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.

Two-state random walk model of lattice diffusion - 1. Self-correlation function

International Nuclear Information System (INIS)

Balakrishnan, V.; Venkataraman, G.

1981-01-01

Diffusion with interruptions (arising from localized oscillations, or traps, or mixing between jump diffusion and fluid-like diffusion, etc.) is a very general phenomenon. Its manifestations range from superionic conductance to the behaviour of hydrogen in metals. Based on a continuous-time random walk approach, we present a comprehensive two-state random walk model for the diffusion of a particle on a lattice, incorporating arbitrary holding-time distributions for both localized residence at the sites and inter-site flights, and also the correct first-waiting-time distributions. A synthesis is thus achieved of the two extremes of jump diffusion (zero flight time) and fluid-like diffusion (zero residence time). Various earlier models emerge as special cases of our theory. Among the noteworthy results obtained are: closed-form solutions (in d dimensions, and with arbitrary directional bias) for temporarily uncorrelated jump diffusion and for the fluid diffusion counterpart; a compact, general formula for the mean square displacement; the effects of a continuous spectrum of time scales in the holding-time distributions, etc. The dynamic mobility and the structure factor for 'oscillatory diffusion' are taken up in part 2. (author)

Reaction-diffusion on the fully-connected lattice: A+A\\rightarrow A

Science.gov (United States)

Turban, Loïc; Fortin, Jean-Yves

2018-04-01

Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong fluctuations in low dimensions. In this work we study this problem on the fully-connected lattice, an infinite-dimensional system in the thermodynamic limit, for which mean-field behaviour is expected. Exact expressions for the particle density distribution at a given time and survival time distribution for a given number of particles are obtained. In particular, we show that the time needed to reach a finite number of surviving particles (vanishing density in the scaling limit) displays strong fluctuations and extreme value statistics, characterized by a universal class of non-Gaussian distributions with singular behaviour.

Diffusion in lattice Lorentz gases with mixtures of point scatterers

International Nuclear Information System (INIS)

Acedo, L.; Santos, A.

1994-01-01

Monte Carlo simulations are carried out to evaluate the diffusion coefficient in some lattice Lorentz gases with mixtures of point scatterers in the limit of a low concentration of scatterers. Two models on a square lattice are considered: (a) right and left stochastic rotators plus pure reflectors and (b) right and left stochastic mirrors plus pure reflectors. The simulation data are compared with the repeated ring approximation (RRA). The agreement is excellent for models in the absence of pure reflectors, suggesting that the RRA gives the correct diffusion coefficient for those cases. As the fraction x B of reflectors increases, the diffusion coefficient decreases and seems to vanish at x B c congruent 0.8 (percolation threshold) with a critical exponent μ congruent 2 (stochastic model) or μ congruent 3 (deterministic rotator model)

Lattice dynamics and thermal diffuse scattering for molecular crystals

International Nuclear Information System (INIS)

Kroon, P.A.

1977-01-01

Thermal diffuse scattering (TDS) corrections on the observed reflection intensities in the accurate determination of crystal structures by X-ray diffraction are emphasized. A lattice-dynamical model and procedure for lattice-dynamical calculations are set up. Expression for first- and second-order TDS intensity distributions are derived. A comparison with other models is made. First-order TDS corrections for naphtalene at 100 K are presented

Analytic treatment of nuclear spin-lattice relaxation for diffusion in a cone model

Science.gov (United States)

Sitnitsky, A. E.

2011-12-01

We consider nuclear spin-lattice relaxation rate resulted from a diffusion equation for rotational wobbling in a cone. We show that the widespread point of view that there are no analytical expressions for correlation functions for wobbling in a cone model is invalid and prove that nuclear spin-lattice relaxation in this model is exactly tractable and amenable to full analytical description. The mechanism of relaxation is assumed to be due to dipole-dipole interaction of nuclear spins and is treated within the framework of the standard Bloemberger, Purcell, Pound-Solomon scheme. We consider the general case of arbitrary orientation of the cone axis relative the magnetic field. The BPP-Solomon scheme is shown to remain valid for systems with the distribution of the cone axes depending only on the tilt relative the magnetic field but otherwise being isotropic. We consider the case of random isotropic orientation of cone axes relative the magnetic field taking place in powders. Also we consider the cases of their predominant orientation along or opposite the magnetic field and that of their predominant orientation transverse to the magnetic field which may be relevant for, e.g., liquid crystals. Besides we treat in details the model case of the cone axis directed along the magnetic field. The latter provides direct comparison of the limiting case of our formulas with the textbook formulas for free isotropic rotational diffusion. The dependence of the spin-lattice relaxation rate on the cone half-width yields results similar to those predicted by the model-free approach.

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

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.

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.

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.

Dynamical behaviour of the coupled diffusion map lattice

International Nuclear Information System (INIS)

Wei Wang; Cerdeira, H.A.

1993-10-01

In this paper we report the dynamical study of a coupled diffusive map lattice with the coupling between the elements only through the bifurcation parameter of the mapping function. The diffusive process of the lattice from an initially random distribution state to a homogeneous one and the stable range of the diffusive homogeneous attractor are discussed. For various coupling strengths we find that there are several types of spatio-temporal structures. In addition, the evolution of the lattice into chaos is studied and a largest Lyapunov exponent is used to characterize the dynamical behaviour. (author). 22 refs, 9 figs

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

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.

Concentration contours in lattics and grain boundary diffusion in a polycrystalline solid

International Nuclear Information System (INIS)

Kim, Yong Soo; Jae, Won Mok; El Saied, Usama; Olander, Donald R.

1995-01-01

Grain boundary diffusion plays significant role in the fission gas release, which is one of the crucial processes dominating nuclear fuel performance. Gaseous fission products such as Xe and Kr generated inside fuel pellet have to diffuse in the lattice and in the grain boundary before they reach open space in the fuel rod. In the mean time, the grains in the fuel pellet grow and shrink according to grain growth kinetics, especially at elevated temperature at which nuclear reactors are operating. Thus the boundary movement ascribed to the grain growth greatly influences the fission gas release rate by lengthening or shortening the lattice diffusion distance, which is the rate limiting step. Sweeping fission gases by the moving boundary contributes to the increment of the fission gas release as well. Lattice and grain boundary diffusion processes in the fission gas release can be studied by 'tracer diffusion' technique, by which grain boundary diffusivity can be estimated and used directly for low burn up fission gas release analysis. However, even for tracer diffusion analysis, taking both the intragranular grain growth and the diffusion processes simultaneously into consideration is not easy. Only a few models accounting for the both processes are available and mostly handle them numerically. Numerical solutions are limited in the practical use. Here in this paper, an approximate analytical solution of the lattice and stationary grain boundary diffusion in a polycrystalline solid is developed for the tracer diffusion techniques. This short closed form solution is compared to available exact and numerical solutions and turns out to be acceptably accurate. It can be applied to the theoretical modeling and the experimental analysis, especially PIE (post irradiation examination), of low burn up fission gas release

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...

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.

Maxwell iteration for the lattice Boltzmann method with diffusive scaling

Science.gov (United States)

Zhao, Weifeng; Yong, Wen-An

2017-03-01

In this work, we present an alternative derivation of the Navier-Stokes equations from Bhatnagar-Gross-Krook models of the lattice Boltzmann method with diffusive scaling. This derivation is based on the Maxwell iteration and can expose certain important features of the lattice Boltzmann solutions. Moreover, it will be seen to be much more straightforward and logically clearer than the existing approaches including the Chapman-Enskog expansion.

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

A realistic molecular-level description of catalytic reactions on single-crystal metal surfaces can be provided by stochastic multisite lattice-gas (msLG) models. This approach has general applicability, although in this report, we will focus on the example of CO-oxidation on the unreconstructed fcc metal (1 0 0) or M(1 0 0) surfaces of common catalyst metals M = Pd, Rh, Pt and Ir (i.e., avoiding regimes where Pt and Ir reconstruct). These models can capture the thermodynamics and kinetics of adsorbed layers for the individual reactants species, such as CO/M(1 0 0) and O/M(1 0 0), as well as the interaction and reaction between different reactant species in mixed adlayers, such as (CO + O)/M(1 0 0). The msLG models allow population of any of hollow, bridge, and top sites. This enables a more flexible and realistic description of adsorption and adlayer ordering, as well as of reaction configurations and configuration-dependent barriers. Adspecies adsorption and interaction energies, as well as barriers for various processes, constitute key model input. The choice of these energies is guided by experimental observations, as well as by extensive Density Functional Theory analysis. Model behavior is assessed via Kinetic Monte Carlo (KMC) simulation. We also address the simulation challenges and theoretical ramifications associated with very rapid diffusion and local equilibration of reactant adspecies such as CO. These msLG models are applied to describe adsorption, ordering, and temperature programmed desorption (TPD) for individual CO/M(1 0 0) and O/M(1 0 0) reactant adlayers. In addition, they are also applied to predict mixed (CO + O)/M(1 0 0) adlayer structure on the nanoscale, the complete bifurcation diagram for reactive steady-states under continuous flow conditions, temperature programmed reaction (TPR) spectra, and titration reactions for the CO-oxidation reaction. Extensive and reasonably successful comparison of model predictions is made with experimental

Cellular automaton model of mass transport with chemical reactions

International Nuclear Information System (INIS)

Karapiperis, T.; Blankleider, B.

1993-10-01

The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes advection and diffusion in a simple way, and as no restriction is placed on the number of particles at a lattice site, it is also able to describe a wide variety of chemical reactions. Assuming molecular chaos and a smooth density function, we obtain the standard reaction-transport equations in the continuum limit. Simulations on one-and two-dimensional lattices show that the discrete model can be used to approximate the solutions of the continuum equations. We discuss discrepancies which arise from correlations between molecules and how these discrepancies disappear as the continuum limit is approached. Of particular interest are simulations displaying long-time behaviour which depends on long-wavelength statistical fluctuations not accounted for by the standard equations. The model is applied to the reactions a + b ↔ c and a + b → c with homogeneous and inhomogeneous initial conditions as well as to systems subject to autocatalytic reactions and displaying spontaneous formation of spatial concentration patterns. (author) 9 figs., 34 refs

Stochastic flows, reaction-diffusion processes, and morphogenesis

International Nuclear Information System (INIS)

Kozak, J.J.; Hatlee, M.D.; Musho, M.K.; Politowicz, P.A.; Walsh, C.A.

1983-01-01

Recently, an exact procedure has been introduced [C. A. Walsh and J. J. Kozak, Phys. Rev. Lett.. 47: 1500 (1981)] for calculating the expected walk length for a walker undergoing random displacements on a finite or infinite (periodic) d-dimensional lattice with traps (reactive sites). The method (which is based on a classification of the symmetry of the sites surrounding the central deep trap and a coding of the fate of the random walker as it encounters a site of given symmetry) is applied here to several problems in lattice statistics for each of which exact results are presented. First, we assess the importance of lattice geometry in influencing the efficiency of reaction-diffusion processs in simple and multiple trap systems by reporting values of for square (cubic) versus hexagonal lattices in d = 2,3. We then show how the method may be applied to variable-step (distance-dependent) walks for a single walker on a given lattice and also demonstrate the calculation of the expected walk length for the case of multiple walkers. Finally, we make contact with recent discussions of ''mixing'' by showing that the degree of chaos associated with flows in certain lattice-systems can be calibrated by monitoring the lattice walks induced by the Poincare map of a certain parabolic function

Diffusion in heterogeneous lattices

Czech Academy of Sciences Publication Activity Database

Tarasenko, Alexander; Jastrabík, Lubomír

2010-01-01

Roč. 256, č. 17 (2010), s. 5137-5144 ISSN 0169-4332 R&D Projects: GA AV ČR KAN301370701; GA MŠk(CZ) 1M06002 Institutional research plan: CEZ:AV0Z10100522 Keywords : lattice- gas systems * diffusion * Monte Carlo simulations Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.795, year: 2010

Combined measurement of surface, grain boundary and lattice diffusion coefficients on olivine bi-crystals

Science.gov (United States)

Marquardt, Katharina; Dohmen, Ralf; Wagner, Johannes

2014-05-01

Diffusion along interface and grain boundaries provides an efficient pathway and may control chemical transport in rocks as well as their mechanical strength. Besides the significant relevance of these diffusion processes for various geologic processes, experimental data are still very limited (e.g., Dohmen & Milke, 2010). Most of these data were measured using polycrystalline materials and the formalism of LeClaire (1951) to fit integrated concentration depth profiles. To correctly apply this formalism, certain boundary conditions of the diffusion problem need to be fulfilled, e.g., surface diffusion is ignored, and furthermore the lattice diffusion coefficient has to be known from other studies or is an additional fitting parameter, which produces some ambiguity in the derived grain boundary diffusion coefficients. We developed an experimental setup where we can measure the lattice and grain boundary diffusion coefficients simultaneously but independent and demonstrate the relevance of surface diffusion for typical grain boundary diffusion experiments. We performed Mg2SiO4 bicrystal diffusion experiments, where a single grain boundary is covered by a thin-film of pure Ni2SiO4 acting as diffusant source, produced by pulsed laser deposition. The investigated grain boundary is a 60° (011)/[100]. This specific grain boundary configuration was modeled using molecular dynamics for comparison with the experimental observations in the transmission electron microscope (TEM). Both, experiment and model are in good agreement regarding the misorientation, whereas there are still some disagreements regarding the strain fields along the grain boundary that are of outmost importance for the strengths of the material. The subsequent diffusion experiments were carried out in the temperature range between 800° and 1450° C. The inter diffusion profiles were measured using the TEMs energy dispersive x-ray spectrometer standardized using the Cliff-Lorimer equation and EMPA

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.

Diffusion in Deterministic Interacting Lattice Systems

Science.gov (United States)

Medenjak, Marko; Klobas, Katja; Prosen, Tomaž

2017-09-01

We study reversible deterministic dynamics of classical charged particles on a lattice with hard-core interaction. It is rigorously shown that the system exhibits three types of transport phenomena, ranging from ballistic, through diffusive to insulating. By obtaining an exact expressions for the current time-autocorrelation function we are able to calculate the linear response transport coefficients, such as the diffusion constant and the Drude weight. Additionally, we calculate the long-time charge profile after an inhomogeneous quench and obtain diffusive profilewith the Green-Kubo diffusion constant. Exact analytical results are corroborated by Monte Carlo simulations.

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.

A lattice-model representation of continuous-time random walks

International Nuclear Information System (INIS)

Campos, Daniel; Mendez, Vicenc

2008-01-01

We report some ideas for constructing lattice models (LMs) as a discrete approach to the reaction-dispersal (RD) or reaction-random walks (RRW) models. The analysis of a rather general class of Markovian and non-Markovian processes, from the point of view of their wavefront solutions, let us show that in some regimes their macroscopic dynamics (front speed) turns out to be different from that by classical reaction-diffusion equations, which are often used as a mean-field approximation to the problem. So, the convenience of a more general framework as that given by the continuous-time random walks (CTRW) is claimed. Here we use LMs as a numerical approach in order to support that idea, while in previous works our discussion was restricted to analytical models. For the two specific cases studied here, we derive and analyze the mean-field expressions for our LMs. As a result, we are able to provide some links between the numerical and analytical approaches studied

A lattice-model representation of continuous-time random walks

Energy Technology Data Exchange (ETDEWEB)

Campos, Daniel [School of Mathematics, Department of Applied Mathematics, University of Manchester, Manchester M60 1QD (United Kingdom); Mendez, Vicenc [Grup de Fisica Estadistica, Departament de Fisica, Universitat Autonoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain)], E-mail: daniel.campos@uab.es, E-mail: vicenc.mendez@uab.es

2008-02-29

We report some ideas for constructing lattice models (LMs) as a discrete approach to the reaction-dispersal (RD) or reaction-random walks (RRW) models. The analysis of a rather general class of Markovian and non-Markovian processes, from the point of view of their wavefront solutions, let us show that in some regimes their macroscopic dynamics (front speed) turns out to be different from that by classical reaction-diffusion equations, which are often used as a mean-field approximation to the problem. So, the convenience of a more general framework as that given by the continuous-time random walks (CTRW) is claimed. Here we use LMs as a numerical approach in order to support that idea, while in previous works our discussion was restricted to analytical models. For the two specific cases studied here, we derive and analyze the mean-field expressions for our LMs. As a result, we are able to provide some links between the numerical and analytical approaches studied.

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)

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.

Diffusion on unstructured triangular grids using Lattice Boltzmann

NARCIS (Netherlands)

Sman, van der R.G.M.

2004-01-01

In this paper, we present a Lattice Boltzmann scheme for diffusion on unstructured triangular grids. In this formulation there is no need for interpolation, as is required in other LB schemes on irregular grids. At the end of the propagation step, the lattice gas particles arrive exactly at

Lattice Boltzmann scheme for diffusion on triangular grids

NARCIS (Netherlands)

Sman, van der R.G.M.

2003-01-01

In this paper we present a Lattice Boltzmann scheme for diffusion on it unstructured triangular grids. In this formulation of a LB for irregular grids there is no need for interpolation, which is required in other LB schemes on irregular grids. At the end of the propagation step the lattice gas

The Role of Lattice Vibrations in Adatom Diffusion at Metal Stepped Surfaces

International Nuclear Information System (INIS)

Durakanoglu, S.

2004-01-01

Diffusion of a single atom on metal surfaces remains a subject of continuing interest in the surface science community because of the important role it plays in several technologically important phenomena such as thin-film and eptaxial growth, catalysis and chemical reactions. Except for a few studies, most of theoretical works, ranging from molecular dynamic simulations to first principle electronic structure calculations, are devoted to determination of the characteristics of the diffusion processes and the energy barriers, neglecting the contribution of lattice vibrations in adatom diffusion. However, in a series of theoretical works on self-diffusion on the flat surfaces of Cu(100), Ag(100) and Ni(100), Ulrike et al.[1-3], showed that the vibrational contributions are important and should be included in any complete description of the temperature dependence of the diffusion coefficient. In this work, it is our aim to examine the role of lattice vibrations in adatom diffusion at stepped surfaces of Cu(100) and Ni(100) within the framework of transition state theory. Ehrlich-Shwoebel energy barriers for an adatom diffusing over a step-edge are calculated through the inclusion of vibrational internal energy. Local vibrational density of states, main ingredient to the vibrational thermodynamic functions, are calculated in the harmonic approximation, using real space Green's function method with the force constants derived from interaction potentials based on the embedded atom method. We emphasize the sensitivity of the local vibrational density of states to the local atomic environment. We, furthermore, discuss the contribution of thermodynamic functions calculated from local vibrational density of states to the prefactors in diffusion coefficient

Theory of spin-lattice relaxation of diffusing light nuclei in glasses

International Nuclear Information System (INIS)

Schirmer, A.; Schirmacher, W.

1988-01-01

NMR data of diffusion-induced spin-lattice relaxation in glasses cannot generally be interpreted in the framework of the classical theory of Bloembergen, Purcell and Pound (BPP). Since it is based on exponential density relaxation, generally bnot found in glasses, the BPP formula must be generalized. Here a combination of standard relaxation theory with a hopping model for diffusion in glasses is present. It is shown that the observed anomaties in the NMR data can be explained as a result of anomalous diffusion. 25 refs.; 1 figure

Parallel diffusion length on thermal neutrons in rod type lattices

International Nuclear Information System (INIS)

Ahmed, T.; Siddiqui, S.A.M.M.; Khan, A.M.

1981-11-01

Calculation of diffusion lengths of thermal neutrons in lead-water and aluminum water lattices in direction parallel to the rods are performed using one group diffusion equation together with Shevelev transport correction. The formalism is then applied to two practical cases, the Kawasaki (Hitachi) and the Douglas point (Candu) reactor lattices. Our results are in good agreement with the observed values. (author)

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

Diffusion coefficients for multi-step persistent random walks on lattices

International Nuclear Information System (INIS)

Gilbert, Thomas; Sanders, David P

2010-01-01

We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which enables us to obtain explicit expressions for the diffusion coefficients of walks with a two-step memory on different classes of one-, two- and higher dimensional lattices.

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.

A Non-Isothermal Chemical Lattice Boltzmann Model Incorporating Thermal Reaction Kinetics and Enthalpy Changes

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Stuart Bartlett

2017-08-01

Full Text Available The lattice Boltzmann method is an efficient computational fluid dynamics technique that can accurately model a broad range of complex systems. As well as single-phase fluids, it can simulate thermohydrodynamic systems and passive scalar advection. In recent years, it also gained attention as a means of simulating chemical phenomena, as interest in self-organization processes increased. This paper will present a widely-used and versatile lattice Boltzmann model that can simultaneously incorporate fluid dynamics, heat transfer, buoyancy-driven convection, passive scalar advection, chemical reactions and enthalpy changes. All of these effects interact in a physically accurate framework that is simple to code and readily parallelizable. As well as a complete description of the model equations, several example systems will be presented in order to demonstrate the accuracy and versatility of the method. New simulations, which analyzed the effect of a reversible reaction on the transport properties of a convecting fluid, will also be described in detail. This extra chemical degree of freedom was utilized by the system to augment its net heat flux. The numerical method outlined in this paper can be readily deployed for a vast range of complex flow problems, spanning a variety of scientific disciplines.

Lattice Boltzmann scheme for mixture modeling: analysis of the continuum diffusion regimes recovering Maxwell-Stefan model and incompressible Navier-Stokes equations.

Science.gov (United States)

Asinari, Pietro

2009-11-01

A finite difference lattice Boltzmann scheme for homogeneous mixture modeling, which recovers Maxwell-Stefan diffusion model in the continuum limit, without the restriction of the mixture-averaged diffusion approximation, was recently proposed [P. Asinari, Phys. Rev. E 77, 056706 (2008)]. The theoretical basis is the Bhatnagar-Gross-Krook-type kinetic model for gas mixtures [P. Andries, K. Aoki, and B. Perthame, J. Stat. Phys. 106, 993 (2002)]. In the present paper, the recovered macroscopic equations in the continuum limit are systematically investigated by varying the ratio between the characteristic diffusion speed and the characteristic barycentric speed. It comes out that the diffusion speed must be at least one order of magnitude (in terms of Knudsen number) smaller than the barycentric speed, in order to recover the Navier-Stokes equations for mixtures in the incompressible limit. Some further numerical tests are also reported. In particular, (1) the solvent and dilute test cases are considered, because they are limiting cases in which the Maxwell-Stefan model reduces automatically to Fickian cases. Moreover, (2) some tests based on the Stefan diffusion tube are reported for proving the complete capabilities of the proposed scheme in solving Maxwell-Stefan diffusion problems. The proposed scheme agrees well with the expected theoretical results.

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

Quantum Lattice-Gas Model for the Diffusion Equation

National Research Council Canada - National Science Library

Yepez, J

2001-01-01

.... It is a minimal model with two qubits per node of a one-dimensional lattice and it is suitable for implementation on a large array of small quantum computers interconnected by nearest-neighbor...

Influence of blocking effect and energetic disorder on diffusion in one-dimensional lattice

International Nuclear Information System (INIS)

Mai Thi Lan; Nguyen Van Hong; Nguyen Thu Nhan; Hoang Van Hue

2014-01-01

The diffusion in one-dimensional disordered lattice with Gaussian distribution of site and transition energies has been studied by mean of kinetic Monte-Carlo simulation. We focus on investigating the influence of energetic disorders and diffusive particle density on diffusivity. In single-particle case, we used both analytical method and kinetic Monte-Carlo simulation to calculate the quantities that relate to diffusive behavior in disordered systems such as the mean time between two consecutive jumps, correlation factor and diffusion coefficient. The calculation shows a good agreement between analytical and simulation results for all disordered lattice types. In many - particle case, the blocking effect results in decreasing correlation factor F and average time τ jump between two consecutive jumps. With increasing the number of particles, the diffusion coefficient D M decreases for site-energy and transition-energy disordered lattices due to the F-effect affect affects stronger than τ-effect. Furthermore, the blocking effect almost is temperature independent for both lattices. (author)

Final disposal of low and intermediate radioactive waste - aspects of diffusion through cement lattice modelling

International Nuclear Information System (INIS)

Mihai, C.

1998-01-01

The present work performed in our department is related to development of safety assessment programme for the National Repository for Radioactive Waste - Baita, Bihor. The rate of radionuclide release in the proximity of National Repository for Radioactive Waste - Baita, Bihor was minimized by taking into account the multibarrier principle. This implies the uses of a complex system of natural and engineered barriers which should neutralize the main processes of radionuclide migration. In the first component of the system mentioned above, cement lattice, the migration of incorporated radionuclides takes place mainly by diffusion process. The diffusion equation is given for the particular case of cylindrical shape of the container, from which the ratio between the released fraction and the initial quantity of radionuclides is obtained. We studied the process of diffusion in three different materials (the radionuclides used were 65 Zn, 51 Cr, 82 Br). The results obtained allowed a pertinent selection of the material for improvement of retardation factors of cement lattice. (author)

Tracer concentration contours in grain lattice and grain boundary diffusion

International Nuclear Information System (INIS)

Kim, Y. S.; Olander, D. R.

