studied. When the movement of precursors is limited to the first nearest neighborhood, the model gives reactive window widths of the order of 0.22 and 0.29 for the square and the hexagonal lattices, respectively, which are quite large compared to those predicted by the LH model. In our model, the reactive window width for a square lattice increases significantly as compared to that for the LH models of the same system on square and hexagonal lattices. The width of the reactive region increases when the precursor motion is extended to the second and the third nearest neighborhood. The continuous transition disappears when the precursor motion is extended to the third nearest neighborhood. The diffusion of B atoms does not change the situation qualitatively for both the precursor and the LH models. However, desorption of the dimer changes the situation significantly; i.e., the width of the reactive window shows an exponential growth with respect to the desorption probability of the dimer for both the precursor and the LH models. In our opinion, the inclusion of precursors in the LH model of the dimer-trimer reactions leads to a better and more realistic description of the heterogeneous catalytic reactions. Consequently, further numerical and theoretical activity in this field will be very useful for understanding complex heterogeneous reactions. (orig./A.B.)

  5. Identification of the population density of a species model with nonlocal diffusion and nonlinear reaction

    Science.gov (United States)

    Tuan, Nguyen Huy; Van Au, Vo; Khoa, Vo Anh; Lesnic, Daniel

    2017-05-01

    The identification of the population density of a logistic equation backwards in time associated with nonlocal diffusion and nonlinear reaction, motivated by biology and ecology fields, is investigated. The diffusion depends on an integral average of the population density whilst the reaction term is a global or local Lipschitz function of the population density. After discussing the ill-posedness of the problem, we apply the quasi-reversibility method to construct stable approximation problems. It is shown that the regularized solutions stemming from such method not only depend continuously on the final data, but also strongly converge to the exact solution in L 2-norm. New error estimates together with stability results are obtained. Furthermore, numerical examples are provided to illustrate the theoretical results.

  6. Modeling the diffusion magnetic resonance imaging signal inside neurons

    International Nuclear Information System (INIS)

    Nguyen, D V; Li, J R; Grebenkov, D S; Le Bihan, D

    2014-01-01

    The Bloch-Torrey partial differential equation (PDE) describes the complex transverse water proton magnetization due to diffusion-encoding magnetic field gradient pulses. The integral of the solution of this PDE yields the diffusion magnetic resonance imaging (dMRI) signal. In a complex medium such as cerebral tissue, it is difficult to explicitly link the dMRI signal to biological parameters such as the cellular geometry or the cellular volume fraction. Studying the dMRI signal arising from a single neuron can provide insight into how the geometrical structure of neurons influences the measured signal. We formulate the Bloch-Torrey PDE inside a single neuron, under no water exchange condition with the extracellular space, and show how to reduce the 3D simulation in the full neuron to a 3D simulation around the soma and 1D simulations in the neurites. We show that this latter approach is computationally much faster than full 3D simulation and still gives accurate results over a wide range of diffusion times

  7. Diffusion tensor imaging in children with tuberous sclerosis complex: tract-based spatial statistics assessment of brain microstructural changes.

    Science.gov (United States)

    Zikou, Anastasia K; Xydis, Vasileios G; Astrakas, Loukas G; Nakou, Iliada; Tzarouchi, Loukia C; Tzoufi, Meropi; Argyropoulou, Maria I

    2016-07-01

    There is evidence of microstructural changes in normal-appearing white matter of patients with tuberous sclerosis complex. To evaluate major white matter tracts in children with tuberous sclerosis complex using tract-based spatial statistics diffusion tensor imaging (DTI) analysis. Eight children (mean age ± standard deviation: 8.5 ± 5.5 years) with an established diagnosis of tuberous sclerosis complex and 8 age-matched controls were studied. The imaging protocol consisted of T1-weighted high-resolution 3-D spoiled gradient-echo sequence and a spin-echo, echo-planar diffusion-weighted sequence. Differences in the diffusion indices were evaluated using tract-based spatial statistics. Tract-based spatial statistics showed increased axial diffusivity in the children with tuberous sclerosis complex in the superior and anterior corona radiata, the superior longitudinal fascicle, the inferior fronto-occipital fascicle, the uncinate fascicle and the anterior thalamic radiation. No significant differences were observed in fractional anisotropy, mean diffusivity and radial diffusivity between patients and control subjects. No difference was found in the diffusion indices between the baseline and follow-up examination in the patient group. Patients with tuberous sclerosis complex have increased axial diffusivity in major white matter tracts, probably related to reduced axonal integrity.

  8. Diffusion tensor imaging in children with tuberous sclerosis complex: tract-based spatial statistics assessment of brain microstructural changes

    International Nuclear Information System (INIS)

    Zikou, Anastasia K.; Xydis, Vasileios G.; Tzarouchi, Loukia C.; Argyropoulou, Maria I.; Astrakas, Loukas G.; Nakou, Iliada; Tzoufi, Meropi

    2016-01-01

    There is evidence of microstructural changes in normal-appearing white matter of patients with tuberous sclerosis complex. To evaluate major white matter tracts in children with tuberous sclerosis complex using tract-based spatial statistics diffusion tensor imaging (DTI) analysis. Eight children (mean age ± standard deviation: 8.5 ± 5.5 years) with an established diagnosis of tuberous sclerosis complex and 8 age-matched controls were studied. The imaging protocol consisted of T1-weighted high-resolution 3-D spoiled gradient-echo sequence and a spin-echo, echo-planar diffusion-weighted sequence. Differences in the diffusion indices were evaluated using tract-based spatial statistics. Tract-based spatial statistics showed increased axial diffusivity in the children with tuberous sclerosis complex in the superior and anterior corona radiata, the superior longitudinal fascicle, the inferior fronto-occipital fascicle, the uncinate fascicle and the anterior thalamic radiation. No significant differences were observed in fractional anisotropy, mean diffusivity and radial diffusivity between patients and control subjects. No difference was found in the diffusion indices between the baseline and follow-up examination in the patient group. Patients with tuberous sclerosis complex have increased axial diffusivity in major white matter tracts, probably related to reduced axonal integrity. (orig.)

  9. Large-eddy simulation with accurate implicit subgrid-scale diffusion

    NARCIS (Netherlands)

    B. Koren (Barry); C. Beets

    1996-01-01

    textabstractA method for large-eddy simulation is presented that does not use an explicit subgrid-scale diffusion term. Subgrid-scale effects are modelled implicitly through an appropriate monotone (in the sense of Spekreijse 1987) discretization method for the advective terms. Special attention is

  10. Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources

    Directory of Open Access Journals (Sweden)

    Ida de Bonis

    2017-09-01

    Full Text Available We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.

  11. Reaction of tantalum-alkyne complexes with isocyanates or acyl cyanides

    International Nuclear Information System (INIS)

    Kataoka, Yasutaka; Oguchi, Yoshiyuki; Yoshizumi, Kazuyuki; Miwatashi, Seiji; Takai, Kazuhiko; Utimoto, Kiitiro

    1992-01-01

    Treatment of alkynes with low-valent tantalum derived from TiCl 5 and zinc produces tantalum-alkyne complexes (not isolated), which react in situ with phenyl isocyanate (or butyl isocyanate) to give (E)-α, β-unsaturated amides stereoselectively. The tantalum-alkyne complexes also react with acyl cyanides in the presence of BF 3 ·OEt 2 to give α-cyanohydrins. In both reactions, filtration of the reaction mixture containing the tantalum-alkyne complexes before addition of isocyanates (or acyl cyanides) is indispensable to obtain good yields. (author)

  12. Travelling wave and convergence in stage-structured reaction-diffusion competitive models with nonlocal delays

    International Nuclear Information System (INIS)

    Xu Rui; Chaplain, M.A.J.; Davidson, F.A.

    2006-01-01

    In this paper, we first investigate a stage-structured competitive model with time delays, harvesting, and nonlocal spatial effect. By using an iterative technique recently developed by Wu and Zou (Wu J, Zou X. Travelling wave fronts of reaction-diffusion systems with delay. J Dynam Differen Equat 2001;13:651-87), sufficient conditions are established for the existence of travelling front solution connecting the two boundary equilibria in the case when there is no positive equilibrium. The travelling wave front corresponds to an invasion by a stronger species which drives the weaker species to extinction. Secondly, we consider a stage-structured competitive model with time delays and nonlocal spatial effect when the domain is finite. We prove the global stability of each of the nonnegative equilibria and demonstrate that the more complex model studied here admits three possible long term behaviors: coexistence, bistability and dominance as is the case for the standard Lotka-Voltera competitive model

  13. Diffusion processes in the relaxed cross sections for the reaction 107109Ag+20Ne

    International Nuclear Information System (INIS)

    Babinet, R.; Moretto, L.G.; Galin, J.; Jared, R.; Moulton, J.; Thompson, S.G.

    1976-01-01

    The fragments emitted in the reaction 107 109 Ag+ 20 Ne at 175 and 252 MeV bombarding energy have been identified in charge up to Z=32. Kinetic energy distributions, cross sections and angular distributions have been measured for each Z. The kinetic energy spectra show the two usual components: the quasielastic component and the relaxed component. The Z-distribution of the latter is fairly flat, slowly decreasing up to Z approximately 15 and then rising again up to Z=30. The variations in the Z-distribution are more pronounced at the lower bombarding energy. The angular distributions associated with the relaxed component are forward peaked for Z-values close to that of the projectile and behave like 1/sintheta for larger Z-values. The forward peaking is very substantial for Z 10 the forward peaking in excess of 1/sintheta disappears around Z=15. These features are interpreted in terms of a diffusion process along the asymmetry coordinate of a short-lived intermediate complex. (Auth.)

