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.

A coupled theory for chemically active and deformable solids with mass diffusion and heat conduction

Science.gov (United States)

Zhang, Xiaolong; Zhong, Zheng

2017-10-01

To analyse the frequently encountered thermo-chemo-mechanical problems in chemically active material applications, we develop a thermodynamically-consistent continuum theory of coupled deformation, mass diffusion, heat conduction and chemical reaction. Basic balance equations of force, mass and energy are presented at first, and then fully coupled constitutive laws interpreting multi-field interactions and evolving equations governing irreversible fluxes are constructed according to the energy dissipation inequality and the chemical kinetics. To consider the essential distinction between mass diffusion and chemical reactions in affecting free energy and dissipations of a highly coupled system, we regard both the concentrations of diffusive species and the extent of reaction as independent state variables. This new formulation then distinguishes between the energy contribution from the diffusive species entering the solid and that from the subsequent chemical reactions occurring among these species and the host solid, which not only interact with stresses or strains in different manners and on different time scales, but also induce different variations of solid microstructures and material properties. Taking advantage of this new description, we further establish a specialized isothermal model to predict precisely the transient chemo-mechanical response of a swelling solid with a proposed volumetric constraint that accounts for material incompressibility. Coupled kinetics is incorporated to capture the volumetric swelling of the solid caused by imbibition of external species and the simultaneous dilation arised from chemical reactions between the diffusing species and the solid. The model is then exemplified with two numerical examples of transient swelling accompanied by chemical reaction. Various ratios of characteristic times of diffusion and chemical reaction are taken into account to shed light on the dependency on kinetic time scales of evolution patterns for

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

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.

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

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium.

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Horowitz, Jordan M

2015-07-28

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

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.

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

International Nuclear Information System (INIS)

Asai, Tetsuya; Adamatzky, Andrew; Amemiya, Yoshihito

2004-01-01

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

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.

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.

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.

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.

Aerosol simulation including chemical and nuclear reactions

International Nuclear Information System (INIS)

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

1985-01-01

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

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

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.

Insights into the mechanisms on chemical reactions: reaction paths for chemical reactions

International Nuclear Information System (INIS)

Dunning, T.H. Jr.; Rosen, E.; Eades, R.A.

1987-01-01

We report reaction paths for two prototypical chemical reactions: Li + HF, an electron transfer reaction, and OH + H 2 , an abstraction reaction. In the first reaction we consider the connection between the energetic terms in the reaction path Hamiltonian and the electronic changes which occur upon reaction. In the second reaction we consider the treatment of vibrational effects in chemical reactions in the reaction path formalism. 30 refs., 9 figs

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

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

Reaction-diffusion path planning in a hybrid chemical and cellular-automaton processor

International Nuclear Information System (INIS)

Adamatzky, Andrew; Lacy Costello, Benjamin de

2003-01-01

To find the shortest collision-free path in a room containing obstacles we designed a chemical processor and coupled it with a cellular-automaton processor. In the chemical processor obstacles are represented by sites of high concentration of potassium iodide and a planar substrate is saturated with palladium chloride. Potassium iodide diffuses into the substrate and reacts with palladium chloride. A dark coloured precipitate of palladium iodide is formed almost everywhere except sites where two or more diffusion wavefronts collide. The less coloured sites are situated at the furthest distance from obstacles. Thus, the chemical processor develops a repulsive field, generated by obstacles. A snapshot of the chemical processor is inputted to a cellular automaton. The automaton behaves like a discrete excitable media; also, every cell of the automaton is supplied with a pointer that shows an origin of the cell's excitation. The excitation spreads along the cells corresponding to precipitate depleted sites of the chemical processor. When the destination-site is excited, waves travel on the lattice and update the orientations of the pointers. Thus, the automaton constructs a spanning tree, made of pointers, that guides a traveler towards the destination point. Thus, the automaton medium generates an attractive field and combination of this attractive field with the repulsive field, generated by the chemical processor, provides us with a solution of the collision-free path problem

Experimental and numerical reaction analysis on sodium-water chemical reaction field

International Nuclear Information System (INIS)

Deguchi, Yoshihiro; Takata, Takashi; Yamaguchi, Akira; Kikuchi, Shin; Ohshima, Hiroyuki

2015-01-01

In a sodium-cooled fast reactor (SFR), liquid sodium is used as a heat transfer fluid because of its excellent heat transport capability. On the other hand, it has strong chemical reactivity with water vapor. One of the design basis accidents of the SFR is the water leakage into the liquid sodium flow by a breach of heat transfer tubes. This process ends up damages on the heat transport equipment in the SFR. Therefore, the study on sodium-water chemical reactions is of paramount importance for security reasons. This study aims to clarify the sodium-water reaction mechanisms using an elementary reaction analysis. A quasi one-dimensional flame model is applied to a sodium-water counter-flow reaction field. The analysis contains 25 elementary reactions, which consist of 17 H_2-O_2 and 8 Na-H_2O reactions. Temperature and species concentrations in the counter-flow reaction field were measured using laser diagnostics such as LIF and CARS. The main reaction in the experimental conditions is Na+H_2O → NaOH+H and OH is produced by H_2O+H → H_2+OH. It is demonstrated that the reaction model in this study well explains the structure of the sodium-water counter-flow diffusion flame. (author)

Acoustic wave propagation in fluids with coupled chemical reactions

International Nuclear Information System (INIS)

Margulies, T.S.; Schwarz, W.H.

1984-08-01

This investigation presents a hydroacoustic theory which accounts for sound absorption and dispersion in a multicomponent mixture of reacting fluids (assuming a set of first-order acoustic equations without diffusion) such that several coupled reactions can occur simultaneously. General results are obtained in the form of a biquadratic characteristic equation (called the Kirchhoff-Langevin equation) for the complex propagation variable chi = - (α + iω/c) in which α is the attenuation coefficient, c is the phase speed of the progressive wave and ω is the angular frequency. Computer simulations of sound absorption spectra have been made for three different chemical systems, each comprised of two-step chemical reactions using physico-chemical data available in the literature. The chemical systems studied include: (1) water-dioxane, (2) aqueous solutions of glycine and (3) cobalt polyphosphate mixtures. Explicit comparisons are made between the exact biquadratic characteristic solution and the approximate equation (sometimes referred to as a Debye equation) previously applied to interpret the experimental data for the chemical reaction contribution to the absorption versus frequency. The relative chemical reaction and classical viscothermal contributions to the sound absorption are also presented. Several discrepancies that can arise when estimating thermodynamic data (chemical reaction heats or volume changes) for multistep chemical reaction systems when making dilute solution or constant density assumptions are discussed

Kinetics of heterogeneous chemical reactions: a theoretical model for the accumulation of pesticides in soil.

Science.gov (United States)

Lin, S H; Sahai, R; Eyring, H

1971-04-01

A theoretical model for the accumulation of pesticides in soil has been proposed and discussed from the viewpoint of heterogeneous reaction kinetics with a basic aim to understand the complex nature of soil processes relating to the environmental pollution. In the bulk of soil, the pesticide disappears by diffusion and a chemical reaction; the rate processes considered on the surface of soil are diffusion, chemical reaction, vaporization, and regular pesticide application. The differential equations involved have been solved analytically by the Laplace-transform method.

Droplet heat transfer and chemical reactions during direct containment heating

International Nuclear Information System (INIS)

Baker, L. Jr.

1986-01-01

A simplified model of heat transfer and chemical reaction has been adapted to evaluate the expected behavior of droplets containing unreacted Zircaloy and stainless steel moving through the containment atmosphere during postulated accidents involving direct containment heating. The model includes internal and external diffusive resistances to reaction. The results indicate that reactions will be incomplete for many conditions characteristic of direct containment heating sequences

A kinetic model for chemical reactions without barriers: transport coefficients and eigenmodes

International Nuclear Information System (INIS)

Alves, Giselle M; Kremer, Gilberto M; Marques, Wilson Jr; Soares, Ana Jacinta

2011-01-01

The kinetic model of the Boltzmann equation proposed in the work of Kremer and Soares 2009 for a binary mixture undergoing chemical reactions of symmetric type which occur without activation energy is revisited here, with the aim of investigating in detail the transport properties of the reactive mixture and the influence of the reaction process on the transport coefficients. Accordingly, the non-equilibrium solutions of the Boltzmann equations are determined through an expansion in Sonine polynomials up to the first order, using the Chapman–Enskog method, in a chemical regime for which the reaction process is close to its final equilibrium state. The non-equilibrium deviations are explicitly calculated for what concerns the thermal–diffusion ratio and coefficients of shear viscosity, diffusion and thermal conductivity. The theoretical and formal analysis developed in the present paper is complemented with some numerical simulations performed for different concentrations of reactants and products of the reaction as well as for both exothermic and endothermic chemical processes. The results reveal that chemical reactions without energy barrier can induce an appreciable influence on the transport properties of the mixture. Oppositely to the case of reactions with activation energy, the coefficients of shear viscosity and thermal conductivity become larger than those of an inert mixture when the reactions are exothermic. An application of the non-barrier model and its detailed transport picture are included in this paper, in order to investigate the dynamics of the local perturbations on the constituent number densities, and velocity and temperature of the whole mixture, induced by spontaneous internal fluctuations. It is shown that for the longitudinal disturbances there exist two hydrodynamic sound modes, one purely diffusive hydrodynamic mode and one kinetic mode

A kinetic model for chemical reactions without barriers: transport coefficients and eigenmodes

Science.gov (United States)

Alves, Giselle M.; Kremer, Gilberto M.; Marques, Wilson, Jr.; Jacinta Soares, Ana

2011-03-01

The kinetic model of the Boltzmann equation proposed in the work of Kremer and Soares 2009 for a binary mixture undergoing chemical reactions of symmetric type which occur without activation energy is revisited here, with the aim of investigating in detail the transport properties of the reactive mixture and the influence of the reaction process on the transport coefficients. Accordingly, the non-equilibrium solutions of the Boltzmann equations are determined through an expansion in Sonine polynomials up to the first order, using the Chapman-Enskog method, in a chemical regime for which the reaction process is close to its final equilibrium state. The non-equilibrium deviations are explicitly calculated for what concerns the thermal-diffusion ratio and coefficients of shear viscosity, diffusion and thermal conductivity. The theoretical and formal analysis developed in the present paper is complemented with some numerical simulations performed for different concentrations of reactants and products of the reaction as well as for both exothermic and endothermic chemical processes. The results reveal that chemical reactions without energy barrier can induce an appreciable influence on the transport properties of the mixture. Oppositely to the case of reactions with activation energy, the coefficients of shear viscosity and thermal conductivity become larger than those of an inert mixture when the reactions are exothermic. An application of the non-barrier model and its detailed transport picture are included in this paper, in order to investigate the dynamics of the local perturbations on the constituent number densities, and velocity and temperature of the whole mixture, induced by spontaneous internal fluctuations. It is shown that for the longitudinal disturbances there exist two hydrodynamic sound modes, one purely diffusive hydrodynamic mode and one kinetic mode.

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.

Investigation of a Monte Carlo model for chemical reactions

International Nuclear Information System (INIS)

Hamm, R.N.; Turner, J.E.; Stabin, M.G.

1998-01-01

Monte Carlo computer simulations are in use at a number of laboratories for calculating time-dependent yields, which can be compared with experiments in the radiolysis of water. We report here on calculations to investigate the validity and consistency of the procedures used for simulating chemical reactions in our code, RADLYS. Model calculations were performed of the rate constants themselves. The rates thus determined showed an expected rapid decline over the first few hundred ps and a very gradual decline thereafter out to the termination of the calculations at 4.5 ns. Results are reported for different initial concentrations and numbers of reactive species. Generally, the calculated rate constants are smallest when the initial concentrations of the reactants are largest. It is found that inhomogeneities that quickly develop in the initial random spatial distribution of reactants persist in time as a result of subsequent chemical reactions, and thus conditions may poorly approximate those assumed from diffusion theory. We also investigated the reaction of a single species of one type placed among a large number of randomly distributed species of another type with which it could react. The distribution of survival times of the single species was calculated by using three different combinations of the diffusion constants for the two species, as is sometimes discussed in diffusion theory. The three methods gave virtually identical results. (orig.)

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

Chemical reactions induced by fast neutron irradiation

International Nuclear Information System (INIS)

Katsumura, Y.

1989-01-01

Here, several studies on fast neutron irradiation effects carried out at the reactor 'YAYOI' are presented. Some indicate a significant difference in the effect from those by γ-ray irradiation but others do not, and the difference changes from subject to subject which we observed. In general, chemical reactions induced by fast neutron irradiation expand in space and time, and there are many aspects. In the time region just after the deposition of neutron energy in the system, intermediates are formed densely and locally reflecting high LET of fast neutrons and, with time, successive reactions proceed parallel to dissipation of localized energy and to diffusion of the intermediates. Finally the reactions are completed in longer time region. If we pick up the effects which reserve the locality of the initial processes, a significant different effect between in fast neutron radiolysis and in γ-ray radiolysis would be derived. If we observe the products generated after dissipation and diffusion in longer time region, a clear difference would not be observed. Therefore, in order to understand the fast neutron irradiation effects, it is necessary to know the fundamental processes of the reactions induced by radiations. (author)

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.

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

Proton conduction based on intracrystalline chemical reaction

International Nuclear Information System (INIS)

Schuck, G.; Lechner, R.E.; Langer, K.

2002-01-01

Proton conductivity in M 3 H(SeO 4 ) 2 crystals (M=K, Rb, Cs) is shown to be due to a dynamic disorder in the form of an intracrystalline chemical equilibrium reaction: alternation between the association of the monomers [HSeO 4 ] 1- and [SeO 4 ] 2- resulting in the dimer [H(SeO 4 ) 2 ] 3- (H-bond formation) and the dissociation of the latter into the two monomers (H-bond breaking). By a combination of quasielastic neutron scattering and FTIR spectroscopy, reaction rates were obtained, as well as rates of proton exchange between selenate ions, leading to diffusion. The results demonstrate that this reaction plays a central role in the mechanism of proton transport in these solid-state protonic conductors. (orig.)