1997-01-01

Grain boundary diffusion plays a significant role in fission gas release, which is one of the crucial processes dominating nuclear fuel performance. Gaseous fission products such as Xe and Kr generated during nuclear fission have to diffuse in the grain lattice and the boundary inside fuel pellets before they reach the open spaces in a fuel rod. These processes can be studied by 'tracer diffusion' techniques, by which grain boundary diffusivity can be estimated and directly used for low burn-up fission gas release analysis. However, only a few models accounting for the both processes are available and mostly handle them numerically due to mathematical complexity. Also the numerical solution has limitations in a practical use. In this paper, an approximate analytical solution in case of stationary grain boundary in a polycrystalline solid is developed for the tracer diffusion techniques. This closed-form solution is compared to available exact and numerical solutions and it turns out that it makes computation not only greatly easier but also more accurate than previous models. It can be applied to theoretical modelings for low burn-up fission gas release phenomena and experimental analyses as well, especially for PIE (post irradiation examination). (author)

Migration of particles on heterogeneous bivariate lattices: the universal analytical expressions for the diffusion coefficients

Czech Academy of Sciences Publication Activity Database

Tarasenko, Alexander; Boháč, Petr; Jastrabík, Lubomír

2015-01-01

Roč. 74, Nov (2015), s. 556-560 ISSN 1386-9477 R&D Projects: GA MŠk LO1409; GA TA ČR TA03010743 Institutional support: RVO:68378271 Keywords : surface diffusion * heterogeneous lattices * lattice-gas models * kinetic Monte Carlo simulation Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.904, year: 2015

Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations

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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.

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

Electrical conductivity and charge diffusion in thermal QCD from the lattice

Energy Technology Data Exchange (ETDEWEB)

Aarts, Gert; Allton, Chris [Department of Physics, College of Science, Swansea University Swansea SA2 8PP (United Kingdom); Amato, Alessandro [Department of Physics, College of Science, Swansea University Swansea SA2 8PP (United Kingdom); Department of Physics and Helsinki Institute of Physics P.O. Box 64, FI-00014 University of Helsinki (Finland); Giudice, Pietro [Universität Münster, Institut für Theoretische Physik Wilhelm-Klemm-Str. 9, D-48149 Münster (Germany); Hands, Simon [Department of Physics, College of Science, Swansea University Swansea SA2 8PP (United Kingdom); Skullerud, Jon-Ivar [Department of Mathematical Physics, National University of Ireland Maynooth Maynooth, Co Kildare (Ireland)

2015-02-27

We present a lattice QCD calculation of the charge diffusion coefficient, the electrical conductivity and various susceptibilities of conserved charges, for a range of temperatures below and above the deconfinement crossover. The calculations include the contributions from up, down and strange quarks. We find that the diffusion coefficient is of the order of 1/(2πT) and has a dip around the crossover temperature. Our results are obtained with lattice simulations containing 2+1 dynamical flavours on anisotropic lattices. The Maximum Entropy Method is used to construct spectral functions from correlators of the conserved vector current.

Lattice Boltzmann method for multi-component, non-continuum mass diffusion

International Nuclear Information System (INIS)

Joshi, Abhijit S; Peracchio, Aldo A; Grew, Kyle N; Chiu, Wilson K S

2007-01-01

Recently, there has been a great deal of interest in extending the lattice Boltzmann method (LBM) to model transport phenomena in the non-continuum regime. Most of these studies have focused on single-component flows through simple geometries. This work examines an ad hoc extension of a recently developed LBM model for multi-component mass diffusion (Joshi et al 2007 J. Phys. D: Appl. Phys. 40 2961) to model mass diffusion in the non-continuum regime. In order to validate the method, LBM results for ternary diffusion in a two-dimensional channel are compared with predictions of the dusty gas model (DGM) over a range of Knudsen numbers. A calibration factor based on the DGM is used in the LBM to correlate Knudsen diffusivity to pore size. Results indicate that the LBM can be a useful tool for predicting non-continuum mass diffusion (Kn > 0.001), but additional research is needed to extend the range of applicability of the algorithm for a larger parameter space. Guidelines are given on using the methodology described in this work to model non-continuum mass transport in more complex geometries where the DGM is not easily applicable. In addition, the non-continuum LBM methodology can be extended to three-dimensions. An envisioned application of this technique is to model non-continuum mass transport in porous solid oxide fuel cell electrodes

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.

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

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

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

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.

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.

Lattice Boltzmann model for numerical relativity.

Science.gov (United States)

Ilseven, E; Mendoza, M

2016-02-01

In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.

Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models

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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.

Lattice animals in diffusion limited binary colloidal system

Science.gov (United States)

Shireen, Zakiya; Babu, Sujin B.

2017-08-01

In a soft matter system, controlling the structure of the amorphous materials has been a key challenge. In this work, we have modeled irreversible diffusion limited cluster aggregation of binary colloids, which serves as a model for chemical gels. Irreversible aggregation of binary colloidal particles leads to the formation of a percolating cluster of one species or both species which are also called bigels. Before the formation of the percolating cluster, the system forms a self-similar structure defined by a fractal dimension. For a one component system when the volume fraction is very small, the clusters are far apart from each other and the system has a fractal dimension of 1.8. Contrary to this, we will show that for the binary system, we observe the presence of lattice animals which has a fractal dimension of 2 irrespective of the volume fraction. When the clusters start inter-penetrating, we observe a fractal dimension of 2.5, which is the same as in the case of the one component system. We were also able to predict the formation of bigels using a simple inequality relation. We have also shown that the growth of clusters follows the kinetic equations introduced by Smoluchowski for diffusion limited cluster aggregation. We will also show that the chemical distance of a cluster in the flocculation regime will follow the same scaling law as predicted for the lattice animals. Further, we will also show that irreversible binary aggregation comes under the universality class of the percolation theory.

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)

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

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

Mechanism of fast lattice diffusion of hydrogen in palladium: Interplay of quantum fluctuations and lattice strain

Science.gov (United States)

Kimizuka, Hajime; Ogata, Shigenobu; Shiga, Motoyuki

2018-01-01

Understanding the underlying mechanism of the nanostructure-mediated high diffusivity of H in Pd is of recent scientific interest and also crucial for industrial applications. Here, we present a decisive scenario explaining the emergence of the fast lattice-diffusion mode of interstitial H in face-centered cubic Pd, based on the quantum mechanical natures of both electrons and nuclei under finite strains. Ab initio path-integral molecular dynamics was applied to predict the temperature- and strain-dependent free energy profiles for H migration in Pd over a temperature range of 150-600 K and under hydrostatic tensile strains of 0.0%-2.4%; such strain conditions are likely to occur in real systems, especially around the elastic fields induced by nanostructured defects. The simulated results revealed that, for preferential H location at octahedral sites, as in unstrained Pd, the activation barrier for H migration (Q ) was drastically increased with decreasing temperature owing to nuclear quantum effects. In contrast, as tetrahedral sites increased in stability with lattice expansion, nuclear quantum effects became less prominent and ceased impeding H migration. This implies that the nature of the diffusion mechanism gradually changes from quantum- to classical-like as the strain is increased. For H atoms in Pd at the hydrostatic strain of ˜2.4 % , we determined that the mechanism promoted fast lattice diffusion (Q =0.11 eV) of approximately 20 times the rate of conventional H diffusion (Q =0.23 eV) in unstrained Pd at a room temperature of 300 K.

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...

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.

Entropy, free energy and phase transitions in the lattice Lotka-Volterra model

International Nuclear Information System (INIS)

Chichigina, O. A.; Tsekouras, G. A.; Provata, A.

2006-01-01

A thermodynamic approach is developed for reactive dynamic models restricted to substrates of arbitrary dimensions, including fractal substrates. The thermodynamic formalism is successfully applied to the lattice Lotka-Volterra (LLV) model of autocatalytic reactions on various lattice substrates. Different regimes of reactions described as phases, and phase transitions, are obtained using this approach. The predictions of thermodynamic theory confirm extensive numerical kinetic Monte Carlo simulations on square and fractal lattices. Extensions of the formalism to multispecies LLV models are also presented

Diffusion of particles over dynamically disordered lattice

Czech Academy of Sciences Publication Activity Database

Tarasenko, Alexander; Jastrabík, Lubomír

2011-01-01

Roč. 13, č. 6 (2011), s. 2300-2306 ISSN 1463-9076 R&D Projects: GA AV ČR KAN301370701; GA MŠk(CZ) 1M06002 Institutional research plan: CEZ:AV0Z10100522 Keywords : diffusion * Monte Carlo simulations * dynamic disordered lattice Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.573, year: 2011

Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations.

Science.gov (United States)

Yang, Xuguang; Shi, Baochang; Chai, Zhenhua

2014-07-01

In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 10(12)).

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.

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.

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.

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.

Communication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice

Energy Technology Data Exchange (ETDEWEB)

Ellery, Adam J.; Simpson, Matthew J. [School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane (Australia); Baker, Ruth E. [Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford (United Kingdom)

2016-05-07

The motion of cells and molecules through biological environments is often hindered by the presence of other cells and molecules. A common approach to modeling this kind of hindered transport is to examine the mean squared displacement (MSD) of a motile tracer particle in a lattice-based stochastic random walk in which some lattice sites are occupied by obstacles. Unfortunately, stochastic models can be computationally expensive to analyze because we must average over a large ensemble of identically prepared realizations to obtain meaningful results. To overcome this limitation we describe an exact method for analyzing a lattice-based model of the motion of an agent moving through a crowded environment. Using our approach we calculate the exact MSD of the motile agent. Our analysis confirms the existence of a transition period where, at first, the MSD does not follow a power law with time. However, after a sufficiently long period of time, the MSD increases in proportion to time. This latter phase corresponds to Fickian diffusion with a reduced diffusivity owing to the presence of the obstacles. Our main result is to provide a mathematically motivated, reproducible, and objective estimate of the amount of time required for the transport to become Fickian. Our new method to calculate this crossover time does not rely on stochastic simulations.

Communication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice

International Nuclear Information System (INIS)

Ellery, Adam J.; Simpson, Matthew J.; Baker, Ruth E.

2016-01-01

The motion of cells and molecules through biological environments is often hindered by the presence of other cells and molecules. A common approach to modeling this kind of hindered transport is to examine the mean squared displacement (MSD) of a motile tracer particle in a lattice-based stochastic random walk in which some lattice sites are occupied by obstacles. Unfortunately, stochastic models can be computationally expensive to analyze because we must average over a large ensemble of identically prepared realizations to obtain meaningful results. To overcome this limitation we describe an exact method for analyzing a lattice-based model of the motion of an agent moving through a crowded environment. Using our approach we calculate the exact MSD of the motile agent. Our analysis confirms the existence of a transition period where, at first, the MSD does not follow a power law with time. However, after a sufficiently long period of time, the MSD increases in proportion to time. This latter phase corresponds to Fickian diffusion with a reduced diffusivity owing to the presence of the obstacles. Our main result is to provide a mathematically motivated, reproducible, and objective estimate of the amount of time required for the transport to become Fickian. Our new method to calculate this crossover time does not rely on stochastic simulations.

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

Lattice gas simulations of replicating domains

International Nuclear Information System (INIS)

Dawson, S.P.; Hasslacher, B.; Pearson, J.E.

1993-01-01

We use the lattice gas cellular automation (LGCA) developed to simulate a process of pattern-formation recently observed in reaction-diffusion systems. We study the reaction mechanism, which is an extension of the Selkov model for glycolytic oscillations. We are able to reproduce the self-replicating domains observed in this work. We use the LGCA simulation to estimate the smallest length-scale on which this process can occur under conditions encountered in the cell. These estimates are similar to those obtained for Turing patterns in the same setting

Lattice gas simulations of replicating domains

Energy Technology Data Exchange (ETDEWEB)

Dawson, S.P.; Hasslacher, B.; Pearson, J.E.

1993-12-31

We use the lattice gas cellular automation (LGCA) developed to simulate a process of pattern-formation recently observed in reaction-diffusion systems. We study the reaction mechanism, which is an extension of the Selkov model for glycolytic oscillations. We are able to reproduce the self-replicating domains observed in this work. We use the LGCA simulation to estimate the smallest length-scale on which this process can occur under conditions encountered in the cell. These estimates are similar to those obtained for Turing patterns in the same setting.

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.

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.

Anomalous spreading of a density front from an infinite continuous source in a concentration-dependent lattice gas automaton diffusion model

CERN Document Server

Kuentz, M

2003-01-01

A two-dimensional lattice gas automaton (LGA) is used for simulating concentration-dependent diffusion in a microscopically random heterogeneous structure. The heterogeneous medium is initialized at a low density rho sub 0 and then submitted to a steep concentration gradient by continuous injection of particles at a concentration rho sub 1 >rho sub 0 from a one-dimensional source to model spreading of a density front. Whereas the nonlinear diffusion equation generally used to describe concentration-dependent diffusion processes predicts a scaling law of the type phi = xt sup - sup 1 sup / sup 2 in one dimension, the spreading process is shown to deviate from the expected t sup 1 sup / sup 2 scaling. The time exponent is found to be larger than 1/2, i.e. diffusion of the density front is enhanced with respect to standard Fickian diffusion. It is also established that the anomalous time exponent decreases as time elapses: anomalous spreading is thus not a timescaling process. We demonstrate that occurrence of a...

Analytical approach for collective diffusion: one-dimensional heterogeneous lattice

Czech Academy of Sciences Publication Activity Database

Tarasenko, Alexander

2016-01-01

Roč. 144, č. 14 (2016), 1-11, č. článku 144105. ISSN 0021-9606 Institutional support: RVO:68378271 Keywords : diffusion * Monte Carlo simulations * one-dimensional heterogeneous lattice Subject RIV: BE - Theoretical Physics Impact factor: 2.965, year: 2016

Unified derivation of the various definitions of lattice cell diffusion coefficients

International Nuclear Information System (INIS)

Hughes, R.P.

1978-01-01

The various definitions of lattice cell diffusion coefficients are discussed within the context of a one-dimensional slab lattice in one energy group. It is shown how each definition, although originally derived in its own particular way, can be derived from a single approach. This makes clear the differences between, and the advantages of, the various definitions

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.

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

A pore-scale model for the cathode electrode of a proton exchange membrane fuel cell by lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Molaeimanesh, Gholam Reza; Akbari, Mohammad Hadi [Shiraz University, Shiraz (Iran, Islamic Republic of)

2015-03-15

A pore-scale model based on the lattice Boltzmann method (LBM) is proposed for the cathode electrode of a PEM fuel cell with heterogeneous and anisotropic porous gas diffusion layer (GDL) and interdigitated flow field. An active approach is implemented to model multi-component transport in GDL, which leads to enhanced accuracy, especially at higher activation over-potentials. The core of the paper is the implementation of an electrochemical reaction with an active approach in a multi-component lattice Boltzmann model for the first time. After model validation, the capability of the presented model is demonstrated through a parametric study. Effects of activation over-potential, pressure differential between inlet and outlet gas channels, land width to channel width ratio, and channel width are investigated. The results show the significant influence of GDL microstructure on the oxygen distribution and current density profile.

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.

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

Ordering phenomena and non-equilibrium properties of lattice gas models

International Nuclear Information System (INIS)

Fiig, T.

1994-03-01

This report falls within the general field of ordering processes and non-equilibrium properties of lattice gas models. The theory of diffuse scattering of lattice gas models originating from a random distribution of clusters is considered. We obtain relations between the diffuse part of the structure factor S dif (q), the correlation function C(r), and the size distribution of clusters D(n). For a number of distributions we calculate S dif (q) exactly in one dimension, and discuss the possibility for a Lorentzian and a Lorentzian square lineshape to arise. We discuss the two- and three-dimensional oxygen ordering processes in the high T c superconductor YBa 2 Cu 3 O 6+x based on a simple anisotropic lattice gas model. We calculate the structural phase diagram by Monte Carlo simulation and compared the results with experimental data. The structure factor of the oxygen ordering properties has been calculated in both two and three dimensions by Monte Carlo simulation. We report on results obtained from large scale computations on the Connection Machine, which are in excellent agreement with recent neutron diffraction data. In addition we consider the effect of the diffusive motion of metal-ion dopants on the oxygen ordering properties on YBa 2 Cu 3 O 6+x . The stationary properties of metastability in long-range interaction models are studied by application of a constrained transfer matrix (CTM) formalism. The model considered, which exhibits several metastable states, is an extension of the Blume Capel model to include weak long-range interactions. We show, that the decay rate of the metastable states is closely related to the imaginary part of the equilibrium free-energy density obtained from the CTM formalism. We discuss a class of lattice gas model for dissipative transport in the framework of a Langevin description, which is capable of producing power law spectra for the density fluctuations. We compare with numerical results obtained from simulations of a

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

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)

A thick-interface model for diffusive and massive phase transformation in substitutional alloys

International Nuclear Information System (INIS)

Svoboda, J.; Vala, J.; Gamsjaeger, E.; Fischer, F.D.

2006-01-01

Based on the application of the thermodynamic extremal principle, a new model for the diffusive and massive phase transformation in multicomponent substitutional alloys is developed. Interfacial reactions such as the rearrangement of the lattice, solute drag and trans-interface diffusion are automatically considered by assigning a finite thickness and a finite mobility to the interface region. As an application of the steady-state solution of the derived evolution equations, the kinetics of the massive γ → α transformation in the Fe-rich Fe-Cr-Ni system is simulated. The thermodynamic properties of the interface may influence significantly the contact conditions at the interface as well as the conditions for the occurrence of the massive transformation and its kinetics. The model is also used for the simulation of the diffusion-induced grain boundary migration in the same system. By application of the model a realistic value for the Gibbs energy per unit interface area is obtained

Lattice Three-Species Models of the Spatial Spread of Rabies among FOXES

Science.gov (United States)

Benyoussef, A.; Boccara, N.; Chakib, H.; Ez-Zahraouy, H.

Lattice models describing the spatial spread of rabies among foxes are studied. In these models, the fox population is divided into three-species: susceptible (S), infected or incubating (I), and infectious or rabid (R). They are based on the fact that susceptible and incubating foxes are territorial while rabid foxes have lost their sense of direction and move erratically. Two different models are investigated: a one-dimensional coupled-map lattice model, and a two-dimensional automata network model. Both models take into account the short-range character of the infection process and the diffusive motion of rabid foxes. Numerical simulations show how the spatial distribution of rabies, and the speed of propagation of the epizootic front depend upon the carrying capacity of the environment and diffusion of rabid foxes out of their territory.

Polar Coordinate Lattice Boltzmann Kinetic Modeling of Detonation Phenomena

International Nuclear Information System (INIS)

Lin Chuan-Dong; Li Ying-Jun; Xu Ai-Guo; Zhang Guang-Cai

2014-01-01

A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution function due to local chemical reaction is dynamically coupled into the modified lattice Boltzmann equation which could recover the Navier—Stokes equations, including contribution of chemical reaction, via the Chapman—Enskog expansion. For the numerical investigations, the main focuses are the nonequilibrium behaviors in these processes. The system at the disc center is always in its thermodynamic equilibrium in the highly symmetric case. The internal kinetic energies in different degrees of freedom around the detonation front do not coincide. The dependence of the reaction rate on the pressure, influences of the shock strength and reaction rate on the departure amplitude of the system from its local thermodynamic equilibrium are probed. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

The role of diffusion measurements in the study of crystal lattice defects

Energy Technology Data Exchange (ETDEWEB)

Kidson, G V

1965-07-15

Measurements of atomic mobility in solids are frequently of direct interest to those concerned with the design, development and utilization of materials in engineering. Increasing attention, however, is currently devoted to an under standing of such properties in terms of the occurrence and nature of point and line defects in the crystals. This paper reviews some recent diffusion studies conducted at C.R,N.L. that provide, in addition to data of interest in nuclear technology, a means of gaining some insight into the more fundamental nature of the lattice defects occurring in the materials. The systems discussed are (i) self diffusion in the high temperature phase of pure zirconium (ii) solute diffusion in lead and (iii) interdiffusion of aluminum and zirconium The unusual and at present incompletely understood results described in (i) are briefly reviewed. Evidence is given to suggest that diffusion occurs either through a dense dislocation network produced as a result of a martensitic phase transformation, or, alternatively, by excess vacancies introduced into the crystal by impurities. In (ii) the extraordinarily rapid diffusion of noble metal solutes in high purity lead single crystals will be discussed n terms of the state of solution of the solute atoms. It will be shown that their diffusion behaviour can be understood by assuming that a fraction f{sub i} of the dissolved solute atoms occupy interstitial sites, The measured diffusion coefficient D{sub m} is related to the interstitial diffusion coefficient by D{sub m} = f{sub i} D{sub i}. In (iii) the formation and rapid growth of single intermetallic compound ZrAl{sub 3} in the diffusion zone formed between pure zirconium and pure aluminum is described and the diffusion mechanism is interpreted in terms of the structure of the compound lattice. The results indicate that ZrAl{sub 3} forms a defect lattice, leading to the relatively rapid migration of aluminum atoms. (author)

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.

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.

Direct numerical simulation of circular-cap bubbles in low viscous liquids using counter diffusion lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Ryu, Seungyeob, E-mail: syryu@kaeri.re.kr [Korea Atomic Energy Research Institute (KAERI), 1045 Daeduk-daero, Yuseong-gu, Daejeon 305-353 (Korea, Republic of); Kim, Youngin; Yoon, Juhyeon [Korea Atomic Energy Research Institute (KAERI), 1045 Daeduk-daero, Yuseong-gu, Daejeon 305-353 (Korea, Republic of); Ko, Sungho, E-mail: sunghoko@cnu.ac.kr [Department of Mechanical Design Engineering, Chungnam National University, 220 Gung-dong, Yuseong-gu, Daejeon 305-764 (Korea, Republic of)

2014-01-15

Highlights: • We directly simulate circular-cap bubbles in low viscous liquids. • The counter diffusion multiphase lattice Boltzmann method is proposed. • The present method is validated through benchmark tests and experimental results. • The high-Reynolds-number bubbles can be simulated without any turbulence models. • The present method is feasible for the direct simulation of bubbly flows. -- Abstract: The counter diffusion lattice Boltzmann method (LBM) is used to directly simulate rising circular-cap bubbles in low viscous liquids. A counter diffusion model for single phase flows has been extended to multiphase flows, and the implicit formulation is converted into an explicit one for easy calculation. Bubbles at high Reynolds numbers ranging from O(10{sup 2}) to O(10{sup 4}) are simulated successfully without any turbulence models, which cannot be done for the existing LBM versions. The characteristics of the circular-cap bubbles are studied for a wide range of Morton numbers and compared with the previous literature. Calculated results agree with the theoretical and experimental data. Consequently, the wake phenomena of circular-cap bubbles and bubble induced turbulence are presented.

The off-center effect on the diffusion coefficient of Cu+ and Li+ in the KCl lattice

International Nuclear Information System (INIS)

Despa, F.

1994-07-01

It is well known that the diffusion coefficients of the Cu + cation in the NaCl and KCl lattices exceeds by three or four orders of magnitude the corresponding self-diffusion coefficients in the intrinsic temperature regions. This fast diffusion of the Cu + has been explained in many papers as an interstitial diffusion although the optical spectra do not confirm the existence of interstitial Cu + . In this paper we propose a new mechanism for fast diffusion. The model assumes that the equilibrium positions of the cationic impurities are noncentral and that the diffusion proceeds by hopping across the potential barrier along the nonlinear paths with the highest probability. The main result shows that the off-center position enhances considerably the diffusion. Theoretical diffusion coefficients have been obtained by modelling the potential barrier. Changes of the configuration entropy and the vibration spectra due to the presence of the noncentral impurity have been included in the model. We proceeded in the Li + cation case as in the case of Cu + cation. We emphasize the good agreement of the model with the experimental data and we show that if the impurity is placed close to the central site the due diffusion coefficient is close to that for the cationic self-diffusion. (author). 37 refs, 6 figs, 3 tabs

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.

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.

Implicit coupling of turbulent diffusion with chemical reaction mechanisms for prognostic atmospheric dispersion models

Energy Technology Data Exchange (ETDEWEB)

Berlowitz, D.R.