  14. Speckle contrast diffuse correlation tomography of complex turbid medium flow

    Energy Technology Data Exchange (ETDEWEB)

    Huang, Chong; Irwin, Daniel; Lin, Yu; Shang, Yu; He, Lian; Kong, Weikai; Yu, Guoqiang [Department of Biomedical Engineering, University of Kentucky, Lexington, Kentucky 40506 (United States); Luo, Jia [Department of Pharmacology and Nutritional Sciences, University of Kentucky, Lexington, Kentucky 40506 (United States)

    2015-07-15

    Purpose: Developed herein is a three-dimensional (3D) flow contrast imaging system leveraging advancements in the extension of laser speckle contrast imaging theories to deep tissues along with our recently developed finite-element diffuse correlation tomography (DCT) reconstruction scheme. This technique, termed speckle contrast diffuse correlation tomography (scDCT), enables incorporation of complex optical property heterogeneities and sample boundaries. When combined with a reflectance-based design, this system facilitates a rapid segue into flow contrast imaging of larger, in vivo applications such as humans. Methods: A highly sensitive CCD camera was integrated into a reflectance-based optical system. Four long-coherence laser source positions were coupled to an optical switch for sequencing of tomographic data acquisition providing multiple projections through the sample. This system was investigated through incorporation of liquid and solid tissue-like phantoms exhibiting optical properties and flow characteristics typical of human tissues. Computer simulations were also performed for comparisons. A uniquely encountered smear correction algorithm was employed to correct point-source illumination contributions during image capture with the frame-transfer CCD and reflectance setup. Results: Measurements with scDCT on a homogeneous liquid phantom showed that speckle contrast-based deep flow indices were within 12% of those from standard DCT. Inclusion of a solid phantom submerged below the liquid phantom surface allowed for heterogeneity detection and validation. The heterogeneity was identified successfully by reconstructed 3D flow contrast tomography with scDCT. The heterogeneity center and dimensions and averaged relative flow (within 3%) and localization were in agreement with actuality and computer simulations, respectively. Conclusions: A custom cost-effective CCD-based reflectance 3D flow imaging system demonstrated rapid acquisition of dense boundary

  15. Passing to the limit in a Wasserstein gradient flow : from diffusion to reaction

    NARCIS (Netherlands)

    Arnrich, S.; Mielke, A.; Peletier, M.A.; Savaré, G.; Veneroni, M.

    2012-01-01

    We study a singular-limit problem arising in the modelling of chemical reactions. At finite e > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is scaled by 1 / e and in the limit e --> 0, the solution concentrates

  16. Simulating social complexity a handbook

    CERN Document Server

    Meyer, Ruth

    2013-01-01

    Social systems are among the most complex known. This poses particular problems for those who wish to understand them. The complexity often makes analytic approaches infeasible and natural language approaches inadequate for relating intricate cause and effect. However, individual- and agent-based computational approaches hold out the possibility of new and deeper understanding of such systems.  Simulating Social Complexity examines all aspects of using agent- or individual-based simulation. This approach represents systems as individual elements having each their own set of differing states and internal processes. The interactions between elements in the simulation represent interactions in the target systems. What makes these elements "social" is that they are usefully interpretable as interacting elements of an observed society. In this, the focus is on human society, but can be extended to include social animals or artificial agents where such work enhances our understanding of human society.  The phenom...

  17. The two-regime method for optimizing stochastic reaction-diffusion simulations

    KAUST Repository

    Flegg, M. B.; Chapman, S. J.; Erban, R.

    2011-01-01

    Spatial organization and noise play an important role in molecular systems biology. In recent years, a number of software packages have been developed for stochastic spatio-temporal simulation, ranging from detailed molecular-based approaches

  18. A coupled mechanical and chemical damage model for concrete affected by alkali–silica reaction

    Energy Technology Data Exchange (ETDEWEB)

    Pignatelli, Rossella, E-mail: rossellapignatelli@gmail.com [Department of Civil and Environmental Engineering, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milano (Italy); Lombardi Ingegneria S.r.l., Via Giotto 36, 20145 Milano (Italy); Comi, Claudia, E-mail: comi@stru.polimi.it [Department of Civil and Environmental Engineering, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milano (Italy); Monteiro, Paulo J.M., E-mail: monteiro@ce.berkeley.edu [Department of Civil and Environmental Engineering, University of California, Berkeley, CA 94720 (United States)

    2013-11-15

    To model the complex degradation phenomena occurring in concrete affected by alkali–silica reaction (ASR), we formulate a poro-mechanical model with two isotropic internal variables: the chemical and the mechanical damage. The chemical damage, related to the evolution of the reaction, is caused by the pressure generated by the expanding ASR gel on the solid concrete skeleton. The mechanical damage describes the strength and stiffness degradation induced by the external loads. As suggested by experimental results, degradation due to ASR is considered to be localized around reactive sites. The effect of the degree of saturation and of the temperature on the reaction development is also modeled. The chemical damage evolution is calibrated using the value of the gel pressure estimated by applying the electrical diffuse double-layer theory to experimental values of the surface charge density in ASR gel specimens reported in the literature. The chemo-damage model is first validated by simulating expansion tests on reactive specimens and beams; the coupled chemo-mechanical damage model is then employed to simulate compression and flexure tests results also taken from the literature. -- Highlights: •Concrete degradation due to ASR in variable environmental conditions is modeled. •Two isotropic internal variables – chemical and mechanical damage – are introduced. •The value of the swelling pressure is estimated by the diffuse double layer theory. •A simplified scheme is proposed to relate macro- and microscopic properties. •The chemo-mechanical damage model is validated by simulating tests in literature.

  19. Kinetics of the reactions of hydrated electrons with metal complexes

    International Nuclear Information System (INIS)

    Korsse, J.

    1983-01-01

    The reactivity of the hydrated electron towards metal complexes is considered. Experiments are described involving metal EDTA and similar complexes. The metal ions studied are mainly Ni 2+ , Co 2+ and Cu 2+ . Rates of the reactions of the complexes with e - (aq) were measured using the pulse radiolysis technique. It is shown that the reactions of e - (aq) with the copper complexes display unusually small kinetic salt effects. The results suggest long-range electron transfer by tunneling. A tunneling model is presented and the experimental results are discussed in terms of this model. Results of approximate molecular orbital calculations of some redox potentials are given, for EDTA chelates as well as for series of hexacyano and hexaquo complexes. Finally, equilibrium constants for the formation of ternary complexes are reported. (Auth./G.J.P.)

  20. On one model problem for the reaction-diffusion-advection equation

    Science.gov (United States)

    Davydova, M. A.; Zakharova, S. A.; Levashova, N. T.

    2017-09-01

    The asymptotic behavior of the solution with boundary layers in the time-independent mathematical model of reaction-diffusion-advection arising when describing the distribution of greenhouse gases in the surface atmospheric layer is studied. On the basis of the asymptotic method of differential inequalities, the existence of a boundary-layer solution and its asymptotic Lyapunov stability as a steady-state solution of the corresponding parabolic problem is proven. One of the results of this work is the determination of the local domain of the attraction of a boundary-layer solution.

  1. Diffusion and dispersion characteristics of hybridized discontinuous Galerkin methods for under-resolved turbulence simulations

    Science.gov (United States)

    Moura, Rodrigo; Fernandez, Pablo; Mengaldo, Gianmarco

    2017-11-01

    We investigate the dispersion and diffusion characteristics of hybridized discontinuous Galerkin (DG) methods. This provides us with insights to develop robust and accurate high-order DG discretizations for under-resolved flow simulations. Using the eigenanalysis technique introduced in (Moura et al., JCP, 2015 and Mengaldo et al., Computers & Fluids, 2017), we present a dispersion-diffusion analysis for the linear advection-diffusion equation. The effect of the accuracy order, the Riemann flux and the viscous stabilization are investigated. Next, we examine the diffusion characteristics of hybridized DG methods for under-resolved turbulent flows. The implicit large-eddy simulation (iLES) of the inviscid and viscous Taylor-Green vortex (TGV) problems are considered to this end. The inviscid case is relevant in the limit of high Reynolds numbers Re , i.e. negligible molecular viscosity, while the viscous case explores the effect of Re on the accuracy and robustness of the simulations. The TGV cases considered here are particularly crucial to under-resolved turbulent free flows away from walls. We conclude the talk with a discussion on the connections between hybridized and standard DG methods for under-resolved flow simulations.

  2. Facile reactions of gold(i) complexes with tri(tert-butyl)azadiboriridine.

    Science.gov (United States)

    Shang, Rong; Saito, Souta; Jimenez-Halla, J Oscar C; Yamamoto, Yohsuke

    2018-04-17

    Direct structural evidence for group 11 metal-mediated B-B bond activation was obtained from reactions of tri(tert-butyl)azadiboriridine (1) with AuCl(L) complexes. The AuCl(SMe2) reaction afforded [η2-B,B-B(tBu)N(tBu)B(tBu)]AuCl (2) by ligand displacement. More donating phosphines as co-ligands led to B-B bond cleavage accompanied by either halide or L migration to form boron-gold complexes 3 (L = PPh3) and 4 (L = PMe3). A similar product 5, which is isostructural to 4, was obtained by the addition of dimethylaminopyridine (DMAP) to 2-4. Complexes 2-5 constitute rare examples of metal complexes bearing two Lewis acidic centres. The effect of the boryl ligand was demonstrated in the formation of a gold(i) complex 6 bearing a 5-membered heterocycle from 3 and tert-butylisonitrile. Plausible reaction mechanisms that led to these complexes and their bonding situation were explored computationally at the DFT level.

  3. Design requirements for ERD in diffusion-dominated media: how do injection interval, bioactive zones and reaction kinetics affect remediation performance?

    Science.gov (United States)

    Chambon, J.; Lemming, G.; Manoli, G.; Broholm, M. M.; Bjerg, P.; Binning, P. J.