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.

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

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.

Distance-dependent diffusion-controlled reaction of •NO and O2•- at chemical equilibrium with ONOO-.

Science.gov (United States)

Botti, Horacio; Möller, Matías N; Steinmann, Daniel; Nauser, Thomas; Koppenol, Willem H; Denicola, Ana; Radi, Rafael

2010-12-16

The fast reaction of (•)NO and O(2)(•-) to give ONOO(-) has been extensively studied at irreversible conditions, but the reasons for the wide variations in observed forward rate constants (3.8 ≤ k(f) ≤ 20 × 10(9) M(-1) s(-1)) remain unexplained. We characterized the diffusion-dependent aqueous (pH > 12) chemical equilibrium of the form (•)NO + O(2)(•-) = ONOO(-) with respect to its dependence on temperature, viscosity, and [ONOO(-)](eq) by determining [ONOO(-)](eq) and [(•)NO](eq). The equilibrium forward reaction rate constant (k(f)(eq)) has negative activation energy, in contrast to that found under irreversible conditions. In contradiction to the law of mass action, we demonstrate that the equilibrium constant depends on ONOO(-) concentration. Therefore, a wide range of k(f)(eq) values could be derived (7.5-21 × 10(9) M(-1) s(-1)). Of general interest, the variations in k(f) can thus be explained by its dependence on the distance between ONOO(-) particles (sites of generation of (•)NO and O(2)(•-)).

Chemical kinetics of gas reactions

CERN Document Server

Kondrat'Ev, V N

2013-01-01

Chemical Kinetics of Gas Reactions explores the advances in gas kinetics and thermal, photochemical, electrical discharge, and radiation chemical reactions. This book is composed of 10 chapters, and begins with the presentation of general kinetic rules for simple and complex chemical reactions. The next chapters deal with the experimental methods for evaluating chemical reaction mechanisms and some theories of elementary chemical processes. These topics are followed by discussions on certain class of chemical reactions, including unimolecular, bimolecular, and termolecular reactions. The rema

Global Controllability of Chemical Reactions

OpenAIRE

Drexler, Dániel András; Tóth, János

2015-01-01

Controllability of chemical reactions is an important problem in chemical engineering science. In control theory, analysis of the controllability of linear systems is well-founded, however the dynamics of chemical reactions is usually nonlinear. Global controllability properties of chemical reactions are analyzed here based on the Lie-algebra of the vector fields associated to elementary reactions. A chemical reaction is controllable almost everywhere if all the reaction rate coefficients can...

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

International Nuclear Information System (INIS)

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

2003-01-01

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

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

Chemical ageing and transformation of diffusivity in semi-solid multi-component organic aerosol particles

Science.gov (United States)

Pfrang, C.; Shiraiwa, M.; Pöschl, U.

2011-07-01

Recent experimental evidence underlines the importance of reduced diffusivity in amorphous semi-solid or glassy atmospheric aerosols. This paper investigates the impact of diffusivity on the ageing of multi-component reactive organic particles approximating atmospheric cooking aerosols. We apply and extend the recently developed KM-SUB model in a study of a 12-component mixture containing oleic and palmitoleic acids. We demonstrate that changes in the diffusivity may explain the evolution of chemical loss rates in ageing semi-solid particles, and we resolve surface and bulk processes under transient reaction conditions considering diffusivities altered by oligomerisation. This new model treatment allows prediction of the ageing of mixed organic multi-component aerosols over atmospherically relevant timescales and conditions. We illustrate the impact of changing diffusivity on the chemical half-life of reactive components in semi-solid particles, and we demonstrate how solidification and crust formation at the particle surface can affect the chemical transformation of organic aerosols.

Chemical ageing and transformation of diffusivity in semi-solid multi-component organic aerosol particles

Directory of Open Access Journals (Sweden)

C. Pfrang

2011-07-01

Full Text Available Recent experimental evidence underlines the importance of reduced diffusivity in amorphous semi-solid or glassy atmospheric aerosols. This paper investigates the impact of diffusivity on the ageing of multi-component reactive organic particles approximating atmospheric cooking aerosols. We apply and extend the recently developed KM-SUB model in a study of a 12-component mixture containing oleic and palmitoleic acids. We demonstrate that changes in the diffusivity may explain the evolution of chemical loss rates in ageing semi-solid particles, and we resolve surface and bulk processes under transient reaction conditions considering diffusivities altered by oligomerisation. This new model treatment allows prediction of the ageing of mixed organic multi-component aerosols over atmospherically relevant timescales and conditions. We illustrate the impact of changing diffusivity on the chemical half-life of reactive components in semi-solid particles, and we demonstrate how solidification and crust formation at the particle surface can affect the chemical transformation of organic aerosols.

Theoretical and experimental study on solid chemical reaction between BaCO3 and TiO2 in microwave field

International Nuclear Information System (INIS)

Liu Hanxing; Guo, Liling; Zou Long; Cao Minhe; Zhou Jian; Ouyang Shixi

2004-01-01

Solid-state chemical reaction mechanism for the reaction between BaCO 3 and TiO 2 in microwave field was investigated based on X-ray power diffraction (XRD) data and theory of diffusion. The compositions of the resultant after reaction under different conditions were studied by employing XRD. The quantitative analyses based on XRD data showed the reaction in microwave field was quite different from that in the conventional method. A model was proposed to explain the change of the ratio between the reactant BaCO 3 , TiO 2 and the resultant BaTiO 3 for the chemical reaction. The formation kinetic of BaTiO 3 from the BaCO 3 and TiO 2 was calculated by employing this theoretical model. The reaction rate between BaCO 3 and TiO 2 in microwave field was much higher than that in conventional method. The activation energy of the atomic diffusions in this solid chemical reaction is only 58 kJ/mol, which was only about 1/4 of 232 kJ/mol in the conventional value. The result suggests that the microwave field enhance atomic diffusion during the reaction

MRI of chemical reactions and processes.

Science.gov (United States)

Britton, Melanie M

2017-08-01

As magnetic resonance imaging (MRI) can spatially resolve a wealth of molecular information available from nuclear magnetic resonance (NMR), it is able to non-invasively visualise the composition, properties and reactions of a broad range of spatially-heterogeneous molecular systems. Hence, MRI is increasingly finding applications in the study of chemical reactions and processes in a diverse range of environments and technologies. This article will explain the basic principles of MRI and how it can be used to visualise chemical composition and molecular properties, providing an overview of the variety of information available. Examples are drawn from the disciplines of chemistry, chemical engineering, environmental science, physics, electrochemistry and materials science. The review introduces a range of techniques used to produce image contrast, along with the chemical and molecular insight accessible through them. Methods for mapping the distribution of chemical species, using chemical shift imaging or spatially-resolved spectroscopy, are reviewed, as well as methods for visualising physical state, temperature, current density, flow velocities and molecular diffusion. Strategies for imaging materials with low signal intensity, such as those containing gases or low sensitivity nuclei, using compressed sensing, para-hydrogen or polarisation transfer, are discussed. Systems are presented which encapsulate the diversity of chemical and physical parameters observable by MRI, including one- and two-phase flow in porous media, chemical pattern formation, phase transformations and hydrodynamic (fingering) instabilities. Lastly, the emerging area of electrochemical MRI is discussed, with studies presented on the visualisation of electrochemical deposition and dissolution processes during corrosion and the operation of batteries, supercapacitors and fuel cells. Crown Copyright © 2017. Published by Elsevier B.V. All rights reserved.

Chemical reactions in the presence of surface modulation and stirring

OpenAIRE

Kamhawi, Khalid; Náraigh, Lennon Ó

2009-01-01

We study the dynamics of simple reactions where the chemical species are confined on a general, time-modulated surface, and subjected to externally-imposed stirring. The study of these inhomogeneous effects requires a model based on a reaction-advection-diffusion equation, which we derive. We use homogenization methods to show that up to second order in a small scaling parameter, the modulation effects on the concentration field are asymptotically equivalent for systems with or without stirri...

Microfluidic chemical reaction circuits

Science.gov (United States)

Lee, Chung-cheng [Irvine, CA; Sui, Guodong [Los Angeles, CA; Elizarov, Arkadij [Valley Village, CA; Kolb, Hartmuth C [Playa del Rey, CA; Huang, Jiang [San Jose, CA; Heath, James R [South Pasadena, CA; Phelps, Michael E [Los Angeles, CA; Quake, Stephen R [Stanford, CA; Tseng, Hsian-rong [Los Angeles, CA; Wyatt, Paul [Tipperary, IE; Daridon, Antoine [Mont-Sur-Rolle, CH

2012-06-26

New microfluidic devices, useful for carrying out chemical reactions, are provided. The devices are adapted for on-chip solvent exchange, chemical processes requiring multiple chemical reactions, and rapid concentration of reagents.

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...

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.

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

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

Infrared laser-induced chemical reactions

International Nuclear Information System (INIS)

Katayama, Mikio

1978-01-01

The experimental means which clearly distinguishes between infrared ray-induced reactions and thermal reactions has been furnished for the first time when an intense monochromatic light source has been obtained by the development of infrared laser. Consequently, infrared laser-induced chemical reactions have started to develop as one field of chemical reaction researches. Researches of laser-induced chemical reactions have become new means for the researches of chemical reactions since they were highlighted as a new promising technique for isotope separation. Specifically, since the success has been reported in 235 U separation using laser in 1974, comparison of this method with conventional separation techniques from the economic point of view has been conducted, and it was estimated by some people that the laser isotope separation is cheaper. This report briefly describes on the excitation of oscillation and reaction rate, and introduces the chemical reactions induced by CW laser and TEA CO 2 laser. Dependence of reaction yield on laser power, measurement of the absorbed quantity of infrared ray and excitation mechanism are explained. Next, isomerizing reactions are reported, and finally, isotope separation is explained. It was found that infrared laser-induced chemical reactions have the selectivity for isotopes. Since it is evident that there are many examples different from thermal and photo-chemical reactions, future collection of the data is expected. (Wakatsuki, Y.)

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

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

Stochastic reaction-diffusion algorithms for macromolecular crowding

Science.gov (United States)

Sturrock, Marc

2016-06-01

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

Convection and reaction in a diffusive boundary layer in a porous medium: nonlinear dynamics.

Science.gov (United States)

Andres, Jeanne Therese H; Cardoso, Silvana S S

2012-09-01

We study numerically the nonlinear interactions between chemical reaction and convective fingering in a diffusive boundary layer in a porous medium. The reaction enhances stability by consuming a solute that is unstably distributed in a gravitational field. We show that chemical reaction profoundly changes the dynamics of the system, by introducing a steady state, shortening the evolution time, and altering the spatial patterns of velocity and concentration of solute. In the presence of weak reaction, finger growth and merger occur effectively, driving strong convective currents in a thick layer of solute. However, as the reaction becomes stronger, finger growth is inhibited, tip-splitting is enhanced and the layer of solute becomes much thinner. Convection enhances the mass flux of solute consumed by reaction in the boundary layer but has a diminishing effect as reaction strength increases. This nonlinear behavior has striking differences to the density fingering of traveling reaction fronts, for which stronger chemical kinetics result in more effective finger merger owing to an increase in the speed of the front. In a boundary layer, a strong stabilizing effect of reaction can maintain a long-term state of convection in isolated fingers of wavelength comparable to that at onset of instability.

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.

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.

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.

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

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)

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.

Reaction Decoder Tool (RDT): extracting features from chemical reactions.

Science.gov (United States)

Rahman, Syed Asad; Torrance, Gilliean; Baldacci, Lorenzo; Martínez Cuesta, Sergio; Fenninger, Franz; Gopal, Nimish; Choudhary, Saket; May, John W; Holliday, Gemma L; Steinbeck, Christoph; Thornton, Janet M

2016-07-01

Extracting chemical features like Atom-Atom Mapping (AAM), Bond Changes (BCs) and Reaction Centres from biochemical reactions helps us understand the chemical composition of enzymatic reactions. Reaction Decoder is a robust command line tool, which performs this task with high accuracy. It supports standard chemical input/output exchange formats i.e. RXN/SMILES, computes AAM, highlights BCs and creates images of the mapped reaction. This aids in the analysis of metabolic pathways and the ability to perform comparative studies of chemical reactions based on these features. This software is implemented in Java, supported on Windows, Linux and Mac OSX, and freely available at https://github.com/asad/ReactionDecoder : asad@ebi.ac.uk or s9asad@gmail.com. © The Author 2016. Published by Oxford University Press.

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

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.

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

Modeling of Reaction Processes Controlled by Diffusion

International Nuclear Information System (INIS)

Revelli, Jorge

2003-01-01

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

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

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)

Diffusion limited reactions in crystalline solids

International Nuclear Information System (INIS)

Fastenau, R.

1982-01-01

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

Chemical burn or reaction

Science.gov (United States)

Chemicals that touch skin can lead to a reaction on the skin, throughout the body, or both. ... leave the person alone and watch carefully for reactions affecting the entire body. Note: If a chemical gets into the eyes, the eyes should be ...

Theoretical study of chemical reaction effects on vertical oscillating plate with variable temperature

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2006-01-01

Full Text Available An exact solution to the flow of a viscous incompressible unsteady flow past an infinite vertical oscillating plate with variable temperature and mass diffusion is presented here, taking into account of the homogeneous chemical reaction of first-order. Both the plate temperature and the concentration level near the plate are raised linearly with respect to time. The dimensionless governing equations has been obtained by the Laplace transform method, when the plate is oscillating harmonically in its own plane. The effects of velocity and concentration are studied for different parameters like phase angle, chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number and time are studied. The solutions are valid only for small values of time t. It is observed that the velocity increases with decreasing phase angle ωt or chemical reaction parameter. .

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...