1996-11-01

In the last few decades the negative impact by humans on the thin atmospheric layer enveloping the earth, the basis for life on this planet, has increased steadily. In order to halt, or at least slow down this development, the knowledge and study of these anthropogenic influence has to be increased and possible remedies have to be suggested. An important tool for these studies are computer models. With their help the atmospheric system can be approximated and the various processes, which have led to the current situation can be quantified. They also serve as an instrument to assess short or medium term strategies to reduce this human impact. However, to assure efficiency as well as accuracy, a careful analysis of the numerous processes involved in the dispersion of pollutants in the atmosphere is called for. This should help to concentrate on the essentials and also prevent excessive usage of sometimes scarce computing resources. The basis of the presented work is the EUMAC Zooming Model (ETM), and particularly the component calculating the dispersion of pollutants in the atmosphere, the model MARS. The model has two main parts: an explicit solver, where the advection and the horizontal diffusion of pollutants are calculated, and an implicit solution mechanism, allowing the joint computation of the change of concentration due to chemical reactions, coupled with the respective influence of the vertical diffusion of the species. The aim of this thesis is to determine particularly the influence of the horizontal components of the turbulent diffusion on the existing implicit solver of the model. Suggestions for a more comprehensive inclusion of the full three dimensional diffusion operator in the implicit solver are made. This is achieved by an appropriate operator splitting. A selection of numerical approaches to tighten the coupling of the diffusion processes with the calculation of the applied chemical reaction mechanisms are examined. (author) figs., tabs., refs.

Simulation of the catalyst layer in PEMFC based on a novel two-phase lattice model

Energy Technology Data Exchange (ETDEWEB)

Zhang Jiejing; Yang Wei; Xu Li [School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin Key Laboratory of Membrane Science and Desalination Technology, Tianjin University, Tianjin 300072 (China); Wang Yuxin, E-mail: yxwang@tju.edu.cn [School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin Key Laboratory of Membrane Science and Desalination Technology, Tianjin University, Tianjin 300072 (China)

2011-08-01

Highlights: > We propose a novel two phase lattice model of catalyst layer in PEMFC. > The model features a catalyst phase and a mixed ionomer and pores phase. > Transport and electrochemical reaction in the lattice are simulated. > The model enables more accurate results than pore-solid two phase model. > Profiles of oxygen level and reaction rate across catalyst layer vary with cell current. - Abstract: A lattice model of catalyst layer in proton exchange membrane fuel cells (PEMFCs), consisting of randomly distributed catalyst phase (C phase) and mixed ionomer-pore phase (IP phase), was established by means of Monte Carlo method. Transport and electrochemical reactions in the model catalyst layer were calculated. The newly proposed C-IP model was compared with previously established pore-solid two phase model. The variation of oxygen level and reaction rate along the thickness of catalyst layer with cell current was discussed. The effect of ionomer distribution across catalyst layer was studied by comparing profiles of oxygen level, reaction rate and overpotential, as well as corresponding polarization curves.

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.

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.

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.

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

A reaction-diffusion model for market fluctuations - A relation between price change and traded volumes

Science.gov (United States)

Yuvan, Steven; Bier, Martin

2018-02-01

Two decades ago Bak et al. (1997) [3] proposed a reaction-diffusion model to describe market fluctuations. In the model buyers and sellers diffuse from opposite ends of a 1D interval that represents a price range. Trades occur when buyers and sellers meet. We show analytically and numerically that the model well reproduces the square-root relation between traded volumes and price changes that is observed in real-life markets. The result is remarkable as this relation has commonly been explained in terms of more elaborate trader strategies. We furthermore explain why the square-root relation is robust under model modifications and we show how real-life bond market data exhibit the square-root relation.

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,...

Off-lattice self-learning kinetic Monte Carlo: application to 2D cluster diffusion on the fcc(111) surface

International Nuclear Information System (INIS)

Kara, Abdelkader; Yildirim, Handan; Rahman, Talat S; Trushin, Oleg

2009-01-01

We report developments of the kinetic Monte Carlo (KMC) method with improved accuracy and increased versatility for the description of atomic diffusivity on metal surfaces. The on-lattice constraint built into our recently proposed self-learning KMC (SLKMC) (Trushin et al 2005 Phys. Rev. B 72 115401) is released, leaving atoms free to occupy 'off-lattice' positions to accommodate several processes responsible for small-cluster diffusion, periphery atom motion and heteroepitaxial growth. This technique combines the ideas embedded in the SLKMC method with a new pattern-recognition scheme fitted to an off-lattice model in which relative atomic positions are used to characterize and store configurations. Application of a combination of the 'drag' and the repulsive bias potential (RBP) methods for saddle point searches allows the treatment of concerted cluster, and multiple- and single-atom, motions on an equal footing. This tandem approach has helped reveal several new atomic mechanisms which contribute to cluster migration. We present applications of this off-lattice SLKMC to the diffusion of 2D islands of Cu (containing 2-30 atoms) on Cu and Ag(111), using the interatomic potential from the embedded-atom method. For the hetero-system Cu/Ag(111), this technique has uncovered mechanisms involving concerted motions such as shear, breathing and commensurate-incommensurate occupancies. Although the technique introduces complexities in storage and retrieval, it does not introduce noticeable extra computational cost.

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.

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.

Lattice dynamical investigations on Zn diffusion in zinc oxide

Indian Academy of Sciences (India)

diffusion and that too by single vacancy mechanism. The results are compared with the .... Instantaneous relative displacement of the diffusing atom with respect to the neigh- bours in the diffusion ring is given as a reaction coordinate,. X =.

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.

Numerical modelling of random walk one-dimensional diffusion

International Nuclear Information System (INIS)

Vamos, C.; Suciu, N.; Peculea, M.

1996-01-01

The evolution of a particle which moves on a discrete one-dimensional lattice, according to a random walk low, approximates better the diffusion process smaller the steps of the spatial lattice and time are. For a sufficiently large assembly of particles one can assume that their relative frequency at lattice knots approximates the distribution function of the diffusion process. This assumption has been tested by simulating on computer two analytical solutions of the diffusion equation: the Brownian motion and the steady state linear distribution. To evaluate quantitatively the similarity between the numerical and analytical solutions we have used a norm given by the absolute value of the difference of the two solutions. Also, a diffusion coefficient at any lattice knots and moment of time has been calculated, by using the numerical solution both from the diffusion equation and the particle flux given by Fick's low. The difference between diffusion coefficient of analytical solution and the spatial lattice mean coefficient of numerical solution constitutes another quantitative indication of the similarity of the two solutions. The results obtained show that the approximation depends first on the number of particles at each knot of the spatial lattice. In conclusion, the random walk is a microscopic process of the molecular dynamics type which permits simulations precision of the diffusion processes with given precision. The numerical method presented in this work may be useful both in the analysis of real experiments and for theoretical studies

Multiple-relaxation-time lattice Boltzmann model for incompressible miscible flow with large viscosity ratio and high Péclet number

Science.gov (United States)

Meng, Xuhui; Guo, Zhaoli

2015-10-01

A lattice Boltzmann model with a multiple-relaxation-time (MRT) collision operator is proposed for incompressible miscible flow with a large viscosity ratio as well as a high Péclet number in this paper. The equilibria in the present model are motivated by the lattice kinetic scheme previously developed by Inamuro et al. [Philos. Trans. R. Soc. London, Ser. A 360, 477 (2002), 10.1098/rsta.2001.0942]. The fluid viscosity and diffusion coefficient depend on both the corresponding relaxation times and additional adjustable parameters in this model. As a result, the corresponding relaxation times can be adjusted in proper ranges to enhance the performance of the model. Numerical validations of the Poiseuille flow and a diffusion-reaction problem demonstrate that the proposed model has second-order accuracy in space. Thereafter, the model is used to simulate flow through a porous medium, and the results show that the proposed model has the advantage to obtain a viscosity-independent permeability, which makes it a robust method for simulating flow in porous media. Finally, a set of simulations are conducted on the viscous miscible displacement between two parallel plates. The results reveal that the present model can be used to simulate, to a high level of accuracy, flows with large viscosity ratios and/or high Péclet numbers. Moreover, the present model is shown to provide superior stability in the limit of high kinematic viscosity. In summary, the numerical results indicate that the present lattice Boltzmann model is an ideal numerical tool for simulating flow with a large viscosity ratio and/or a high Péclet number.

Lattice diffusion of a single molecule in solution

Science.gov (United States)

Ruggeri, Francesca; Krishnan, Madhavi

2017-12-01

The ability to trap a single molecule in an electrostatic potential well in solution has opened up new possibilities for the use of molecular electrical charge to study macromolecular conformation and dynamics at the level of the single entity. Here we study the diffusion of a single macromolecule in a two-dimensional lattice of electrostatic traps in solution. We report the ability to measure both the size and effective electrical charge of a macromolecule by observing single-molecule transport trajectories, typically a few seconds in length, using fluorescence microscopy. While, as shown previously, the time spent by the molecule in a trap is a strong function of its effective charge, we demonstrate here that the average travel time between traps in the landscape yields its hydrodynamic radius. Tailoring the pitch of the lattice thus yields two different experimentally measurable time scales that together uniquely determine both the size and charge of the molecule. Since no information is required on the location of the molecule between consecutive departure and arrival events at lattice sites, the technique is ideally suited to measurements on weakly emitting entities such as single molecules.

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.

Reaction-diffusion processes in zero transverse dimensions as toy models for high-energy QCD

International Nuclear Information System (INIS)

Armesto, Nestor; Bondarenko, Sergey; Quiroga-Arias, Paloma; Milhano, Jose Guilherme

2008-01-01

We examine numerically different zero-dimensional reaction-diffusion processes as candidate toy models for high-energy QCD evolution. Of the models examined-Reggeon Field Theory, Directed Percolation and Reversible Processes-only the latter shows the behaviour commonly expected, namely an increase of the scattering amplitude with increasing rapidity. Further, we find that increasing recombination terms, quantum loops and the heuristic inclusion of a running of the couplings, generically slow down the evolution.

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

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.

Coarse-mesh method for multidimensional, mixed-lattice diffusion calculations

International Nuclear Information System (INIS)

Dodds, H.L. Jr.; Honeck, H.C.; Hostetler, D.E.

1977-01-01

A coarse-mesh finite difference method has been developed for multidimensional, mixed-lattice reactor diffusion calculations, both statics and kinetics, in hexagonal geometry. Results obtained with the coarse-mesh (CM) method have been compared with a conventional mesh-centered finite difference method and with experiment. The results of this comparison indicate that the accuracy of the CM method for highly heterogeneous (mixed) lattices using one point per hexagonal mesh element (''hex'') is about the same as the conventional method with six points per hex. Furthermore, the computing costs (i.e., central processor unit time and core storage requirements) of the CM method with one point per hex are about the same as the conventional method with one point per hex

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

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.

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.

A mass-conserving multiphase lattice Boltzmann model for simulation of multiphase flows

Science.gov (United States)

Niu, Xiao-Dong; Li, You; Ma, Yi-Ren; Chen, Mu-Feng; Li, Xiang; Li, Qiao-Zhong

2018-01-01

In this study, a mass-conserving multiphase lattice Boltzmann (LB) model is proposed for simulating the multiphase flows. The proposed model developed in the present study is to improve the model of Shao et al. ["Free-energy-based lattice Boltzmann model for simulation of multiphase flows with density contrast," Phys. Rev. E 89, 033309 (2014)] by introducing a mass correction term in the lattice Boltzmann model for the interface. The model of Shao et al. [(the improved Zheng-Shu-Chew (Z-S-C model)] correctly considers the effect of the local density variation in momentum equation and has an obvious improvement over the Zheng-Shu-Chew (Z-S-C) model ["A lattice Boltzmann model for multiphase flows with large density ratio," J. Comput. Phys. 218(1), 353-371 (2006)] in terms of solution accuracy. However, due to the physical diffusion and numerical dissipation, the total mass of each fluid phase cannot be conserved correctly. To solve this problem, a mass correction term, which is similar to the one proposed by Wang et al. ["A mass-conserved diffuse interface method and its application for incompressible multiphase flows with large density ratio," J. Comput. Phys. 290, 336-351 (2015)], is introduced into the lattice Boltzmann equation for the interface to compensate the mass losses or offset the mass increase. Meanwhile, to implement the wetting boundary condition and the contact angle, a geometric formulation and a local force are incorporated into the present mass-conserving LB model. The proposed model is validated by verifying the Laplace law, simulating both one and two aligned droplets splashing onto a liquid film, droplets standing on an ideal wall, droplets with different wettability splashing onto smooth wax, and bubbles rising under buoyancy. Numerical results show that the proposed model can correctly simulate multiphase flows. It was found that the mass is well-conserved in all cases considered by the model developed in the present study. The developed

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

A nonlocal and periodic reaction-diffusion-advection model of a single phytoplankton species.

Science.gov (United States)

Peng, Rui; Zhao, Xiao-Qiang

2016-02-01

In this article, we are concerned with a nonlocal reaction-diffusion-advection model which describes the evolution of a single phytoplankton species in a eutrophic vertical water column where the species relies solely on light for its metabolism. The new feature of our modeling equation lies in that the incident light intensity and the death rate are assumed to be time periodic with a common period. We first establish a threshold type result on the global dynamics of this model in terms of the basic reproduction number R0. Then we derive various characterizations of R0 with respect to the vertical turbulent diffusion rate, the sinking or buoyant rate and the water column depth, respectively, which in turn give rather precise conditions to determine whether the phytoplankton persist or become extinct. Our theoretical results not only extend the existing ones for the time-independent case, but also reveal new interesting effects of the modeling parameters and the time-periodic heterogeneous environment on persistence and extinction of the phytoplankton species, and thereby suggest important implications for phytoplankton growth control.

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.

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.

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.

Lattice location of diffused Zn atoms in GaAs and InP single crystals

International Nuclear Information System (INIS)

Chan, L.Y.; Yu, K.M.; Ben-Tzur, M.; Haller, E.E.; Jaklevic, J.M.; Walukiewicz, W.; Hanson, C.M.

1991-01-01

We have investigated the saturation phenomenon of the free carrier concentration in p-type GaAs and InP single crystals doped by zinc diffusion. The free hole saturation occurs at 10 20 cm -3 for GaAs, but the maximum concentration for InP appears at mid 10 18 cm -3 . The difference in the saturation hole concentrations for these materials is investigated by studying the incorporation and the lattice location of the impurity zinc, an acceptor when located on a group III atom site. Zinc is diffused into the III-V wafers in a sealed quartz ampoule. Particle-induced x-ray emission with ion-channeling techniques are employed to determine the exact lattice location of the zinc atoms. We have found that over 90% of all zinc atoms occupy Ga sites in the diffused GaAs samples, while for the InP case, the zinc substitutionality is dependent on the cooling rate of the sample after high-temperature diffusion. For the slowly cooled sample, a large fraction (∼90%) of the zinc atoms form random precipitates of Zn 3 P 2 and elemental Zn. However, when rapidly cooled only 60% of the zinc forms such precipitates while the rest occupies specific sites in the InP. We analyze our results in terms of the amphoteric native defect model. We show that the difference in the electrical activity of the Zn atoms in GaAs and InP is a consequence of the different location of the Fermi level stabilization energy in these two materials

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....

Transition point prediction in a multicomponent lattice Boltzmann model: Forcing scheme dependencies

Science.gov (United States)

Küllmer, Knut; Krämer, Andreas; Joppich, Wolfgang; Reith, Dirk; Foysi, Holger

2018-02-01

Pseudopotential-based lattice Boltzmann models are widely used for numerical simulations of multiphase flows. In the special case of multicomponent systems, the overall dynamics are characterized by the conservation equations for mass and momentum as well as an additional advection diffusion equation for each component. In the present study, we investigate how the latter is affected by the forcing scheme, i.e., by the way the underlying interparticle forces are incorporated into the lattice Boltzmann equation. By comparing two model formulations for pure multicomponent systems, namely the standard model [X. Shan and G. D. Doolen, J. Stat. Phys. 81, 379 (1995), 10.1007/BF02179985] and the explicit forcing model [M. L. Porter et al., Phys. Rev. E 86, 036701 (2012), 10.1103/PhysRevE.86.036701], we reveal that the diffusion characteristics drastically change. We derive a generalized, potential function-dependent expression for the transition point from the miscible to the immiscible regime and demonstrate that it is shifted between the models. The theoretical predictions for both the transition point and the mutual diffusion coefficient are validated in simulations of static droplets and decaying sinusoidal concentration waves, respectively. To show the universality of our analysis, two common and one new potential function are investigated. As the shift in the diffusion characteristics directly affects the interfacial properties, we additionally show that phenomena related to the interfacial tension such as the modeling of contact angles are influenced as well.

Transition point prediction in a multicomponent lattice Boltzmann model: Forcing scheme dependencies.

Science.gov (United States)

Küllmer, Knut; Krämer, Andreas; Joppich, Wolfgang; Reith, Dirk; Foysi, Holger

2018-02-01

Pseudopotential-based lattice Boltzmann models are widely used for numerical simulations of multiphase flows. In the special case of multicomponent systems, the overall dynamics are characterized by the conservation equations for mass and momentum as well as an additional advection diffusion equation for each component. In the present study, we investigate how the latter is affected by the forcing scheme, i.e., by the way the underlying interparticle forces are incorporated into the lattice Boltzmann equation. By comparing two model formulations for pure multicomponent systems, namely the standard model [X. Shan and G. D. Doolen, J. Stat. Phys. 81, 379 (1995)JSTPBS0022-471510.1007/BF02179985] and the explicit forcing model [M. L. Porter et al., Phys. Rev. E 86, 036701 (2012)PLEEE81539-375510.1103/PhysRevE.86.036701], we reveal that the diffusion characteristics drastically change. We derive a generalized, potential function-dependent expression for the transition point from the miscible to the immiscible regime and demonstrate that it is shifted between the models. The theoretical predictions for both the transition point and the mutual diffusion coefficient are validated in simulations of static droplets and decaying sinusoidal concentration waves, respectively. To show the universality of our analysis, two common and one new potential function are investigated. As the shift in the diffusion characteristics directly affects the interfacial properties, we additionally show that phenomena related to the interfacial tension such as the modeling of contact angles are influenced as well.

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.

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

Hysteresis and Phase Transitions in a Lattice Regularization of an Ill-Posed Forward-Backward Diffusion Equation

Science.gov (United States)

Helmers, Michael; Herrmann, Michael

2018-03-01

We consider a lattice regularization for an ill-posed diffusion equation with a trilinear constitutive law and study the dynamics of phase interfaces in the parabolic scaling limit. Our main result guarantees for a certain class of single-interface initial data that the lattice solutions satisfy asymptotically a free boundary problem with a hysteretic Stefan condition. The key challenge in the proof is to control the microscopic fluctuations that are inevitably produced by the backward diffusion when a particle passes the spinodal region.

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.

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.

A Reaction-Diffusion Model for Synapse Growth and Long-Term Memory

Science.gov (United States)

Liu, Kang; Lisman, John; Hagan, Michael

Memory storage involves strengthening of synaptic transmission known as long-term potentiation (LTP). The late phase of LTP is associated with structural processes that enlarge the synapse. Yet, synapses must be stable, despite continual subunit turnover, over the lifetime of an encoded memory. These considerations suggest that synapses are variable-size stable structure (VSSS), meaning they can switch between multiple metastable structures with different sizes. The mechanisms underlying VSSS are poorly understood. While experiments and theory have suggested that the interplay between diffusion and receptor-scaffold interactions can lead to a preferred stable size for synaptic domains, such a mechanism cannot explain how synapses adopt widely different sizes. Here we develop a minimal reaction-diffusion model of VSSS for synapse growth, incorporating the recent observation from super-resolution microscopy that neural activity can build compositional heterogeneities within synaptic domains. We find that introducing such heterogeneities can change the stable domain size in a controlled manner. We discuss a potential connection between this model and experimental data on synapse sizes, and how it provides a possible mechanism to structurally encode graded long-term memory. We acknowledge the support from NSF INSPIRE Award number IOS-1526941 (KL, MFH, JL) and the Brandeis Center for Bioinspired Soft Materials, an NSF MRSEC, DMR- 1420382 (MFH).

Lattice Higgs models

International Nuclear Information System (INIS)

Jersak, J.

1986-01-01

This year has brought a sudden interest in lattice Higgs models. After five years of only modest activity we now have many new results obtained both by analytic and Monte Carlo methods. This talk is a review of the present state of lattice Higgs models with particular emphasis on the recent development

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.

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.

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

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.

On thermal vibration effects in diffusion model calculations of blocking dips

International Nuclear Information System (INIS)

Fuschini, E.; Ugozzoni, A.

1983-01-01

In the framework of the diffusion model, a method for calculating blocking dips is suggested that takes into account thermal vibrations of the crystal lattice. Results of calculations of the diffusion factor and the transverse energy distribution taking into accoUnt scattering of the channeled particles at thermal vibrations of lattice nuclei, are presented. Calculations are performed for α-particles with the energy of 2.12 MeV at 300 K scattered by Al crystal. It is shown that calculations performed according to the above method prove the necessity of taking into account effects of multiple scattering under blocking conditions

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

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.

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.

Traveling wave solutions of a biological reaction-convection-diffusion equation model by using $(G'/G$ expansion method

Directory of Open Access Journals (Sweden)

Shahnam Javadi

2013-07-01

Full Text Available In this paper, the $(G'/G$-expansion method is applied to solve a biological reaction-convection-diffusion model arising in mathematical biology. Exact traveling wave solutions are obtained by this method. This scheme can be applied to a wide class of nonlinear partial differential equations.

A drift-diffusion-reaction model for excitonic photovoltaic bilayers: Photovoltaic bilayers: Asymptotic analysis and a 2D hdg finite element scheme

KAUST Repository

Brinkman, Daniel; Fellner, Klemens J.; Markowich, Peter A.; Wolfram, Marie Therese

2013-01-01

We present and discuss a mathematical model for the operation of bilayer organic photovoltaic devices. Our model couples drift-diffusion-recombination equations for the charge carriers (specifically, electrons and holes) with a reaction

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.

The Lattice and Thermal Radiation Conductivity of Thermal Barrier Coatings: Models and Experiments

Science.gov (United States)

Zhu, Dongming; Spuckler, Charles M.

2010-01-01

The lattice and radiation conductivity of ZrO2-Y2O3 thermal barrier coatings was evaluated using a laser heat flux approach. A diffusion model has been established to correlate the coating apparent thermal conductivity to the lattice and radiation conductivity. The radiation conductivity component can be expressed as a function of temperature, coating material scattering, and absorption properties. High temperature scattering and absorption of the coating systems can be also derived based on the testing results using the modeling approach. A comparison has been made for the gray and nongray coating models in the plasma-sprayed thermal barrier coatings. The model prediction is found to have a good agreement with experimental observations.

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

A reaction-diffusion model for radiation-induced bystander effects.

Science.gov (United States)

Olobatuyi, Oluwole; de Vries, Gerda; Hillen, Thomas

2017-08-01

We develop and analyze a reaction-diffusion model to investigate the dynamics of the lifespan of a bystander signal emitted when cells are exposed to radiation. Experimental studies by Mothersill and Seymour 1997, using malignant epithelial cell lines, found that an emitted bystander signal can still cause bystander effects in cells even 60 h after its emission. Several other experiments have also shown that the signal can persist for months and even years. Also, bystander effects have been hypothesized as one of the factors responsible for the phenomenon of low-dose hyper-radiosensitivity and increased radioresistance (HRS/IRR). Here, we confirm this hypothesis with a mathematical model, which we fit to Joiner's data on HRS/IRR in a T98G glioma cell line. Furthermore, we use phase plane analysis to understand the full dynamics of the signal's lifespan. We find that both single and multiple radiation exposure can lead to bystander signals that either persist temporarily or permanently. We also found that, in an heterogeneous environment, the size of the domain exposed to radiation and the number of radiation exposures can determine whether a signal will persist temporarily or permanently. Finally, we use sensitivity analysis to identify those cell parameters that affect the signal's lifespan and the signal-induced cell death the most.

A general treatment of one- to three-dimensional diffusion reaction kinetics of interstitial clusters: Implications for the evolution of voids

International Nuclear Information System (INIS)

Trinkaus, H.; Singh, B.N.; Golubov, S.I.