    2011-12-01

    Enhanced Reductive Dechlorination (ERD) has been successfully used in high permeability media, such as sand aquifers, and is considered to be a promising technology for low permeability settings. Pilot and full-scale applications of ERD at several sites in Denmark have shown that the main challenge is to get contact between the injected bacteria and electron donor and the contaminants trapped in the low-permeability matrix. Sampling of intact cores from the low-permeability matrix has shown that the bioactive zones (where degradation occurs) are limited in the matrix, due to the slow diffusion transport processes, and this affects the timeframes for the remediation. Due to the limited ERD applications and the complex transport and reactive processes occurring in low-permeability media, design guidelines are currently not available for ERD in such settings, and remediation performance assessments are limited. The objective of this study is to combine existing knowledge from several sites with numerical modeling to assess the effect of the injection interval, development of bioactive zones and reaction kinetics on the remediation efficiency for ERD in diffusion-dominated media. A numerical model is developed to simulate ERD at a contaminated site, where the source area (mainly TCE) is located in a clayey till with fractures and interbedded sand lenses. Such contaminated sites are common in North America and Europe. Hydro-geological characterization provided information on geological heterogeneities and hydraulic parameters, which are relevant for clay till sites in general. The numerical model couples flow and transport in the fracture network and low-permeability matrix. Sequential degradation of TCE to ethene is modeled using Monod kinetics, and the kinetic parameters are obtained from laboratory experiments. The influence of the reaction kinetics on remediation efficiency is assessed by varying the biomass concentration of the specific degraders. The injected

  4. Prospective randomized study of contrast reaction management curricula: Computer-based interactive simulation versus high-fidelity hands-on simulation

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Carolyn L., E-mail: wangcl@uw.edu [Department of Radiology, University of Washington, Box 357115, 1959 NE Pacific Street, Seattle, WA 98195-7115 (United States); Schopp, Jennifer G.; Kani, Kimia [Department of Radiology, University of Washington, Box 357115, 1959 NE Pacific Street, Seattle, WA 98195-7115 (United States); Petscavage-Thomas, Jonelle M. [Penn State Hershey Medical Center, Department of Radiology, 500 University Drive, Hershey, PA 17033 (United States); Zaidi, Sadaf; Hippe, Dan S.; Paladin, Angelisa M.; Bush, William H. [Department of Radiology, University of Washington, Box 357115, 1959 NE Pacific Street, Seattle, WA 98195-7115 (United States)

    2013-12-01

    Purpose: We developed a computer-based interactive simulation program for teaching contrast reaction management to radiology trainees and compared its effectiveness to high-fidelity hands-on simulation training. Materials and methods: IRB approved HIPAA compliant prospective study of 44 radiology residents, fellows and faculty who were randomized into either the high-fidelity hands-on simulation group or computer-based simulation group. All participants took separate written tests prior to and immediately after their intervention. Four months later participants took a delayed written test and a hands-on high-fidelity severe contrast reaction scenario performance test graded on predefined critical actions. Results: There was no statistically significant difference between the computer and hands-on groups’ written pretest, immediate post-test, or delayed post-test scores (p > 0.6 for all). Both groups’ scores improved immediately following the intervention (p < 0.001). The delayed test scores 4 months later were still significantly higher than the pre-test scores (p ≤ 0.02). The computer group's performance was similar to the hands-on group on the severe contrast reaction simulation scenario test (p = 0.7). There were also no significant differences between the computer and hands-on groups in performance on the individual core competencies of contrast reaction management during the contrast reaction scenario. Conclusion: It is feasible to develop a computer-based interactive simulation program to teach contrast reaction management. Trainees that underwent computer-based simulation training scored similarly on written tests and on a hands-on high-fidelity severe contrast reaction scenario performance test as those trained with hands-on high-fidelity simulation.

  5. Prospective randomized study of contrast reaction management curricula: Computer-based interactive simulation versus high-fidelity hands-on simulation

    International Nuclear Information System (INIS)

    Wang, Carolyn L.; Schopp, Jennifer G.; Kani, Kimia; Petscavage-Thomas, Jonelle M.; Zaidi, Sadaf; Hippe, Dan S.; Paladin, Angelisa M.; Bush, William H.

    2013-01-01

    Purpose: We developed a computer-based interactive simulation program for teaching contrast reaction management to radiology trainees and compared its effectiveness to high-fidelity hands-on simulation training. Materials and methods: IRB approved HIPAA compliant prospective study of 44 radiology residents, fellows and faculty who were randomized into either the high-fidelity hands-on simulation group or computer-based simulation group. All participants took separate written tests prior to and immediately after their intervention. Four months later participants took a delayed written test and a hands-on high-fidelity severe contrast reaction scenario performance test graded on predefined critical actions. Results: There was no statistically significant difference between the computer and hands-on groups’ written pretest, immediate post-test, or delayed post-test scores (p > 0.6 for all). Both groups’ scores improved immediately following the intervention (p < 0.001). The delayed test scores 4 months later were still significantly higher than the pre-test scores (p ≤ 0.02). The computer group's performance was similar to the hands-on group on the severe contrast reaction simulation scenario test (p = 0.7). There were also no significant differences between the computer and hands-on groups in performance on the individual core competencies of contrast reaction management during the contrast reaction scenario. Conclusion: It is feasible to develop a computer-based interactive simulation program to teach contrast reaction management. Trainees that underwent computer-based simulation training scored similarly on written tests and on a hands-on high-fidelity severe contrast reaction scenario performance test as those trained with hands-on high-fidelity simulation

  6. Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries.

    Science.gov (United States)

    Shafiey, Hassan; Gan, Xinjun; Waxman, David

    2017-11-01

    To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

  7. Simulation of Electron and Ion Transport in Methane-Air Counterflow Diffusion Flames

    Science.gov (United States)

    Choi, Sangkyu; Bisetti, Fabrizio; Chung, Suk Ho

    2010-11-01

    The spatial distribution of charged species in a methane-air counterflow diffusion flame is simulated with a detailed ion chemistry. The electric field induced by the distribution of charged species is calculated and compared to that obtained invoking the ambipolar diffusion assumption. The two calculations showed identical profiles for charged species and electric field. The profiles of ion mole fractions show two peaks: one near the maximum temperature and a second peak on the oxidizer side. The major ions near the maximum temperature are electron, C2H3O+ and H3O+. CHO3- and H3O+ contribute to the second peak. These profiles are quite different from those adopting a simplified three-step mechanism based solely on E-, CHO+ and H3O+, which shows only a single peak. Reaction pathway analyses showed that near the flame region, the proton is transferred by the path of CHO+ -> H3O+ -> C2H3O+ -> CHO+ in a circulating manner. In the second peak, CHO3- is produced though the pathway of E- -> O- -> OH- -> CHO3-. The sensitivity of the charged species profiles to transport properties is investigated, and it is found that the variation of charged species profiles near peak temperature is relatively small, while on the oxidizer side, it is quite sensitive to transport properties.

  8. Alternans and Spiral Breakup in an Excitable Reaction-Diffusion System: A Simulation Study.

    Science.gov (United States)

    Gani, M Osman; Ogawa, Toshiyuki

    2014-01-01

    The determination of the mechanisms of spiral breakup in excitable media is still an open problem for researchers. In the context of cardiac electrophysiological activities, spiral breakup exhibits complex spatiotemporal pattern known as ventricular fibrillation. The latter is the major cause of sudden cardiac deaths all over the world. In this paper, we numerically study the instability of periodic planar traveling wave solution in two dimensions. The emergence of stable spiral pattern is observed in the considered model. This pattern occurs when the heart is malfunctioning (i.e., ventricular tachycardia). We show that the spiral wave breakup is a consequence of the transverse instability of the planar traveling wave solutions. The alternans, that is, the oscillation of pulse widths, is observed in our simulation results. Moreover, we calculate the widths of spiral pulses numerically and observe that the stable spiral pattern bifurcates to an oscillatory wave pattern in a one-parameter family of solutions. The spiral breakup occurs far below the bifurcation when the maximum and the minimum excited states become more distinct, and hence the alternans becomes more pronounced.

  9. Design and Evaluation of a Prompting Instrument to Support Learning within the Diffusion Simulation Game

    Science.gov (United States)

    Kwon, Seolim; Lara, Miguel; Enfield, Jake; Frick, Theodore

    2013-01-01

    Conducting an iterative usability testing, a set of prompts used as a form of instructional support was developed in order to facilitate the comprehension of the diffusion of innovations theory (Rogers, 2003) in a simulation game called the Diffusion Simulation Game (DSG) (Molenda & Rice, 1979). The six subjects who participated in the study…

  10. Allergic Contact Dermatitis with Diffuse Erythematous Reaction from Diisopropanolamine in a Compress

    Directory of Open Access Journals (Sweden)

    Tomoko Rind

    2010-04-01

    Full Text Available Compresses containing a nonsteroidal antiinflammatory drug (NSAID are commonly used in Japan. However, this treatment may induce both allergic and photoallergic contact dermatitis from the NSAIDs and their ingredients. Here, we describe a case of allergic contact dermatitis with diffuse erythematous reaction due to diisopropanolamine in the applied compress. The absorption of diisopropanolamine might have been enhanced by the occlusive condition.

  11. Ionic Diffusion and Kinetic Homogeneous Chemical Reactions in the Pore Solution of Porous Materials with Moisture Transport

    DEFF Research Database (Denmark)

    Johannesson, Björn

    2009-01-01

    Results from a systematic continuum mixture theory will be used to establish the governing equations for ionic diffusion and chemical reactions in the pore solution of a porous material subjected to moisture transport. The theory in use is the hybrid mixture theory (HMT), which in its general form......’s law of diffusion and the generalized Darcy’s law will be used together with derived constitutive equations for chemical reactions within phases. The mass balance equations for the constituents and the phases together with the constitutive equations gives the coupled set of non-linear differential...... general description of chemical reactions among constituents is described. The Petrov – Galerkin approach are used in favour of the standard Galerkin weighting in order to improve the solution when the convective part of the problem is dominant. A modified type of Newton – Raphson scheme is derived...

  12. Simulation of diffusion time of small molecules in protein crystals.

    Science.gov (United States)

    Geremia, Silvano; Campagnolo, Mara; Demitri, Nicola; Johnson, Louise N

    2006-03-01

    A simple model for evaluation of diffusion times of small molecule into protein crystals has been developed, which takes into account the physical and chemical properties both of protein crystal and the diffusing molecules. The model also includes consideration of binding and the binding affinity of a ligand to the protein. The model has been validated by simulation of experimental set-ups of several examples found in the literature. These experiments cover a wide range of situations: from small to relatively large diffusing molecules, crystals having low, medium, or high protein density, and different size. The reproduced experiments include ligand exchange in protein crystals by soaking techniques. Despite the simplifying assumptions of the model, theoretical and experimental data are in agreement with available data, with experimental diffusion times ranging from a few seconds to several hours. The method has been used successfully for planning intermediate cryotrapping experiments in maltodextrin phosphorylase crystals.