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

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

Science.gov (United States)

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

2018-05-01

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

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

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.

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

Coupled Diffusion and Reaction Processes in Rock Matrices: Impact on Dilute Groundwater Plumes

Science.gov (United States)

2015-12-28

35    3.6.3-Diffusion-Reaction Cell Construction using 40 mL Vials Gas tight extraction cells were designed and constructed to serve as a means to...ground surface GC gas chromatograph HPLC high-performance liquid chromatography ISCO in situ chemical oxidation MNA monitored natural attenuation...fracture-matrix interface. Mazurek et al. (1996) showed that fractures within shales were coated with birnessite and gypsum. Thus, the impacts 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...

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.

Finite element modeling of contaminant transport in soils including the effect of chemical reactions.

Science.gov (United States)

Javadi, A A; Al-Najjar, M M

2007-05-17

The movement of chemicals through soils to the groundwater is a major cause of degradation of water resources. In many cases, serious human and stock health implications are associated with this form of pollution. Recent studies have shown that the current models and methods are not able to adequately describe the leaching of nutrients through soils, often underestimating the risk of groundwater contamination by surface-applied chemicals, and overestimating the concentration of resident solutes. Furthermore, the effect of chemical reactions on the fate and transport of contaminants is not included in many of the existing numerical models for contaminant transport. In this paper a numerical model is presented for simulation of the flow of water and air and contaminant transport through unsaturated soils with the main focus being on the effects of chemical reactions. The governing equations of miscible contaminant transport including advection, dispersion-diffusion and adsorption effects together with the effect of chemical reactions are presented. The mathematical framework and the numerical implementation of the model are described in detail. The model is validated by application to a number of test cases from the literature and is then applied to the simulation of a physical model test involving transport of contaminants in a block of soil with particular reference to the effects of chemical reactions. Comparison of the results of the numerical model with the experimental results shows that the model is capable of predicting the effects of chemical reactions with very high accuracy. The importance of consideration of the effects of chemical reactions is highlighted.

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.

Chemical transport reactions

CERN Document Server

Schäfer, Harald

2013-01-01

Chemical Transport Reactions focuses on the processes and reactions involved in the transport of solid or liquid substances to form vapor phase reaction products. The publication first offers information on experimental and theoretical principles and the transport of solid substances and its special applications. Discussions focus on calculation of the transport effect of heterogeneous equilibria for a gas motion between equilibrium spaces; transport effect and the thermodynamic quantities of the transport reaction; separation and purification of substances by means of material transport; and

Chemical order-disorder in alloys. Study by neutrons diffuse diffusion

International Nuclear Information System (INIS)

Novion, C. de; Beuneu, B.

1993-01-01

Applications of neutrons diffuse diffusion for short distance chemical order in FCC transition metals solid solutions (Pd-V, Ni-V, Ni-Cr) and understoichiometric carbides or nitrides of transition metals (TiC 1-x , NbC 1-x , TiN 1-x ) are shortly presented with theoretical and experimental aspects. (A.B.)

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.

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.

Characterization of the reaction layer in U-7wt%Mo/Al diffusion couples

Energy Technology Data Exchange (ETDEWEB)

Mirandou, M.I.; Balart, S.N.; Ortiz, M.; Granovsky, M.S. E-mail: granovsk@cnea.gov.ar

2003-11-15

The reaction layer in chemical diffusion couples U-7wt%Mo/Al was investigated using optical and scanning electron microscopy, electron probe microanalysis and X-ray diffraction (XRD) techniques. When the U-7wt%Mo alloy was previously homogenized and the {gamma}(U, Mo) phase was retained, the formation of (U, Mo)Al{sub 3} and (U, Mo)Al{sub 4} was observed at 580 deg. C. Also a very thin band was detected close to the Al side, the structure of the ternary compound Al{sub 20}UMo{sub 2} might be assigned to it. When the decomposition of the {gamma}(U, Mo) took place, a drastic change in the diffusion behavior was observed. In this case, XRD indicated the presence of phases with the structures of (U, Mo)Al{sub 3}, Al{sub 43}U{sub 6}Mo{sub 4}, {gamma}(U, Mo) and {alpha}(U) in the reaction layer.

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.

On the mechanism of effective chemical reactions with turbulent mixing of reactants and finite rate of molecular reactions

Energy Technology Data Exchange (ETDEWEB)

Vorotilin, V. P., E-mail: VPVorotilin@yandex.ru [Russian Academy of Sciences, Institute of Applied Mechanics (Russian Federation)

2017-01-15

A generalization of the theory of chemical transformation processes under turbulent mixing of reactants and arbitrary values of the rate of molecular reactions is presented that was previously developed for the variant of an instantaneous reaction [13]. The use of the features of instantaneous reactions when considering the general case, namely, the introduction of the concept of effective reaction for the reactant volumes and writing a closing conservation equation for these volumes, became possible due to the partition of the whole amount of reactants into “active” and “passive” classes; the reactants of the first class are not mixed and react by the mechanism of instantaneous reactions, while the reactants of the second class approach each other only through molecular diffusion, and therefore their contribution to the reaction process can be neglected. The physical mechanism of reaction for the limit regime of an ideal mixing reactor (IMR) is revealed and described. Although formally the reaction rate in this regime depends on the concentration of passive fractions of the reactants, according to the theory presented, the true (hidden) mechanism of the reaction is associated only with the reaction of the active fractions of the reactants with vanishingly small concentration in the volume of the reactor. It is shown that the rate constant of fast chemical reactions can be evaluated when the mixing intensity of reactants is much less than that needed to reach the mixing conditions in an IMR.

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.

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,...

Unsteady Bioconvection Squeezing Flow in a Horizontal Channel with Chemical Reaction and Magnetic Field Effects

Directory of Open Access Journals (Sweden)

Qingkai Zhao

2017-01-01

Full Text Available The time-dependent mixed bioconvection flow of an electrically conducting fluid between two infinite parallel plates in the presence of a magnetic field and a first-order chemical reaction is investigated. The fully coupled nonlinear systems describing the total mass, momentum, thermal energy, mass diffusion, and microorganisms equations are reduced to a set of ordinary differential equations via a set of new similarity transformations. The detailed analysis illustrating the influences of various physical parameters such as the magnetic, squeezing, and chemical reaction parameters and the Schmidt and Prandtl numbers on the distributions of temperature and microorganisms as well as the skin friction and the Nusselt number is presented. The conclusion is drawn that the flow field, temperature, and chemical reaction profiles are significantly influenced by magnetic parameter, heat generation/absorption parameter, and chemical parameter. Some examples of potential applications of such bioconvection could be found in pharmaceutical industry, microfluidic devices, microbial enhanced oil recovery, modeling oil, and gas-bearing sedimentary basins.

Convergence to equilibrium of renormalised solutions to nonlinear chemical reaction–diffusion systems

Science.gov (United States)

Fellner, Klemens; Tang, Bao Quoc

2018-06-01

The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex balanced condition. By applying the so-called entropy method, we show that if the system does not have boundary equilibria, i.e. equilibrium states lying on the boundary of R_+^N, then any renormalised solution converges exponentially to the complex balanced equilibrium with a rate, which can be computed explicitly up to a finite-dimensional inequality. This inequality is proven via a contradiction argument and thus not explicitly. An explicit method of proof, however, is provided for a specific application modelling a reversible enzyme reaction by exploiting the specific structure of the conservation laws. Our approach is also useful to study the trend to equilibrium for systems possessing boundary equilibria. More precisely, to show the convergence to equilibrium for systems with boundary equilibria, we establish a sufficient condition in terms of a modified finite-dimensional inequality along trajectories of the system. By assuming this condition, which roughly means that the system produces too much entropy to stay close to a boundary equilibrium for infinite time, the entropy method shows exponential convergence to equilibrium for renormalised solutions to complex balanced systems with boundary equilibria.

Chemical kinetics and reaction mechanism

International Nuclear Information System (INIS)

Jung, Ou Sik; Park, Youn Yeol

1996-12-01

This book is about chemical kinetics and reaction mechanism. It consists of eleven chapters, which deal with reaction and reaction speed on reaction mechanism, simple reaction by rate expression, reversible reaction and simultaneous reaction, successive reaction, complicated reaction mechanism, assumption for reaction mechanism, transition state theory, successive reaction and oscillating reaction, reaction by solution, research method high except kinetics on reaction mechanism, high reaction of kinetics like pulsed radiolysis.

The efficiency of driving chemical reactions by a physical non-equilibrium is kinetically controlled.

Science.gov (United States)

Göppel, Tobias; Palyulin, Vladimir V; Gerland, Ulrich

2016-07-27

An out-of-equilibrium physical environment can drive chemical reactions into thermodynamically unfavorable regimes. Under prebiotic conditions such a coupling between physical and chemical non-equilibria may have enabled the spontaneous emergence of primitive evolutionary processes. Here, we study the coupling efficiency within a theoretical model that is inspired by recent laboratory experiments, but focuses on generic effects arising whenever reactant and product molecules have different transport coefficients in a flow-through system. In our model, the physical non-equilibrium is represented by a drift-diffusion process, which is a valid coarse-grained description for the interplay between thermophoresis and convection, as well as for many other molecular transport processes. As a simple chemical reaction, we consider a reversible dimerization process, which is coupled to the transport process by different drift velocities for monomers and dimers. Within this minimal model, the coupling efficiency between the non-equilibrium transport process and the chemical reaction can be analyzed in all parameter regimes. The analysis shows that the efficiency depends strongly on the Damköhler number, a parameter that measures the relative timescales associated with the transport and reaction kinetics. Our model and results will be useful for a better understanding of the conditions for which non-equilibrium environments can provide a significant driving force for chemical reactions in a prebiotic setting.

Curved fronts in the Belousov-Zhabotinskii reaction-diffusion systems in R2

Science.gov (United States)

Niu, Hong-Tao; Wang, Zhi-Cheng; Bu, Zhen-Hui

2018-05-01

In this paper we consider a diffusion system with the Belousov-Zhabotinskii (BZ for short) chemical reaction. Following Brazhnik and Tyson [4] and Pérez-Muñuzuri et al. [45], who predicted V-shaped fronts theoretically and discovered V-shaped fronts by experiments respectively, we give a rigorous mathematical proof of their results. We establish the existence of V-shaped traveling fronts in R2 by constructing a proper supersolution and a subsolution. Furthermore, we establish the stability of the V-shaped front in R2.

Chemical potential and reaction electronic flux in symmetry controlled reactions.

Science.gov (United States)

Vogt-Geisse, Stefan; Toro-Labbé, Alejandro

2016-07-15

In symmetry controlled reactions, orbital degeneracies among orbitals of different symmetries can occur along a reaction coordinate. In such case Koopmans' theorem and the finite difference approximation provide a chemical potential profile with nondifferentiable points. This results in an ill-defined reaction electronic flux (REF) profile, since it is defined as the derivative of the chemical potential with respect to the reaction coordinate. To overcome this deficiency, we propose a new way for the calculation of the chemical potential based on a many orbital approach, suitable for reactions in which symmetry is preserved. This new approach gives rise to a new descriptor: symmetry adapted chemical potential (SA-CP), which is the chemical potential corresponding to a given irreducible representation of a symmetry group. A corresponding symmetry adapted reaction electronic flux (SA-REF) is also obtained. Using this approach smooth chemical potential profiles and well defined REFs are achieved. An application of SA-CP and SA-REF is presented by studying the Cs enol-keto tautomerization of thioformic acid. Two SA-REFs are obtained, JA'(ξ) and JA'' (ξ). It is found that the tautomerization proceeds via an in-plane delocalized 3-center 4-electron O-H-S hypervalent bond which is predicted to exist only in the transition state (TS) region. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

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.

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...

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.

A coupled mechanical and chemical damage model for concrete affected by alkali–silica reaction

Energy Technology Data Exchange (ETDEWEB)

Pignatelli, Rossella, E-mail: rossellapignatelli@gmail.com [Department of Civil and Environmental Engineering, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milano (Italy); Lombardi Ingegneria S.r.l., Via Giotto 36, 20145 Milano (Italy); Comi, Claudia, E-mail: comi@stru.polimi.it [Department of Civil and Environmental Engineering, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milano (Italy); Monteiro, Paulo J.M., E-mail: monteiro@ce.berkeley.edu [Department of Civil and Environmental Engineering, University of California, Berkeley, CA 94720 (United States)

2013-11-15

To model the complex degradation phenomena occurring in concrete affected by alkali–silica reaction (ASR), we formulate a poro-mechanical model with two isotropic internal variables: the chemical and the mechanical damage. The chemical damage, related to the evolution of the reaction, is caused by the pressure generated by the expanding ASR gel on the solid concrete skeleton. The mechanical damage describes the strength and stiffness degradation induced by the external loads. As suggested by experimental results, degradation due to ASR is considered to be localized around reactive sites. The effect of the degree of saturation and of the temperature on the reaction development is also modeled. The chemical damage evolution is calibrated using the value of the gel pressure estimated by applying the electrical diffuse double-layer theory to experimental values of the surface charge density in ASR gel specimens reported in the literature. The chemo-damage model is first validated by simulating expansion tests on reactive specimens and beams; the coupled chemo-mechanical damage model is then employed to simulate compression and flexure tests results also taken from the literature. -- Highlights: •Concrete degradation due to ASR in variable environmental conditions is modeled. •Two isotropic internal variables – chemical and mechanical damage – are introduced. •The value of the swelling pressure is estimated by the diffuse double layer theory. •A simplified scheme is proposed to relate macro- and microscopic properties. •The chemo-mechanical damage model is validated by simulating tests in literature.

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)

Modeling chemical reactions for drug design.