2008-05-01

In recent years, it has been shown that a number of striking features in the microstructural evolution occurring in metals under cascade damage generating irradiation (e.g. enhanced swelling near grain boundaries, decoration of dislocations with SIA loops, saturation of void growth and void lattice formation) can be rationalised in terms of intra-cascade clustering of vacancies and self-interstitial atoms (SIAs), differences in the thermal stability and mobility of the resulting clusters and one-dimensional (1D) glide diffusion of SIA clusters ('production bias model'). The 1D diffusion of SIA clusters is generally disturbed by changes between equivalent 1D diffusion paths and by transversal diffusion by self-climb, resulting in diffusion reaction kinetics between the 1D and 3D limiting cases. In this paper, a general treatment of such kinetics operating in systems containing random distributions of sinks is presented. The complicated partial sink strengths of different components of the system for the annihilation of SIA clusters are expressed by those for the simple 1D and 3D limiting cases. The effects of direction changes and transversal diffusion are first considered separately and are then combined. The significance of the present treatment for damage accumulation under cascade damage conditions is illustrated by applying it to the discussion of void growth characteristics, particularly of the conditions for saturation of void growth. (au)

A general treatment of one- to three-dimensional diffusion reaction kinetics of interstitial clusters: Implications for the evolution of voids

Energy Technology Data Exchange (ETDEWEB)

Trinkaus, H. (Inst. Festkoerperforschung, Forschungszentrum Juelich (Germany)); Singh, B.N. (Risoe DTU, Roskilde (Denmark)); Golubov, S.I. (Oak Ridge National Lab., Materials Science and Technology Div., TN (United States))

2008-05-15

In recent years, it has been shown that a number of striking features in the microstructural evolution occurring in metals under cascade damage generating irradiation (e.g. enhanced swelling near grain boundaries, decoration of dislocations with SIA loops, saturation of void growth and void lattice formation) can be rationalised in terms of intra-cascade clustering of vacancies and self-interstitial atoms (SIAs), differences in the thermal stability and mobility of the resulting clusters and one-dimensional (1D) glide diffusion of SIA clusters ('production bias model'). The 1D diffusion of SIA clusters is generally disturbed by changes between equivalent 1D diffusion paths and by transversal diffusion by self-climb, resulting in diffusion reaction kinetics between the 1D and 3D limiting cases. In this paper, a general treatment of such kinetics operating in systems containing random distributions of sinks is presented. The complicated partial sink strengths of different components of the system for the annihilation of SIA clusters are expressed by those for the simple 1D and 3D limiting cases. The effects of direction changes and transversal diffusion are first considered separately and are then combined. The significance of the present treatment for damage accumulation under cascade damage conditions is illustrated by applying it to the discussion of void growth characteristics, particularly of the conditions for saturation of void growth. (au)

A strongly nonlinear reaction-diffusion model for a deterministic diffusive epidemic

International Nuclear Information System (INIS)

Kirane, M.; Kouachi, S.

1992-10-01

In the present paper the mathematical validity of a model on the spread of an infectious disease is proved. This model was proposed by Bailey. The mathematical validity is proved by means of a positivity, uniqueness and existence theorem. In spite of the apparent simplicity of the problem, the solution requires a delicate set of techniques. It seems very difficult to extend these techniques to a model in more than one dimension without imposing conditions on the diffusivities. (author). 7 refs

Reactivity and reaction rate measurements in U--D2O lattices with coaxial fuel

International Nuclear Information System (INIS)

Pellarin, D.J.; Morris, B.M.

1976-12-01

Integral reaction rate parameters, intracell thermal neutron flux profiles, and material bucklings were measured for D 2 O-moderated uniform lattices in the exponential facility at the Savannah River Laboratory. Two different slightly enriched coaxial uranium fuel assemblies were examined over a wide range of triangular lattice pitches. Integral parameters are reported for inner and outer fuel separately providing data for a more detailed and rigorous comparison with computation than has been previously available. Results are compared with RAHAB calculations using ENDF/B-IV cross sections. Large discrepancies in agreement between calculation and experiment, outside of experimental errors and uncertainties in the input cross sections, probably result from the resonance capture models used by RAHAB

Layer features of the lattice gas model for self-organized criticality

International Nuclear Information System (INIS)

Pesheva, N.C.; Brankov, J.G.

1995-06-01

A layer-by-layer description of the asymmetric lattice gas model for 1/f-noise suggested by Jensen [Phys. Rev. Lett. 64, 3103 (1990)] is presented. The power spectra of the lattice layers in the direction perpendicular to the particle flux is studied in order to understand how the white noise at the input boundary evolves, on the average, into 1/f-noise for the system. The effects of high boundary drive and uniform driving force on the power spectrum of the total number of diffusing particles are considered. In the case of nearest-neighbor particle interactions, high statistics simulation results show that the power spectra of single lattice layers are characterized by different β x exponents such that β x → 1.9 as one approaches the outer boundary. (author). 10 refs, 6 figs

An extended fractal growth regime in the diffusion limited aggregation including edge diffusion

Directory of Open Access Journals (Sweden)

Aritra Ghosh

2016-01-01

Full Text Available We have investigated on-lattice diffusion limited aggregation (DLA involving edge diffusion and compared the results with the standard DLA model. For both cases, we observe the existence of a crossover from the fractal to the compact regime as a function of sticking coefficient. However, our modified DLA model including edge diffusion shows an extended fractal growth regime like an earlier theoretical result using realistic growth models and physical parameters [Zhang et al., Phys. Rev. Lett. 73 (1994 1829]. While the results of Zhang et al. showed the existence of the extended fractal growth regime only on triangular but not on square lattices, we find its existence on the square lattice. There is experimental evidence of this growth regime on a square lattice. The standard DLA model cannot characterize fractal morphology as the fractal dimension (Hausdorff dimension, DH is insensitive to morphology. It also predicts DH = DP (the perimeter dimension. For the usual fractal structures, observed in growth experiments on surfaces, the perimeter dimension can differ significantly (DH ≠ DP depending on the morphology. Our modified DLA model shows minor sensitivity to this difference.

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.

Energy gains from lattice-enabled nuclear reactions

International Nuclear Information System (INIS)

Nagel, David J.

2015-01-01

The energy gain of a system is defined as the ratio of its output energy divided by the energy provided to operate the system. Most familiar systems have energy gains less than one due to various inefficiencies. By contrast, lattice-enabled nuclear reactions (LENR) offer high energy gains. Theoretical values in excess of 1000 are possible. Energy gains over 100 have already been reported. But, they have not yet been sustained for commercially significant durations. This article summarizes the current status of LENR energy gains. (author)

Lattice continuum and diffusional creep.

Science.gov (United States)

Mesarovic, Sinisa Dj

2016-04-01

Diffusional creep is characterized by growth/disappearance of lattice planes at the crystal boundaries that serve as sources/sinks of vacancies, and by diffusion of vacancies. The lattice continuum theory developed here represents a natural and intuitive framework for the analysis of diffusion in crystals and lattice growth/loss at the boundaries. The formulation includes the definition of the Lagrangian reference configuration for the newly created lattice, the transport theorem and the definition of the creep rate tensor for a polycrystal as a piecewise uniform, discontinuous field. The values associated with each crystalline grain are related to the normal diffusional flux at grain boundaries. The governing equations for Nabarro-Herring creep are derived with coupled diffusion and elasticity with compositional eigenstrain. Both, bulk diffusional dissipation and boundary dissipation accompanying vacancy nucleation and absorption, are considered, but the latter is found to be negligible. For periodic arrangements of grains, diffusion formally decouples from elasticity but at the cost of a complicated boundary condition. The equilibrium of deviatorically stressed polycrystals is impossible without inclusion of interface energies. The secondary creep rate estimates correspond to the standard Nabarro-Herring model, and the volumetric creep is small. The initial (primary) creep rate is estimated to be much larger than the secondary creep rate.

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

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.

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.

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

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.

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).

Atomistic models of Cu diffusion in CuInSe2 under variations in composition

Science.gov (United States)

Sommer, David E.; Dunham, Scott T.

2018-03-01

We construct an analytic model for the composition dependence of the vacancy-mediated Cu diffusion coefficient in undoped CuInSe2 using parameters from density functional theory. The applicability of this model is supported numerically with kinetic lattice Monte Carlo and Onsager transport tensors. We discuss how this model relates to experimental measurements of Cu diffusion, arguing that our results can account for significant contributions to the bulk diffusion of Cu tracers in non-stoichiometric CuInSe2.

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.

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.

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.

Trace diffusion of different nuclear reactions products in polycrystalline tantalum

International Nuclear Information System (INIS)

Beyer, G.J.; Fromm, W.D.; Novgorodov, A.F.

1976-07-01

Measurements of the lattice diffusion coefficients for carrier free isotopes of Hf, Lu, Yb, Tm, Tb, Gd, Eu, Ba, Cs, Y, Sr, Rb and As in polycrystalline tantalum were made over the temperature range 1700 Fsub(As)>Fsub(lanthanides)>Fsub(Sr)>Fsub(Ba)>Fsub(Hf)>Fsub(Rb)>Fsub(Cs). The data indicate, that the Arrhenius relation was obeyed over the entire temperature range. Within the lanthanide-group no differences in the diffusion velocities could be detected, this fact points to a diffusion mechanism of Me 3+ -ions of lanthanides, Me 2+ -ions of earth alkaline elements and Me + -ions of alkaline elements. (author)

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...

Diffusion coefficients for periodically induced multi-step persistent walks on regular lattices

International Nuclear Information System (INIS)

Gilbert, Thomas; Sanders, David P

2012-01-01

We present a generalization of our formalism for the computation of diffusion coefficients of multi-step persistent random walks on regular lattices to walks which include zero-displacement states. This situation is especially relevant to systems where tracer particles move across potential barriers as a result of the action of a periodic forcing whose period sets the timescale between transitions. (paper)

The Bond Fluctuation Model and Other Lattice Models

Science.gov (United States)

Müller, Marcus

Lattice models constitute a class of coarse-grained representations of polymeric materials. They have enjoyed a longstanding tradition for investigating the universal behavior of long chain molecules by computer simulations and enumeration techniques. A coarse-grained representation is often necessary to investigate properties on large time- and length scales. First, some justification for using lattice models will be given and the benefits and limitations will be discussed. Then, the bond fluctuation model by Carmesin and Kremer [1] is placed into the context of other lattice models and compared to continuum models. Some specific techniques for measuring the pressure in lattice models will be described. The bond fluctuation model has been employed in more than 100 simulation studies in the last decade and only few selected applications can be mentioned.

Competing reaction processes on a lattice as a paradigm for catalyst deactivation

Science.gov (United States)

Abad, E.; Kozak, J. J.

2015-02-01

We mobilize both a generating function approach and the theory of finite Markov processes to compute the probability of irreversible absorption of a randomly diffusing species on a lattice with competing reaction centers. We consider an N-site lattice populated by a single deep trap, and N -1 partially absorbing traps (absorption probability 0 characteristic Ω =0 and Ω =2 . The results obtained allow a characterization of catalyst deactivation processes on planar surfaces and on catalyst pellets where only a single catalytic site remains fully active (deep trap), the other sites being only partially active as a result of surface poisoning. The central result of our study is that the predicted dependence of the reaction efficiency on system size N and on s is in qualitative accord with previously reported experimental results, notably catalysts exhibiting selective poisoning due to surface sites that have different affinities for chemisorption of the poisoning agent (e.g., acid zeolite catalysts). Deviations from the efficiency of a catalyst with identical sites are quantified, and we find that such deviations display a significant dependence on the topological details of the surface (for fixed values of N and s we find markedly different results for, say, a planar surface and for the polyhedral surface of a catalyst pellet). Our results highlight the importance of surface topology for the efficiency of catalytic conversion processes on inhomogeneous substrates, and in particular for those aimed at industrial applications. From our exact analysis we extract results for the two limiting cases s ≈1 and s ≈0 , corresponding respectively to weak and strong catalyst poisoning (decreasing s leads to a monotonic decrease in the efficiency of catalytic conversion). The results for the s ≈0 case are relevant for the dual problem of light-energy conversion via trapping of excitations in the chlorophyll antenna network. Here, decreasing the probability of excitation

Entire solutions for bistable lattice differential equations with obstacles

CERN Document Server

Hoffman, Aaron; Vleck, E S Van

2018-01-01

The authors consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions they show that wave-like solutions exist when obstacles (characterized by "holes") are present in the lattice. Their work generalizes to the discrete spatial setting the results obtained in Berestycki, Hamel, and Matuno (2009) for the propagation of waves around obstacles in continuous spatial domains. The analysis hinges upon the development of sub and super-solutions for a class of discrete bistable reaction-diffusion problems and on a generalization of a classical result due to Aronson and Weinberger that concerns the spreading of localized disturbances.

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

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.

The pseudo-compartment method for coupling partial differential equation and compartment-based models of diffusion.

Science.gov (United States)

Yates, Christian A; Flegg, Mark B

2015-05-06

Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs), which assumes there are sufficient densities of particles that a continuum approximation is valid. However, owing to recent advances in computational power, the simulation and therefore postulation, of computationally intensive individual-based models has become a popular way to investigate the effects of noise in reaction-diffusion systems in which regions of low copy numbers exist. The specific stochastic models with which we shall be concerned in this manuscript are referred to as 'compartment-based' or 'on-lattice'. These models are characterized by a discretization of the computational domain into a grid/lattice of 'compartments'. Within each compartment, particles are assumed to be well mixed and are permitted to react with other particles within their compartment or to transfer between neighbouring compartments. Stochastic models provide accuracy, but at the cost of significant computational resources. For models that have regions of both low and high concentrations, it is often desirable, for reasons of efficiency, to employ coupled multi-scale modelling paradigms. In this work, we develop two hybrid algorithms in which a PDE in one region of the domain is coupled to a compartment-based model in the other. Rather than attempting to balance average fluxes, our algorithms answer a more fundamental question: 'how are individual particles transported between the vastly different model descriptions?' First, we present an algorithm derived by carefully redefining the continuous PDE concentration as a probability distribution. While this first algorithm shows very strong convergence to analytical solutions of test problems, it can be cumbersome to simulate. Our second algorithm is a simplified and more efficient implementation of

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...

Phase transitions in a lattice population model

International Nuclear Information System (INIS)

Windus, Alastair; Jensen, Henrik J

2007-01-01

We introduce a model for a population on a lattice with diffusion and birth/death according to 2A→3A and A→Φ for a particle A. We find that the model displays a phase transition from an active to an absorbing state which is continuous in 1 + 1 dimensions and of first-order in higher dimensions in agreement with the mean field equation. For the (1 + 1)-dimensional case, we examine the critical exponents and a scaling function for the survival probability and show that it belongs to the universality class of directed percolation. In higher dimensions, we look at the first-order phase transition by plotting a histogram of the population density and use the presence of phase coexistence to find an accurate value for the critical point in 2 + 1 dimensions

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.

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.

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.

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.

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/.

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.

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.

Diffusion induced nuclear reactions in metals: a possible source of heat in the core

International Nuclear Information System (INIS)

Hamza, V.M.; Iyer, S.S.S.

1989-01-01

It has recently been proposed that diffusion of light nuclei in metals can give rise to unusual electrical charge distributions in their lattice structures, inducing thereby certain nuclear reactions that are otherwise uncommon. In the light of these results we advance the hypothesis that such nuclear reactions take place in the metal rich core of the earth, based on following observations: 1 - The solubility of hydrogen in metals is relatively high compared to that in silicates. 2 - Studies of rare gas samples in intraplate volcanos and diamonds show that 3 He/ He ratio increases with depth in the mantle. 3 - There are indications that He is positively correlated with enrichment of metals in lavas. We propose that hydrogen incorporated into metallic phases at the time of planetary accretion was carried to the core by downward migration of metal rich melts during the early states of proto-earth. Preliminary estimates suggest that cold fusion reactions can give rise to an average rate of heat generation of 8.2x10 12 W and may thus serve as a supplementary source of energy for the geomagnetic dynamo. (author)

Comparison of measured and calculated reaction rate distributions in an scwr-like test lattice

Energy Technology Data Exchange (ETDEWEB)

Raetz, Dominik, E-mail: dominik.raetz@psi.ch [Paul Scherrer Institut, CH-5232 Villigen PSI (Switzerland); Jordan, Kelly A., E-mail: kelly.jordan@psi.ch [Paul Scherrer Institut, CH-5232 Villigen PSI (Switzerland); Murphy, Michael F., E-mail: mike.murphy@psi.ch [Paul Scherrer Institut, CH-5232 Villigen PSI (Switzerland); Perret, Gregory, E-mail: gregory.perret@psi.ch [Paul Scherrer Institut, CH-5232 Villigen PSI (Switzerland); Chawla, Rakesh, E-mail: rakesh.chawla@psi.ch [Paul Scherrer Institut, CH-5232 Villigen PSI (Switzerland); Ecole Polytechnique Federale de Lausanne (EPFL), CH-1015 Lausanne, EPFL (Switzerland)

2011-04-15

High resolution gamma-ray spectroscopy measurements were performed on 61 rods of an SCWR-like fuel lattice, after irradiation in the central test zone of the PROTEUS zero-power research reactor at the Paul Scherrer Institute in Switzerland. The derived reaction rates are the capture rate in {sup 238}U (C{sub 8}) and the total fission rate (F{sub tot}), and also the reaction rate ratio C{sub 8}/F{sub tot}. Each of these has been mapped rod-wise on the lattice and compared to calculated results from whole-reactor Monte Carlo simulations with MCNPX. Ratios of calculated to experimental values (C/E's) have been assessed for the C{sub 8}, F{sub tot} and C{sub 8}/F{sub tot} distributions across the lattice. These C/E's show excellent agreement between the calculations and the measurements. For the {sup 238}U capture rate distribution, the 1{sigma} level in the comparisons corresponds to an uncertainty of {+-}0.8%, while for the total fission rate the corresponding value is {+-}0.4%. The uncertainty for C{sub 8}/F{sub tot}, assessed as a reaction rate ratio characterizing each individual rod position in the test lattice, is significantly higher at {+-}2.2%. To determine the reproducibility of these results, the measurements were performed twice, once in 2006 and again in 2009. The agreement between these two measurement sets is within the respective statistical uncertainties.

Lattice gas cellular automata and lattice Boltzmann models an introduction

CERN Document Server

Wolf-Gladrow, Dieter A

2000-01-01

Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.

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.

Lattice Boltzmann based multicomponent reactive transport model coupled with geochemical solver for scale simulations

NARCIS (Netherlands)

Patel, R.A.; Perko, J.; Jaques, D.; De Schutter, G.; Ye, G.; Van Breugel, K.

2013-01-01

A Lattice Boltzmann (LB) based reactive transport model intended to capture reactions and solid phase changes occurring at the pore scale is presented. The proposed approach uses LB method to compute multi component mass transport. The LB multi-component transport model is then coupled with the

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

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

Quantum lattice model solver HΦ

Science.gov (United States)

Kawamura, Mitsuaki; Yoshimi, Kazuyoshi; Misawa, Takahiro; Yamaji, Youhei; Todo, Synge; Kawashima, Naoki

2017-08-01

HΦ [aitch-phi ] is a program package based on the Lanczos-type eigenvalue solution applicable to a broad range of quantum lattice models, i.e., arbitrary quantum lattice models with two-body interactions, including the Heisenberg model, the Kitaev model, the Hubbard model and the Kondo-lattice model. While it works well on PCs and PC-clusters, HΦ also runs efficiently on massively parallel computers, which considerably extends the tractable range of the system size. In addition, unlike most existing packages, HΦ supports finite-temperature calculations through the method of thermal pure quantum (TPQ) states. In this paper, we explain theoretical background and user-interface of HΦ. We also show the benchmark results of HΦ on supercomputers such as the K computer at RIKEN Advanced Institute for Computational Science (AICS) and SGI ICE XA (Sekirei) at the Institute for the Solid State Physics (ISSP).

An Active Lattice Model in a Bayesian Framework

DEFF Research Database (Denmark)

Carstensen, Jens Michael

1996-01-01

A Markov Random Field is used as a structural model of a deformable rectangular lattice. When used as a template prior in a Bayesian framework this model is powerful for making inferences about lattice structures in images. The model assigns maximum probability to the perfect regular lattice...... by penalizing deviations in alignment and lattice node distance. The Markov random field represents prior knowledge about the lattice structure, and through an observation model that incorporates the visual appearance of the nodes, we can simulate realizations from the posterior distribution. A maximum...... a posteriori (MAP) estimate, found by simulated annealing, is used as the reconstructed lattice. The model was developed as a central part of an algorithm for automatic analylsis of genetic experiments, positioned in a lattice structure by a robot. The algorithm has been successfully applied to many images...

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.

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.

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

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...

Global Existence Analysis of Cross-Diffusion Population Systems for Multiple Species

Science.gov (United States)

Chen, Xiuqing; Daus, Esther S.; Jüngel, Ansgar

2018-02-01

The existence of global-in-time weak solutions to reaction-cross-diffusion systems for an arbitrary number of competing population species is proved. The equations can be derived from an on-lattice random-walk model with general transition rates. In the case of linear transition rates, it extends the two-species population model of Shigesada, Kawasaki, and Teramoto. The equations are considered in a bounded domain with homogeneous Neumann boundary conditions. The existence proof is based on a refined entropy method and a new approximation scheme. Global existence follows under a detailed balance or weak cross-diffusion condition. The detailed balance condition is related to the symmetry of the mobility matrix, which mirrors Onsager's principle in thermodynamics. Under detailed balance (and without reaction) the entropy is nonincreasing in time, but counter-examples show that the entropy may increase initially if detailed balance does not hold.

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...

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.

Stochastic motion of a particle in a model fluctuating medium

International Nuclear Information System (INIS)

Moreau, M.; Gaveau, B.; Perera, A.; Frankowicz, M.

1993-01-01

We present several models of time fluctuating media with finite memory, consisting in one and two-dimensional lattices, the Modes of which fluctuate between two internal states according to a Poisson process. A particle moves on the lattice, the diffusion by the Modes depending on their internal state. Such models can be used for the microscopic theory of reaction constants in a dense phase, or for the study of diffusion or reactivity in a complex medium. In a number of cases, the transmission probability of the medium is computed exactly; it is shown that stochastic resonances can occur, an optimal transmission being obtained for a convenient choice of parameters. In more general situations, approximate solutions are given in the case of short and moderate memory of the obstacles. The diffusion in an infinite two-dimensional lattice is studied, and the memory is shown to affect the distribution of the particles rather than the diffusion law. (author). 25 refs, 5 figs

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.

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.

Kinetic models for irreversible processes on a lattice

Energy Technology Data Exchange (ETDEWEB)

Wolf, N.O.

1979-04-01

The development and application of kinetic lattice models are considered. For the most part, the discussions are restricted to lattices in one-dimension. In Chapter 1, a brief overview of kinetic lattice model formalisms and an extensive literature survey are presented. A review of the kinetic models for non-cooperative lattice events is presented in Chapter 2. The development of cooperative lattice models and solution of the resulting kinetic equations for an infinite and a semi-infinite lattice are thoroughly discussed in Chapters 3 and 4. The cooperative models are then applied to the problem of theoretically dtermining the sticking coefficient for molecular chemisorption in Chapter 5. In Chapter 6, other possible applications of these models and several model generalizations are considered. Finally, in Chapter 7, an experimental study directed toward elucidating the mechanistic factors influencing the chemisorption of methane on single crystal tungsten is reported. In this it differs from the rest of the thesis which deals with the statistical distributions resulting from a given mechanism.

Kinetic models for irreversible processes on a lattice

International Nuclear Information System (INIS)

Wolf, N.O.

1979-04-01

The development and application of kinetic lattice models are considered. For the most part, the discussions are restricted to lattices in one-dimension. In Chapter 1, a brief overview of kinetic lattice model formalisms and an extensive literature survey are presented. A review of the kinetic models for non-cooperative lattice events is presented in Chapter 2. The development of cooperative lattice models and solution of the resulting kinetic equations for an infinite and a semi-infinite lattice are thoroughly discussed in Chapters 3 and 4. The cooperative models are then applied to the problem of theoretically dtermining the sticking coefficient for molecular chemisorption in Chapter 5. In Chapter 6, other possible applications of these models and several model generalizations are considered. Finally, in Chapter 7, an experimental study directed toward elucidating the mechanistic factors influencing the chemisorption of methane on single crystal tungsten is reported. In this it differs from the rest of the thesis which deals with the statistical distributions resulting from a given mechanism

Lattice Boltzmann heat transfer model for permeable voxels

Science.gov (United States)

Pereira, Gerald G.; Wu, Bisheng; Ahmed, Shakil

2017-12-01

We develop a gray-scale lattice Boltzmann (LB) model to study fluid flow combined with heat transfer for flow through porous media where voxels may be partially solid (or void). Heat transfer in rocks may lead to deformation, which in turn can modulate the fluid flow and so has significant contribution to rock permeability. The LB temperature field is compared to a finite difference solution of the continuum partial differential equations for fluid flow in a channel. Excellent quantitative agreement is found for both Poiseuille channel flow and Brinkman flow. The LB model is then applied to sample porous media such as packed beds and also more realistic sandstone rock sample, and both the convective and diffusive regimes are recovered when varying the thermal diffusivity. It is found that while the rock permeability can be comparatively small (order milli-Darcy), the temperature field can show significant variation depending on the thermal convection of the fluid. This LB method has significant advantages over other numerical methods such as finite and boundary element methods in dealing with coupled fluid flow and heat transfer in rocks which have irregular and nonsmooth pore spaces.

Diffusion of innovations in Axelrod’s model

Science.gov (United States)

Tilles, Paulo F. C.; Fontanari, José F.