  13. Stochastic Simulation of Biomolecular Reaction Networks Using the Biomolecular Network Simulator Software

    National Research Council Canada - National Science Library

    Frazier, John; Chusak, Yaroslav; Foy, Brent

    2008-01-01

    .... The software uses either exact or approximate stochastic simulation algorithms for generating Monte Carlo trajectories that describe the time evolution of the behavior of biomolecular reaction networks...

  14. Convergence to a pulsating travelling wave for an epidemic reaction-diffusion system with non-diffusive susceptible population.

    Science.gov (United States)

    Ducrot, Arnaud; Giletti, Thomas

    2014-09-01

    In this work we study the asymptotic behaviour of the Kermack-McKendrick reaction-diffusion system in a periodic environment with non-diffusive susceptible population. This problem was proposed by Kallen et al. as a model for the spatial spread for epidemics, where it can be reasonable to assume that the susceptible population is motionless. For arbitrary dimensional space we prove that large classes of solutions of such a system have an asymptotic spreading speed in large time, and that the infected population has some pulse-like asymptotic shape. The analysis of the one-dimensional problem is more developed, as we are able to uncover a much more accurate description of the profile of solutions. Indeed, we will see that, for some initially compactly supported infected population, the profile of the solution converges to some pulsating travelling wave with minimal speed, that is to some entire solution moving at a constant positive speed and whose profile's shape is periodic in time.

  15. Simulations of nuclear reactions for a future HIE-ISOLDE spectrometer

    Energy Technology Data Exchange (ETDEWEB)

    Tveten, Gry [University of Oslo (Norway); CERN (Switzerland); Cederkall, Joakim [Lund University (Sweden); CERN (Switzerland); Blumenfeld, Yorick [CERN (Switzerland)

    2009-07-01

    The planned High Intensity and Energy (HIE) upgrade of the radioactive beam facility ISOLDE will enable post-acceleration of radioactive beams up to an energy of about 10 MeV/u, thus opening the door to nuclear reaction studies. In the case of transfer reactions in inverse kinematics a recoil separator is often well suited or even needed to tell recoils and beam apart and to select the exit channel or to do spectroscopic studies. Two different types of spectrometer designs are being considered for HIE-ISOLDE, namely a recoil mass separator or a ray-tracing type of spectrometer. A set of nuclear transfer reactions in inverse kinematics have been simulated using realistic parameters for HIE-ISOLDE. The performance of the two types of spectrometer designs is compared and their scientific possibilities and limitations discussed based on the simulation results. To evaluate the validity of the simulations a data set from PRISMA at LNL is also compared with simulation results and a comparison between simulations and these data will be presented.

  16. Cluster geometry and survival probability in systems driven by reaction-diffusion dynamics

    International Nuclear Information System (INIS)

    Windus, Alastair; Jensen, Henrik J

    2008-01-01

    We consider a reaction-diffusion model incorporating the reactions A→φ, A→2A and 2A→3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order absorbing phase transition to an extinct state. A tricritical point separates the two phase lines. While we comment on this critical behaviour, the main focus of the paper is on the geometry of the population clusters that form. We observe the different cluster structures that arise at criticality for the three different types of critical behaviour and show that there exists a linear relationship for the survival probability against initial cluster size at the tricritical point only.

  17. Mass transfer with complex reversible chemical reactions. II: Parallel reversible chemical reactions

    NARCIS (Netherlands)

    Versteeg, Geert; van Beckum, F.P.H.; Kuipers, J.A.M.; van Swaaij, Willibrordus Petrus Maria

    1990-01-01

    An absorption model has been developed which can be used to calculate rapidly absorption rates for the phenomenon mass transfer accompanied by multiple complex parallel reversible chemical reactions. This model can be applied for the calculation of the mass transfer rates, enhancement factors and

  18. Mass transfer with complex reversible chemical reactions. II: parallel reversible chemical reactions

    NARCIS (Netherlands)

    Versteeg, G.F.; Kuipers, J.A.M.; Beckum, van F.P.H.; van Swaaij, W.P.M.

    1990-01-01

    An absorption model has been developed which can be used to calculate rapidly absorption rates for the phenomenon mass transfer accompanied by multiple complex parallel reversible chemical reactions. This model can be applied for the calculation of the mass transfer rates, enhancement factors and

  19. COEL: A Cloud-based Reaction Network Simulator

    Directory of Open Access Journals (Sweden)

    Peter eBanda

    2016-04-01

    Full Text Available Chemical Reaction Networks (CRNs are a formalism to describe the macroscopic behavior of chemical systems. We introduce COEL, a web- and cloud-based CRN simulation framework that does not require a local installation, runs simulations on a large computational grid, provides reliable database storage, and offers a visually pleasing and intuitive user interface. We present an overview of the underlying software, the technologies, and the main architectural approaches employed. Some of COEL's key features include ODE-based simulations of CRNs and multicompartment reaction networks with rich interaction options, a built-in plotting engine, automatic DNA-strand displacement transformation and visualization, SBML/Octave/Matlab export, and a built-in genetic-algorithm-based optimization toolbox for rate constants.COEL is an open-source project hosted on GitHub (http://dx.doi.org/10.5281/zenodo.46544, which allows interested research groups to deploy it on their own sever. Regular users can simply use the web instance at no cost at http://coel-sim.org. The framework is ideally suited for a collaborative use in both research and education.

  20. Molecular dynamics simulation of helium and oxygen diffusion in UO2±x

    International Nuclear Information System (INIS)

    Govers, K.; Lemehov, S.; Hou, M.; Verwerft, M.

    2009-01-01

    Atomic scale simulation techniques based on empirical potentials have been considered in the present work to get insight on helium diffusion in uranium dioxide. By varying the stoichiometry, together with the system temperature, the performed molecular dynamics simulations indicate two diffusion regimes for He. The first one presents a low activation energy (0.5 eV) and suggests oxygen vacancies assisted migration. This regime seems to provide the major contribution to diffusion when structural defects are present (extrinsic defects, imposed, e.g. by the stoichiometry). The second regime presents a higher activation energy, around 2 eV, and dominates in the higher temperature range or at perfect stoichiometry, suggesting an intrinsic migration process. Considering the dependence of He behaviour with oxygen defects, oxygen diffusion has been considered as well in the different stoichiometry domains. Finally, further investigations were made with nudged elastic bands calculations for a better interpretation of the operating migration mechanisms, both for He and O.

  1. Simulation Studies of Diffusion-Release and Effusive-Flow of Short-Lived Radioactive Isotopes

    CERN Document Server

    Zhang, Yan; Kawai, Yoko

    2005-01-01

    Delay times associated with diffusion release from targets and effusive-flow transport of radioactive isotopes to ion sources are principal intensity limiters at ISOL-based radioactive ion beam facilities, and simulation studies with computer models are cost effective methods for designing targets and vapor transport systems with minimum delay times to avoid excessive decay losses of short lived ion species. A finite difference code, Diffuse II, was recently developed at the Oak Ridge National Laboratory to study diffusion-release of short-lived species from three principal target geometries. Simulation results are in close agreement with analytical solutions to Fick’s second equation. Complementary to the development of Diffuse II, the Monte-Carlo code, Effusion, was developed to address issues related to the design of fast vapor transport systems. Results, derived by using Effusion, are also found to closely agree with experimental measurements. In this presentation, the codes will be used in conc...

  2. Reaction chemistry of nitrogen species in hydrothermal systems: Simple reactions, waste simulants, and actual wastes

    International Nuclear Information System (INIS)

    Dell'Orco, P.; Luan, L.; Proesmans, P.; Wilmanns, E.

    1995-01-01

    Results are presented from hydrothermal reaction systems containing organic components, nitrogen components, and an oxidant. Reaction chemistry observed in simple systems and in simple waste simulants is used to develop a model which presents global nitrogen chemistry in these reactive systems. The global reaction path suggested is then compared with results obtained for the treatment of an actual waste stream containing only C-N-0-H species

  3. Spatiotemporal chaos of self-replicating spots in reaction-diffusion systems.

    Science.gov (United States)

    Wang, Hongli; Ouyang, Qi

    2007-11-23

    The statistical properties of self-replicating spots in the reaction-diffusion Gray-Scott model are analyzed. In the chaotic regime of the system, the spots that dominate the spatiotemporal chaos grow and divide in two or decay into the background randomly and continuously. The rates at which the spots are created and decay are observed to be linearly dependent on the number of spots in the system. We derive a probabilistic description of the spot dynamics based on the statistical independence of spots and thus propose a characterization of the spatiotemporal chaos dominated by replicating spots.

  4. Discrete maximum principle for FE solutions of the diffusion-reaction problem on prismatic meshes

    Czech Academy of Sciences Publication Activity Database

    Hannukainen, A.; Korotov, S.; Vejchodský, Tomáš

    2009-01-01

    Roč. 226, č. 2 (2009), s. 275-287 ISSN 0377-0427 R&D Projects: GA AV ČR IAA100760702 Institutional research plan: CEZ:AV0Z10190503 Keywords : diffusion-reaction problem * maximum principle * prismatic finite elements Subject RIV: BA - General Mathematics Impact factor: 1.292, year: 2009

  5. Diffusion in higher dimensional SYK model with complex fermions

    Science.gov (United States)

    Cai, Wenhe; Ge, Xian-Hui; Yang, Guo-Hong

    2018-01-01

    We construct a new higher dimensional SYK model with complex fermions on bipartite lattices. As an extension of the original zero-dimensional SYK model, we focus on the one-dimension case, and similar Hamiltonian can be obtained in higher dimensions. This model has a conserved U(1) fermion number Q and a conjugate chemical potential μ. We evaluate the thermal and charge diffusion constants via large q expansion at low temperature limit. The results show that the diffusivity depends on the ratio of free Majorana fermions to Majorana fermions with SYK interactions. The transport properties and the butterfly velocity are accordingly calculated at low temperature. The specific heat and the thermal conductivity are proportional to the temperature. The electrical resistivity also has a linear temperature dependence term.