Science.gov (United States)

Gasteiger, Johann

2007-01-01

Chemical reactions are involved at many stages of the drug design process. This starts with the analysis of biochemical pathways that are controlled by enzymes that might be downregulated in certain diseases. In the lead discovery and lead optimization process compounds have to be synthesized in order to test them for their biological activity. And finally, the metabolism of a drug has to be established. A better understanding of chemical reactions could strongly help in making the drug design process more efficient. We have developed methods for quantifying the concepts an organic chemist is using in rationalizing reaction mechanisms. These methods allow a comprehensive modeling of chemical reactivity and thus are applicable to a wide variety of chemical reactions, from gas phase reactions to biochemical pathways. They are empirical in nature and therefore allow the rapid processing of large sets of structures and reactions. We will show here how methods have been developed for the prediction of acidity values and of the regioselectivity in organic reactions, for designing the synthesis of organic molecules and of combinatorial libraries, and for furthering our understanding of enzyme-catalyzed reactions and of the metabolism of drugs.

Numerical study of chemical reactions in a surface microdischarge tube with mist flow based on experiment

International Nuclear Information System (INIS)

Shibata, T; Nishiyama, H

2014-01-01

Recently, a water treatment method of spraying solution into a discharge region has been developed and shows high energy efficiency. In this study, a simulation model of a water treatment method using a surface microdischarge (SMD) tube with mist flow is proposed for further understanding the detailed chemical reactions. Our model has three phases (plasma, gas and liquid) and three simulation steps. The carrier gas is humid air including 2% or 3% water vapour. The chemical species diffusion characteristics in the SMD tube and the concentrations in a droplet are clarified in a wide pH interval. The simulation results show that the chemical species generated on the SMD tube inner wall are diffused to the central axis and dissolved into fine droplets. Especially, OH radicals dissolve into droplets a few mm away from the SMD tube wall because of acidification of the droplets. Furthermore, the hydrogen peroxide density, which is the most important indicator of a radical reaction in water, is influenced by the initial solution pH. This pH dependence results from ozone self-decomposition in water. (paper)

Numerical study of chemical reactions in a surface microdischarge tube with mist flow based on experiment

Science.gov (United States)

Shibata, T.; Nishiyama, H.

2014-03-01

Recently, a water treatment method of spraying solution into a discharge region has been developed and shows high energy efficiency. In this study, a simulation model of a water treatment method using a surface microdischarge (SMD) tube with mist flow is proposed for further understanding the detailed chemical reactions. Our model has three phases (plasma, gas and liquid) and three simulation steps. The carrier gas is humid air including 2% or 3% water vapour. The chemical species diffusion characteristics in the SMD tube and the concentrations in a droplet are clarified in a wide pH interval. The simulation results show that the chemical species generated on the SMD tube inner wall are diffused to the central axis and dissolved into fine droplets. Especially, OH radicals dissolve into droplets a few mm away from the SMD tube wall because of acidification of the droplets. Furthermore, the hydrogen peroxide density, which is the most important indicator of a radical reaction in water, is influenced by the initial solution pH. This pH dependence results from ozone self-decomposition in water.

Investigations of chemical reactions between U-Zr alloy and FBR cladding materials

International Nuclear Information System (INIS)

Ishii, Tetsuya; Ukai, Shigeharu

2005-07-01

U-Pu-Zr alloys are candidate materials for commercial FBR fuel. However, informations about chemical reactions with cladding materials developed by JNC for commercial FBR have not been well obtained. In this work, the reaction zones formed in four diffusion couples U-10wt.%Zr/PNC-FMS, U-10wt.%Zr/9Cr-ODS, U-10wt.%Zr/12Cr-ODS, and U-10wt.%Zr/Fe at about 1013K have been examined and following results were obtained. 1) At about 1013K, in the U-10wt.%Zr/Fe couple, the liquid phase zones were obtained. In the other couples U-10wt.%Zr/PNC-FMS, U-10wt.%Zr/9Cr-ODS and U-10wt.%Zr/12Cr-ODS, no liquid phase zones were obtained. The obtained chemical reaction zones in the later 3 couples were similar to the reported ones obtained in U-Zr/Fe couples without liquid phase formation. In comparison with the reaction zones obtained in the U-10wt.%Zr/Fe couple, the reaction zones inside cladding materials obtained in the PNC-FMS, 9Cr-ODS, and 12Cr-ODS couples were thin. 2) From the investigations of relationship between the obtained depths of the chemical reaction zones inside cladding materials and composition of the cladding materials, it was considered that the depth of chemical reaction zone would depend on the Cr content of the cladding materials and the depth would decrease with increasing Cr content, resulting in prevention of liquid phase formation. 3) From the investigations of the mechanisms of chemical reactions between U-Pu-Zr/cladding materials, it was considered that the same effect of Cr obtained in the U-Zr/cladding materials would be expected in U-Pu-Zr/cladding materials. Those seemed to indicate that the threshold temperatures of liquid phase formation for U-Pu-Zr/PNC-FMS, U-Pu-Zr/9Cr-ODS, and U-Pu-Zr/12Cr-ODS might be higher than that for U-Pu-Zr/Fe. (author)

Chemical reactions confined within carbon nanotubes.

Science.gov (United States)

Miners, Scott A; Rance, Graham A; Khlobystov, Andrei N

2016-08-22

In this critical review, we survey the wide range of chemical reactions that have been confined within carbon nanotubes, particularly emphasising how the pairwise interactions between the catalysts, reactants, transition states and products of a particular molecular transformation with the host nanotube can be used to control the yields and distributions of products of chemical reactions. We demonstrate that nanoscale confinement within carbon nanotubes enables the control of catalyst activity, morphology and stability, influences the local concentration of reactants and products thus affecting equilibria, rates and selectivity, pre-arranges the reactants for desired reactions and alters the relative stability of isomeric products. We critically evaluate the relative advantages and disadvantages of the confinement of chemical reactions inside carbon nanotubes from a chemical perspective and describe how further developments in the controlled synthesis of carbon nanotubes and the incorporation of multifunctionality are essential for the development of this ever-expanding field, ultimately leading to the effective control of the pathways of chemical reactions through the rational design of multi-functional carbon nanoreactors.

Amazing variational approach to chemical reactions

OpenAIRE

Fernández, Francisco M.

2009-01-01

In this letter we analyse an amazing variational approach to chemical reactions. Our results clearly show that the variational expressions are unsuitable for the analysis of empirical data obtained from chemical reactions.

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

ReactionMap: an efficient atom-mapping algorithm for chemical reactions.

Science.gov (United States)

Fooshee, David; Andronico, Alessio; Baldi, Pierre

2013-11-25

Large databases of chemical reactions provide new data-mining opportunities and challenges. Key challenges result from the imperfect quality of the data and the fact that many of these reactions are not properly balanced or atom-mapped. Here, we describe ReactionMap, an efficient atom-mapping algorithm. Our approach uses a combination of maximum common chemical subgraph search and minimization of an assignment cost function derived empirically from training data. We use a set of over 259,000 balanced atom-mapped reactions from the SPRESI commercial database to train the system, and we validate it on random sets of 1000 and 17,996 reactions sampled from this pool. These large test sets represent a broad range of chemical reaction types, and ReactionMap correctly maps about 99% of the atoms and about 96% of the reactions, with a mean time per mapping of 2 s. Most correctly mapped reactions are mapped with high confidence. Mapping accuracy compares favorably with ChemAxon's AutoMapper, versions 5 and 6.1, and the DREAM Web tool. These approaches correctly map 60.7%, 86.5%, and 90.3% of the reactions, respectively, on the same data set. A ReactionMap server is available on the ChemDB Web portal at http://cdb.ics.uci.edu .

Coupling between solute transport and chemical reactions models

International Nuclear Information System (INIS)

Samper, J.; Ajora, C.

1993-01-01

During subsurface transport, reactive solutes are subject to a variety of hydrodynamic and chemical processes. The major hydrodynamic processes include advection and convection, dispersion and diffusion. The key chemical processes are complexation including hydrolysis and acid-base reactions, dissolution-precipitation, reduction-oxidation, adsorption and ion exchange. The combined effects of all these processes on solute transport must satisfy the principle of conservation of mass. The statement of conservation of mass for N mobile species leads to N partial differential equations. Traditional solute transport models often incorporate the effects of hydrodynamic processes rigorously but oversimplify chemical interactions among aqueous species. Sophisticated chemical equilibrium models, on the other hand, incorporate a variety of chemical processes but generally assume no-flow systems. In the past decade, coupled models accounting for complex hydrological and chemical processes, with varying degrees of sophistication, have been developed. The existing models of reactive transport employ two basic sets of equations. The transport of solutes is described by a set of partial differential equations, and the chemical processes, under the assumption of equilibrium, are described by a set of nonlinear algebraic equations. An important consideration in any approach is the choice of primary dependent variables. Most existing models cannot account for the complete set of chemical processes, cannot be easily extended to include mixed chemical equilibria and kinetics, and cannot handle practical two and three dimensional problems. The difficulties arise mainly from improper selection of the primary variables in the transport equations. (Author) 38 refs

Chemical vapor deposition of refractory ternary nitrides for advanced diffusion barriers

Energy Technology Data Exchange (ETDEWEB)

Custer, Jonathan S.; Fleming, James G.; Roherty-Osmun, Elizabeth; Smith, Paul Martin

1998-09-22

Refractory ternary nitride films for diffusion barriers in microelectronics have been grown using chemical vapor deposition. Thin films of titanium-silicon-nitride, tungsten-boron-nitride, and tungsten-silicon-nitride of various compositions have been deposited on 150 mm Si wafers. The microstructure of the films are either fully amorphous for the tungsten based films, or nauocrystalline TiN in an amorphous matrix for titanium-silicon-nitride. All films exhibit step coverages suitable for use in future microelectronics generations. Selected films have been tested as diffusion barriers between copper and silicon, and generally perform extremely weH. These fiIms are promising candidates for advanced diffusion barriers for microelectronics applications. The manufacturing of silicon wafers into integrated circuits uses many different process and materials. The manufacturing process is usually divided into two parts: the front end of line (FEOL) and the back end of line (BEOL). In the FEOL the individual transistors that are the heart of an integrated circuit are made on the silicon wafer. The responsibility of the BEOL is to wire all the transistors together to make a complete circuit. The transistors are fabricated in the silicon itself. The wiring is made out of metal, currently aluminum and tungsten, insulated by silicon dioxide, see Figure 1. Unfortunately, silicon will diffuse into aluminum, causing aluminum spiking of junctions, killing transistors. Similarly, during chemical vapor deposition (CVD) of tungsten from ~fj, the reactivity of the fluorine can cause "worn-holes" in the silicon, also destroying transistors. The solution to these problems is a so-called diffusion barrier, which will allow current to pass from the transistors to the wiring, but will prevent reactions between silicon and the metal.

Mass transfer in porous media with heterogeneous chemical reaction

Directory of Open Access Journals (Sweden)

Souza S.M.A.G.Ulson de

2003-01-01

Full Text Available In this paper, the modeling of the mass transfer process in packed-bed reactors is presented and takes into account dispersion in the main fluid phase, internal diffusion of the reactant in the pores of the catalyst, and surface reaction inside the catalyst. The method of volume averaging is applied to obtain the governing equation for use on a small scale. The local mass equilibrium is assumed for obtaining the one-equation model for use on a large scale. The closure problems are developed subject to the length-scale constraints and the model of a spatially periodic porous medium. The expressions for effective diffusivity, hydrodynamic dispersion, total dispersion and the Darcy's law permeability tensors are presented. Solution of the set of final equations permits the variations of velocity and concentration of the chemical species along the packed-bed reactors to be obtained.

Mining chemical reactions using neighborhood behavior and condensed graphs of reactions approaches.

Science.gov (United States)

de Luca, Aurélie; Horvath, Dragos; Marcou, Gilles; Solov'ev, Vitaly; Varnek, Alexandre

2012-09-24

This work addresses the problem of similarity search and classification of chemical reactions using Neighborhood Behavior (NB) and Condensed Graphs of Reaction (CGR) approaches. The CGR formalism represents chemical reactions as a classical molecular graph with dynamic bonds, enabling descriptor calculations on this graph. Different types of the ISIDA fragment descriptors generated for CGRs in combination with two metrics--Tanimoto and Euclidean--were considered as chemical spaces, to serve for reaction dissimilarity scoring. The NB method has been used to select an optimal combination of descriptors which distinguish different types of chemical reactions in a database containing 8544 reactions of 9 classes. Relevance of NB analysis has been validated in generic (multiclass) similarity search and in clustering with Self-Organizing Maps (SOM). NB-compliant sets of descriptors were shown to display enhanced mapping propensities, allowing the construction of better Self-Organizing Maps and similarity searches (NB and classical similarity search criteria--AUC ROC--correlate at a level of 0.7). The analysis of the SOM clusters proved chemically meaningful CGR substructures representing specific reaction signatures.

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.

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.

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.

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

Femtosecond laser control of chemical reactions

CSIR Research Space (South Africa)

Du Plessis, A

2010-08-31

Full Text Available Femtosecond laser control of chemical reactions is made possible through the use of pulse-shaping techniques coupled to a learning algorithm feedback loop – teaching the laser pulse to control the chemical reaction. This can result in controllable...

Pattern formation in three-dimensional reaction-diffusion systems

Science.gov (United States)

Callahan, T. K.; Knobloch, E.

1999-08-01

Existing group theoretic analysis of pattern formation in three dimensions [T.K. Callahan, E. Knobloch, Symmetry-breaking bifurcations on cubic lattices, Nonlinearity 10 (1997) 1179-1216] is used to make specific predictions about the formation of three-dimensional patterns in two models of the Turing instability, the Brusselator model and the Lengyel-Epstein model. Spatially periodic patterns having the periodicity of the simple cubic (SC), face-centered cubic (FCC) or body-centered cubic (BCC) lattices are considered. An efficient center manifold reduction is described and used to identify parameter regimes permitting stable lamellæ, SC, FCC, double-diamond, hexagonal prism, BCC and BCCI states. Both models possess a special wavenumber k* at which the normal form coefficients take on fixed model-independent ratios and both are described by identical bifurcation diagrams. This property is generic for two-species chemical reaction-diffusion models with a single activator and inhibitor.