2015-11-01

Axelrod's model for the dissemination of culture contains two key factors required to model the process of diffusion of innovations, namely, social influence (i.e., individuals become more similar when they interact) and homophily (i.e., individuals interact preferentially with similar others). The strength of these social influences are controlled by two parameters: $F$, the number of features that characterizes the cultures and $q$, the common number of states each feature can assume. Here we assume that the innovation is a new state of a cultural feature of a single individual -- the innovator -- and study how the innovation spreads through the networks among the individuals. For infinite regular lattices in one (1D) and two dimensions (2D), we find that initially the successful innovation spreads linearly with the time $t$, but in the long-time limit it spreads diffusively ($\\sim t^{1/2}$) in 1D and sub-diffusively ($\\sim t/\\ln t$) in 2D. For finite lattices, the growth curves for the number of adopters are typically concave functions of $t$. For random graphs with a finite number of nodes $N$, we argue that the classical S-shaped growth curves result from a trade-off between the average connectivity $K$ of the graph and the per feature diversity $q$. A large $q$ is needed to reduce the pace of the initial spreading of the innovation and thus delimit the early-adopters stage, whereas a large $K$ is necessary to ensure the onset of the take-off stage at which the number of adopters grows superlinearly with $t$. In an infinite random graph we find that the number of adopters of a successful innovation scales with $t^\\gamma$ with $\\gamma =1$ for $K> 2$ and $1/2 < \\gamma < 1$ for $K=2$. We suggest that the exponent $\\gamma$ may be a useful index to characterize the process of diffusion of successful innovations in diverse scenarios.

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

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

Drift mechanism of mass transfer on heterogeneous reaction in crystalline silicon substrate

Energy Technology Data Exchange (ETDEWEB)

Kukushkin, S.A. [Institute of Problems of Mechanical Engineering, Russian Academy of Science, St Petersburg, 199178 (Russian Federation); St. Petersburg National Research University of Information Technologies, Mechanics and Optics, 197101 (Russian Federation); Osipov, A.V., E-mail: Andrey.V.Osipov@gmail.com [Institute of Problems of Mechanical Engineering, Russian Academy of Science, St Petersburg, 199178 (Russian Federation); St. Petersburg National Research University of Information Technologies, Mechanics and Optics, 197101 (Russian Federation)

2017-05-01

This work aims to study the pressure dependence of the thickness of the epitaxial silicon carbide film growing from crystalline silicon due to the heterogeneous reaction with gaseous carbon monoxide. It turned out that this dependence exhibits the clear maximum. On further pressure increasing the film thickness decreases. The theoretical model has been developed which explains such a character of the dependence by the fact that the gaseous silicon monoxide reaction product inhibits the drift of the gaseous reagent through the channels of a crystal lattice, thus decreasing their hydraulic diameter. In the proposed hydraulic model, the dependences of the film thickness both on the gas pressure and time have been calculated. It was shown that not only the qualitative but also quantitative correspondence between theoretical and experimental results takes place. As one would expect, due to the Einstein relation, at short growth times the drift model coincides with the diffusion one. Consequences of this drift mechanism of epitaxial film growing are discussed. - Graphical abstract: This work aims to study the pressure dependence of the thickness of the epitaxial silicon carbide film growing from crystalline silicon due to the heterogeneous reaction with gaseous carbon monoxide. It turned out that this dependence exhibits the clear maximum. On further pressure increasing the film thickness decreases. The theoretical model has been developed which explains such a character of the dependence by the fact that the gaseous silicon monoxide reaction product inhibits the drift of the gaseous reagent through the channels of a crystal lattice, thus decreasing their hydraulic diameter. - Highlights: • It is established that the greater pressure, the smaller is the reaction rate. • The reaction product prevents penetration of the reagent into a reaction zone. • For description the hydraulic model of crystal lattice channels is developed. • Theoretical results for polytropic

Confining Domains Lead to Reaction Bursts: Reaction Kinetics in the Plasma Membrane

Science.gov (United States)

Kalay, Ziya; Fujiwara, Takahiro K.; Kusumi, Akihiro

2012-01-01

Confinement of molecules in specific small volumes and areas within a cell is likely to be a general strategy that is developed during evolution for regulating the interactions and functions of biomolecules. The cellular plasma membrane, which is the outermost membrane that surrounds the entire cell, was considered to be a continuous two-dimensional liquid, but it is becoming clear that it consists of numerous nano-meso-scale domains with various lifetimes, such as raft domains and cytoskeleton-induced compartments, and membrane molecules are dynamically trapped in these domains. In this article, we give a theoretical account on the effects of molecular confinement on reversible bimolecular reactions in a partitioned surface such as the plasma membrane. By performing simulations based on a lattice-based model of diffusion and reaction, we found that in the presence of membrane partitioning, bimolecular reactions that occur in each compartment proceed in bursts during which the reaction rate is sharply and briefly increased even though the asymptotic reaction rate remains the same. We characterized the time between reaction bursts and the burst amplitude as a function of the model parameters, and discussed the biological significance of the reaction bursts in the presence of strong inhibitor activity. PMID:22479350

Confining domains lead to reaction bursts: reaction kinetics in the plasma membrane.

Directory of Open Access Journals (Sweden)

Ziya Kalay

Full Text Available Confinement of molecules in specific small volumes and areas within a cell is likely to be a general strategy that is developed during evolution for regulating the interactions and functions of biomolecules. The cellular plasma membrane, which is the outermost membrane that surrounds the entire cell, was considered to be a continuous two-dimensional liquid, but it is becoming clear that it consists of numerous nano-meso-scale domains with various lifetimes, such as raft domains and cytoskeleton-induced compartments, and membrane molecules are dynamically trapped in these domains. In this article, we give a theoretical account on the effects of molecular confinement on reversible bimolecular reactions in a partitioned surface such as the plasma membrane. By performing simulations based on a lattice-based model of diffusion and reaction, we found that in the presence of membrane partitioning, bimolecular reactions that occur in each compartment proceed in bursts during which the reaction rate is sharply and briefly increased even though the asymptotic reaction rate remains the same. We characterized the time between reaction bursts and the burst amplitude as a function of the model parameters, and discussed the biological significance of the reaction bursts in the presence of strong inhibitor activity.

Coupled reaction-diffusion equations to model the fission gas release in the irradiation of the uranium dioxide

International Nuclear Information System (INIS)

Moyano, Edgardo A.; Scarpettini, Alberto F.

2003-01-01

A semi linear model of weakly coupled parabolic p.d.e. with reaction-diffusion is investigated. The system describes fission gas transfer from grain interior of UO 2 to grain boundaries. The problem is studied in a bounded domain. Using the upper-lower solutions method, two monotone sequences for the finite differences equations are constructed. Reasons are mentioned that allow to affirm that in the proposed functional sector the algorithm converges to the unique solution of the differential system. (author)

Analyses of Lattice Traffic Flow Model on a Gradient Highway

International Nuclear Information System (INIS)

Gupta Arvind Kumar; Redhu Poonam; Sharma Sapna

2014-01-01

The optimal current difference lattice hydrodynamic model is extended to investigate the traffic flow dynamics on a unidirectional single lane gradient highway. The effect of slope on uphill/downhill highway is examined through linear stability analysis and shown that the slope significantly affects the stability region on the phase diagram. Using nonlinear stability analysis, the Burgers, Korteweg-deVries (KdV) and modified Korteweg-deVries (mKdV) equations are derived in stable, metastable and unstable region, respectively. The effect of reaction coefficient is examined and concluded that it plays an important role in suppressing the traffic jams on a gradient highway. The theoretical findings have been verified through numerical simulation which confirm that the slope on a gradient highway significantly influence the traffic dynamics and traffic jam can be suppressed efficiently by considering the optimal current difference effect in the new lattice model. (nuclear physics)

A generalized diffusion model for growth of nanoparticles synthesized by colloidal methods.

Science.gov (United States)

Wen, Tianlong; Brush, Lucien N; Krishnan, Kannan M

2014-04-01

A nanoparticle growth model is developed to predict and guide the syntheses of monodisperse colloidal nanoparticles in the liquid phase. The model, without any a priori assumptions, is based on the Fick's law of diffusion, conservation of mass and the Gibbs-Thomson equation for crystal growth. In the limiting case, this model reduces to the same expression as the currently accepted model that requires the assumption of a diffusion layer around each nanoparticle. The present growth model bridges the two limiting cases of the previous model i.e. complete diffusion controlled and adsorption controlled growth of nanoparticles. Specifically, the results show that a monodispersion of nanoparticles can be obtained both with fast monomer diffusion and with surface reaction under conditions of small diffusivity to surface reaction constant ratio that results is growth 'focusing'. This comprehensive description of nanoparticle growth provides new insights and establishes the required conditions for fabricating monodisperse nanoparticles critical for a wide range of applications. Copyright © 2013 Elsevier Inc. All rights reserved.

Hyper-lattice algebraic model for data warehousing

CERN Document Server

Sen, Soumya; Chaki, Nabendu

2016-01-01

This book presents Hyper-lattice, a new algebraic model for partially ordered sets, and an alternative to lattice. The authors analyze some of the shortcomings of conventional lattice structure and propose a novel algebraic structure in the form of Hyper-lattice to overcome problems with lattice. They establish how Hyper-lattice supports dynamic insertion of elements in a partial order set with a partial hierarchy between the set members. The authors present the characteristics and the different properties, showing how propositions and lemmas formalize Hyper-lattice as a new algebraic structure.

Modeling convection-diffusion-reaction systems for microfluidic molecular communications with surface-based receivers in Internet of Bio-Nano Things.

Directory of Open Access Journals (Sweden)

Murat Kuscu

Full Text Available We consider a microfluidic molecular communication (MC system, where the concentration-encoded molecular messages are transported via fluid flow-induced convection and diffusion, and detected by a surface-based MC receiver with ligand receptors placed at the bottom of the microfluidic channel. The overall system is a convection-diffusion-reaction system that can only be solved by numerical methods, e.g., finite element analysis (FEA. However, analytical models are key for the information and communication technology (ICT, as they enable an optimisation framework to develop advanced communication techniques, such as optimum detection methods and reliable transmission schemes. In this direction, we develop an analytical model to approximate the expected time course of bound receptor concentration, i.e., the received signal used to decode the transmitted messages. The model obviates the need for computationally expensive numerical methods by capturing the nonlinearities caused by laminar flow resulting in parabolic velocity profile, and finite number of ligand receptors leading to receiver saturation. The model also captures the effects of reactive surface depletion layer resulting from the mass transport limitations and moving reaction boundary originated from the passage of finite-duration molecular concentration pulse over the receiver surface. Based on the proposed model, we derive closed form analytical expressions that approximate the received pulse width, pulse delay and pulse amplitude, which can be used to optimize the system from an ICT perspective. We evaluate the accuracy of the proposed model by comparing model-based analytical results to the numerical results obtained by solving the exact system model with COMSOL Multiphysics.

Modeling convection-diffusion-reaction systems for microfluidic molecular communications with surface-based receivers in Internet of Bio-Nano Things.

Science.gov (United States)

Kuscu, Murat; Akan, Ozgur B

2018-01-01

We consider a microfluidic molecular communication (MC) system, where the concentration-encoded molecular messages are transported via fluid flow-induced convection and diffusion, and detected by a surface-based MC receiver with ligand receptors placed at the bottom of the microfluidic channel. The overall system is a convection-diffusion-reaction system that can only be solved by numerical methods, e.g., finite element analysis (FEA). However, analytical models are key for the information and communication technology (ICT), as they enable an optimisation framework to develop advanced communication techniques, such as optimum detection methods and reliable transmission schemes. In this direction, we develop an analytical model to approximate the expected time course of bound receptor concentration, i.e., the received signal used to decode the transmitted messages. The model obviates the need for computationally expensive numerical methods by capturing the nonlinearities caused by laminar flow resulting in parabolic velocity profile, and finite number of ligand receptors leading to receiver saturation. The model also captures the effects of reactive surface depletion layer resulting from the mass transport limitations and moving reaction boundary originated from the passage of finite-duration molecular concentration pulse over the receiver surface. Based on the proposed model, we derive closed form analytical expressions that approximate the received pulse width, pulse delay and pulse amplitude, which can be used to optimize the system from an ICT perspective. We evaluate the accuracy of the proposed model by comparing model-based analytical results to the numerical results obtained by solving the exact system model with COMSOL Multiphysics.

MURLI, 1-D Flux, Reaction Rate in Cylindrical Geometry Thermal Reactor Lattice by Transport

International Nuclear Information System (INIS)

Huria, H.C.

1985-01-01

1 - Description of problem or function: MURLI is an integral transport theory code to calculate fluxes and reaction rates in one- dimensional cylindrical geometry lattice cells of a thermal reactor. For a specified buckling, it computes k-effective using few-group diffusion theory and a few-group collapsed set of Cross sections. The code can optionally be used to solve a first order differential equation for the number density of fissile, fertile and fission product nuclei as a function of time, and to recalculate fluxes, reaction rates and k-effective at different stages of burnup. A 27-group cross section data library is included. There are four pseudo-fission products each associated with the decay chains of plutonium and uranium isotopes in addition to Rh-105, Xe-135, Np-239, U-236, Am-241, Am-242 and Am-243. There is also data for one lumped pseudo-fission product. 2 - Method of solution: Multiple collision probabilities and escape probabilities are calculated for each cylindrical shell region assuming protons are born uniformly and isotropically over the entire region volume. The equations of integral transport theory can then be solved for neutron flux. The first order differential burnup equation is solved by a fourth order Runge-Kutta method. 3 - Restrictions on the complexity of the problem: There are maxima of 8 fissionable elements, 8 resonant elements, and 20 spatial regions

Remarks on lattice gauge models

International Nuclear Information System (INIS)

Grosse, H.

1981-01-01

The author reports a study of the phase structure of lattice gauge models where one takes as a gauge group a non-abelian discrete subgroup of SU(3). In addition he comments on a lattice action proposed recently by Manton and observes that it violates a positivity property. (Auth.)

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.

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.

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

Cellular automaton model of coupled mass transport and chemical reactions

International Nuclear Information System (INIS)

Karapiperis, T.

1994-01-01

Mass transport, coupled with chemical reactions, is modelled as a cellular automaton in which solute molecules perform a random walk on a lattice and react according to a local probabilistic rule. Assuming molecular chaos and a smooth density function, we obtain the standard reaction-transport equations in the continuum limit. The model is applied to the reactions a + b ↔c and a + b →c, where we observe interesting macroscopic effects resulting from microscopic fluctuations and spatial correlations between molecules. We also simulate autocatalytic reaction schemes displaying spontaneous formation of spatial concentration patterns. Finally, we propose and discuss the limitations of a simple model for mineral-solute interaction. (author) 5 figs., 20 refs

Carbon isotope exchange between gaseous CO2 and thin solution films: Artificial cave experiments and a complete diffusion-reaction model

Science.gov (United States)

Hansen, Maximilian; Scholz, Denis; Froeschmann, Marie-Louise; Schöne, Bernd R.; Spötl, Christoph

2017-08-01

Speleothem stable carbon isotope (δ13C) records provide important paleoclimate and paleo-environmental information. However, the interpretation of these records in terms of past climate or environmental change remains challenging because of various processes affecting the δ13C signals. A process that has only been sparsely discussed so far is carbon isotope exchange between the gaseous CO2 of the cave atmosphere and the dissolved inorganic carbon (DIC) contained in the thin solution film on the speleothem, which may be particularly important for strongly ventilated caves. Here we present a novel, complete reaction diffusion model describing carbon isotope exchange between gaseous CO2 and the DIC in thin solution films. The model considers all parameters affecting carbon isotope exchange, such as diffusion into, out of and within the film, the chemical reactions occurring within the film as well as the dependence of diffusion and the reaction rates on isotopic mass and temperature. To verify the model, we conducted laboratory experiments under completely controlled, cave-analogue conditions at three different temperatures (10, 20, 30 °C). We exposed thin (≈0.1 mm) films of a NaHCO3 solution with four different concentrations (1, 2, 5 and 10 mmol/l, respectively) to a nitrogen atmosphere containing a specific amount of CO2 (1000 and 3000 ppmV). The experimentally observed temporal evolution of the pH and δ13C values of the DIC is in good agreement with the model predictions. The carbon isotope exchange times in our experiments range from ca. 200 to ca. 16,000 s and strongly depend on temperature, film thickness, atmospheric pCO2 and the concentration of DIC. For low pCO2 (between 500 and 1000 ppmV, as for strongly ventilated caves), our time constants are substantially lower than those derived in a previous study, suggesting a potentially stronger influence of carbon isotope exchange on speleothem δ13C values. However, this process should only have an

Remarks on lattice gauge models

International Nuclear Information System (INIS)

Grosse, H.

1981-01-01

The author reports on a study of the phase structure of lattice gauge models where one takes as a gauge group a non-abelian discrete subgroup of SU(3). In addition he comments on a lattice action proposed recently by Manton (1980) and observes that it violates a positivity property. (Auth.)

Towards the simplest hydrodynamic lattice-gas model.

Science.gov (United States)

Boghosian, Bruce M; Love, Peter J; Meyer, David A

2002-03-15

It has been known since 1986 that it is possible to construct simple lattice-gas cellular automata whose hydrodynamics are governed by the Navier-Stokes equations in two dimensions. The simplest such model heretofore known has six bits of state per site on a triangular lattice. In this work, we demonstrate that it is possible to construct a model with only five bits of state per site on a Kagome lattice. Moreover, the model has a simple, deterministic set of collision rules and is easily implemented on a computer. In this work, we derive the equilibrium distribution function for this lattice-gas automaton and carry out the Chapman-Enskog analysis to determine the form of the Navier-Stokes equations.

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.

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.

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....

A new consistent definition of the homogenized diffusion coefficient of a lattice, limitations of the homogenization concept, and discussion of previously defined coefficients

International Nuclear Information System (INIS)

Deniz, V.C.

1978-01-01

The problem concerned with the correct definition of the homogenized diffusion coefficient of a lattice, and the concurrent problem of whether or not a homogenized diffusion equation can be formally set up, is studied by a space-energy angle dependent treatment for a general lattice cell; using an operator notation which applies to any eigen-problem. It is shown that the diffusion coefficient should represent only leakage effects. A new definition of the diffusion coefficient is given, which combines within itself the individual merits of each of the two definitions of Benoist, and reduces to the 'uncorrected' Benoist coefficient in certain cases. The conditions under which a homogenized diffusion equation can be obtained are discussed. A compatison is made between the approach via a diffusion equation and the approach via the eigen-coefficients of Deniz. Previously defined diffusion coefficients are discussed, and it is shown that the transformed eigen-coefficients proposed by Gelbard and by Larsen are unsuitable as diffusion coefficients, and that the cell-edge normalization of the Bonalumi coefficient is not physically justifiable. (author)

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.

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.

Lattice sigma models with exact supersymmetry

International Nuclear Information System (INIS)

Simon Catterall; Sofiane Ghadab

2004-01-01

We show how to construct lattice sigma models in one, two and four dimensions which exhibit an exact fermionic symmetry. These models are discretized and twisted versions of conventional supersymmetric sigma models with N=2 supersymmetry. The fermionic symmetry corresponds to a scalar BRST charge built from the original supercharges. The lattice theories possess local actions and exhibit no fermion doubling. In the two and four dimensional theories we show that these lattice theories are invariant under additional discrete symmetries. We argue that the presence of these exact symmetries ensures that no fine tuning is required to achieve N=2 supersymmetry in the continuum limit. As a concrete example we show preliminary numerical results from a simulation of the O(3) supersymmetric sigma model in two dimensions. (author)

Hamiltonian approach to the lattice massive Schwinger model

International Nuclear Information System (INIS)

Sidorov, A.V.; Zastavenko, L.G.

1996-01-01

The authors consider the limit e 2 /m 2 much-lt 1 of the lattice massive Schwinger model, i.e., the lattice massive QED in two space-time dimensions, up to lowest order in the effective coupling constant e 2 /m 2 . Here, m is the fermion mass parameter and e is the electron charge. They compare their lattice QED model with the analogous continuous space and lattice space models, (CSM and LSM), which do not take account of the zero momentum mode, z.m.m., of the vector potential. The difference is that (due to extra z.m.m. degree of freedom) to every eigenstate of the CSM and LSM there corresponds a family of eigenstates of the authors lattice QED with the parameter λ. They restrict their consideration to small values of the parameter λ. Then, the energies of the particle states of their lattice QED and LSM do coincide (in their approximation). In the infinite periodicity length limit the Hamiltonian of the authors lattice QED (as well as the Hamiltonian of the LSM) possesses two different Hilbert spaces of eigenfunctions. Thus, in this limit the authors lattice QED model (as well as LSM) describes something like two connected, but different, worlds

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

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

Multispeed models in off-lattice Boltzmann simulations

NARCIS (Netherlands)

Bardow, A.; Karlin, I.V.; Gusev, A.A.

2008-01-01

The lattice Boltzmann method is a highly promising approach to the simulation of complex flows. Here, we realize recently proposed multispeed lattice Boltzmann models [S. Chikatamarla et al., Phys. Rev. Lett. 97 190601 (2006)] by exploiting the flexibility offered by off-lattice Boltzmann methods.

A new consistent definition of the homogenized diffusion coefficient of a lattice, limitations of the homogenization concept, and discussion of previously defined coefficients

International Nuclear Information System (INIS)

Deniz, V.C.

1980-01-01

The problem concerned with the correct definition of the homogenized diffusion coefficient of a lattice, and the concurrent problem of whether or not a homogenized diffusion equation can be formally set up, is studied by a space-energy-angle dependent treatment for a general lattice cell using an operator notation which applies to any eigen-problem. A new definition of the diffusion coefficient is given, which combines within itself the individual merits of the two definitions of Benoist. The relation between the new coefficient and the ''uncorrected'' Benoist coefficient is discussed by considering continuous-spectrum and multi-group diffusion equations. Other definitions existing in the literature are briefly discussed. It is concluded that a diffusion coefficient should represent only leakage effects. A comparison is made between the homogenization approach and the approach via eigen-coefficients, and brief indications are given of a possible scheme for the latter. (author)

Monte Carlo based diffusion coefficients for LMFBR analysis

International Nuclear Information System (INIS)

Van Rooijen, Willem F.G.; Takeda, Toshikazu; Hazama, Taira

2010-01-01

A method based on Monte Carlo calculations is developed to estimate the diffusion coefficient of unit cells. The method uses a geometrical model similar to that used in lattice theory, but does not use the assumption of a separable fundamental mode used in lattice theory. The method uses standard Monte Carlo flux and current tallies, and the continuous energy Monte Carlo code MVP was used without modifications. Four models are presented to derive the diffusion coefficient from tally results of flux and partial currents. In this paper the method is applied to the calculation of a plate cell of the fast-spectrum critical facility ZEBRA. Conventional calculations of the diffusion coefficient diverge in the presence of planar voids in the lattice, but our Monte Carlo method can treat this situation without any problem. The Monte Carlo method was used to investigate the influence of geometrical modeling as well as the directional dependence of the diffusion coefficient. The method can be used to estimate the diffusion coefficient of complicated unit cells, the limitation being the capabilities of the Monte Carlo code. The method will be used in the future to confirm results for the diffusion coefficient obtained of the Monte Carlo code. The method will be used in the future to confirm results for the diffusion coefficient obtained with deterministic codes. (author)

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

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

Turing instability for a competitor-competitor-mutualist model with nonlinear cross-diffusion effects

International Nuclear Information System (INIS)

Wen, Zijuan; Fu, Shengmao

2016-01-01

This paper deals with a strongly coupled reaction-diffusion system modeling a competitor-competitor-mutualist three-species model with diffusion, self-diffusion and nonlinear cross-diffusion and subject to Neumann boundary conditions. First, we establish the persistence of a corresponding reaction-diffusion system without self- and cross-diffusion. Second, the global asymptotic stability of the unique positive equilibrium for weakly coupled PDE system is established by using a comparison method. Moreover, under certain conditions about the intra- and inter-species effects, we prove that the uniform positive steady state is linearly unstable for the cross-diffusion system when one of the cross-diffusions is large enough. The results indicate that Turing instability can be driven solely from strong diffusion effect of the first species (or the second species or the third species) due to the pressure of the second species (or the first species).

Semi-analytical solutions of the Schnakenberg model of a reaction-diffusion cell with feedback

Science.gov (United States)

Al Noufaey, K. S.

2018-06-01

This paper considers the application of a semi-analytical method to the Schnakenberg model of a reaction-diffusion cell. The semi-analytical method is based on the Galerkin method which approximates the original governing partial differential equations as a system of ordinary differential equations. Steady-state curves, bifurcation diagrams and the region of parameter space in which Hopf bifurcations occur are presented for semi-analytical solutions and the numerical solution. The effect of feedback control, via altering various concentrations in the boundary reservoirs in response to concentrations in the cell centre, is examined. It is shown that increasing the magnitude of feedback leads to destabilization of the system, whereas decreasing this parameter to negative values of large magnitude stabilizes the system. The semi-analytical solutions agree well with numerical solutions of the governing equations.