  6. Diffusion coefficient of three-dimensional Yukawa liquids

    International Nuclear Information System (INIS)

    Dzhumagulova, K. N.; Ramazanov, T. S.; Masheeva, R. U.

    2013-01-01

    The purpose of this work is an investigation of the diffusion coefficient of the dust component in complex plasma. The computer simulation of the Yukawa liquids was made on the basis of the Langevin equation, which takes into account the influence of buffer plasma on the dust particles dynamics. The Green–Kubo relation was used to calculate the diffusion coefficient. Calculations of the diffusion coefficient for a wide range of the system parameters were performed. Using obtained numerical data, we constructed the interpolation formula for the diffusion coefficient. We also show that the interpolation formula correctly describes experimental data obtained under microgravity conditions

  7. Physiological environment induce quick response - slow exhaustion reactions

    Directory of Open Access Journals (Sweden)

    Noriko eHiroi

    2011-09-01

    Full Text Available In vivo environments are highly crowded and inhomogeneous, which may affect reaction processes in cells. In this study we examined the effects of intracellular crowding and an inhomogeneity on the behavior of in vivo reactions by calculating the spectral dimension (ds, which can be translated into the reaction rate function. We compared estimates of anomaly parameters obtained from Fluorescence Correlation Spectroscopy (FCS data with fractal dimensions derived from Transmission Electron Microscopy (TEM image analysis. FCS analysis indicated that the anomalous property was linked to physiological structure. Subsequent TEM analysis provided an in vivo illustration; soluble molecules likely percolate between intracellular clusters, which are constructed in a self-organizing manner. We estimated a cytoplasmic spectral dimension ds to be 1.39 ± 0.084. This result suggests that in vivo reactions initially run faster than the same reactions in a homogeneous space; this conclusion is consistent with the anomalous character indicated by FCS analysis. We further showed that these results were compatible with our Monte-Carlo simulation in which the anomalous behavior of mobile molecules correlates with the intracellular environment, leading to description as a percolation cluster, as demonstrated using TEM analysis. We confirmed by the simulation that the above-mentioned in vivo like properties are different from those of homogeneously concentrated environments. Additionally, simulation results indicated that crowding level of an environment might affect diffusion rate of reactant. Such knowledge of the spatial information enables us to construct realistic models for in vivo diffusion and reaction systems.

  8. Characterization of reversible reactions of isocyanides with molybdenum dithiolate complexes

    International Nuclear Information System (INIS)

    Miller, D.J.; DuBois, M.R.

    1980-01-01

    Dimeric molybdenum complexes with bridging dithiocarbonimidate ligands of the formula [C 5 H 5 MoS 2 CNR] 2 (where R = CH 3 , CH 2 C 6 H 5 , C 6 H 11 , and n-C 4 H 9 ) have been synthesized and characterized. The syntheses involve the room-temperature reactions of excess isocyanides with solutions of the dimeric complex [C 5 H 5 MoSC 3 H 6 S] 2 . During the course of these reactions, propene is displaced from the sulfur atoms of the bridging dithiolate ligands. Addition of excess alkene reverses the above reactions. Equilibrium constants have been calculated for the following reactions by integration of NMR resonances: [CH 3 C 5 H 4 MoSC 2 H 4 S] 2 + RNC reversible (CH 3 C 5 H 4 Mo) 2 (SC 2 H 4 S)(S 2 CNR) + C == C, K 1 = 2.9 +- 0.2; (CH 3 C 5 H 4 Mo) 2 (SC 2 H 4 S)(S 2 CNR) + RNC reversible [CH 3 C 5 H 4 MoS 2 CNR] 2 + C == C, K 2 = 0.7 +- 0.1 (R = CH 2 C 6 H 5 ). The dithiocarbonimidate complexes react cleanly with the electrophiles CH 3 OSO 2 F and HOSO 2 CF 3 to form [C 5 H 5 MoS 2 CNRR'] 2 2+ where R' = H or CH 3 . These products have been characterized by spectral and conductivity methods. The reactions of the dithiocarbonimidate complexes with reducing agents and with carbon monoxide are discussed. 1 figure, 2 tables

  9. High-Fidelity Contrast Reaction Simulation Training: Performance Comparison of Faculty, Fellows, and Residents.

    Science.gov (United States)

    Pfeifer, Kyle; Staib, Lawrence; Arango, Jennifer; Kirsch, John; Arici, Mel; Kappus, Liana; Pahade, Jay

    2016-01-01

    Reactions to contrast material are uncommon in diagnostic radiology, and vary in clinical presentation from urticaria to life-threatening anaphylaxis. Prior studies have demonstrated a high error rate in contrast reaction management, with smaller studies using simulation demonstrating variable data on effectiveness. We sought to assess the effectiveness of high-fidelity simulation in teaching contrast reaction management for residents, fellows, and attendings. A 20-question multiple-choice test assessing contrast reaction knowledge, with Likert-scale questions assessing subjective comfort levels of management of contrast reactions, was created. Three simulation scenarios that represented a moderate reaction, a severe reaction, and a contrast reaction mimic were completed in a one-hour period in a simulation laboratory. All participants completed a pretest and a posttest at one month. A six-month delayed posttest was given, but was optional for all participants. A total of 150 radiologists participated (residents = 52; fellows = 24; faculty = 74) in the pretest and posttest; and 105 participants completed the delayed posttest (residents = 31; fellows = 17; faculty = 57). A statistically significant increase was found in the one-month posttest (P < .00001) and the six-month posttest scores (P < .00001) and Likert scores (P < .001) assessing comfort level in managing all contrast reactions, compared with the pretest. Test scores and comfort level for moderate and severe reactions significantly decreased at six months, compared with the one-month posttest (P < .05). High-fidelity simulation is an effective learning tool, allowing practice of "high-acuity" situation management in a nonthreatening environment; the simulation training resulted in significant improvement in test scores, as well as an increase in subjective comfort in management of reactions, across all levels of training. A six-month refresher course is suggested, to maintain knowledge and comfort level in

  10. Nonlinear simulation of electromagnetic current diffusive interchange mode turbulence

    International Nuclear Information System (INIS)

    Yagi, M.; Itoh, S.I.; Fukuyama, A.

    1998-01-01

    The anomalous transport in toroidal plasmas has been investigated extensively. It is pointed out that the nonlinear instability is important in driving the microturbulence[1], i.e., the self-sustained plasma turbulence. This concept is explained as follows; when the electron motion along the magnetic field line is resisted by the background turbulence, it gives rise to the effective resistivity and enhances the level of the turbulence. The nonlinear simulation of the electrostatic current diffusive interchange mode (CDIM) in the two dimensional sheared slab geometry has been performed as an example. The occurrence of the nonlinear instability and the self-sustainment of the plasma turbulence were confirmed by this simulation[2]. On the other hand, the electromagnetic turbulence is sustained in the high pressure limit. The possibility of the self-organization with more variety has been pointed out[3]. It is important to study the electromagnetic turbulence based on the nonlinear simulation. In this paper, the model equation for the electrostatic CDIM turbulence[2] is extended for both electrostatic and electromagnetic turbulence. (1) Not only E x B convective nonlinearity but also the electromagnetic nonlinearity which is related to the parallel flow are incorporated into the model equation. (2) The electron and ion pressure evolution equations are solved separately, making it possible to distinguish the electron and ion thermal diffusivities. The two dimensional nonlinear simulation of the electromagnetic CDIM is performed based on the extended fluid model. This paper is organized as follows. The model equation is explained in section II. The result of simulation is shown in section III. The conclusion and discussion are given in section IV. (author)

  11. Bifurcation analysis of a delay reaction-diffusion malware propagation model with feedback control

    Science.gov (United States)

    Zhu, Linhe; Zhao, Hongyong; Wang, Xiaoming

    2015-05-01

    With the rapid development of network information technology, information networks security has become a very critical issue in our work and daily life. This paper attempts to develop a delay reaction-diffusion model with a state feedback controller to describe the process of malware propagation in mobile wireless sensor networks (MWSNs). By analyzing the stability and Hopf bifurcation, we show that the state feedback method can successfully be used to control unstable steady states or periodic oscillations. Moreover, formulas for determining the properties of the bifurcating periodic oscillations are derived by applying the normal form method and center manifold theorem. Finally, we conduct extensive simulations on large-scale MWSNs to evaluate the proposed model. Numerical evidences show that the linear term of the controller is enough to delay the onset of the Hopf bifurcation and the properties of the bifurcation can be regulated to achieve some desirable behaviors by choosing the appropriate higher terms of the controller. Furthermore, we obtain that the spatial-temporal dynamic characteristics of malware propagation are closely related to the rate constant for nodes leaving the infective class for recovered class and the mobile behavior of nodes.

  12. Proton exchange in acid–base complexes induced by reaction coordinates with heavy atom motions

    International Nuclear Information System (INIS)

    Alavi, Saman; Taghikhani, Mahdi

    2012-01-01

    Highlights: ► Proton exchange in acid–base complexes is studied. ► The structures, binding energies, and normal mode vibrations are calculated. ► Transition state structures of proton exchange mechanism are determined. ► In the complexes studied, the reaction coordinate involves heavy atom rocking. ► The reaction coordinate is not simply localized in the proton movements. - Abstract: We extend previous work on nitric acid–ammonia and nitric acid–alkylamine complexes to illustrate that proton exchange reaction coordinates involve the rocking motion of the base moiety in many double hydrogen-bonded gas phase strong acid–strong base complexes. The complexes studied involve the biologically and atmospherically relevant glycine, formic, acetic, propionic, and sulfuric acids with ammonia/alkylamine bases. In these complexes, the magnitude of the imaginary frequencies associated with the proton exchange transition states are −1 . This contrasts with widely studied proton exchange reactions between symmetric carboxylic acid dimers or asymmetric DNA base pair and their analogs where the reaction coordinate is localized in proton motions and the magnitude of the imaginary frequencies for the transition states are >1100 cm −1 . Calculations on complexes of these acids with water are performed for comparison. Variations of normal vibration modes along the reaction coordinate in the complexes are described.