Two-scale large deviations for chemical reaction kinetics through second quantization path integral

International Nuclear Information System (INIS)

Li, Tiejun; Lin, Feng

2016-01-01

Motivated by the study of rare events for a typical genetic switching model in systems biology, in this paper we aim to establish the general two-scale large deviations for chemical reaction systems. We build a formal approach to explicitly obtain the large deviation rate functionals for the considered two-scale processes based upon the second quantization path integral technique. We get three important types of large deviation results when the underlying two timescales are in three different regimes. This is realized by singular perturbation analysis to the rate functionals obtained by the path integral. We find that the three regimes possess the same deterministic mean-field limit but completely different chemical Langevin approximations. The obtained results are natural extensions of the classical large volume limit for chemical reactions. We also discuss its implication on the single-molecule Michaelis–Menten kinetics. Our framework and results can be applied to understand general multi-scale systems including diffusion processes. (paper)

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....

Study of flow past an exponentially accelerated isothermal vertical plate in the presence of chemical reaction

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2010-01-01

Full Text Available Theoretical study of unsteady flow past an exponentially accelerated infinite isothermal vertical plate with variable mass diffusion has been presented in the presence of homogeneous chemical reaction of first order. The plate temperature is raised to Tw and species concentration level near the plate is made to rise linearly with time. The dimensionless governing equations are solved using Laplace-transform technique. The velocity profiles are studied for different physical parameters like chemical reaction parameter, thermal Grashof number, mass Grashof number, a and time. It is observed that the velocity increases with increasing values of a or t. But the trend is just reversed with respect to K.

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...

Coupling effects of chemical stresses and external mechanical stresses on diffusion

International Nuclear Information System (INIS)

Xuan Fuzhen; Shao Shanshan; Wang Zhengdong; Tu Shantung

2009-01-01

Interaction between diffusion and stress fields has been investigated extensively in the past. However, most of the previous investigations were focused on the effect of chemical stress on diffusion due to the unbalanced mass transport. In this work, the coupling effects of external mechanical stress and chemical stress on diffusion are studied. A self-consistent diffusion equation including the chemical stress and external mechanical stress gradient is developed under the framework of the thermodynamic theory and Fick's law. For a thin plate subjected to unidirectional tensile stress fields, the external stress coupled diffusion equation is solved numerically with the help of the finite difference method for one-side and both-side charging processes. Results show that, for such two types of charging processes, the external stress gradient will accelerate the diffusion process and thus increase the value of concentration while reducing the magnitude of chemical stress when the direction of diffusion is identical to that of the stress gradient. In contrast, when the direction of diffusion is opposite to that of the stress gradient, the external stress gradient will obstruct the process of solute penetration by decreasing the value of concentration and increasing the magnitude of chemical stress. For both-side charging process, compared with that without the coupling effect of external stress, an asymmetric distribution of concentration is produced due to the asymmetric mechanical stress field feedback to diffusion.

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.

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.

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.

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

Controlled surface diffusion in plasma-enhanced chemical vapor deposition of GaN nanowires

International Nuclear Information System (INIS)

Hou, W C; Hong, Franklin Chau-Nan

2009-01-01

This study investigates the growth of GaN nanowires by controlling the surface diffusion of Ga species on sapphire in a plasma-enhanced chemical vapor deposition (CVD) system. Under nitrogen-rich growth conditions, Ga has a tendency to adsorb on the substrate surface diffusing to nanowires to contribute to their growth. The significance of surface diffusion on the growth of nanowires is dependent on the environment of the nanowire on the substrate surface as well as the gas phase species and compositions. Under nitrogen-rich growth conditions, the growth rate is strongly dependent on the surface diffusion of gallium, but the addition of 5% hydrogen in nitrogen plasma instantly diminishes the surface diffusion effect. Gallium desorbs easily from the surface by reaction with hydrogen. On the other hand, under gallium-rich growth conditions, nanowire growth is shown to be dominated by the gas phase deposition, with negligible contribution from surface diffusion. This is the first study reporting the inhibition of surface diffusion effects by hydrogen addition, which can be useful in tailoring the growth and characteristics of nanowires. Without any evidence of direct deposition on the nanowire surface, gallium and nitrogen are shown to dissolve into the catalyst for growing the nanowires at 900 deg. C.

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

Microfabricated sleeve devices for chemical reactions

Science.gov (United States)

Northrup, M. Allen

2003-01-01

A silicon-based sleeve type chemical reaction chamber that combines heaters, such as doped polysilicon for heating, and bulk silicon for convection cooling. The reaction chamber combines a critical ratio of silicon and non-silicon based materials to provide the thermal properties desired. For example, the chamber may combine a critical ratio of silicon and silicon nitride to the volume of material to be heated (e.g., a liquid) in order to provide uniform heating, yet low power requirements. The reaction chamber will also allow the introduction of a secondary tube (e.g., plastic) into the reaction sleeve that contains the reaction mixture thereby alleviating any potential materials incompatibility issues. The reaction chamber may be utilized in any chemical reaction system for synthesis or processing of organic, inorganic, or biochemical reactions, such as the polymerase chain reaction (PCR) and/or other DNA reactions, such as the ligase chain reaction, which are examples of a synthetic, thermal-cycling-based reaction. The reaction chamber may also be used in synthesis instruments, particularly those for DNA amplification and synthesis.

Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation

Directory of Open Access Journals (Sweden)

Petr Stehlík

2015-01-01

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

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.

Computational Analyses of Complex Flows with Chemical Reactions

Science.gov (United States)

Bae, Kang-Sik

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

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.

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.

Plasmon-driven sequential chemical reactions in an aqueous environment.

Science.gov (United States)

Zhang, Xin; Wang, Peijie; Zhang, Zhenglong; Fang, Yurui; Sun, Mengtao

2014-06-24

Plasmon-driven sequential chemical reactions were successfully realized in an aqueous environment. In an electrochemical environment, sequential chemical reactions were driven by an applied potential and laser irradiation. Furthermore, the rate of the chemical reaction was controlled via pH, which provides indirect evidence that the hot electrons generated from plasmon decay play an important role in plasmon-driven chemical reactions. In acidic conditions, the hot electrons were captured by the abundant H(+) in the aqueous environment, which prevented the chemical reaction. The developed plasmon-driven chemical reactions in an aqueous environment will significantly expand the applications of plasmon chemistry and may provide a promising avenue for green chemistry using plasmon catalysis in aqueous environments under irradiation by sunlight.

Chemical reactions as $\\Gamma$-limit of diffusion

NARCIS (Netherlands)

Peletier, M.A.; Savaré, G.; Veneroni, M.

2012-01-01

We study the limit of high activation energy of a special Fokker–Planck equation known as the Kramers–Smoluchowski equation (KS). This equation governs the time evolution of the probability density of a particle performing a Brownian motion under the influence of a chemical potential

Complex Chemical Reaction Networks from Heuristics-Aided Quantum Chemistry.

Science.gov (United States)

Rappoport, Dmitrij; Galvin, Cooper J; Zubarev, Dmitry Yu; Aspuru-Guzik, Alán

2014-03-11

While structures and reactivities of many small molecules can be computed efficiently and accurately using quantum chemical methods, heuristic approaches remain essential for modeling complex structures and large-scale chemical systems. Here, we present a heuristics-aided quantum chemical methodology applicable to complex chemical reaction networks such as those arising in cell metabolism and prebiotic chemistry. Chemical heuristics offer an expedient way of traversing high-dimensional reactive potential energy surfaces and are combined here with quantum chemical structure optimizations, which yield the structures and energies of the reaction intermediates and products. Application of heuristics-aided quantum chemical methodology to the formose reaction reproduces the experimentally observed reaction products, major reaction pathways, and autocatalytic cycles.

Surface chemical reactions probed with scanning force microscopy

NARCIS (Netherlands)

Werts, M.P L; van der Vegte, E.W.; Hadziioannou, G

1997-01-01

In this letter we report the study of surface chemical reactions with scanning force microscopy (SFM) with chemical specificity. Using chemically modified SFM probes, we can determine the local surface reaction conversion during a chemical surface modification. The adhesion forces between a

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.

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.

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.

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.

Incidents of chemical reactions in cell equipment

Energy Technology Data Exchange (ETDEWEB)

Baldwin, N.M.; Barlow, C.R. [Uranium Enrichment Organization, Oak Ridge, TN (United States)

1991-12-31

Strongly exothermic reactions can occur between equipment structural components and process gases under certain accident conditions in the diffusion enrichment cascades. This paper describes the conditions required for initiation of these reactions, and describes the range of such reactions experienced over nearly 50 years of equipment operation in the US uranium enrichment program. Factors are cited which can promote or limit the destructive extent of these reactions, and process operations are described which are designed to control the reactions to minimize equipment damage, downtime, and the possibility of material releases.

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.

Runaway chemical reaction exposes community to highly toxic chemicals

International Nuclear Information System (INIS)

Kaszniak, Mark; Vorderbrueggen, John

2008-01-01

The U.S. Chemical Safety and Hazard Investigation Board (CSB) conducted a comprehensive investigation of a runaway chemical reaction at MFG Chemical (MFG) in Dalton, Georgia on April 12, 2004 that resulted in the uncontrolled release of a large quantity of highly toxic and flammable allyl alcohol and allyl chloride into the community. Five people were hospitalized and 154 people required decontamination and treatment for exposure to the chemicals. This included police officers attempting to evacuate the community and ambulance personnel who responded to 911 calls from residents exposed to the chemicals. This paper presents the findings of the CSB report (U.S. Chemical Safety and Hazard Investigation Board (CSB), Investigation Report: Toxic Chemical Vapor Cloud Release, Report No. 2004-09-I-GA, Washington DC, April 2006) including a discussion on tolling practices; scale-up of batch reaction processes; Process Safety Management (PSM) and Risk Management Plan (RMP) implementation; emergency planning by the company, county and the city; and emergency response and mitigation actions taken during the incident. The reactive chemical testing and atmospheric dispersion modeling conducted by CSB after the incident and recommendations adopted by the Board are also discussed

Rate kernel theory for pseudo-first-order kinetics of diffusion-influenced reactions and application to fluorescence quenching kinetics.

Science.gov (United States)

Yang, Mino

2007-06-07

Theoretical foundation of rate kernel equation approaches for diffusion-influenced chemical reactions is presented and applied to explain the kinetics of fluorescence quenching reactions. A many-body master equation is constructed by introducing stochastic terms, which characterize the rates of chemical reactions, into the many-body Smoluchowski equation. A Langevin-type of memory equation for the density fields of reactants evolving under the influence of time-independent perturbation is derived. This equation should be useful in predicting the time evolution of reactant concentrations approaching the steady state attained by the perturbation as well as the steady-state concentrations. The dynamics of fluctuation occurring in equilibrium state can be predicted by the memory equation by turning the perturbation off and consequently may be useful in obtaining the linear response to a time-dependent perturbation. It is found that unimolecular decay processes including the time-independent perturbation can be incorporated into bimolecular reaction kinetics as a Laplace transform variable. As a result, a theory for bimolecular reactions along with the unimolecular process turned off is sufficient to predict overall reaction kinetics including the effects of unimolecular reactions and perturbation. As the present formulation is applied to steady-state kinetics of fluorescence quenching reactions, the exact relation between fluorophore concentrations and the intensity of excitation light is derived.

Modelling of structural effects on chemical reactions in turbulent flows

Energy Technology Data Exchange (ETDEWEB)

Gammelsaeter, H.R.

1997-12-31

Turbulence-chemistry interactions are analysed using algebraic moment closure for the chemical reaction term. The coupling between turbulence and chemical length and time scales generate a complex interaction process. This interaction process is called structural effects in this work. The structural effects are shown to take place on all scales between the largest scale of turbulence and the scales of the molecular motions. The set of equations describing turbulent correlations involved in turbulent reacting flows are derived. Interactions are shown schematically using interaction charts. Algebraic equations for the turbulent correlations in the reaction rate are given using the interaction charts to include the most significant couplings. In the frame of fundamental combustion physics, the structural effects appearing on the small scales of turbulence are proposed modelled using a discrete spectrum of turbulent scales. The well-known problem of averaging the Arrhenius law, the specific reaction rate, is proposed solved using a presumed single variable probability density function and a sub scale model for the reaction volume. Although some uncertainties are expected, the principles are addressed. Fast chemistry modelling is shown to be consistent in the frame of algebraic moment closure when the turbulence-chemistry interaction is accounted for in the turbulent diffusion. The modelling proposed in this thesis is compared with experimental data for an laboratory methane flame and advanced probability density function modelling. The results show promising features. Finally it is shown a comparison with full scale measurements for an industrial burner. All features of the burner are captured with the model. 41 refs., 33 figs.

Chemical reaction due to stronger Ramachandran interaction

Indian Academy of Sciences (India)

actions between two polarized atoms are responsible for initiating a chemical reaction, either before or after ... Chemical reaction; Ramachandran interaction; anisotropic and asymmetric polarization; ionization ..... man sequence exactly, including the generalized mech- ..... We now move on and rearrange Eq. (8) to arrive at.

Reduction of chemical reaction models

Science.gov (United States)

Frenklach, Michael

1991-01-01

An attempt is made to reconcile the different terminologies pertaining to reduction of chemical reaction models. The approaches considered include global modeling, response modeling, detailed reduction, chemical lumping, and statistical lumping. The advantages and drawbacks of each of these methods are pointed out.

Enhancing chemical reactions

Science.gov (United States)

Morrey, John R.