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

Random attractors for stochastic lattice reversible Gray-Scott systems with additive noise

Directory of Open Access Journals (Sweden)

Hongyan Li

2015-10-01

Full Text Available In this article, we prove the existence of a random attractor of the stochastic three-component reversible Gray-Scott system on infinite lattice with additive noise. We use a transformation of addition involved with Ornstein-Uhlenbeck process, for proving the pullback absorbing property and the pullback asymptotic compactness of the reaction diffusion system with cubic nonlinearity.

Effects of soft interactions and bound mobility on diffusion in crowded environments: a model of sticky and slippery obstacles

Science.gov (United States)

Stefferson, Michael W.; Norris, Samantha L.; Vernerey, Franck J.; Betterton, Meredith D.; E Hough, Loren

2017-08-01

Crowded environments modify the diffusion of macromolecules, generally slowing their movement and inducing transient anomalous subdiffusion. The presence of obstacles also modifies the kinetics and equilibrium behavior of tracers. While previous theoretical studies of particle diffusion have typically assumed either impenetrable obstacles or binding interactions that immobilize the particle, in many cellular contexts bound particles remain mobile. Examples include membrane proteins or lipids with some entry and diffusion within lipid domains and proteins that can enter into membraneless organelles or compartments such as the nucleolus. Using a lattice model, we studied the diffusive movement of tracer particles which bind to soft obstacles, allowing tracers and obstacles to occupy the same lattice site. For sticky obstacles, bound tracer particles are immobile, while for slippery obstacles, bound tracers can hop without penalty to adjacent obstacles. In both models, binding significantly alters tracer motion. The type and degree of motion while bound is a key determinant of the tracer mobility: slippery obstacles can allow nearly unhindered diffusion, even at high obstacle filling fraction. To mimic compartmentalization in a cell, we examined how obstacle size and a range of bound diffusion coefficients affect tracer dynamics. The behavior of the model is similar in two and three spatial dimensions. Our work has implications for protein movement and interactions within cells.

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.

Lattice models and conformal field theories

International Nuclear Information System (INIS)

Saleur, H.

1988-01-01

Theoretical studies concerning the connection between critical physical systems and the conformal theories are reviewed. The conformal theory associated to a critical (integrable) lattice model is derived. The obtention of the central charge, critical exponents and torus partition function, using renormalization group arguments, is shown. The quantum group structure, in the integrable lattice models, and the theory of Visaro algebra representations are discussed. The relations between off-critical integrable models and conformal theories, in finite geometries, are studied

On the relationship between two popular lattice models for polymer melts

Science.gov (United States)

Subramanian, Gopinath; Shanbhag, Sachin

2008-10-01

A mapping between two well known lattice bond-fluctuation models for polymers [I. Carmesin and K. Kremer, Macromolecules 21, 2819 (1988); J. S. Shaffer, J. Chem. Phys. 101, 4205 (1994)] is investigated by performing primitive path analysis to identify the average number of monomers per entanglement. Simulations conducted using both models, and previously published data are compared in an attempt to establish relationships between molecular weight, lengthscale, and timescale. Using these relationships, an examination of the self-diffusion coefficient yields excellent agreement not only between the two models, but also with experimental data on polystyrene, polybutadiene, and polydimethylsiloxane. However, it is shown that even with the limited set of criteria examined in this paper, a true mapping between these two models is elusive. Nevertheless, a practical guide to convert between models is provided.

Aliasing modes in the lattice Schwinger model

International Nuclear Information System (INIS)

Campos, Rafael G.; Tututi, Eduardo S.

2007-01-01

We study the Schwinger model on a lattice consisting of zeros of the Hermite polynomials that incorporates a lattice derivative and a discrete Fourier transform with many properties. Such a lattice produces a Klein-Gordon equation for the boson field and the exact value of the mass in the asymptotic limit if the boundaries are not taken into account. On the contrary, if the lattice is considered with boundaries new modes appear due to aliasing effects. In the continuum limit, however, this lattice yields also a Klein-Gordon equation with a reduced mass

Finite-lattice form factors in free-fermion models

International Nuclear Information System (INIS)

Iorgov, N; Lisovyy, O

2011-01-01

We consider the general Z 2 -symmetric free-fermion model on the finite periodic lattice, which includes as special cases the Ising model on the square and triangular lattices and the Z n -symmetric BBS τ (2) -model with n = 2. Translating Kaufman's fermionic approach to diagonalization of Ising-like transfer matrices into the language of Grassmann integrals, we determine the transfer matrix eigenvectors and observe that they coincide with the eigenvectors of a square lattice Ising transfer matrix. This allows us to find exact finite-lattice form factors of spin operators for the statistical model and the associated finite-length quantum chains, of which the most general is equivalent to the XY chain in a transverse field

Thermal neutron scattering from a hydrogen-metal system in terms of a general multi-sublattice jump diffusion model

International Nuclear Information System (INIS)

Kutner, R.; Sosnowska, I.

1977-01-01

A Multi-Sublattice Jump Diffusion Model (MSJD) for hydrogen diffusion through interstitial-site lattices is presented. The MSJD approach may, in principle, be considered as an extension of the Rowe et al (J. Phys. Chem. Solids; 32:41 (1971)) model. Jump diffusion to any neighbours with different jump times which may be asymmetric in space is discussed. On the basis of the model a new method of calculating the diffusion tensor is advanced. The quasielastic, double differential cross section for thermal neutron scattering is obtained in terms of the MSJD model. The model can be used for systems in which interstitial jump diffusion of impurity particles occurs. In Part II the theoretical results are compared with those for quasielastic neutron scattering from the αNbHsub(x) system. (author)

Poly-epoxide lattices used for the coating of radioactive wastes: aging analysis in storage conditions and effects on the diffusional properties of materials

International Nuclear Information System (INIS)

Damian Pellissier, C.

1999-01-01

This work deals with the long term forecasting of the aging behaviour of epoxy-amine lattices used for the coating of radioactive wastes. In storage conditions, the oxygen of air, the radiations and the water are the three factors at the origin of the aging. The main goals have been to study the morphology changes during the aging and to model the oxidation phenomena. The transport properties allow to determine the oxygen diffusivities and solubilities. A wide range of poly-epoxide lattices has been studied, from the classical DGEBA/DDM classical lattice to the commercial coating matrix with contains both an important molar fraction of mono-epoxy and a plasticizer which lowers the vitreous transition temperature from 175 deg. C to 55 deg. C. The analysis of the diffusional parameters of these lattices shows that the solubility increases and the diffusivity decreases when the reticulation increases or when the lattice contains no plasticizer. The transport parameters necessary for the modeling laws have been determined for all lattices. The aging under thermo-activated air involves oxidation reactions which take place preferentially at the level of epoxy constituents and lead to the formation of carbonyl and amide polar oxygenated functions and to chain cleavage with the departure of phenol-type volatile products or higher mass compounds. Using a theoretical model, the hyperbolic-type oxide sites concentration profile has been precised and an important parameter, the thickness of the oxidized layer has been calculated. The radio-oxidation, performed in extreme conditions with respect to the real storage conditions, leads to the formation of polar functions without any significant degradation of lattices. The hygro-thermal aging is characterized, for the commercial matrix only, by the leaching possibility of various products initially present in the lattice and of hydrolysis products, and by the occurrence of osmotic pressure bags at the origin of cracks. This raises

Improved models of dense anharmonic lattices

Energy Technology Data Exchange (ETDEWEB)

Rosenau, P., E-mail: rosenau@post.tau.ac.il; Zilburg, A.

2017-01-15

We present two improved quasi-continuous models of dense, strictly anharmonic chains. The direct expansion which includes the leading effect due to lattice dispersion, results in a Boussinesq-type PDE with a compacton as its basic solitary mode. Without increasing its complexity we improve the model by including additional terms in the expanded interparticle potential with the resulting compacton having a milder singularity at its edges. A particular care is applied to the Hertz potential due to its non-analyticity. Since, however, the PDEs of both the basic and the improved model are ill posed, they are unsuitable for a study of chains dynamics. Using the bond length as a state variable we manipulate its dispersion and derive a well posed fourth order PDE. - Highlights: • An improved PDE model of a Newtonian lattice renders compacton solutions. • Compactons are classical solutions of the improved model and hence amenable to standard analysis. • An alternative well posed model enables to study head on interactions of lattices' solitary waves. • Well posed modeling of Hertz potential.

Lattice-enabled nuclear reactions in the nickel and hydrogen gas system

International Nuclear Information System (INIS)

Nagel, David J.

2015-01-01

Thousands of lattice-enabled nuclear reaction (LENR) experiments involving electrochemical loading of deuterium into palladium have been conducted and reported in hundreds of papers. But, it appears that the first commercial LENR power generators will employ gas loading of hydrogen onto nickel. This article reviews the scientific base for LENR in the gas-loaded Ni-H system, and some of the tests of pre-commercial prototype generators based on this combination. (author)

Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis

KAUST Repository

Ibragimov, Akif; Ritter, Laura; Walton, Jay R.

2010-01-01

This paper presents a linear, asymptotic stability analysis for a reaction-diffusionconvection system modeling atherogenesis, the initiation of atherosclerosis, as an inflammatory instability. Motivated by the disease paradigm articulated by Ross

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

Diffusion and transport in locally disordered driven lattices

International Nuclear Information System (INIS)

Wulf, Thomas; Okupnik, Alexander; Schmelcher, Peter

2016-01-01

We study the effect of disorder on the particle density evolution in a classical Hamiltonian driven lattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence of strong tails in the density distribution which even increases towards larger positions is shown, thus yielding a highly non-Gaussian particle density evolution. As the key underlying mechanism, we identify the conversion between different components of the unperturbed systems mixed phase space which is induced by the disorder. Based on the introduction of individual conversion rates between chaotic and regular components, a theoretical model is developed which correctly predicts the scaling of the particle density. The effect of disorder on the transport properties is studied where a significant enhancement of the transport for cases of localized disorder is shown, thereby contrasting strongly the merely weak modification of the transport for global disorder.

Diffusion and transport in locally disordered driven lattices

Energy Technology Data Exchange (ETDEWEB)

Wulf, Thomas, E-mail: Thomas.Wulf@physnet.uni-hamburg.de; Okupnik, Alexander [Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany); Schmelcher, Peter, E-mail: Peter.Schmelcher@physnet.uni-hamburg.de [Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany); The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)

2016-09-15

We study the effect of disorder on the particle density evolution in a classical Hamiltonian driven lattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence of strong tails in the density distribution which even increases towards larger positions is shown, thus yielding a highly non-Gaussian particle density evolution. As the key underlying mechanism, we identify the conversion between different components of the unperturbed systems mixed phase space which is induced by the disorder. Based on the introduction of individual conversion rates between chaotic and regular components, a theoretical model is developed which correctly predicts the scaling of the particle density. The effect of disorder on the transport properties is studied where a significant enhancement of the transport for cases of localized disorder is shown, thereby contrasting strongly the merely weak modification of the transport for global disorder.

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.

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.

Diffusion and reaction within porous packing media: a phenomenological model.

Science.gov (United States)

Jones, W L; Dockery, J D; Vogel, C R; Sturman, P J

1993-04-25

A phenomenological model has been developed to describe biomass distribution and substrate depletion in porous diatomaceous earth (DE) pellets colonized by Pseudomonas aeruginosa. The essential features of the model are diffusion, attachment and detachment to/from pore walls of the biomass, diffusion of substrate within the pellet, and external mass transfer of both substrate and biomass in the bulk fluid of a packed bed containing the pellets. A bench-scale reactor filled with DE pellets was inoculated with P. aeruginosa and operated in plug flow without recycle using a feed containing glucose as the limiting nutrient. Steady-state effluent glucose concentrations were measured at various residence times, and biomass distribution within the pellet was measured at the lowest residence time. In the model, microorganism/substrate kinetics and mass transfer characteristics were predicted from the literature. Only the attachment and detachment parameters were treated as unknowns, and were determined by fitting biomass distribution data within the pellets to the mathematical model. The rate-limiting step in substrate conversion was determined to be internal mass transfer resistance; external mass transfer resistance and microbial kinetic limitations were found to be nearly negligible. Only the outer 5% of the pellets contributed to substrate conversion.

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.

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.

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.

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

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.

A lattice model for influenza spreading.

Directory of Open Access Journals (Sweden)

Antonella Liccardo

Full Text Available We construct a stochastic SIR model for influenza spreading on a D-dimensional lattice, which represents the dynamic contact network of individuals. An age distributed population is placed on the lattice and moves on it. The displacement from a site to a nearest neighbor empty site, allows individuals to change the number and identities of their contacts. The dynamics on the lattice is governed by an attractive interaction between individuals belonging to the same age-class. The parameters, which regulate the pattern dynamics, are fixed fitting the data on the age-dependent daily contact numbers, furnished by the Polymod survey. A simple SIR transmission model with a nearest neighbors interaction and some very basic adaptive mobility restrictions complete the model. The model is validated against the age-distributed Italian epidemiological data for the influenza A(H1N1 during the [Formula: see text] season, with sensible predictions for the epidemiological parameters. For an appropriate topology of the lattice, we find that, whenever the accordance between the contact patterns of the model and the Polymod data is satisfactory, there is a good agreement between the numerical and the experimental epidemiological data. This result shows how rich is the information encoded in the average contact patterns of individuals, with respect to the analysis of the epidemic spreading of an infectious disease.

Self diffusion of sodium ion in sodium chloride

International Nuclear Information System (INIS)

Haridasan, T.M.; Lawrence, N.

1985-09-01

The problem of cation self diffusion in NaCl for a single vacancy mechanism is attempted using a reaction coordinate approach employing the phonons in the system. The vacancy is given an active role by estimating the displacements of its nearest neighbour Cl - ions in the environment of the vacancy through the lattice Green's functions and the t matrix formalism. The jump frequency, the isotope effect and diffusion coefficients estimated by this approach agree well with the experimentally deduced values. These results support the experimental conclusion of about 30% of vacancy pairs in the cation diffusion in NaCl. (author)

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.

Immiscible multicomponent lattice Boltzmann model for fluids with ...

Indian Academy of Sciences (India)

College of Mechanical Engineering, Tongji University, 4800# Cao'an Road, ... was developed from a discretized fluid model known as the lattice gas automata ... of two immiscible fluids, several lattice Boltzmann (LB) models have been ...

Gauge theories and integrable lattice models

International Nuclear Information System (INIS)

Witten, E.

1989-01-01

Investigations of new knot polynomials discovered in the last few years have shown them to be intimately connected with soluble models of two dimensional lattice statistical mechanics. In this paper, these results, which in time may illuminate the whole question of why integrable lattice models exist, are reconsidered from the point of view of three dimensional gauge theory. Expectation values of Wilson lines in three dimensional Chern-Simons gauge theories can be computed by evaluating the partition functions of certain lattice models on finite graphs obtained by projecting the Wilson lines to the plane. The models in question - previously considered in both the knot theory and statistical mechanics literature - are IRF models in which the local Boltzmann weights are the matrix elements of braiding matrices in rational conformal field theories. These matrix elements, in turn, can be represented in three dimensional gauge theory in terms of the expectation value of a certain tetrahedral configuration of Wilson lines. This representation makes manifest a surprising symmetry of the braiding matrix elements in conformal field theory. (orig.)

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 \

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

A Unified Theory of Non-Ideal Gas Lattice Boltzmann Models

Science.gov (United States)

Luo, Li-Shi

1998-01-01

A non-ideal gas lattice Boltzmann model is directly derived, in an a priori fashion, from the Enskog equation for dense gases. The model is rigorously obtained by a systematic procedure to discretize the Enskog equation (in the presence of an external force) in both phase space and time. The lattice Boltzmann model derived here is thermodynamically consistent and is free of the defects which exist in previous lattice Boltzmann models for non-ideal gases. The existing lattice Boltzmann models for non-ideal gases are analyzed and compared with the model derived here.

Mesoscopic effects in an agent-based bargaining model in regular lattices.

Science.gov (United States)

Poza, David J; Santos, José I; Galán, José M; López-Paredes, Adolfo

2011-03-09

The effect of spatial structure has been proved very relevant in repeated games. In this work we propose an agent based model where a fixed finite population of tagged agents play iteratively the Nash demand game in a regular lattice. The model extends the multiagent bargaining model by Axtell, Epstein and Young modifying the assumption of global interaction. Each agent is endowed with a memory and plays the best reply against the opponent's most frequent demand. We focus our analysis on the transient dynamics of the system, studying by computer simulation the set of states in which the system spends a considerable fraction of the time. The results show that all the possible persistent regimes in the global interaction model can also be observed in this spatial version. We also find that the mesoscopic properties of the interaction networks that the spatial distribution induces in the model have a significant impact on the diffusion of strategies, and can lead to new persistent regimes different from those found in previous research. In particular, community structure in the intratype interaction networks may cause that communities reach different persistent regimes as a consequence of the hindering diffusion effect of fluctuating agents at their borders.

Mesoscopic effects in an agent-based bargaining model in regular lattices.

Directory of Open Access Journals (Sweden)

David J Poza

Full Text Available The effect of spatial structure has been proved very relevant in repeated games. In this work we propose an agent based model where a fixed finite population of tagged agents play iteratively the Nash demand game in a regular lattice. The model extends the multiagent bargaining model by Axtell, Epstein and Young modifying the assumption of global interaction. Each agent is endowed with a memory and plays the best reply against the opponent's most frequent demand. We focus our analysis on the transient dynamics of the system, studying by computer simulation the set of states in which the system spends a considerable fraction of the time. The results show that all the possible persistent regimes in the global interaction model can also be observed in this spatial version. We also find that the mesoscopic properties of the interaction networks that the spatial distribution induces in the model have a significant impact on the diffusion of strategies, and can lead to new persistent regimes different from those found in previous research. In particular, community structure in the intratype interaction networks may cause that communities reach different persistent regimes as a consequence of the hindering diffusion effect of fluctuating agents at their borders.

Anomalous diffusion in niobium. Study of solute diffusion mechanism of iron in niobium

International Nuclear Information System (INIS)

Ablitzer, D.

1977-01-01

In order to explain anomalously high diffusion velocities observed for iron diffusion in niobium, the following parameters were measured: isotope effect, b factor (which expresses the effect of iron on niobium self-diffusion), self-diffusion coefficient of niobium, solute diffusion coefficient of iron in niobium. The results obtained show that neither pure vacancy models, nor diffusion in the lattice defects (dislocations, sub-boundaries, grain boundaries), nor pure interstitialy mechanisms, nor simple or cyclic exchange mechanisms agree with experiments. A mechanism is proposed which considers an equilibrium between substitution iron atoms and interstitial iron atoms. The diffusion of iron then occurs through interstitial vancancy pairs [fr

Trojan War displayed as a full annihilation-diffusion-reaction model

Science.gov (United States)

Flores, J. C.

2017-02-01

The diffusive pair annihilation model with embedded topological domains and archaeological data is applied in an analysis of the hypothetical Trojan-Greek war during the late Bronze Age. Estimations of parameter are explicitly made for critical dynamics of the model. In particular, the 8-metre walls of Troy could be viewed as the effective shield that provided the technological difference between the two armies. Suggestively, the numbers in The Iliad are quite sound, being in accord with Lanchester's laws of warfare.

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.

A drift-diffusion-reaction model for excitonic photovoltaic bilayers: Photovoltaic bilayers: Asymptotic analysis and a 2D hdg finite element scheme

KAUST Repository

Brinkman, Daniel

2013-05-01

We present and discuss a mathematical model for the operation of bilayer organic photovoltaic devices. Our model couples drift-diffusion-recombination equations for the charge carriers (specifically, electrons and holes) with a reaction-diffusion equation for the excitons/polaron pairs and Poisson\\'s equation for the self-consistent electrostatic potential. The material difference (i.e. the HOMO/LUMO gap) of the two organic substrates forming the bilayer device is included as a work-function potential. Firstly, we perform an asymptotic analysis of the scaled one-dimensional stationary state system: (i) with focus on the dynamics on the interface and (ii) with the goal of simplifying the bulk dynamics away from the interface. Secondly, we present a two-dimensional hybrid discontinuous Galerkin finite element numerical scheme which is very well suited to resolve: (i) the material changes, (ii) the resulting strong variation over the interface, and (iii) the necessary upwinding in the discretization of drift-diffusion equations. Finally, we compare the numerical results with the approximating asymptotics. © 2013 World Scientific Publishing Company.

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.

Multisite Interactions in Lattice-Gas Models

Science.gov (United States)

Einstein, T. L.; Sathiyanarayanan, R.

For detailed applications of lattice-gas models to surface systems, multisite interactions often play at least as significant a role as interactions between pairs of adatoms that are separated by a few lattice spacings. We recall that trio (3-adatom, non-pairwise) interactions do not inevitably create phase boundary asymmetries about half coverage. We discuss a sophisticated application to an experimental system and describe refinements in extracting lattice-gas energies from calculations of total energies of several different ordered overlayers. We describe how lateral relaxations complicate matters when there is direct interaction between the adatoms, an issue that is important when examining the angular dependence of step line tensions. We discuss the connector model as an alternative viewpoint and close with a brief account of recent work on organic molecule overlayers.

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.

Lattice chiral symmetry and the Wess-Zumino model

International Nuclear Information System (INIS)

Fujikawa, Kazuo; Ishibashi, Masato

2002-01-01

A lattice regularization of the supersymmetric Wess-Zumino model is studied by using Ginsparg-Wilson operators. We recognize a certain conflict between the lattice chiral symmetry and the Majorana condition for Yukawa couplings, or in Weyl representation a conflict between the lattice chiral symmetry and Yukawa couplings. This conflict is also related, though not directly, to the fact that the kinetic (Kaehler) term and the superpotential term are clearly distinguished in the continuum Wess-Zumino model, whereas these two terms are mixed in the Ginsparg-Wilson operators. We illustrate a case where lattice chiral symmetry together with naive Bose-Fermi symmetry is imposed by preserving a SUSY-like symmetry in the free part of the Lagrangian; one-loop level non-renormalization of the superpotential is then maintained for finite lattice spacing, though the finite parts of wave function renormalization deviate from the supersymmetric value. All these properties hold for the general Ginsparg-Wilson algebra independently of the detailed construction of lattice Dirac operators

Multispeed Lattice Boltzmann Model with Space-Filling Lattice for Transcritical Shallow Water Flows

Directory of Open Access Journals (Sweden)

Y. Peng

2017-01-01

Full Text Available Inspired by the recent success of applying multispeed lattice Boltzmann models with a non-space-filling lattice for simulating transcritical shallow water flows, the capabilities of their space-filling counterpart are investigated in this work. Firstly, two lattice models with five integer discrete velocities are derived by using the method of matching hydrodynamics moments and then tested with two typical 1D problems including the dam-break flow over flat bed and the steady flow over bump. In simulations, the derived space-filling multispeed models, together with the stream-collision scheme, demonstrate better capability in simulating flows with finite Froude number. However, the performance is worse than the non-space-filling model solved by finite difference scheme. The stream-collision scheme with second-order accuracy may be the reason since a numerical scheme with second-order accuracy is prone to numerical oscillations at discontinuities, which is worthwhile for further study.

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.

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.

Magnetic nanoparticles in fluid environment: combining molecular dynamics and Lattice-Boltzmann

Energy Technology Data Exchange (ETDEWEB)

Melenev, Petr, E-mail: melenev@icmm.ru [Ural Federal University, 4, Turgeneva str., 620000 Ekaterinburg (Russian Federation); Institute of Continuous Media Mechanics, 1, Koroleva str., 614013 Perm (Russian Federation)

2017-06-01

Hydrodynamic interactions between magnetic nanoparticles suspended in the Newtonian liquid are accounted for using a combination of the lattice Boltzmann method and molecular dynamics simulations. Nanoparticle is modelled by the system of molecular dynamics material points (which form structure resembles raspberry) coupled to the lattice Boltzmann fluid. The hydrodynamic coupling between the colloids is studied by simulations of the thermo-induced rotational diffusion of two raspberry objects. It was found that for the considered range of model parameters the approaching of the raspberries leads to slight retard of the relaxation process. The presence of the weak magnetic dipolar interaction between the objects leads to modest decrease of the relaxation time and the extent of the acceleration of the diffusion is intensified along with magnetic forces. - Highlights: • The combination of molecular dynamics and lattice Boltzmann method is utilized for the reveal of the role of hydrodynamic interaction in rotational dynamics of colloid particles. • The verification of the model parameters is done based on the comparison with the results of Langevin dynamics. • For the task of free rotational diffusion of the pair of colloid particles the influence of the hydrodynamic interactions on the relaxation time is examined in the case of nonmagnetic particles and at the presence of weak dipolar interaction.

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.

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

Galilean invariant lattice Boltzmann scheme for natural convection on square and rectangular lattices

NARCIS (Netherlands)

Sman, van der R.G.M.

2006-01-01

In this paper we present lattice Boltzmann (LB) schemes for convection diffusion coupled to fluid flow on two-dimensional rectangular lattices. Via inverse Chapman-Enskog analysis of LB schemes including source terms, we show that for consistency with physics it is required that the moments of the

Depressurization accident analysis of MPBR by PBRSIM with chemical reaction model

International Nuclear Information System (INIS)

No, Hee Cheon; Kadak, A. C.