  13. Simulations of reactive transport and precipitation with smoothed particle hydrodynamics

    Science.gov (United States)

    Tartakovsky, Alexandre M.; Meakin, Paul; Scheibe, Timothy D.; Eichler West, Rogene M.

    2007-03-01

    A numerical model based on smoothed particle hydrodynamics (SPH) was developed for reactive transport and mineral precipitation in fractured and porous materials. Because of its Lagrangian particle nature, SPH has several advantages for modeling Navier-Stokes flow and reactive transport including: (1) in a Lagrangian framework there is no non-linear term in the momentum conservation equation, so that accurate solutions can be obtained for momentum dominated flows and; (2) complicated physical and chemical processes such as surface growth due to precipitation/dissolution and chemical reactions are easy to implement. In addition, SPH simulations explicitly conserve mass and linear momentum. The SPH solution of the diffusion equation with fixed and moving reactive solid-fluid boundaries was compared with analytical solutions, Lattice Boltzmann [Q. Kang, D. Zhang, P. Lichtner, I. Tsimpanogiannis, Lattice Boltzmann model for crystal growth from supersaturated solution, Geophysical Research Letters, 31 (2004) L21604] simulations and diffusion limited aggregation (DLA) [P. Meakin, Fractals, scaling and far from equilibrium. Cambridge University Press, Cambridge, UK, 1998] model simulations. To illustrate the capabilities of the model, coupled three-dimensional flow, reactive transport and precipitation in a fracture aperture with a complex geometry were simulated.

  14. Diffusion and Interface Effects during Preparation of All-Solid Microstructured Fibers

    Directory of Open Access Journals (Sweden)

    Kobelke Jens

    2014-09-01

    Full Text Available All-solid microstructured optical fibers (MOF allow the realization of very flexible optical waveguide designs. They are prepared by stacking of doped silica rods or canes in complex arrangements. Typical dopants in silica matrices are germanium and phosphorus to increase the refractive index (RI, or boron and fluorine to decrease the RI. However, the direct interface contact of stacking elements often causes interrelated chemical reactions or evaporation during thermal processing. The obtained fiber structures after the final drawing step thus tend to deviate from the targeted structure risking degrading their favored optical functionality. Dopant profiles and design parameters (e.g., the RI homogeneity of the cladding are controlled by the combination of diffusion and equilibrium conditions of evaporation reactions. We show simulation results of diffusion and thermal dissociation in germanium and fluorine doped silica rod arrangements according to the monitored geometrical disturbances in stretched canes or drawn fibers. The paper indicates geometrical limits of dopant structures in sub-µm-level depending on the dopant concentration and the thermal conditions during the drawing process. The presented results thus enable an optimized planning of the preform parameters avoiding unwanted alterations in dopant concentration profiles or in design parameters encountered during the drawing process.

  15. Simulation of reaction–diffusion processes in three dimensions using CUDA

    NARCIS (Netherlands)

    Molnár Jr., Ferenc; Izsak, F.; Mészáros, Róbert; Lagzi, István

    2011-01-01

    Numerical solution of reaction–diffusion equations in three dimensions is one of the most challenging applied mathematical problems. Since these simulations are very time consuming, any ideas and strategies aiming at the reduction of CPU time are important topics of research. A general and robust

  16. Physics of Fresh Produce Safety: Role of Diffusion and Tissue Reaction in Sanitization of Leafy Green Vegetables with Liquid and Gaseous Ozone-Based Sanitizers.

    Science.gov (United States)

    Shynkaryk, Mykola V; Pyatkovskyy, Taras; Mohamed, Hussein M; Yousef, Ahmed E; Sastry, Sudhir K

    2015-12-01

    Produce safety has received much recent attention, with the emphasis being largely on discovery of how microbes invade produce. However, the sanitization operation deserves more attention than it has received. The ability of a sanitizer to reach the site of pathogens is a fundamental prerequisite for efficacy. This work addresses the transport processes of ozone (gaseous and liquid) sanitizer for decontamination of leafy greens. The liquid sanitizer was ineffective against Escherichia coli K-12 in situations where air bubbles may be trapped within cavities. A model was developed for diffusion of sanitizer into the interior of produce. The reaction rate of ozone with the surface of a lettuce leaf was determined experimentally and was used in a numerical simulation to evaluate ozone concentrations within the produce and to determine the time required to reach different locations. For aqueous ozone, the penetration depth was limited to several millimeters by ozone self-decomposition due to the significant time required for diffusion. In contrast, gaseous sanitizer was able to reach a depth of 100 mm in several minutes without depletion in the absence of reaction with surfaces. However, when the ozone gas reacted with the produce surface, gas concentration was significantly affected. Simulation data were validated experimentally by measuring ozone concentrations at the bottom of a cylinder made of lettuce leaf. The microbiological test confirmed the relationship between ozone transport, its self-decomposition, reaction with surrounding materials, and the degree of inactivation of E. coli K-12. Our study shows that decontamination of fresh produce, through direct contact with the sanitizer, is more feasible with gaseous than with aqueous sanitizers. Therefore, sanitization during a high-speed washing process is effective only for decontaminating the wash water.

  17. Diffusion kinetics of the glucose/glucose oxidase system in swift heavy ion track-based biosensors

    Science.gov (United States)

    Fink, Dietmar; Vacik, Jiri; Hnatowicz, V.; Muñoz Hernandez, G.; Garcia Arrelano, H.; Alfonta, Lital; Kiv, Arik

    2017-05-01

    For understanding of the diffusion kinetics and their optimization in swift heavy ion track-based biosensors, recently a diffusion simulation was performed. This simulation aimed at yielding the degree of enrichment of the enzymatic reaction products in the highly confined space of the etched ion tracks. A bunch of curves was obtained for the description of such sensors that depend only on the ratio of the diffusion coefficient of the products to that of the analyte within the tracks. As hitherto none of these two diffusion coefficients is accurately known, the present work was undertaken. The results of this paper allow one to quantify the previous simulation and hence yield realistic predictions of glucose-based biosensors. At this occasion, also the influence of the etched track radius on the diffusion coefficients was measured and compared with earlier prediction.

  18. Propagator formalism and computer simulation of restricted diffusion behaviors of inter-molecular multiple-quantum coherences

    International Nuclear Information System (INIS)

    Cai Congbo; Chen Zhong; Cai Shuhui; Zhong Jianhui

    2005-01-01

    In this paper, behaviors of single-quantum coherences and inter-molecular multiple-quantum coherences under restricted diffusion in nuclear magnetic resonance experiments were investigated. The propagator formalism based on the loss of spin phase memory during random motion was applied to describe the diffusion-induced signal attenuation. The exact expression of the signal attenuation under the short gradient pulse approximation for restricted diffusion between two parallel plates was obtained using this propagator method. For long gradient pulses, a modified formalism was proposed. The simulated signal attenuation under the effects of gradient pulses of different width based on the Monte Carlo method agrees with the theoretical predictions. The propagator formalism and computer simulation can provide convenient, intuitive and precise methods for the study of the diffusion behaviors

  19. Convergence to Equilibrium in Energy-Reaction-Diffusion Systems Using Vector-Valued Functional Inequalities

    Science.gov (United States)

    Mielke, Alexander; Mittnenzweig, Markus

    2018-04-01

    We discuss how the recently developed energy dissipation methods for reaction diffusion systems can be generalized to the non-isothermal case. For this, we use concave entropies in terms of the densities of the species and the internal energy, where the importance is that the equilibrium densities may depend on the internal energy. Using the log-Sobolev estimate and variants for lower-order entropies as well as estimates for the entropy production of the nonlinear reactions, we give two methods to estimate the relative entropy by the total entropy production, namely a somewhat restrictive convexity method, which provides explicit decay rates, and a very general, but weaker compactness method.

  20. Cluster geometry and survival probability in systems driven by reaction-diffusion dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Windus, Alastair; Jensen, Henrik J [The Institute for Mathematical Sciences, 53 Prince' s Gate, South Kensington, London SW7 2PG (United Kingdom)], E-mail: h.jensen@imperial.ac.uk

    2008-11-15

    We consider a reaction-diffusion model incorporating the reactions A{yields}{phi}, A{yields}2A and 2A{yields}3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order absorbing phase transition to an extinct state. A tricritical point separates the two phase lines. While we comment on this critical behaviour, the main focus of the paper is on the geometry of the population clusters that form. We observe the different cluster structures that arise at criticality for the three different types of critical behaviour and show that there exists a linear relationship for the survival probability against initial cluster size at the tricritical point only.

  1. The Influence of Receptor-Mediated Interactions on Reaction-Diffusion Mechanisms of Cellular Self-organisation

    Czech Academy of Sciences Publication Activity Database

    Klika, Václav; Baker, R. E.; Headon, D.; Gaffney, E. A.

    2012-01-01

    Roč. 74, č. 4 (2012), s. 935-957 ISSN 0092-8240 Institutional research plan: CEZ:AV0Z20760514 Keywords : reaction-diffusion * receptor-mediated patterning * turing models Subject RIV: BO - Biophysics Impact factor: 2.023, year: 2012 http://www.springerlink.com/content/9713544x6871w4n6/?MUD=MP

  2. Computer simulation of the steam--graphite reaction under isothermal and steady-state conditions

    International Nuclear Information System (INIS)

    Joy, D.S.; Stem, S.C.

    1975-05-01

    A mathematical model was formulated to describe the isothermal, steady-state diffusion and reaction of steam in a graphite matrix. A generalized Langmuir-Hinshelwood equation is used to represent the steam-graphite reaction rate. The model also includes diffusion in the gas phase adjacent to the graphite matrix. A computer program, written to numerically integrate the resulting differential equations, is described. The coupled nonlinear differential equations in the graphite phase are solved using the IBM Continuous System Modeling Program. Classical finite difference techniques are used for the gas-phase calculations. An iterative procedure is required to couple the two sets of calculations. Several sample problems are presented to demonstrate the utility of the model. (U.S.)