1978-01-01

Methods of enhancing selected chemical reactions. The population of a selected high vibrational energy state of a reactant molecule is increased substantially above its population at thermal equilibrium by directing onto the molecule a beam of radiant energy from a laser having a combination of frequency and intensity selected to pump the selected energy state, and the reaction is carried out with the temperature, pressure, and concentrations of reactants maintained at a combination of values selected to optimize the reaction in preference to thermal degradation by transforming the absorbed energy into translational motion. The reaction temperature is selected to optimize the reaction. Typically a laser and a frequency doubler emit radiant energy at frequencies of .nu. and 2.nu. into an optical dye within an optical cavity capable of being tuned to a wanted frequency .delta. or a parametric oscillator comprising a non-centrosymmetric crystal having two indices of refraction, to emit radiant energy at the frequencies of .nu., 2.nu., and .delta. (and, with a parametric oscillator, also at 2.nu.-.delta.). Each unwanted frequency is filtered out, and each desired frequency is focused to the desired radiation flux within a reaction chamber and is reflected repeatedly through the chamber while reactants are fed into the chamber and reaction products are removed therefrom.

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 \

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

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.

Optimizing Chemical Reactions with Deep Reinforcement Learning.

Science.gov (United States)

Zhou, Zhenpeng; Li, Xiaocheng; Zare, Richard N

2017-12-27

Deep reinforcement learning was employed to optimize chemical reactions. Our model iteratively records the results of a chemical reaction and chooses new experimental conditions to improve the reaction outcome. This model outperformed a state-of-the-art blackbox optimization algorithm by using 71% fewer steps on both simulations and real reactions. Furthermore, we introduced an efficient exploration strategy by drawing the reaction conditions from certain probability distributions, which resulted in an improvement on regret from 0.062 to 0.039 compared with a deterministic policy. Combining the efficient exploration policy with accelerated microdroplet reactions, optimal reaction conditions were determined in 30 min for the four reactions considered, and a better understanding of the factors that control microdroplet reactions was reached. Moreover, our model showed a better performance after training on reactions with similar or even dissimilar underlying mechanisms, which demonstrates its learning ability.

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

Flows and chemical reactions in heterogeneous mixtures

CERN Document Server

Prud'homme, Roger

2014-01-01

This book - a sequel of previous publications 'Flows and Chemical Reactions' and 'Chemical Reactions in Flows and Homogeneous Mixtures' - is devoted to flows with chemical reactions in heterogeneous environments.  Heterogeneous media in this volume include interfaces and lines. They may be the site of radiation. Each type of flow is the subject of a chapter in this volume. We consider first, in Chapter 1, the question of the generation of environments biphasic individuals: dusty gas, mist, bubble flow.  Chapter 2 is devoted to the study at the mesoscopic scale: particle-fluid exchange of mom

Silicon-based sleeve devices for chemical reactions

Science.gov (United States)

Northrup, M. Allen; Mariella, Jr., Raymond P.; Carrano, Anthony V.; Balch, Joseph W.

1996-01-01

A silicon-based sleeve type chemical reaction chamber that combines heaters, such as doped polysilicon for heating, and bulk silicon for convection cooling. The reaction chamber combines a critical ratio of silicon and silicon nitride to the volume of material to be heated (e.g., a liquid) in order to provide uniform heating, yet low power requirements. The reaction chamber will also allow the introduction of a secondary tube (e.g., plastic) into the reaction sleeve that contains the reaction mixture thereby alleviating any potential materials incompatibility issues. The reaction chamber may be utilized in any chemical reaction system for synthesis or processing of organic, inorganic, or biochemical reactions, such as the polymerase chain reaction (PCR) and/or other DNA reactions, such as the ligase chain reaction, which are examples of a synthetic, thermal-cycling-based reaction. The reaction chamber may also be used in synthesis instruments, particularly those for DNA amplification and synthesis.

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

Investigation of Evaluation method of chemical runaway reaction

International Nuclear Information System (INIS)

Sato, Yoshihiko; Sasaya, Shinji; Kurakata, Koichiro; Nojiri, Ichiro

2002-02-01

Safety study 'Study of evaluation of abnormal occurrence for chemical substances in the nuclear fuel facilities' will be carried out from 2001 to 2005. In this study, the prediction of thermal hazards of chemical substances will be investigated and prepared. The hazard prediction method of chemical substances will be constructed from these results. Therefore, the hazard prediction methods applied in the chemical engineering in which the chemical substances with the hazard of fire and explosion were often treated were investigated. CHETAH (The ASTM Computer Program for Chemical Thermodynamic and Energy Release Evaluation) developed by ASTM (American Society for Testing and Materials) and TSS (Thermal Safety Software) developed by CISP (ChemInform St. Petersburg) were introduced and the fire and explosion hazards of chemical substances and reactions in the reprocessing process were evaluated. From these evaluated results, CHETAH could almost estimate the heat of reaction at 10% accuracy. It was supposed that CHETAH was useful as a screening for the hazards of fire and explosion of the new chemical substances and so on. TSS could calculate the reaction rate and the reaction behavior from the data measured by the various calorimeters rapidly. It was supposed that TSS was useful as an evaluation method for the hazards of fire and explosion of the new chemical reactions and so on. (author)

A thermodynamic framework for thermo-chemo-elastic interactions in chemically active materials

Science.gov (United States)

Zhang, XiaoLong; Zhong, Zheng

2017-08-01

In this paper, a general thermodynamic framework is developed to describe the thermo-chemo-mechanical interactions in elastic solids undergoing mechanical deformation, imbibition of diffusive chemical species, chemical reactions and heat exchanges. Fully coupled constitutive relations and evolving laws for irreversible fluxes are provided based on entropy imbalance and stoichiometry that governs reactions. The framework manifests itself with a special feature that the change of Helmholtz free energy is attributed to separate contributions of the diffusion-swelling process and chemical reaction-dilation process. Both the extent of reaction and the concentrations of diffusive species are taken as independent state variables, which describe the reaction-activated responses with underlying variation of microstructures and properties of a material in an explicit way. A specialized isothermal formulation for isotropic materials is proposed that can properly account for volumetric constraints from material incompressibility under chemo-mechanical loadings, in which inhomogeneous deformation is associated with reaction and diffusion under various kinetic time scales. This framework can be easily applied to model the transient volumetric swelling of a solid caused by imbibition of external chemical species and simultaneous chemical dilation arising from reactions between the diffusing species and the solid.

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.

Modeling of turbulent chemical reaction

Science.gov (United States)

Chen, J.-Y.

1995-01-01

Viewgraphs are presented on modeling turbulent reacting flows, regimes of turbulent combustion, regimes of premixed and regimes of non-premixed turbulent combustion, chemical closure models, flamelet model, conditional moment closure (CMC), NO(x) emissions from turbulent H2 jet flames, probability density function (PDF), departures from chemical equilibrium, mixing models for PDF methods, comparison of predicted and measured H2O mass fractions in turbulent nonpremixed jet flames, experimental evidence of preferential diffusion in turbulent jet flames, and computation of turbulent reacting flows.

Chemical tailoring of teicoplanin with site-selective reactions.

Science.gov (United States)

Pathak, Tejas P; Miller, Scott J

2013-06-05

Semisynthesis of natural product derivatives combines the power of fermentation with orthogonal chemical reactions. Yet, chemical modification of complex structures represents an unmet challenge, as poor selectivity often undermines efficiency. The complex antibiotic teicoplanin eradicates bacterial infections. However, as resistance emerges, the demand for improved analogues grows. We have discovered chemical reactions that achieve site-selective alteration of teicoplanin. Utilizing peptide-based additives that alter reaction selectivities, certain bromo-teicoplanins are accessible. These new compounds are also scaffolds for selective cross-coupling reactions, enabling further molecular diversification. These studies enable two-step access to glycopeptide analogues not available through either biosynthesis or rapid total chemical synthesis alone. The new compounds exhibit a spectrum of activities, revealing that selective chemical alteration of teicoplanin may lead to analogues with attenuated or enhanced antibacterial properties, in particular against vancomycin- and teicoplanin-resistant strains.

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.

A coupled mechanical-chemical model for reflecting the influence of stress on oxidation reactions in thermal barrier coating

Science.gov (United States)

Chen, Lin; Yueming, Li

2018-06-01

In this paper, a coupled mechanical-chemical model is established based on the thermodynamic framework, in which the contribution of chemical expansion to free energy is introduced. The stress-dependent chemical potential equilibrium at the gas-solid interface and the stress gradient-dependent diffusion equation as well as a so-called generalized force which is conjugate to the oxidation rate are derived from the proposed model, which could reflect the influence of stresses on the oxidation reaction. Based on the proposed coupled mechanical-chemical model, a user element subroutine is developed in ABAQUS. The numerical simulation of the high temperature oxidation in the thermal barrier coating is carried out to verify the accuracy of the proposed model, and then the influence of stresses on the oxidation reaction is investigated. In thermally grown oxide, the considerable stresses would be induced by permanent volumetric swelling during the oxidation. The stresses play an important role in the chemical potential equilibrium at the gas-solid interface and strongly affect the oxidation reaction. The gradient of the stresses, however, only occurs in the extremely thin oxidation front layer, which plays a very limited role in the oxidation reaction. The generalized force could be divided into the stress-dependent and the stress-independent parts. Comparing with the stress-independent part, the stress-dependent part is smaller, which has little influence on oxidation reaction.

Kinetics of intercalation of fluorescent probes in magnesium-aluminium layered double hydroxide within a multiscale reaction-diffusion framework

Science.gov (United States)

Saliba, Daniel; Al-Ghoul, Mazen

2016-11-01

We report the synthesis of magnesium-aluminium layered double hydroxide (LDH) using a reaction-diffusion framework (RDF) that exploits the multiscale coupling of molecular diffusion with chemical reactions, nucleation and growth of crystals. In an RDF, the hydroxide anions are allowed to diffuse into an organic gel matrix containing the salt mixture needed for the precipitation of the LDH. The chemical structure and composition of the synthesized magnesium-aluminium LDHs are determined using powder X-ray diffraction (PXRD), thermo-gravimetric analysis, differential scanning calorimetry, solid-state nuclear magnetic resonance (SSNMR), Fourier transform infrared and energy dispersive X-ray spectroscopy. This novel technique also allows the investigation of the mechanism of intercalation of some fluorescent probes, such as the neutral three-dimensional rhodamine B (RhB) and the negatively charged two-dimensional 8-hydroxypyrene-1,3,6-trisulfonic acid (HPTS), using in situ steady-state fluorescence spectroscopy. The incorporation of these organic dyes inside the interlayer region of the LDH is confirmed via fluorescence microscopy, solid-state lifetime, SSNMR and PXRD. The activation energies of intercalation of the corresponding molecules (RhB and HPTS) are computed and exhibit dependence on the geometry of the involved probe (two or three dimensions), the charge of the fluorescent molecule (anionic, cationic or neutral) and the cationic ratio of the corresponding LDH. This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

Explorations into Chemical Reactions and Biochemical Pathways.

Science.gov (United States)

Gasteiger, Johann

2016-12-01

A brief overview of the work in the research group of the present author on extracting knowledge from chemical reaction data is presented. Methods have been developed to calculate physicochemical effects at the reaction site. It is shown that these physicochemical effects can quite favourably be used to derive equations for the calculation of data on gas phase reactions and on reactions in solution such as aqueous acidity of alcohols or carboxylic acids or the hydrolysis of amides. Furthermore, it is shown that these physicochemical effects are quite effective for assigning reactions into reaction classes that correspond to chemical knowledge. Biochemical reactions constitute a particularly interesting and challenging task for increasing our understanding of living species. The BioPath.Database is a rich source of information on biochemical reactions and has been used for a variety of applications of chemical, biological, or medicinal interests. Thus, it was shown that biochemical reactions can be assigned by the physicochemical effects into classes that correspond to the classification of enzymes by the EC numbers. Furthermore, 3D models of reaction intermediates can be used for searching for novel enzyme inhibitors. It was shown in a combined application of chemoinformatics and bioinformatics that essential pathways of diseases can be uncovered. Furthermore, a study showed that bacterial flavor-forming pathways can be discovered. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Interaction between diffusion and chemical stresses

International Nuclear Information System (INIS)

Yang Fuqian

2005-01-01

The present work studies the interaction between chemical stresses and diffusion. A new relation between hydrostatic stress and concentration of solute atoms is established. For a solid free of action of body force, the Laplacian of the hydrostatic stress is proportional to the Laplacian of the concentration of solute atoms, that is, deviation of the hydrostatic stress from its local average is proportional to deviation of the local concentration of solute atoms. A general relationship among surface concentration of solute atoms, normal stress and surface deformation of a solid is then derived, in which the normal stress is dependent on the mean curvature of the undeformed surface and tangential components of the surface displacement. A closed-form solution of the steady state concentration of solute atoms in a thin plate is obtained. It turns out that linear distribution of solute atoms in the plate is non-existent due to the interaction between chemical stresses and diffusion

Mass transfer with complex reversible chemical reactions. II: Parallel reversible chemical reactions

NARCIS (Netherlands)

Versteeg, Geert; van Beckum, F.P.H.; Kuipers, J.A.M.; van Swaaij, Willibrordus Petrus Maria

1990-01-01

An absorption model has been developed which can be used to calculate rapidly absorption rates for the phenomenon mass transfer accompanied by multiple complex parallel reversible chemical reactions. This model can be applied for the calculation of the mass transfer rates, enhancement factors and

Mass transfer with complex reversible chemical reactions. II: parallel reversible chemical reactions

NARCIS (Netherlands)

Versteeg, G.F.; Kuipers, J.A.M.; Beckum, van F.P.H.; van Swaaij, W.P.M.