2002-01-01

The simple model for natural circulation is implemented into PBR S IM to provide air inlet velocity from the containment air space. For the friction and form loss only the pebble region is considered conservatively modeling laminar flow through a packed bed. For the chemical reaction model of PBR S IM the oxidation rate is determined as the minimum value of three mechanisms estimated at each time step: oxygen mass flow rate entering the bottom of the reflector, oxidation rate by kinetics, and oxygen mass flow rate arriving at the graphite surface by diffusion. Oxygen mass flux arriving at the graphite surface by diffusion is estimated based on energy-mass analogy. Two types of exothermic chemical reaction are considered: (C + zO 2 → xCO + yCO 2 ) and (2CO + O 2 2CO 2 ). The heterogeneous and homogeneous chemical reaction rates by kinetics are determined by INEEL and Bruno correlations, respectively. The instantaneous depressurization accident of MPBR is simulated using PBR S IM with chemical model. The air inlet velocity is initially rapidly dropped within 10 hr and reaches a saturation value of about 1.5cm/s. The oxidation rate by the diffusion process becomes lower than that by the chemical kinetics above 600K. The maximum pebble bed temperatures without and with chemical reaction reach the peak values of 1560 and 1617 .deg. C at 80 hr and 92 hr, respectively. As the averaged temperatures in the bottom reflector and the pebble bed regions increase with time, (C+1/2O2 ->CO) reaction becomes dominant over (C+O 2 →CO 2 ) reaction. Also, the CO generated by (C+1/2O 2 →CO) reaction will be consumed by (2CO+O 2 →2CO 2 ) reaction and the energy homogeneously generated by this CO depletion reaction becomes dominant over the heterogeneous reaction

Statistical mechanics of directed models of polymers in the square lattice

CERN Document Server

Rensburg, J V

2003-01-01

Directed square lattice models of polymers and vesicles have received considerable attention in the recent mathematical and physical sciences literature. These are idealized geometric directed lattice models introduced to study phase behaviour in polymers, and include Dyck paths, partially directed paths, directed trees and directed vesicles models. Directed models are closely related to models studied in the combinatorics literature (and are often exactly solvable). They are also simplified versions of a number of statistical mechanics models, including the self-avoiding walk, lattice animals and lattice vesicles. The exchange of approaches and ideas between statistical mechanics and combinatorics have considerably advanced the description and understanding of directed lattice models, and this will be explored in this review. The combinatorial nature of directed lattice path models makes a study using generating function approaches most natural. In contrast, the statistical mechanics approach would introduce...

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.

What Can the Diffusion Model Tell Us About Prospective Memory?

Science.gov (United States)

Horn, Sebastian S.; Bayen, Ute J.; Smith, Rebekah E.

2011-01-01

Cognitive process models, such as Ratcliff’s (1978) diffusion model, are useful tools for examining cost- or interference effects in event-based prospective memory (PM). The diffusion model includes several parameters that provide insight into how and why ongoing-task performance may be affected by a PM task and is ideally suited to analyze performance because both reaction time and accuracy are taken into account. Separate analyses of these measures can easily yield misleading interpretations in cases of speed-accuracy tradeoffs. The diffusion model allows us to measure possible criterion shifts and is thus an important methodological improvement over standard analyses. Performance in an ongoing lexical decision task (Smith, 2003) was analyzed with the diffusion model. The results suggest that criterion shifts play an important role when a PM task is added, but do not fully explain the cost effect on RT. PMID:21443332

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.

Reaction-diffusion models of decontamination

DEFF Research Database (Denmark)

Hjorth, Poul G.

A contaminant, which also contains a polymer is in the form of droplets on a solid surface. It is to be removed by the action of a decontaminant, which is applied in aqueous solution. The contaminant is only sparingly soluble in water, so the reaction mechanism is that it slowly dissolves...

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 ...

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.

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.

Representations of the Virasoro algebra from lattice models

International Nuclear Information System (INIS)

Koo, W.M.; Saleur, H.

1994-01-01

We investigate in detail how the Virasoro algebra appears in the scaling limit of the simplest lattice models of XXZ or RSOS type. Our approach is straightforward but to our knowledge had never been tried so far. We simply formulate a conjecture for the lattice stress-energy tensor motivated by the exact derivation of lattice global Ward identities. We then check that the proper algebraic relations are obeyed in the scaling limit. The latter is under reasonable control thanks to the Bethe-ansatz solution. The results, which are mostly numerical for technical reasons, are remarkably precise. They are also corroborated by exact pieces of information from various sources, in particular Temperley-Lieb algebra representation theory. Most features of the Virasoro algebra (like central term, null vectors, metric properties, etc.) can thus be observed using the lattice models. This seems of general interest for lattice field theory, and also more specifically for finding relations between conformal invariance and lattice integrability, since a basis for the irreducible representations of the Virasoro algebra should now follow (at least in principle) from Bethe-ansatz computations. ((orig.))

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.

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.

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

Multiplex polymerase chain reaction-based prognostic models in diffuse large B-cell lymphoma patients treated with R-CHOP

DEFF Research Database (Denmark)

Green, Tina M; Jensen, Andreas K; Holst, René

2016-01-01

We present a multiplex analysis for genes known to have prognostic value in an attempt to design a clinically useful classification model in patients with diffuse large B-cell lymphoma (DLBCL). Real-time polymerase chain reaction was used to measure transcript levels of 28 relevant genes in 194 de...... models. The best model was validated in data from an online available R-CHOP treated cohort. With progression-free survival (PFS) as primary endpoint, the best performing IPI independent model incorporated the LMO2 and HLADQA1 as well as gene interactions for GCSAMxMIB1, GCSAMxCTGF and FOXP1xPDE4B....... This model assigned 33% of patients (n = 60) to poor outcome with an estimated 3-year PFS of 40% vs. 87% for low risk (n = 61) and intermediate (n = 60) risk groups (P model incorporated LMO2 and BCL2 and assigned 33% of the patients with a 3-year PFS of 35% vs...

Dynamic Characteristics and Model for Centralization Reaction of Acidic Tailings From Heap Leaching of Uranium Ore

International Nuclear Information System (INIS)

Ding Dexin; Liu Yulong; Li Guangyue; Wang Youtuan

2010-01-01

Centralization tests were carried out on acidic tailings from heap leaching of uranium ore by using CaO, NaOH and NH 4 OH. The variations of pH with time were measured for the three centralization systems and the dynamic models for the systems were set up by regressing the measured data. The centralization process consists of the fast reaction phase representing the reaction between the centralization agent and the acid on the surface of the tailing's particles and the slow diffusion-reaction phase representing the diffusion-reaction between the centralization agent and the acid within the tailing's particles. The non-linear coupling and feedback function model for the diffusion-reaction of the centralization agent can reflect the process and mode of the centralization reaction. There is a non-linear oscillation in the variation of pH within the centralization systems. The dynamic model for the tailing's centralization reaction can fit the pH variation within the centralization systems. (authors)

Numerical simulation of direct methanol fuel cells using lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Delavar, Mojtaba Aghajani; Farhadi, Mousa; Sedighi, Kurosh [Faculty of Mechanical Engineering, Babol University of Technology, Babol, P.O. Box 484 (Iran)

2010-09-15

In this study Lattice Boltzmann Method (LBM) as an alternative of conventional computational fluid dynamics method is used to simulate Direct Methanol Fuel Cell (DMFC). A two dimensional lattice Boltzmann model with 9 velocities, D2Q9, is used to solve the problem. The computational domain includes all seven parts of DMFC: anode channel, catalyst and diffusion layers, membrane and cathode channel, catalyst and diffusion layers. The model has been used to predict the flow pattern and concentration fields of different species in both clear and porous channels to investigate cell performance. The results have been compared well with results in literature for flow in porous and clear channels and cell polarization curves of the DMFC at different flow speeds and feed methanol concentrations. (author)

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

Construction and analysis of lattice Boltzmann methods applied to a 1D convection-diffusion equation

International Nuclear Information System (INIS)

Dellacherie, Stephane

2014-01-01

To solve the 1D (linear) convection-diffusion equation, we construct and we analyze two LBM schemes built on the D1Q2 lattice. We obtain these LBM schemes by showing that the 1D convection-diffusion equation is the fluid limit of a discrete velocity kinetic system. Then, we show in the periodic case that these LBM schemes are equivalent to a finite difference type scheme named LFCCDF scheme. This allows us, firstly, to prove the convergence in L∞ of these schemes, and to obtain discrete maximum principles for any time step in the case of the 1D diffusion equation with different boundary conditions. Secondly, this allows us to obtain most of these results for the Du Fort-Frankel scheme for a particular choice of the first iterate. We also underline that these LBM schemes can be applied to the (linear) advection equation and we obtain a stability result in L∞ under a classical CFL condition. Moreover, by proposing a probabilistic interpretation of these LBM schemes, we also obtain Monte-Carlo algorithms which approach the 1D (linear) diffusion equation. At last, we present numerical applications justifying these results. (authors)

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.)

A lattice gas model on a tangled chain

International Nuclear Information System (INIS)

Mejdani, R.

1993-04-01

We have used a model of a lattice gas defined on a tangled chain to study the enzyme kinetics by a modified transfer matrix method. By using a simple iterative algorithm we have obtained different kinds of saturation curves for different configurations of the tangled chain and different types of the additional interactions. In some special cases of configurations and interactions we have found the same equations for the saturation curves, which we have obtained before studying the lattice gas model with nearest neighbor interactions or the lattice gas model with alternate nearest neighbor interactions, using different techniques as the correlated walks' theory, the partition point technique or the transfer matrix model. This more general model and the new results could be useful for the experimental investigations. (author). 20 refs, 6 figs

Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices.

Science.gov (United States)

Español, Malena I; Golovaty, Dmitry; Wilber, J Patrick

2018-01-01

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

Bayesian Analysis of Geostatistical Models With an Auxiliary Lattice

KAUST Repository

Park, Jincheol; Liang, Faming

2012-01-01

of observations is large. In this article, we propose an auxiliary lattice-based approach for tackling this difficulty. By introducing an auxiliary lattice to the space of observations and defining a Gaussian Markov random field on the auxiliary lattice, our model

Study of the diffusion of lithium and sodium ions in solids under regardment of the dimensionality of the crystal lattice; Untersuchung der Diffusion von Lithium- und Natrium-Ionen in Festkoerpern unter Beruecksichtigung der Dimensionalitaet des Kristallgitters

Energy Technology Data Exchange (ETDEWEB)

Volgmann, Kai Tristan

2016-07-29

Low-dimensional diffusion was investigated to improve the understanding of the fundamentals of ion movement in condensed matter. Different model systems with different dimensionality of cation migration pathways were investigated using solidstate nuclear magnetic resonance (NMR) spectroscopy and impedance spectroscopy. Both experimental methods made it possible to complementarily study both Li and Na mobility over a wide range of jump rates. Metallic lithium as a well-known model system for isotropic diffusion was investigated using {sup 7}Li field-cycling NMR. The spin-lattice relaxation (SLR) rates were separated into an electronic contribution and a diffusion-induced contribution. The Korringa product was calculated from the actual measurements. The main focus was the comparison of different theoretical models describing the Li motion in metallic lithium. The well-known model by Bloembergen, Purcell and Pound already reproduced the data well, but two models by Sholl improved the results taking into account the type of crystal lattice and jump correlation effects. A single-vacancy diffusion mechanism was observed, but a double-vacancy mechanism was not excluded as elevated temperatures near the melting point of lithium were not available. Li{sub 0.7}Nb{sub 3}S{sub 4} is isostructural to Li{sub 0.7}Nb{sub 3}Se{sub 4} which was reported as possible 1D Li ion conductor due to its channel structure. Thus, Li{sub 0.7}Nb{sub 3}S{sub 4} was investigated as 1D model system using solid-state NMR spectroscopy. Multinuclear NMR spectroscopy gave insights into structural properties. Li dynamics was observed by several NMR methods over a wide temperature range. {sup 7}Li NMR motional narrowing led to an estimate of the activation energy for local Li hopping. {sup 7}Li NMR spin-alignment echo (SAE) was used for the determination of Li jump rates on a macroscopic scale. Possible dimensionality effects were investigated by {sup 7}Li NMR SLR. Out of the phase system Li{sub 2}O

On the characterization and software implementation of general protein lattice models.

Directory of Open Access Journals (Sweden)

Alessio Bechini

Full Text Available models of proteins have been widely used as a practical means to computationally investigate general properties of the system. In lattice models any sterically feasible conformation is represented as a self-avoiding walk on a lattice, and residue types are limited in number. So far, only two- or three-dimensional lattices have been used. The inspection of the neighborhood of alpha carbons in the core of real proteins reveals that also lattices with higher coordination numbers, possibly in higher dimensional spaces, can be adopted. In this paper, a new general parametric lattice model for simplified protein conformations is proposed and investigated. It is shown how the supporting software can be consistently designed to let algorithms that operate on protein structures be implemented in a lattice-agnostic way. The necessary theoretical foundations are developed and organically presented, pinpointing the role of the concept of main directions in lattice-agnostic model handling. Subsequently, the model features across dimensions and lattice types are explored in tests performed on benchmark protein sequences, using a Python implementation. Simulations give insights on the use of square and triangular lattices in a range of dimensions. The trend of potential minimum for sequences of different lengths, varying the lattice dimension, is uncovered. Moreover, an extensive quantitative characterization of the usage of the so-called "move types" is reported for the first time. The proposed general framework for the development of lattice models is simple yet complete, and an object-oriented architecture can be proficiently employed for the supporting software, by designing ad-hoc classes. The proposed framework represents a new general viewpoint that potentially subsumes a number of solutions previously studied. The adoption of the described model pushes to look at protein structure issues from a more general and essential perspective, making

Kinetic Monte Carlo simulations of travelling pulses and spiral waves in the lattice Lotka-Volterra model.

Science.gov (United States)

Makeev, Alexei G; Kurkina, Elena S; Kevrekidis, Ioannis G

2012-06-01

Kinetic Monte Carlo simulations are used to study the stochastic two-species Lotka-Volterra model on a square lattice. For certain values of the model parameters, the system constitutes an excitable medium: travelling pulses and rotating spiral waves can be excited. Stable solitary pulses travel with constant (modulo stochastic fluctuations) shape and speed along a periodic lattice. The spiral waves observed persist sometimes for hundreds of rotations, but they are ultimately unstable and break-up (because of fluctuations and interactions between neighboring fronts) giving rise to complex dynamic behavior in which numerous small spiral waves rotate and interact with each other. It is interesting that travelling pulses and spiral waves can be exhibited by the model even for completely immobile species, due to the non-local reaction kinetics.

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.)

A reaction-diffusion model to capture disparity selectivity in primary visual cortex.

Directory of Open Access Journals (Sweden)

Mohammed Sultan Mohiuddin Siddiqui

Full Text Available Decades of experimental studies are available on disparity selective cells in visual cortex of macaque and cat. Recently, local disparity map for iso-orientation sites for near-vertical edge preference is reported in area 18 of cat visual cortex. No experiment is yet reported on complete disparity map in V1. Disparity map for layer IV in V1 can provide insight into how disparity selective complex cell receptive field is organized from simple cell subunits. Though substantial amounts of experimental data on disparity selective cells is available, no model on receptive field development of such cells or disparity map development exists in literature. We model disparity selectivity in layer IV of cat V1 using a reaction-diffusion two-eye paradigm. In this model, the wiring between LGN and cortical layer IV is determined by resource an LGN cell has for supporting connections to cortical cells and competition for target space in layer IV. While competing for target space, the same type of LGN cells, irrespective of whether it belongs to left-eye-specific or right-eye-specific LGN layer, cooperate with each other while trying to push off the other type. Our model captures realistic 2D disparity selective simple cell receptive fields, their response properties and disparity map along with orientation and ocular dominance maps. There is lack of correlation between ocular dominance and disparity selectivity at the cell population level. At the map level, disparity selectivity topography is not random but weakly clustered for similar preferred disparities. This is similar to the experimental result reported for macaque. The details of weakly clustered disparity selectivity map in V1 indicate two types of complex cell receptive field organization.

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.

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 ...

Chemically-induced liquid film migration with low lattice diffusivity relative to the migration rate in Mo-Ni-(W)

International Nuclear Information System (INIS)

Lee, K.R.

1992-01-01

This paper reports that when a 90Mo-10Ni alloy (by wt) liquid phase sintered at 1400 degrees C is heat-treated at 1400 degrees C after replacing the matrix with a melt of 44Ni-34Mo-22W (by wt), the liquid films between the grains migrate, leaving behind an Mo alloy enriched with W. The ratio of the lattice diffusivity of W in Mo, D, to the initial migration velocity, v. (D/v) is estimated to be between 0.03 and 0.18 angstrom. Hence it appears that there is no lattice diffusion of W ahead of the migrating liquid film, and is such a case the driving force has been suggested to be the chemical free energy. But the observed v is approximately same as that to be expected if the driving force is assumed to be diffusional coherency strain energy. Likewise, a previous study of den Broeder and Nakahara shows that the rate of chemically-induced grain boundary migration in Cu-Ni shows a smooth variation with temperature as D/v decreases from values much larger than the interatomic spacing to values much smaller with decreasing temperature. The coherency strain energy thus appears to be a general driving force for the migration even when the apparent diffusion length indicated by D/v is smaller than the interatomic spacing

Boundedness for a system of reaction-diffusion equations with more general Arrhenius term. Pt. 1

International Nuclear Information System (INIS)

Okoya, S.S.

1992-11-01

In this paper, we consider an extended model of a coupled nonlinear reaction-diffusion equation with Neumann-Neumann boundary conditions. We obtain upper linear growth bound for one of the components. We also find the corresponding bound for the case of Dirichlet-Dirichlet boundary conditions. (author). 12 refs

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.

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.

Extended Hubbard models for ultracold atoms in optical lattices

International Nuclear Information System (INIS)

Juergensen, Ole

2015-01-01

In this thesis, the phase diagrams and dynamics of various extended Hubbard models for ultracold atoms in optical lattices are studied. Hubbard models are the primary description for many interacting particles in periodic potentials with the paramount example of the electrons in solids. The very same models describe the behavior of ultracold quantum gases trapped in the periodic potentials generated by interfering beams of laser light. These optical lattices provide an unprecedented access to the fundamentals of the many-particle physics that govern the properties of solid-state materials. They can be used to simulate solid-state systems and validate the approximations and simplifications made in theoretical models. This thesis revisits the numerous approximations underlying the standard Hubbard models with special regard to optical lattice experiments. The incorporation of the interaction between particles on adjacent lattice sites leads to extended Hubbard models. Offsite interactions have a strong influence on the phase boundaries and can give rise to novel correlated quantum phases. The extended models are studied with the numerical methods of exact diagonalization and time evolution, a cluster Gutzwiller approximation, as well as with the strong-coupling expansion approach. In total, this thesis demonstrates the high relevance of beyond-Hubbard processes for ultracold atoms in optical lattices. Extended Hubbard models can be employed to tackle unexplained problems of solid-state physics as well as enter previously inaccessible regimes.

Extended Hubbard models for ultracold atoms in optical lattices

Energy Technology Data Exchange (ETDEWEB)

Juergensen, Ole

2015-06-05

In this thesis, the phase diagrams and dynamics of various extended Hubbard models for ultracold atoms in optical lattices are studied. Hubbard models are the primary description for many interacting particles in periodic potentials with the paramount example of the electrons in solids. The very same models describe the behavior of ultracold quantum gases trapped in the periodic potentials generated by interfering beams of laser light. These optical lattices provide an unprecedented access to the fundamentals of the many-particle physics that govern the properties of solid-state materials. They can be used to simulate solid-state systems and validate the approximations and simplifications made in theoretical models. This thesis revisits the numerous approximations underlying the standard Hubbard models with special regard to optical lattice experiments. The incorporation of the interaction between particles on adjacent lattice sites leads to extended Hubbard models. Offsite interactions have a strong influence on the phase boundaries and can give rise to novel correlated quantum phases. The extended models are studied with the numerical methods of exact diagonalization and time evolution, a cluster Gutzwiller approximation, as well as with the strong-coupling expansion approach. In total, this thesis demonstrates the high relevance of beyond-Hubbard processes for ultracold atoms in optical lattices. Extended Hubbard models can be employed to tackle unexplained problems of solid-state physics as well as enter previously inaccessible regimes.

Application to supersymmetric models of Dirac-kaehler formalism on the lattice

International Nuclear Information System (INIS)

Zimerman, A.H.

1987-01-01

Using Dirac-Kaehler techniques we formulate some supersymmetric models on the lattice. Specifically we consider the Wess-Zumino model with N=2 in two dimensions which is formulated on a space lattice in its Hamiltonian version (continuous time) as well as on the space-time lattice in its Lagrangean version (euclidean space). On the space lattice (Hamiltonian formulation) we study also the supersymmetric Yanh-Mills model with N=4 in four dimensions. After the introduction of lattice covariant derivatives for fields in the adjoint representation of a compact group we write down some new relations which we have obtained and which constitute generalizations on the lattice of those which are known in the continuous case. (author) [pt

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.

Muon diffusion in noble metals

International Nuclear Information System (INIS)

Schillaci, M.E.; Boekema, C.; Heffner, R.H.; Hutson, R.L.; Leon, M.; Olsen, C.E.; Dodds, S.A.; MacLaughlin, D.E.; Richards, P.M.

1982-01-01

Diffusion-induced muon depolarization was measured in dilute AgGd and AgEr in the temperature range 200 to 700 0 K and have thereby determined the muon diffusion parameters in Ag. The diffusion parameters for μ + in Cu, Ag, and Au are compared with those of hydrogen. For Ag and Au, the μ + parameters are similar to those of hydrogen, whereas for Cu, the μ + parameters are much smaller. Lattice-activated tunneling and over-barrier hopping are investigated with computational models

Investigating the thermal dissociation of viral capsid by lattice model

Science.gov (United States)

Chen, Jingzhi; Chevreuil, Maelenn; Combet, Sophie; Lansac, Yves; Tresset, Guillaume

2017-11-01

The dissociation of icosahedral viral capsids was investigated by a homogeneous and a heterogeneous lattice model. In thermal dissociation experiments with cowpea chlorotic mottle virus and probed by small-angle neutron scattering, we observed a slight shrinkage of viral capsids, which can be related to the strengthening of the hydrophobic interaction between subunits at increasing temperature. By considering the temperature dependence of hydrophobic interaction in the homogeneous lattice model, we were able to give a better estimate of the effective charge. In the heterogeneous lattice model, two sets of lattice sites represented different capsid subunits with asymmetric interaction strengths. In that case, the dissociation of capsids was found to shift from a sharp one-step transition to a gradual two-step transition by weakening the hydrophobic interaction between AB and CC subunits. We anticipate that such lattice models will shed further light on the statistical mechanics underlying virus assembly and disassembly.

Investigation and Modelling of Diesel Hydrotreating Reactions

DEFF Research Database (Denmark)

Boesen, Rasmus Risum

on a commercial CoMo catalyst, and a simple kinetic model is presented. Hydrogenation of fused aromatic rings are known to be fast, and it is possible, that the reaction rates are limited by either internal or external mass transfer. An experiment conducted at industrial temperatures and pressure, using...... naphthalene as a model compound, have shown, that intra-particle diffusion resistance are likely to limit the reaction rate. In order to produce ULSD it is necessary to remove sulfur from some of the most refrac- tive sulfur compounds, such as sterically hindered dibenzothiophenes. Basic nitrogen com- pounds...... are known to inhibit certain hydrotreating reactions. Experimental results are pre- sented, showing the effect of 3 different nitrogen compounds, acridine, 1,4-dimethylcarabazole and 3-methylindole, on the hydrodesulfurization of a real feed and of a model compound, 4,6-dimethyldibenzothiophene. It is shown...

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.

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.

Modelling of Innovation Diffusion

Directory of Open Access Journals (Sweden)

Arkadiusz Kijek

2010-01-01

Full Text Available Since the publication of the Bass model in 1969, research on the modelling of the diffusion of innovation resulted in a vast body of scientific literature consisting of articles, books, and studies of real-world applications of this model. The main objective of the diffusion model is to describe a pattern of spread of innovation among potential adopters in terms of a mathematical function of time. This paper assesses the state-of-the-art in mathematical models of innovation diffusion and procedures for estimating their parameters. Moreover, theoretical issues related to the models presented are supplemented with empirical research. The purpose of the research is to explore the extent to which the diffusion of broadband Internet users in 29 OECD countries can be adequately described by three diffusion models, i.e. the Bass model, logistic model and dynamic model. The results of this research are ambiguous and do not indicate which model best describes the diffusion pattern of broadband Internet users but in terms of the results presented, in most cases the dynamic model is inappropriate for describing the diffusion pattern. Issues related to the further development of innovation diffusion models are discussed and some recommendations are given. (original abstract

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.