  3. Markovian dynamics on complex reaction networks

    Energy Technology Data Exchange (ETDEWEB)

    Goutsias, J., E-mail: goutsias@jhu.edu; Jenkinson, G., E-mail: jenkinson@jhu.edu

    2013-08-10

    Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological, ecological, social, neural, and multi-agent networks. A common approach to modeling such networks is by a master equation that governs the dynamic evolution of the joint probability mass function of the underlying population process and naturally leads to Markovian dynamics for such process. Due however to the nonlinear nature of most reactions and the large size of the underlying state-spaces, computation and analysis of the resulting stochastic population dynamics is a difficult task. This review article provides a coherent and comprehensive coverage of recently developed approaches and methods to tackle this problem. After reviewing a general framework for modeling Markovian reaction networks and giving specific examples, the authors present numerical and computational techniques capable of evaluating or approximating the solution of the master equation, discuss a recently developed approach for studying the stationary behavior of Markovian reaction networks using a potential energy landscape perspective, and provide an introduction to the emerging theory of thermodynamic analysis of such networks. Three representative problems of opinion formation, transcription regulation, and neural network dynamics are used as illustrative examples.

  4. Markovian dynamics on complex reaction networks

    International Nuclear Information System (INIS)

    Goutsias, J.; Jenkinson, G.

    2013-01-01

    Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological, ecological, social, neural, and multi-agent networks. A common approach to modeling such networks is by a master equation that governs the dynamic evolution of the joint probability mass function of the underlying population process and naturally leads to Markovian dynamics for such process. Due however to the nonlinear nature of most reactions and the large size of the underlying state-spaces, computation and analysis of the resulting stochastic population dynamics is a difficult task. This review article provides a coherent and comprehensive coverage of recently developed approaches and methods to tackle this problem. After reviewing a general framework for modeling Markovian reaction networks and giving specific examples, the authors present numerical and computational techniques capable of evaluating or approximating the solution of the master equation, discuss a recently developed approach for studying the stationary behavior of Markovian reaction networks using a potential energy landscape perspective, and provide an introduction to the emerging theory of thermodynamic analysis of such networks. Three representative problems of opinion formation, transcription regulation, and neural network dynamics are used as illustrative examples

  5. Modeling the suppression of boron transient enhanced diffusion in silicon by substitutional carbon incorporation

    Science.gov (United States)

    Ngau, Julie L.; Griffin, Peter B.; Plummer, James D.

    2001-08-01

    Recent work has indicated that the suppression of boron transient enhanced diffusion (TED) in carbon-rich Si is caused by nonequilibrium Si point defect concentrations, specifically the undersaturation of Si self-interstitials, that result from the coupled out-diffusion of carbon interstitials via the kick-out and Frank-Turnbull reactions. This study of boron TED reduction in Si1-x-yGexCy during 750 °C inert anneals has revealed that the use of an additional reaction that further reduces the Si self-interstitial concentration is necessary to describe accurately the time evolved diffusion behavior of boron. In this article, we present a comprehensive model which includes {311} defects, boron-interstitial clusters, a carbon kick-out reaction, a carbon Frank-Turnbull reaction, and a carbon interstitial-carbon substitutional (CiCs) pairing reaction that successfully simulates carbon suppression of boron TED at 750 °C for anneal times ranging from 10 s to 60 min.

  6. Modeling the suppression of boron transient enhanced diffusion in silicon by substitutional carbon incorporation

    International Nuclear Information System (INIS)

    Ngau, Julie L.; Griffin, Peter B.; Plummer, James D.

    2001-01-01

    Recent work has indicated that the suppression of boron transient enhanced diffusion (TED) in carbon-rich Si is caused by nonequilibrium Si point defect concentrations, specifically the undersaturation of Si self-interstitials, that result from the coupled out-diffusion of carbon interstitials via the kick-out and Frank--Turnbull reactions. This study of boron TED reduction in Si 1-x-y Ge x C y during 750 o C inert anneals has revealed that the use of an additional reaction that further reduces the Si self-interstitial concentration is necessary to describe accurately the time evolved diffusion behavior of boron. In this article, we present a comprehensive model which includes {311} defects, boron-interstitial clusters, a carbon kick-out reaction, a carbon Frank--Turnbull reaction, and a carbon interstitial-carbon substitutional (C i C s ) pairing reaction that successfully simulates carbon suppression of boron TED at 750 o C for anneal times ranging from 10 s to 60 min. copyright 2001 American Institute of Physics

  7. Effects of electrostatic interactions on electron transfer reactions

    International Nuclear Information System (INIS)

    Hickel, B.

    1987-01-01

    The fast reactions of electron transfer are studied by pulse radiolysis. This technique allows the creation in about 10 -8 second radicals and radical ions with high redox potentials. For solvated electrons electrostatic interaction on the kinetics of reactions limited by diffusion is described by Debye's equation when ion mobility is known. Deviation from theory can occur in ion pairs formation. This is evidenced experimentally for anions by cation complexation with a cryptate. Relatively slow reactions are more sensitive to electrostatic interactions than limited by diffusion. If ion pairs are not formed kinetics constant depends on dielectric constant of solvent and reaction radius. Experimentally is studied the effect of electrostatic interaction on the rate constants of solvated electrons with anions and cations in water-ethanol mixtures where the dielectric constant change from 80 to 25 at room temperature. 17 refs

  8. PENTrack-a simulation tool for ultracold neutrons, protons, and electrons in complex electromagnetic fields and geometries

    Science.gov (United States)

    Schreyer, W.; Kikawa, T.; Losekamm, M. J.; Paul, S.; Picker, R.

    2017-06-01

    Modern precision experiments trapping low-energy particles require detailed simulations of particle trajectories and spin precession to determine systematic measurement limitations and apparatus deficiencies. We developed PENTrack, a tool that allows to simulate trajectories of ultracold neutrons and their decay products-protons and electrons-and the precession of their spins in complex geometries and electromagnetic fields. The interaction of ultracold neutrons with matter is implemented with the Fermi-potential formalism and diffuse scattering using Lambert and microroughness models. The results of several benchmark simulations agree with STARucn v1.2, uncovered several flaws in Geant4 v10.2.2, and agree with experimental data. Experiment geometry and electromagnetic fields can be imported from commercial computer-aided-design and finite-element software. All simulation parameters are defined in simple text files allowing quick changes. The simulation code is written in C++ and is freely available at github.com/wschreyer/PENTrack.git.

  9. Identifying Slow Molecular Motions in Complex Chemical Reactions.

    Science.gov (United States)

    Piccini, GiovanniMaria; Polino, Daniela; Parrinello, Michele

    2017-09-07

    We have studied the cyclization reaction of deprotonated 4-chloro-1-butanethiol to tetrahydrothiophene by means of well-tempered metadynamics. To properly select the collective variables, we used the recently proposed variational approach to conformational dynamics within the framework of metadyanmics. This allowed us to select the appropriate linear combinations from a set of collective variables representing the slow degrees of freedom that best describe the slow modes of the reaction. We performed our calculations at three different temperatures, namely, 300, 350, and 400 K. We show that the choice of such collective variables allows one to easily interpret the complex free-energy surface of such a reaction by univocal identification of the conformers belonging to reactants and product states playing a fundamental role in the reaction mechanism.

  10. PHAST--a program for simulating ground-water flow, solute transport, and multicomponent geochemical reactions

    Science.gov (United States)

    Parkhurst, David L.; Kipp, Kenneth L.; Engesgaard, Peter; Charlton, Scott R.

    2004-01-01

    The computer program PHAST simulates multi-component, reactive solute transport in three-dimensional saturated ground-water flow systems. PHAST is a versatile ground-water flow and solute-transport simulator with capabilities to model a wide range of equilibrium and kinetic geochemical reactions. The flow and transport calculations are based on a modified version of HST3D that is restricted to constant fluid density and constant temperature. The geochemical reactions are simulated with the geochemical model PHREEQC, which is embedded in PHAST. PHAST is applicable to the study of natural and contaminated ground-water systems at a variety of scales ranging from laboratory experiments to local and regional field scales. PHAST can be used in studies of migration of nutrients, inorganic and organic contaminants, and radionuclides; in projects such as aquifer storage and recovery or engineered remediation; and in investigations of the natural rock-water interactions in aquifers. PHAST is not appropriate for unsaturated-zone flow, multiphase flow, density-dependent flow, or waters with high ionic strengths. A variety of boundary conditions are available in PHAST to simulate flow and transport, including specified-head, flux, and leaky conditions, as well as the special cases of rivers and wells. Chemical reactions in PHAST include (1) homogeneous equilibria using an ion-association thermodynamic model; (2) heterogeneous equilibria between the aqueous solution and minerals, gases, surface complexation sites, ion exchange sites, and solid solutions; and (3) kinetic reactions with rates that are a function of solution composition. The aqueous model (elements, chemical reactions, and equilibrium constants), minerals, gases, exchangers, surfaces, and rate expressions may be defined or modified by the user. A number of options are available to save results of simulations to output files. The data may be saved in three formats: a format suitable for viewing with a text editor; a

  11. Effective dynamics along given reaction coordinates, and reaction rate theory.

    Science.gov (United States)

    Zhang, Wei; Hartmann, Carsten; Schütte, Christof

    2016-12-22

    In molecular dynamics and related fields one considers dynamical descriptions of complex systems in full (atomic) detail. In order to reduce the overwhelming complexity of realistic systems (high dimension, large timescale spread, limited computational resources) the projection of the full dynamics onto some reaction coordinates is examined in order to extract statistical information like free energies or reaction rates. In this context, the effective dynamics that is induced by the full dynamics on the reaction coordinate space has attracted considerable attention in the literature. In this article, we contribute to this discussion: we first show that if we start with an ergodic diffusion process whose invariant measure is unique then these properties are inherited by the effective dynamics. Then, we give equations for the effective dynamics, discuss whether the dominant timescales and reaction rates inferred from the effective dynamics are accurate approximations of such quantities for the full dynamics, and compare our findings to results from approaches like Mori-Zwanzig, averaging, or homogenization. Finally, by discussing the algorithmic realization of the effective dynamics, we demonstrate that recent algorithmic techniques like the "equation-free" approach and the "heterogeneous multiscale method" can be seen as special cases of our approach.