1990-01-01

An absorption model has been developed which can be used to calculate rapidly absorption rates for the phenomenon mass transfer accompanied by multiple complex parallel reversible chemical reactions. This model can be applied for the calculation of the mass transfer rates, enhancement factors and

HEAT AND MASS TRANSFER EFFECTS ON FLOW PAST PARABOLIC STARTING MOTION OF ISOTHERMAL VERTICAL PLATE IN THE PRESENCE OF FIRST ORDER CHEMICAL REACTION

Directory of Open Access Journals (Sweden)

R. Muthucumaraswamy

2013-06-01

Full Text Available An exact solution of unsteady flow past a parabolic starting motion of the infinite isothermal vertical plate with uniform mass diffusion, in the presence of a homogeneous chemical reaction of the first order, has been studied. The plate temperature and the concentration level near the plate are raised uniformly. The dimensionless governing equations are solved using the Laplace transform technique. The effect of velocity profiles are studied for different physical parameters, such as chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number, and time. It is observed that velocity increases with increasing values of thermal Grashof number or mass Grashof number. The trend is reversed with respect to the chemical reaction parameter.

Modelling Students' Visualisation of Chemical Reaction

Science.gov (United States)

Cheng, Maurice M. W.; Gilbert, John K.

2017-01-01

This paper proposes a model-based notion of "submicro representations of chemical reactions". Based on three structural models of matter (the simple particle model, the atomic model and the free electron model of metals), we suggest there are two major models of reaction in school chemistry curricula: (a) reactions that are simple…

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.

Non-equilibrium reaction rates in chemical kinetic equations

Science.gov (United States)

Gorbachev, Yuriy

2018-05-01

Within the recently proposed asymptotic method for solving the Boltzmann equation for chemically reacting gas mixture, the chemical kinetic equations has been derived. Corresponding one-temperature non-equilibrium reaction rates are expressed in terms of specific heat capacities of the species participate in the chemical reactions, bracket integrals connected with the internal energy transfer in inelastic non-reactive collisions and energy transfer coefficients. Reactions of dissociation/recombination of homonuclear and heteronuclear diatomic molecules are considered. It is shown that all reaction rates are the complex functions of the species densities, similarly to the unimolecular reaction rates. For determining the rate coefficients it is recommended to tabulate corresponding bracket integrals, additionally to the equilibrium rate constants. Correlation of the obtained results with the irreversible thermodynamics is established.

Kinetics of chemical reactions initiated by hot atoms

International Nuclear Information System (INIS)

Firsova, L.P.

1977-01-01

Modern ideas about kinetics of chemical reactions of hot atoms are generalized. The main points of the phenomenological theories (''kinetic theory'' of Wolfgang-Estrup hot reactions and the theory of ''reactions integral probability'' of Porter) are given. Physico-chemical models of elastic and non-elastic collisions are considered which are used in solving Boltzmann integro-differential equations and stochastic equations in the Porter theory. The principal formulas are given describing probabilities or yields of chemical reactions, initiated with hot atoms, depending on the distribution functions of hot particles with respect to energy. Briefly described are the techniques and the results of applying the phenomenological theories for interpretation of the experimental data obtained during nuclear reactions with hot atoms, photochemical investigations, etc. 96 references are given

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.

Numerical investigation of biogas diffusion flames characteristics under several operation conditions in counter-flow configuration with an emphasis on thermal and chemical effects of CO2 in the fuel mixture

Science.gov (United States)

Mameri, A.; Tabet, F.; Hadef, A.

2017-08-01

This study addresses the influence of several operating conditions (composition and ambient pressure) on biogas diffusion flame structure and NO emissions with particular attention on thermal and chemical effect of CO2. The biogas flame is modeled by a counter flow diffusion flame and analyzed in mixture fraction space using flamelet approach. The GRI Mech-3.0 mechanism that involves 53 species and 325 reactions is adopted for the oxidation chemistry. It has been observed that flame properties are very sensitive to biogas composition and pressure. CO2 addition decreases flame temperature by both thermal and chemical effects. Added CO2 may participate in chemical reaction due to thermal dissociation (chemical effect). Excessively supplied CO2 plays the role of pure diluent (thermal effect). The ambient pressure rise increases temperature and reduces flame thickness, radiation losses and dissociation amount. At high pressure, recombination reactions coupled with chain carrier radicals reduction, diminishes NO mass fraction.

Mesoscale simulations of shockwave energy dissipation via chemical reactions.

Science.gov (United States)

Antillon, Edwin; Strachan, Alejandro

2015-02-28

We use a particle-based mesoscale model that incorporates chemical reactions at a coarse-grained level to study the response of materials that undergo volume-reducing chemical reactions under shockwave-loading conditions. We find that such chemical reactions can attenuate the shockwave and characterize how the parameters of the chemical model affect this behavior. The simulations show that the magnitude of the volume collapse and velocity at which the chemistry propagates are critical to weaken the shock, whereas the energetics in the reactions play only a minor role. Shock loading results in transient states where the material is away from local equilibrium and, interestingly, chemical reactions can nucleate under such non-equilibrium states. Thus, the timescales for equilibration between the various degrees of freedom in the material affect the shock-induced chemistry and its ability to attenuate the propagating shock.

Contributions of chemical and diffusive exchange to T1ρ dispersion.

Science.gov (United States)

Cobb, Jared Guthrie; Xie, Jingping; Gore, John C

2013-05-01

Variations in local magnetic susceptibility may induce magnetic field gradients that affect the signals acquired for MR imaging. Under appropriate diffusion conditions, such fields produce effects similar to slow chemical exchange. These effects may also be found in combination with other chemical exchange processes at multiple time scales. We investigate these effects with simulations and measurements to determine their contributions to rotating frame (R1ρ ) relaxation in model systems. Simulations of diffusive and chemical exchange effects on R1ρ dispersion were performed using the Bloch equations. Additionally, R1ρ dispersion was measured in suspensions of Sephadex and latex beads with varying spin locking fields at 9.4 T. A novel analysis method was used to iteratively fit for apparent chemical and diffusive exchange rates with a model by Chopra et al. Single- and double-inflection points in R1ρ dispersion profiles were observed, respectively, in simulations of slow diffusive exchange alone and when combined with rapid chemical exchange. These simulations were consistent with measurements of R1ρ in latex bead suspensions and small-diameter Sephadex beads that showed single- and double-inflection points, respectively. These observations, along with measurements following changes in temperature and pH, are consistent with the combined effects of slow diffusion and rapid -OH exchange processes. Copyright © 2012 Wiley Periodicals, Inc.

Kinetic modelling of hydro-treatment reactions by study of different chemical groups; Modelisation cinetique des reactions d`hydrotraitement par regroupement en familles chimiques

Energy Technology Data Exchange (ETDEWEB)

Bonnardot, J

1998-11-19

Hydro-treatment of petroleum shortcuts permits elimination of unwanted components in order to increase combustion in engine and to decrease atmospheric pollution. Hydro-desulfurization (HDS), Hydro-denitrogenation (HDN) and Hydrogenation of aromatics (HDA) of a LCO (Light Cycle Oil)-Type gas oil have been studied using a new pilot at a fixed temperature with a NiMo/Al{sub 2}O{sub 3} catalyst. A hydrodynamic study showed that reactions occurring in the up-flow fixed bed reactor that has been used during the experiments, were governed exclusively by chemical reaction rates and not by diffusion. Through detailed chemical analysis, height chemical groups have been considered: three aromatics groups, one sulfided group, one nitrogenized and NH{sub 3}, H{sub 2}S, H{sub 2}. Two Langmuir-Hinshelwood-type kinetic models with either one or two types of sites have been established. The model with two types of site - one site of hydrogenation and one site of hydrogenolysis - showed a better fit in the modeling of the experimental results. This model enables to forecast the influence of partial pressure of H{sub 2}S and partial pressure of H{sub 2} on hydro-treatment reactions of a LCO-type gas oil. (author) 119 refs.

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

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.)

Chemical reactions in solvents and melts

CERN Document Server

Charlot, G

1969-01-01

Chemical Reactions in Solvents and Melts discusses the use of organic and inorganic compounds as well as of melts as solvents. This book examines the applications in organic and inorganic chemistry as well as in electrochemistry. Organized into two parts encompassing 15 chapters, this book begins with an overview of the general properties and the different types of reactions, including acid-base reactions, complex formation reactions, and oxidation-reduction reactions. This text then describes the properties of inert and active solvents. Other chapters consider the proton transfer reactions in

Kinetic studies of elementary chemical reactions

Energy Technology Data Exchange (ETDEWEB)

Durant, J.L. Jr. [Sandia National Laboratories, Livermore, CA (United States)

1993-12-01

This program concerning kinetic studies of elementary chemical reactions is presently focussed on understanding reactions of NH{sub x} species. To reach this goal, the author is pursuing experimental studies of reaction rate coefficients and product branching fractions as well as using electronic structure calculations to calculate transition state properties and reaction rate calculations to relate these properties to predicted kinetic behavior. The synergy existing between the experimental and theoretical studies allow one to gain a deeper insight into more complex elementary reactions.

Neutral theory of chemical reaction networks

International Nuclear Information System (INIS)

Lee, Sang Hoon; Holme, Petter; Minnhagen, Petter; Bernhardsson, Sebastian; Kim, Beom Jun

2012-01-01

To what extent do the characteristic features of a chemical reaction network reflect its purpose and function? In general, one argues that correlations between specific features and specific functions are key to understanding a complex structure. However, specific features may sometimes be neutral and uncorrelated with any system-specific purpose, function or causal chain. Such neutral features are caused by chance and randomness. Here we compare two classes of chemical networks: one that has been subjected to biological evolution (the chemical reaction network of metabolism in living cells) and one that has not (the atmospheric planetary chemical reaction networks). Their degree distributions are shown to share the very same neutral system-independent features. The shape of the broad distributions is to a large extent controlled by a single parameter, the network size. From this perspective, there is little difference between atmospheric and metabolic networks; they are just different sizes of the same random assembling network. In other words, the shape of the degree distribution is a neutral characteristic feature and has no functional or evolutionary implications in itself; it is not a matter of life and death. (paper)

Automatic NMR-based identification of chemical reaction types in mixtures of co-occurring reactions.

Science.gov (United States)

Latino, Diogo A R S; Aires-de-Sousa, João

2014-01-01

The combination of chemoinformatics approaches with NMR techniques and the increasing availability of data allow the resolution of problems far beyond the original application of NMR in structure elucidation/verification. The diversity of applications can range from process monitoring, metabolic profiling, authentication of products, to quality control. An application related to the automatic analysis of complex mixtures concerns mixtures of chemical reactions. We encoded mixtures of chemical reactions with the difference between the (1)H NMR spectra of the products and the reactants. All the signals arising from all the reactants of the co-occurring reactions were taken together (a simulated spectrum of the mixture of reactants) and the same was done for products. The difference spectrum is taken as the representation of the mixture of chemical reactions. A data set of 181 chemical reactions was used, each reaction manually assigned to one of 6 types. From this dataset, we simulated mixtures where two reactions of different types would occur simultaneously. Automatic learning methods were trained to classify the reactions occurring in a mixture from the (1)H NMR-based descriptor of the mixture. Unsupervised learning methods (self-organizing maps) produced a reasonable clustering of the mixtures by reaction type, and allowed the correct classification of 80% and 63% of the mixtures in two independent test sets of different similarity to the training set. With random forests (RF), the percentage of correct classifications was increased to 99% and 80% for the same test sets. The RF probability associated to the predictions yielded a robust indication of their reliability. This study demonstrates the possibility of applying machine learning methods to automatically identify types of co-occurring chemical reactions from NMR data. Using no explicit structural information about the reactions participants, reaction elucidation is performed without structure elucidation of

Automatic NMR-based identification of chemical reaction types in mixtures of co-occurring reactions.

Directory of Open Access Journals (Sweden)

Diogo A R S Latino

Full Text Available The combination of chemoinformatics approaches with NMR techniques and the increasing availability of data allow the resolution of problems far beyond the original application of NMR in structure elucidation/verification. The diversity of applications can range from process monitoring, metabolic profiling, authentication of products, to quality control. An application related to the automatic analysis of complex mixtures concerns mixtures of chemical reactions. We encoded mixtures of chemical reactions with the difference between the (1H NMR spectra of the products and the reactants. All the signals arising from all the reactants of the co-occurring reactions were taken together (a simulated spectrum of the mixture of reactants and the same was done for products. The difference spectrum is taken as the representation of the mixture of chemical reactions. A data set of 181 chemical reactions was used, each reaction manually assigned to one of 6 types. From this dataset, we simulated mixtures where two reactions of different types would occur simultaneously. Automatic learning methods were trained to classify the reactions occurring in a mixture from the (1H NMR-based descriptor of the mixture. Unsupervised learning methods (self-organizing maps produced a reasonable clustering of the mixtures by reaction type, and allowed the correct classification of 80% and 63% of the mixtures in two independent test sets of different similarity to the training set. With random forests (RF, the percentage of correct classifications was increased to 99% and 80% for the same test sets. The RF probability associated to the predictions yielded a robust indication of their reliability. This study demonstrates the possibility of applying machine learning methods to automatically identify types of co-occurring chemical reactions from NMR data. Using no explicit structural information about the reactions participants, reaction elucidation is performed without structure

Chemical kinetics: on the heterogeneous catalysis processes leading to an exchange between two phases. Example: isotopic exchange reactions; Cinetique chimique: sur les processus de catalyse 'heterogene' conduisant a un echange entre deux phases. Exemple: reactions d'echange isotopique

Energy Technology Data Exchange (ETDEWEB)

Dirian, G; Grandcollot, P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1961-07-01

For an exchange reaction between a gaseous and a liquid phase proceeding by 'heterogeneous' catalysis in the liquid phase, diffusion in the liquid and the chemical reaction are two simultaneous and indivisible processes. We have nevertheless been able to establish criteria making it possible to distinguish between a really homogeneous kinetic process and a pseudo-homogeneous one. (author) [French] Pour une reaction d'echange entre une phase gazeuse et une phase liquide procedant par catalyse 'heterogene' en phase liquide, la diffusion dans le liquide et la reaction chimique sont deux etapes simultanees et indissociables. Nous avons pu neanmoins etablir des criteres permettant de distinguer entre une cinetique homogene vraie et une cinetique pseudo-homogene. (auteur)

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.)