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.

Dynamic structure factor for liquid He4 and quantum lattice model

International Nuclear Information System (INIS)

Lee, M.H.

1975-01-01

It has been realized for some time now that the quantum lattice model (or the anisotropic Heisenberg antiferromagnetic model) is a useful model for studying the properties of quantum liquids especially near the lambda transition. The static critical values calculated from the quantum lattice model are in good agreement with the observed values. Furthermore, it was shown recently that there are collective modes in the quantum lattice model which are equivalent to the plasmons. Hence, it would seem to be interesting to study the dynamic structure factor for the quantum lattice model and to make a comparison with experiment. Work on the dynamic structure factor is reported here. (Auth.)

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

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

Equivalence of interest rate models and lattice gases.

Science.gov (United States)

Pirjol, Dan

2012-04-01

We consider the class of short rate interest rate models for which the short rate is proportional to the exponential of a Gaussian Markov process x(t) in the terminal measure r(t)=a(t)exp[x(t)]. These models include the Black-Derman-Toy and Black-Karasinski models in the terminal measure. We show that such interest rate models are equivalent to lattice gases with attractive two-body interaction, V(t(1),t(2))=-Cov[x(t(1)),x(t(2))]. We consider in some detail the Black-Karasinski model with x(t) as an Ornstein-Uhlenbeck process, and show that it is similar to a lattice gas model considered by Kac and Helfand, with attractive long-range two-body interactions, V(x,y)=-α(e(-γ|x-y|)-e(-γ(x+y))). An explicit solution for the model is given as a sum over the states of the lattice gas, which is used to show that the model has a phase transition similar to that found previously in the Black-Derman-Toy model in the terminal measure.

Diffusive Fractionation of Lithium Isotopes in Olivine Grain Boundaries

Science.gov (United States)

Homolova, V.; Watson, E. B.

2012-12-01

produced in the grain boundaries versus the lattices of the individual grains of the 'dunite rock'. The model assumes a linear grain boundary juxtaposed to the long side of a rectangular crystal lattice. During a simulation, the diffusant may directly enter the lattice or the grain boundary. Once in the grain boundary, the diffusant may then continue to diffuse away from the source until the end of the simulation or, alternatively, it may be incorporated into the lattice at some point during its travels down the grain boundary. The model system is similar to that considered by Whipple-LeClaire (1963) and our model results agree well with their analytical solution. Preliminary modeling results show that the distinctive minimum in the isotopic ratio is only produced when diffusive fractionation occurs in the grain boundary and not when the fractionation occurs only in the lattice. This suggests that the isotopic profile observed in the experiments may be a product of diffusive fractionation in grain boundaries. Implications of these results extend to the longevity of Li isotopic heterogeneities in the mantle, and suggest that the isotopes of other elements, which have a large relative mass difference, may also be diffusively fractionated by grain boundary diffusion.

A comparison of lattice parameters for CANDU-type lattices obtained using MCNP, WIMS, and WIMS with resonance reaction rates from MCNP

International Nuclear Information System (INIS)

Craig, D.S.

1989-03-01

The Monte Carlo code MCNP was used to check the accuracy of the WIMS calculation of the resolved resonance capture rate in CANDU-type lattices. Reactivities, relative conversion ratios, and fast fission factors are compared with experiments. Values of ρ 28 and reaction rates for U-238 are given as a function of position in the fuel bundle. A check was made on the correction made in WIMS to allow for endcaps on the fuel bundles. (26 refs)

(Non-) Gibbsianness and Phase Transitions in Random Lattice Spin Models

NARCIS (Netherlands)

Külske, C.

1999-01-01

We consider disordered lattice spin models with finite-volume Gibbs measures µΛ[η](dσ). Here σ denotes a lattice spin variable and η a lattice random variable with product distribution P describing the quenched disorder of the model. We ask: when will the joint measures limΛ↑Zd P(dη)µΛ[η](dσ) be

Grain rotation and lattice deformation during photoinduced chemical reactions revealed by in situ X-ray nanodiffraction.

Science.gov (United States)

Huang, Zhifeng; Bartels, Matthias; Xu, Rui; Osterhoff, Markus; Kalbfleisch, Sebastian; Sprung, Michael; Suzuki, Akihiro; Takahashi, Yukio; Blanton, Thomas N; Salditt, Tim; Miao, Jianwei

2015-07-01

In situ X-ray diffraction (XRD) and transmission electron microscopy (TEM) have been used to investigate many physical science phenomena, ranging from phase transitions, chemical reactions and crystal growth to grain boundary dynamics. A major limitation of in situ XRD and TEM is a compromise that has to be made between spatial and temporal resolution. Here, we report the development of in situ X-ray nanodiffraction to measure high-resolution diffraction patterns from single grains with up to 5 ms temporal resolution. We observed, for the first time, grain rotation and lattice deformation in chemical reactions induced by X-ray photons: Br(-) + hv → Br + e(-) and e(-) + Ag(+) → Ag(0). The grain rotation and lattice deformation associated with the chemical reactions were quantified to be as fast as 3.25 rad s(-1) and as large as 0.5 Å, respectively. The ability to measure high-resolution diffraction patterns from individual grains with a temporal resolution of several milliseconds is expected to find broad applications in materials science, physics, chemistry and nanoscience.

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

Transport lattice models of heat transport in skin with spatially heterogeneous, temperature-dependent perfusion

Directory of Open Access Journals (Sweden)

Martin Gregory T

2004-11-01

Full Text Available Abstract Background Investigation of bioheat transfer problems requires the evaluation of temporal and spatial distributions of temperature. This class of problems has been traditionally addressed using the Pennes bioheat equation. Transport of heat by conduction, and by temperature-dependent, spatially heterogeneous blood perfusion is modeled here using a transport lattice approach. Methods We represent heat transport processes by using a lattice that represents the Pennes bioheat equation in perfused tissues, and diffusion in nonperfused regions. The three layer skin model has a nonperfused viable epidermis, and deeper regions of dermis and subcutaneous tissue with perfusion that is constant or temperature-dependent. Two cases are considered: (1 surface contact heating and (2 spatially distributed heating. The model is relevant to the prediction of the transient and steady state temperature rise for different methods of power deposition within the skin. Accumulated thermal damage is estimated by using an Arrhenius type rate equation at locations where viable tissue temperature exceeds 42°C. Prediction of spatial temperature distributions is also illustrated with a two-dimensional model of skin created from a histological image. Results The transport lattice approach was validated by comparison with an analytical solution for a slab with homogeneous thermal properties and spatially distributed uniform sink held at constant temperatures at the ends. For typical transcutaneous blood gas sensing conditions the estimated damage is small, even with prolonged skin contact to a 45°C surface. Spatial heterogeneity in skin thermal properties leads to a non-uniform temperature distribution during a 10 GHz electromagnetic field exposure. A realistic two-dimensional model of the skin shows that tissue heterogeneity does not lead to a significant local temperature increase when heated by a hot wire tip. Conclusions The heat transport system model of the

Muon diffusion in noble metals

International Nuclear Information System (INIS)

Schillaci, M.E.; Bokema, C.; Heffner, R.H.; Hutson, R.L.; Leon, M.; Olsen, C.E.; Dodds, S.A.; MacLaughlin, D.E.; Richards, P.M.

1983-01-01

Diffusion-induced muon depolarization in dilute AgGd and AgEr were measured in the temperature range 200-700 K and have thereby determined the muon diffusion parameters in Ag. The diffusion parameters for μ + in Cu, Ag, and Au are compared with those of hydrogen. For Ag and Au, the μ + parameters are similar to those of hydrogen, whereas for Cu, the μ + parameters are much smaller. Lattice-activated tunneling and over-barrier hopping are investigated with computational models. 15 references, 1 figure, 2 tables

Critical, statistical, and thermodynamical properties of lattice models

Energy Technology Data Exchange (ETDEWEB)

Varma, Vipin Kerala

2013-10-15

In this thesis we investigate zero temperature and low temperature properties - critical, statistical and thermodynamical - of lattice models in the contexts of bosonic cold atom systems, magnetic materials, and non-interacting particles on various lattice geometries. We study quantum phase transitions in the Bose-Hubbard model with higher body interactions, as relevant for optical lattice experiments of strongly interacting bosons, in one and two dimensions; the universality of the Mott insulator to superfluid transition is found to remain unchanged for even large three body interaction strengths. A systematic renormalization procedure is formulated to fully re-sum these higher (three and four) body interactions into the two body terms. In the strongly repulsive limit, we analyse the zero and low temperature physics of interacting hard-core bosons on the kagome lattice at various fillings. Evidence for a disordered phase in the Ising limit of the model is presented; in the strong coupling limit, the transition between the valence bond solid and the superfluid is argued to be first order at the tip of the solid lobe.

Critical, statistical, and thermodynamical properties of lattice models

International Nuclear Information System (INIS)

Varma, Vipin Kerala

2013-10-01

In this thesis we investigate zero temperature and low temperature properties - critical, statistical and thermodynamical - of lattice models in the contexts of bosonic cold atom systems, magnetic materials, and non-interacting particles on various lattice geometries. We study quantum phase transitions in the Bose-Hubbard model with higher body interactions, as relevant for optical lattice experiments of strongly interacting bosons, in one and two dimensions; the universality of the Mott insulator to superfluid transition is found to remain unchanged for even large three body interaction strengths. A systematic renormalization procedure is formulated to fully re-sum these higher (three and four) body interactions into the two body terms. In the strongly repulsive limit, we analyse the zero and low temperature physics of interacting hard-core bosons on the kagome lattice at various fillings. Evidence for a disordered phase in the Ising limit of the model is presented; in the strong coupling limit, the transition between the valence bond solid and the superfluid is argued to be first order at the tip of the solid lobe.

A CUMULATIVE MIGRATION METHOD FOR COMPUTING RIGOROUS TRANSPORT CROSS SECTIONS AND DIFFUSION COEFFICIENTS FOR LWR LATTICES WITH MONTE CARLO

Energy Technology Data Exchange (ETDEWEB)

Zhaoyuan Liu; Kord Smith; Benoit Forget; Javier Ortensi

2016-05-01

A new method for computing homogenized assembly neutron transport cross sections and dif- fusion coefficients that is both rigorous and computationally efficient is proposed in this paper. In the limit of a homogeneous hydrogen slab, the new method is equivalent to the long-used, and only-recently-published CASMO transport method. The rigorous method is used to demonstrate the sources of inaccuracy in the commonly applied “out-scatter” transport correction. It is also demonstrated that the newly developed method is directly applicable to lattice calculations per- formed by Monte Carlo and is capable of computing rigorous homogenized transport cross sections for arbitrarily heterogeneous lattices. Comparisons of several common transport cross section ap- proximations are presented for a simple problem of infinite medium hydrogen. The new method has also been applied in computing 2-group diffusion data for an actual PWR lattice from BEAVRS benchmark.

Determination of axial diffusion coefficients by the Monte-Carlo method

International Nuclear Information System (INIS)

Milgram, M.

1994-01-01

A simple method to calculate the homogenized diffusion coefficient for a lattice cell using Monte-Carlo techniques is demonstrated. The method relies on modelling a finite reactor volume to induce a curvature in the flux distribution, and then follows a large number of histories to obtain sufficient statistics for a meaningful result. The goal is to determine the diffusion coefficient with sufficient accuracy to test approximate methods built into deterministic lattice codes. Numerical results are given. (author). 4 refs., 8 figs

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.

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.

An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice

International Nuclear Information System (INIS)

Bezzola, Andri; Bales, Benjamin B.; Alkire, Richard C.; Petzold, Linda R.

2014-01-01

We present an exact and efficient algorithm for reaction–diffusion–nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands

An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice

Energy Technology Data Exchange (ETDEWEB)

Bezzola, Andri, E-mail: andri.bezzola@gmail.com [Mechanical Engineering Department, University of California, Santa Barbara, CA 93106 (United States); Bales, Benjamin B., E-mail: bbbales2@gmail.com [Mechanical Engineering Department, University of California, Santa Barbara, CA 93106 (United States); Alkire, Richard C., E-mail: r-alkire@uiuc.edu [Department of Chemical Engineering, University of Illinois, Urbana, IL 61801 (United States); Petzold, Linda R., E-mail: petzold@engineering.ucsb.edu [Mechanical Engineering Department and Computer Science Department, University of California, Santa Barbara, CA 93106 (United States)

2014-01-01

We present an exact and efficient algorithm for reaction–diffusion–nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands.

Anomalous diffusion in neutral evolution of model proteins

Science.gov (United States)

Nelson, Erik D.; Grishin, Nick V.

2015-06-01

Protein evolution is frequently explored using minimalist polymer models, however, little attention has been given to the problem of structural drift, or diffusion. Here, we study neutral evolution of small protein motifs using an off-lattice heteropolymer model in which individual monomers interact as low-resolution amino acids. In contrast to most earlier models, both the length and folded structure of the polymers are permitted to change. To describe structural change, we compute the mean-square distance (MSD) between monomers in homologous folds separated by n neutral mutations. We find that structural change is episodic, and, averaged over lineages (for example, those extending from a single sequence), exhibits a power-law dependence on n . We show that this exponent depends on the alignment method used, and we analyze the distribution of waiting times between neutral mutations. The latter are more disperse than for models required to maintain a specific fold, but exhibit a similar power-law tail.

On techniques of ATR lattice computation

International Nuclear Information System (INIS)

1997-08-01

Lattice computation is to compute the average nuclear constants of unit fuel lattice which are required for computing core nuclear characteristics such as core power distribution and reactivity characteristics. The main nuclear constants are infinite multiplying rate, neutron movement area, cross section for diffusion computation, local power distribution and isotope composition. As for the lattice computation code, WIMS-ATR is used, which is based on the WIMS-D code developed in U.K., and for the purpose of heightening the accuracy of analysis, which was improved by adding heavy water scattering cross section considering the temperature dependence by Honeck model. For the computation of the neutron absorption by control rods, LOIEL BLUE code is used. The extrapolation distance of neutron flux on control rod surfaces is computed by using THERMOS and DTF codes, and the lattice constants of adjoining lattices are computed by using the WIMS-ATR code. As for the WIMS-ATR code, the computation flow and nuclear data library, and as for the LOIEL BLUE code, the computation flow are explained. The local power distribution in fuel assemblies determined by the WIMS-ATR code was verified with the measured data, and the results are reported. (K.I.)

Critical manifold of the kagome-lattice Potts model

International Nuclear Information System (INIS)

Jacobsen, Jesper Lykke; Scullard, Christian R

2012-01-01

Any two-dimensional infinite regular lattice G can be produced by tiling the plane with a finite subgraph B⊆G; we call B a basis of G. We introduce a two-parameter graph polynomial P B (q, v) that depends on B and its embedding in G. The algebraic curve P B (q, v) = 0 is shown to provide an approximation to the critical manifold of the q-state Potts model, with coupling v = e K − 1, defined on G. This curve predicts the phase diagram not only in the physical ferromagnetic regime (v > 0), but also in the antiferromagnetic (v B (q, v) = 0 provides the exact critical manifold in the limit of infinite B. Furthermore, for some lattices G—or for the Ising model (q = 2) on any G—the polynomial P B (q, v) factorizes for any choice of B: the zero set of the recurrent factor then provides the exact critical manifold. In this sense, the computation of P B (q, v) can be used to detect exact solvability of the Potts model on G. We illustrate the method for two choices of G: the square lattice, where the Potts model has been exactly solved, and the kagome lattice, where it has not. For the square lattice we correctly reproduce the known phase diagram, including the antiferromagnetic transition and the singularities in the Berker–Kadanoff phase at certain Beraha numbers. For the kagome lattice, taking the smallest basis with six edges we recover a well-known (but now refuted) conjecture of F Y Wu. Larger bases provide successive improvements on this formula, giving a natural extension of Wu’s approach. We perform large-scale numerical computations for comparison and find excellent agreement with the polynomial predictions. For v > 0 the accuracy of the predicted critical coupling v c is of the order 10 −4 or 10 −5 for the six-edge basis, and improves to 10 −6 or 10 −7 for the largest basis studied (with 36 edges). This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of

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.

Subgrid models for mass and thermal diffusion in turbulent mixing

International Nuclear Information System (INIS)

Lim, H; Yu, Y; Glimm, J; Li, X-L; Sharp, D H

2010-01-01

We propose a new method for the large eddy simulation (LES) of turbulent mixing flows. The method yields convergent probability distribution functions (PDFs) for temperature and concentration and a chemical reaction rate when applied to reshocked Richtmyer-Meshkov (RM) unstable flows. Because such a mesh convergence is an unusual and perhaps original capability for LES of RM flows, we review previous validation studies of the principal components of the algorithm. The components are (i) a front tracking code, FronTier, to control numerical mass diffusion and (ii) dynamic subgrid scale (SGS) models to compensate for unresolved scales in the LES. We also review the relevant code comparison studies. We compare our results to a simple model based on 1D diffusion, taking place in the geometry defined statistically by the interface (the 50% isoconcentration surface between the two fluids). Several conclusions important to physics could be drawn from our study. We model chemical reactions with no closure approximations beyond those in the LES of the fluid variables itself, and as with dynamic SGS models, these closures contain no adjustable parameters. The chemical reaction rate is specified by the joint PDF for temperature and concentration. We observe a bimodal distribution for the PDF and we observe significant dependence on fluid transport parameters.

Model for lattice dynamics of hexagonal close packed metals

Energy Technology Data Exchange (ETDEWEB)

Singh, R K [Tata Inst. of Fundamental Research, Bombay (India); Kumar, S [Meerut Coll. (India). Dept. of Physics

1977-11-19

A lattice dynamical model, which satisfies the requirements of translational invariance as well as the static equilibrium of hexagonal close packed lattice, has been proposed and applied to study the phonon dispersion relations in magnesium. The results revealed by this model have been claimed to be better than earlier ones.

Quantum diffusion in semi-infinite periodic and quasiperiodic systems

International Nuclear Information System (INIS)

Zhang Kaiwang

2008-01-01

This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C(t) ∼ t −δ and d(t) ∼ t β . However, it finds that 0 < δ < 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed

On the equivalence of continuum and lattice models for fluids

International Nuclear Information System (INIS)

Panagiotopoulos, Athanassios Z.

2000-01-01

It was demonstrated that finely discretized lattice models for fluids with particles interacting via Lennard-Jones or exponential-6 potentials have essentially identical thermodynamic and structural properties to their continuum counterparts. Grand canonical histogram reweighting Monte Carlo calculations were performed for systems with repulsion exponents between 11 and 22. Critical parameters were determined from mixed-field finite-size scaling methods. Numerical equivalence of lattice and continuous space models, within simulation uncertainties, was observed for lattices with ratio of particle diameter σ to grid spacing of 10. The lattice model calculations were more efficient computationally by factors between 10 and 20. It was also shown that Lennard-Jones and exponential-6 based models with identical critical properties can be constructed by appropriate choice of the repulsion exponent. (c) 2000 American Institute of Physics

Reaction Diffusion Voronoi Diagrams: From Sensors Data to Computing

Directory of Open Access Journals (Sweden)

Alejandro Vázquez-Otero

2015-05-01

Full Text Available In this paper, a new method to solve computational problems using reaction diffusion (RD systems is presented. The novelty relies on the use of a model configuration that tailors its spatiotemporal dynamics to develop Voronoi diagrams (VD as a part of the system’s natural evolution. The proposed framework is deployed in a solution of related robotic problems, where the generalized VD are used to identify topological places in a grid map of the environment that is created from sensor measurements. The ability of the RD-based computation to integrate external information, like a grid map representing the environment in the model computational grid, permits a direct integration of sensor data into the model dynamics. The experimental results indicate that this method exhibits significantly less sensitivity to noisy data than the standard algorithms for determining VD in a grid. In addition, previous drawbacks of the computational algorithms based on RD models, like the generation of volatile solutions by means of excitable waves, are now overcome by final stable states.

Quantum mechanics of lattice gas automata: One-particle plane waves and potentials

International Nuclear Information System (INIS)

Meyer, D.A.

1997-01-01

Classical lattice gas automata effectively simulate physical processes, such as diffusion and fluid flow (in certain parameter regimes), despite their simplicity at the microscale. Motivated by current interest in quantum computation we recently defined quantum lattice gas automata; in this paper we initiate a project to analyze which physical processes these models can effectively simulate. Studying the single particle sector of a one-dimensional quantum lattice gas we find discrete analogs of plane waves and wave packets, and then investigate their behavior in the presence of inhomogeneous potentials. copyright 1997 The American Physical Society

Effect of noise on defect chaos in a reaction-diffusion model.

Science.gov (United States)

Wang, Hongli; Ouyang, Qi

2005-06-01

The influence of noise on defect chaos due to breakup of spiral waves through Doppler and Eckhaus instabilities is investigated numerically with a modified Fitzhugh-Nagumo model. By numerical simulations we show that the noise can drastically enhance the creation and annihilation rates of topological defects. The noise-free probability distribution function for defects in this model is found not to fit with the previously reported squared-Poisson distribution. Under the influence of noise, the distributions are flattened, and can fit with the squared-Poisson or the modified-Poisson distribution. The defect lifetime and diffusive property of defects under the influence of noise are also checked in this model.

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.

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...

Chiral Schwinger model and lattice fermionic regularizations

International Nuclear Information System (INIS)

Kieu, T.D.; Sen, D.; Xue, S.

1988-01-01

The chiral Schwinger model is studied on the lattice with use of Wilson fermions. The arbitrary mass term for the gauge boson is shown to originate from the arbitrariness of the Wilson parameter, which is required to avoid the doubling phenomenon on the lattice. The necessity for such a term is thus demonstrated in contrast to the mere admissibility as indicated by previous continuum calculations

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.

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.

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

Diffusion processes and memory effects

International Nuclear Information System (INIS)

Mokshin, Anatolii V; Yulmetyev, Renat M; Haenggi, Peter

2005-01-01

We report the results of the numerical estimation of statistical memory effects in diffusion for two various systems: Lennard-Jones fluids and the model of the Brownian particle in a one-dimensional harmonic lattice. We have found the relation between the diffusion coefficient and the non-Markovity parameter, which is linear for the Lennard-Jones systems in liquid state. The relation between the memory measure and the excess entropy is also discussed here

Three-dimensional lattice Boltzmann model for compressible flows.

Science.gov (United States)

Sun, Chenghai; Hsu, Andrew T

2003-07-01

A three-dimensional compressible lattice Boltzmann model is formulated on a cubic lattice. A very large particle-velocity set is incorporated in order to enable a greater variation in the mean velocity. Meanwhile, the support set of the equilibrium distribution has only six directions. Therefore, this model can efficiently handle flows over a wide range of Mach numbers and capture shock waves. Due to the simple form of the equilibrium distribution, the fourth-order velocity tensors are not involved in the formulation. Unlike the standard lattice Boltzmann model, no special treatment is required for the homogeneity of fourth-order velocity tensors on square lattices. The Navier-Stokes equations were recovered, using the Chapman-Enskog method from the Bhatnagar-Gross-Krook (BGK) lattice Boltzmann equation. The second-order discretization error of the fluctuation velocity in the macroscopic conservation equation was eliminated by means of a modified collision invariant. The model is suitable for both viscous and inviscid compressible flows with or without shocks. Since the present scheme deals only with the equilibrium distribution that depends only on fluid density, velocity, and internal energy, boundary conditions on curved wall are easily implemented by an extrapolation of macroscopic variables. To verify the scheme for inviscid flows, we have successfully simulated a three-dimensional shock-wave propagation in a box and a normal shock of Mach number 10 over a wedge. As an application to viscous flows, we have simulated a flat plate boundary layer flow, flow over a cylinder, and a transonic flow over a NACA0012 airfoil cascade.

A lattice-valued linguistic decision model for nuclear safeguards applications

International Nuclear Information System (INIS)

Ruan, D.; Liu, J.; Carchon, R.

2001-01-01

In this study, we focus our attention on decision making models to process uncertainty-based information directly without transforming them into any particular membership function, i.e., directly using linguistic information (linguistic values) instead of numbers (numerical values). By analyzing the feature of linguistic values ordered by their means of common usage, we argue that the set of linguistic values should be characterized by a lattice structure. We propose the lattice structure based on a logical algebraic structure i.e., lattice implication algebra. Finally, we obtain a multi-objective decision-making model by extending Yager's multi-objective model from the following aspects: (1) extension of linguistic information: from a set of linear ordered linguistic labels (values) to that of lattice-valued linguistic labels; (2) extension of the combination function M, which is used to combine the individual ratings with the weights of criteria. We propose an implication operation form of M. The implication operation can be drawn from lattice implication algebra. As an illustration, we will finally apply this decision model to the evaluation problem in safeguard relevant information. (orig.)

Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys

Science.gov (United States)

Balakrishna, Ananya Renuka; Carter, W. Craig

2018-04-01