  12. Lie and Q-Conditional Symmetries of Reaction-Diffusion-Convection Equations with Exponential Nonlinearities and Their Application for Finding Exact Solutions

    Directory of Open Access Journals (Sweden)

    Roman Cherniha

    2018-04-01

    Full Text Available This review is devoted to search for Lie and Q-conditional (nonclassical symmetries and exact solutions of a class of reaction-diffusion-convection equations with exponential nonlinearities. A complete Lie symmetry classification of the class is derived via two different algorithms in order to show that the result depends essentially on the type of equivalence transformations used for the classification. Moreover, a complete description of Q-conditional symmetries for PDEs from the class in question is also presented. It is shown that all the well-known results for reaction-diffusion equations with exponential nonlinearities follow as particular cases from the results derived for this class of reaction-diffusion-convection equations. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found by means of different techniques. Finally, an application of the exact solutions for solving boundary-value problems arising in population dynamics is presented.

  13. Adaptive exponential synchronization of delayed neural networks with reaction-diffusion terms

    International Nuclear Information System (INIS)

    Sheng Li; Yang Huizhong; Lou Xuyang

    2009-01-01

    This paper presents an exponential synchronization scheme for a class of neural networks with time-varying and distributed delays and reaction-diffusion terms. An adaptive synchronization controller is derived to achieve the exponential synchronization of the drive-response structure of neural networks by using the Lyapunov stability theory. At the same time, the update laws of parameters are proposed to guarantee the synchronization of delayed neural networks with all parameters unknown. It is shown that the approaches developed here extend and improve the ideas presented in recent literatures.

  14. Simulation of the diffusion equation on a type-II quantum computer

    International Nuclear Information System (INIS)

    Berman, G.P.; Kamenev, D.I.; Ezhov, A.A.; Yepez, J.

    2002-01-01

    A lattice-gas algorithm for the one-dimensional diffusion equation is realized using radio frequency pulses in a one-dimensional spin system. The model is a large array of quantum two-qubit nodes interconnected by the nearest-neighbor classical communication channels. We present a quantum protocol for implementation of the quantum collision operator and a method for initialization and reinitialization of quantum states. Numerical simulations of the quantum-classical dynamics are in good agreement with the analytic solution for the diffusion equation

  15. Solid state reaction studies in Fe{sub 3}O{sub 4}–TiO{sub 2} system by diffusion couple method

    Energy Technology Data Exchange (ETDEWEB)

    Ren, Zhongshan [State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083 (China); School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083 (China); Hu, Xiaojun, E-mail: huxiaojun@ustb.edu.cn [State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083 (China); School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083 (China); Xue, Xiangxin [School of Materials and Metallurgy, Northeastern University, Shenyang 110006 (China); Chou, Kuochih [State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083 (China); School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083 (China)

    2013-12-15

    Highlights: •The solid state reactions of Fe2O3-TiO2 system was studied by the diffusion couple method. •Different products were formed by diffusion, and the FeTiO3 was more stable phase. •The inter-diffusion coefficients and diffusion activation energy were estimated. -- Abstract: The solid state reactions in Fe{sub 3}O{sub 4}–TiO{sub 2} system has been studied by diffusion couple experiments at 1323–1473 K, in which the oxygen partial pressure was controlled by the CO–CO{sub 2} gas mixture. The XRD analysis was used to confirm the phases of the inter-compound, and the concentration profiles were determined by electron probe microanalysis (EPMA). Based on the concentration profile of Ti, the inter-diffusion coefficients in Fe{sub 3}O{sub 4} phase, which were both temperature and concentration of Ti ions dependent, were calculated by the modified Boltzmann–Matano method. According to the relation between the thickness of diffusion layer and temperature, the diffusion coefficient of the Fe{sub 3}O{sub 4}–TiO{sub 2} system was obtained. According to the Arrhenius equation, the estimated diffusion activation energy was about 282.1 ± 18.8 kJ mol{sup −1}.

  16. Pattern formation in three-dimensional reaction-diffusion systems

    Science.gov (United States)

    Callahan, T. K.; Knobloch, E.

    1999-08-01

    Existing group theoretic analysis of pattern formation in three dimensions [T.K. Callahan, E. Knobloch, Symmetry-breaking bifurcations on cubic lattices, Nonlinearity 10 (1997) 1179-1216] is used to make specific predictions about the formation of three-dimensional patterns in two models of the Turing instability, the Brusselator model and the Lengyel-Epstein model. Spatially periodic patterns having the periodicity of the simple cubic (SC), face-centered cubic (FCC) or body-centered cubic (BCC) lattices are considered. An efficient center manifold reduction is described and used to identify parameter regimes permitting stable lamellæ, SC, FCC, double-diamond, hexagonal prism, BCC and BCCI states. Both models possess a special wavenumber k* at which the normal form coefficients take on fixed model-independent ratios and both are described by identical bifurcation diagrams. This property is generic for two-species chemical reaction-diffusion models with a single activator and inhibitor.

  17. Sensitive determination of trace mercury by UV-visible diffuse reflectance spectroscopy after complexation and membrane filtration-enrichment.

    Science.gov (United States)

    Yin, Changhai; Iqbal, Jibran; Hu, Huilian; Liu, Bingxiang; Zhang, Lei; Zhu, Bilin; Du, Yiping

    2012-09-30

    A simple, sensitive and selective solid phase reflectometry method is proposed for the determination of trace mercury in aqueous samples. The complexation reagent dithizone was firstly injected into the properly buffered solution with vigorous stirring, which started a simultaneous formation of nanoparticles suspension of dithizone and its complexation reaction with the mercury(II) ions to make Hg-dithizone nanoparticles. After a definite time, the mixture was filtered with membrane, and then quantified directly on the surface of the membrane by using integrating sphere accessory of the UV-visible spectrophotometer. The quantitative analysis was carried out at a wavelength of 485 nm since it yielded the largest difference in diffuse reflectance spectra before and after reaction with mercury(II).A good linear correlation in the range of 0.2-4.0 μg/L with a squared correlation coefficient (R(2)) of 0.9944 and a detection limit of 0.12 μg/L were obtained. The accuracy of the method was evaluated by the analysis of spiked mercury(II) concentrations determined using this method along with those determined by the atomic fluorescence mercury vapourmeter and the results obtained were in good agreement. The proposed method was applied to the determination of mercury in tap water and river water samples with the recovery in an acceptable range (95.7-105.3%). Copyright © 2012 Elsevier B.V. All rights reserved.

  18. Convection and reaction in a diffusive boundary layer in a porous medium: nonlinear dynamics.

    Science.gov (United States)

    Andres, Jeanne Therese H; Cardoso, Silvana S S

    2012-09-01

    We study numerically the nonlinear interactions between chemical reaction and convective fingering in a diffusive boundary layer in a porous medium. The reaction enhances stability by consuming a solute that is unstably distributed in a gravitational field. We show that chemical reaction profoundly changes the dynamics of the system, by introducing a steady state, shortening the evolution time, and altering the spatial patterns of velocity and concentration of solute. In the presence of weak reaction, finger growth and merger occur effectively, driving strong convective currents in a thick layer of solute. However, as the reaction becomes stronger, finger growth is inhibited, tip-splitting is enhanced and the layer of solute becomes much thinner. Convection enhances the mass flux of solute consumed by reaction in the boundary layer but has a diminishing effect as reaction strength increases. This nonlinear behavior has striking differences to the density fingering of traveling reaction fronts, for which stronger chemical kinetics result in more effective finger merger owing to an increase in the speed of the front. In a boundary layer, a strong stabilizing effect of reaction can maintain a long-term state of convection in isolated fingers of wavelength comparable to that at onset of instability.

  19. Multidimensional simulation of radon diffusion through earthen covers

    International Nuclear Information System (INIS)

    Mayer, D.W.; Gee, G.W.

    1983-01-01

    The purpose of this report is to document applications of the RADMD model used at PNL to perform analyses of radon diffusion through uranium mill tailings cover systems. The accuracy of the numerical formulation of the RADMD model was demonstrated through a comparison with a two-dimensional analytic solution to the radon diffusion equation. Excellent agreement was obtained between two-dimensional radon concentration profiles predicted by RADMD and those obtained with the analytic solution. A simulation was made of radon diffusion into a test canister using the two dimensional capabilities of RADMD. The radon flux profile was computed and illustrates the effects of the canister on the surface radon flux. The influence of the canister on the radon flux was shown to be significant under certain circumstances. Defects in earthen cover systems were evaluated using the three dimensional capabilities of RADMD. The results support the expectation that defective covers can increase the surface flux from a covered talings pile. Compared to a cover with no defects, radon flux could be elevated by as much as a factor of three when 20% of the radon control layer area contained pockets of reduced moisture. The effects of temporal and spatial variations in moisture content have been modeled by coupling RADMD with a variable saturated flow model. Two dimensional simulations were made of the time dependence of radon flux from a tailings site before and after cover placement. The results demonstrated the expected flux reduction produced by a thick earthen cover. Time dependence of the radon flux after cover placement was attributed to slight changes in moisture content of the cover material with time. The particular cover studied had a compacted clay layer that effectively attenuated the radon

  20. Classical simulations of heavy-ion fusion reactions and weakly ...

    Indian Academy of Sciences (India)

    82, No. 5. — journal of. May 2014 physics pp. 879–891. Classical simulations of heavy-ion fusion reactions and weakly-bound projectile breakup reactions ... on the collision energy and the moment of inertia of the deformed nucleus. ... where each individual nucleus consists of a number of protons and neutrons, in some.