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 ...

Reaction Hamiltonian and state-to-state description of chemical reactions

International Nuclear Information System (INIS)

Ruf, B.A.; Kresin, V.Z.; Lester, W.A. Jr.

1985-08-01

A chemical reaction is treated as a quantum transition from reactants to products. A specific reaction Hamiltonian (in second quantization formalism) is introduced. The approach leads to Franck-Condon-like factor, and adiabatic method in the framework of the nuclear motion problems. The influence of reagent vibrational state on the product energy distribution has been studied following the reaction Hamiltonian method. Two different cases (fixed available energy and fixed translational energy) are distinguished. Results for several biomolecular reactions are presented. 40 refs., 5 figs

Determination of trapping parameters and the chemical diffusion coefficient from hydrogen permeation experiments

International Nuclear Information System (INIS)

Svoboda, J.; Mori, G.; Prethaler, A.; Fischer, F.D.

2014-01-01

Highlights: • A modeling study for diffusion of hydrogen with traps is presented. • Introduction of a new chemical diffusion coefficient. • Density of traps and average depth of traps can be determined. • Lattice diffusion and sub-surface concentration of atomic hydrogen can be determined. - Abstract: An improved diffusion theory accounting for trapping effects is applied to evaluation of hydrogen permeation experiments performed for pure iron and pearlitic and martensitic steels. The trapping parameters as molar volume and depth of traps are determined by fitting experiments by simulations based on the theory. The concentration-dependent chemical diffusion coefficient of hydrogen is extracted indicating that the trapping effect on diffusion in pure iron and pearlitic steel is negligible. However, it is significant for martensitic steel, for which the chemical diffusion coefficient cannot be considered as concentration-independent as it is established in current standards

Heterogeneously Catalysed Chemical Reactions in Carbon Dioxide Medium

DEFF Research Database (Denmark)

Musko, Nikolai E.

In this PhD-study the different areas of chemical engineering, heterogeneous catalysis, supercritical fluids, and phase equilibrium thermodynamics have been brought together for selected reactions. To exploit the beneficial properties of supercritical fluids in heterogeneous catalysis, experimental...... studies of catalytic chemical reactions in dense and supercritical carbon dioxide have been complemented by the theoretical calculations of phase equilibria using advanced thermodynamic models. In the recent years, the use of compressed carbon dioxide as innovative, non-toxic and non-flammable, cheap......, and widely available reaction medium for many practical and industrial applications has drastically increased. Particularly attractive are heterogeneously catalysed chemical reactions. The beneficial use of CO2 is attributed to its unique properties at dense and supercritical states (at temperatures...

Emergency Evacuation of Hazardous Chemical Accidents Based on Diffusion Simulation

Directory of Open Access Journals (Sweden)

Jiang-Hua Zhang

2017-01-01

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

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.

Measurement of oxygen chemical diffusion in PuO2-x and analysis of oxygen diffusion in PuO2-x and (Pu,U)O2-x

International Nuclear Information System (INIS)

Kato, Masato; Uchida, Teppei; Sunaoshi, Takeo

2013-01-01

Oxygen chemical diffusion in PuO 2-x was investigated in the temperature range of 1473-1873 K by thermogravimetry as functions of oxygen-to-metal (O/M) ratios and temperatures. The oxygen chemical diffusion coefficients, D were determined assuming that the reduction curves were dominated by a diffusion process. The O/M ratio and Pu content dependence on the chemical diffusion coefficients were evaluated. The chemical diffusion coefficient had its minimum value at around O/M=1.98 and decreased with increasing Pu content in (U,Pu)O 2-x . The self-diffusion coefficients were evaluated. A model for describing the relationship among O/M ratio, oxygen chemical diffusion, and self-diffusion was proposed based on defect chemistry. (copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

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.

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

Chemical changes in groundwater and their reaction rates

International Nuclear Information System (INIS)

Talma, A.S.

1981-01-01

The evolution of the major ion concentrations of groundwater (Na, K, Ca, Mg, HCO 3 , SO 4 , Cl and NO 3 ) can be described as the consequence of a number of competing chemical reactions. With the aid of the naturally occuring radioactive and stable isotopes some of these reactions can be separated, identified and followed in space and time. In some field studies, especialy of artesian water, the rates of reactions can be estimated. A number of processes observed in South African sandstones aquifers are discussed and the variable reaction rates demonstrated. Reactions that can be identified include carbonate solution, chemical weathering, salt leaching, cation exchange and redox processes

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

Measurement of chemical diffusion coefficients in liquid binary alloys

International Nuclear Information System (INIS)

Keita, M.; Steinemann, S.; Kuenzi, H.U.

1976-01-01

New measurements of the chemical diffusion coefficient in liquid binary alloys are presented. The wellknown geometry of the 'capillary-reservoir' is used and the concentration is obtained from a resistivity measurement. The method allows to follow continuously the diffusion process in the liquid state. A precision of at least 10% in the diffusion coefficient is obtained with a reproductibility better than 5%. The systems Hg-In, Al-Sn, Al-Si have been studied. Diffusion coefficients are obtained as a function of temperature, concentration, and geometrical factors related to the capillary (diameter, relative orientation of density gradient and gravity). (orig.) [de

Temperature dependence on sodium-water chemical reaction

International Nuclear Information System (INIS)

Tamura, Kenta; Deguchi, Yoshihiro; Suzuki, Koichi; Takata, Takashi; Yamaguchi, Akira; Kikuchi, Shin; Ohshima, Hiroyuki

2012-01-01

In a sodium-cooled fast reactor (SFR), liquid sodium is used as a heat transfer fluid because of its excellent heat transport capability. On the other hand, it has strong chemical reactivity with water vapor. One of the design basis accidents of the SFR is the water leakage into the liquid sodium flow by a breach of heat transfer tubes. This process ends up damages on the heat transport equipment in the SFR. Therefore, the study on sodium-water chemical reactions is of paramount importance for security reasons. This study aims to clarify the sodium-water reaction mechanisms using laser diagnostics. A quasi one-dimensional flame model is also applied to a sodium-water counter-flow reaction field. Temperature, H 2 , H 2 O, OH, Na and Particulate matter were measured using laser induced fluorescence and CARS in the counter-flow reaction field. The temperature of the reaction field was also modified to reduce the condensation of Na in the reaction zone. (author)

Ignition in Convective-Diffusive Systems

National Research Council Canada - National Science Library

Law, Chung

1999-01-01

... efficiency as well as the knock and emission characteristics. The ignition event is clearly controlled by the chemical reactions of fuel oxidation and the fluid mechanics of convective and diffusive transport...

A new type of power energy for accelerating chemical reactions: the nature of a microwave-driving force for accelerating chemical reactions.

Science.gov (United States)

Zhou, Jicheng; Xu, Wentao; You, Zhimin; Wang, Zhe; Luo, Yushang; Gao, Lingfei; Yin, Cheng; Peng, Renjie; Lan, Lixin

2016-04-27

The use of microwave (MW) irradiation to increase the rate of chemical reactions has attracted much attention recently in nearly all fields of chemistry due to substantial enhancements in reaction rates. However, the intrinsic nature of the effects of MW irradiation on chemical reactions remains unclear. Herein, the highly effective conversion of NO and decomposition of H2S via MW catalysis were investigated. The temperature was decreased by several hundred degrees centigrade. Moreover, the apparent activation energy (Ea') decreased substantially under MW irradiation. Importantly, for the first time, a model of the interactions between microwave electromagnetic waves and molecules is proposed to elucidate the intrinsic reason for the reduction in the Ea' under MW irradiation, and a formula for the quantitative estimation of the decrease in the Ea' was determined. MW irradiation energy was partially transformed to reduce the Ea', and MW irradiation is a new type of power energy for speeding up chemical reactions. The effect of MW irradiation on chemical reactions was determined. Our findings challenge both the classical view of MW irradiation as only a heating method and the controversial MW non-thermal effect and open a promising avenue for the development of novel MW catalytic reaction technology.

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

Stereodynamics: From elementary processes to macroscopic chemical reactions

Energy Technology Data Exchange (ETDEWEB)

Kasai, Toshio [Department of Chemistry, National Taiwan University, Taipei 106, Taiwan (China); Graduate School of Science, Department of Chemistry, Osaka University, Toyonaka, 560-0043 Osaka (Japan); Che, Dock-Chil [Graduate School of Science, Department of Chemistry, Osaka University, Toyonaka, 560-0043 Osaka (Japan); Tsai, Po-Yu [Department of Chemistry, National Taiwan University, Taipei 106, Taiwan (China); Department of Chemistry, National Chung Hsing University, Taichung 402, Taiwan (China); Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan (China); Lin, King-Chuen [Department of Chemistry, National Taiwan University, Taipei 106, Taiwan (China); Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan (China); Palazzetti, Federico [Scuola Normale Superiore, Pisa (Italy); Dipartimento di Chimica Biologia e Biotecnologie, Università di Perugia, 06123 Perugia (Italy); Aquilanti, Vincenzo [Dipartimento di Chimica Biologia e Biotecnologie, Università di Perugia, 06123 Perugia (Italy); Istituto di Struttura della Materia, Consiglio Nazionale delle Ricerche, Roma (Italy); Instituto de Fisica, Universidade Federal da Bahia, Salvador (Brazil)

2015-12-31

This paper aims at discussing new facets on stereodynamical behaviors in chemical reactions, i.e. the effects of molecular orientation and alignment on reactive processes. Further topics on macroscopic processes involving deviations from Arrhenius behavior in the temperature dependence of chemical reactions and chirality effects in collisions are also discussed.

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

Unequal diffusivities case of homogeneous–heterogeneous reactions within viscoelastic fluid flow in the presence of induced magnetic-field and nonlinear thermal radiation

Directory of Open Access Journals (Sweden)

I.L. Animasaun

2016-06-01

Full Text Available This article presents the effects of nonlinear thermal radiation and induced magnetic field on viscoelastic fluid flow toward a stagnation point. It is assumed that there exists a kind of chemical reaction between chemical species A and B. The diffusion coefficients of the two chemical species in the viscoelastic fluid flow are unequal. Since chemical species B is a catalyst at the horizontal surface, hence homogeneous and heterogeneous schemes are of the isothermal cubic autocatalytic reaction and first order reaction respectively. The transformed governing equations are solved numerically using Runge–Kutta integration scheme along with Newton’s method. Good agreement is obtained between present and published numerical results for a limiting case. The influence of some pertinent parameters on skin friction coefficient, local heat transfer rate, together with velocity, induced magnetic field, temperature, and concentration profiles is illustrated graphically and discussed. Based on all of these assumptions, results indicate that the effects of induced magnetic and viscoelastic parameters on velocity, transverse velocity and velocity of induced magnetic field are almost the same but opposite in nature. The strength of heterogeneous reaction parameter is very helpful to reduce the concentration of bulk fluid and increase the concentration of catalyst at the surface.

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.

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.

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

Science.gov (United States)

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

2006-12-01

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

Chemical reactions in reverse micelle systems

Science.gov (United States)

Matson, Dean W.; Fulton, John L.; Smith, Richard D.; Consani, Keith A.

1993-08-24

This invention is directed to conducting chemical reactions in reverse micelle or microemulsion systems comprising a substantially discontinuous phase including a polar fluid, typically an aqueous fluid, and a microemulsion promoter, typically a surfactant, for facilitating the formation of reverse micelles in the system. The system further includes a substantially continuous phase including a non-polar or low-polarity fluid material which is a gas under standard temperature and pressure and has a critical density, and which is generally a water-insoluble fluid in a near critical or supercritical state. Thus, the microemulsion system is maintained at a pressure and temperature such that the density of the non-polar or low-polarity fluid exceeds the critical density thereof. The method of carrying out chemical reactions generally comprises forming a first reverse micelle system including an aqueous fluid including reverse micelles in a water-insoluble fluid in the supercritical state. Then, a first reactant is introduced into the first reverse micelle system, and a chemical reaction is carried out with the first reactant to form a reaction product. In general, the first reactant can be incorporated into, and the product formed in, the reverse micelles. A second reactant can also be incorporated in the first reverse micelle system which is capable of reacting with the first reactant to form a product.

Chemical memory reactions induced bursting dynamics in gene expression.

Science.gov (United States)

Tian, Tianhai

2013-01-01

Memory is a ubiquitous phenomenon in biological systems in which the present system state is not entirely determined by the current conditions but also depends on the time evolutionary path of the system. Specifically, many memorial phenomena are characterized by chemical memory reactions that may fire under particular system conditions. These conditional chemical reactions contradict to the extant stochastic approaches for modeling chemical kinetics and have increasingly posed significant challenges to mathematical modeling and computer simulation. To tackle the challenge, I proposed a novel theory consisting of the memory chemical master equations and memory stochastic simulation algorithm. A stochastic model for single-gene expression was proposed to illustrate the key function of memory reactions in inducing bursting dynamics of gene expression that has been observed in experiments recently. The importance of memory reactions has been further validated by the stochastic model of the p53-MDM2 core module. Simulations showed that memory reactions is a major mechanism for realizing both sustained oscillations of p53 protein numbers in single cells and damped oscillations over a population of cells. These successful applications of the memory modeling framework suggested that this innovative theory is an effective and powerful tool to study memory process and conditional chemical reactions in a wide range of complex biological systems.

Entropy Generation in a Chemical Reaction

Science.gov (United States)

Miranda, E. N.

2010-01-01

Entropy generation in a chemical reaction is analysed without using the general formalism of non-equilibrium thermodynamics at a level adequate for advanced undergraduates. In a first approach to the problem, the phenomenological kinetic equation of an elementary first-order reaction is used to show that entropy production is always positive. A…

An autonomous organic reaction search engine for chemical reactivity

Science.gov (United States)

Dragone, Vincenza; Sans, Victor; Henson, Alon B.; Granda, Jaroslaw M.; Cronin, Leroy

2017-06-01

The exploration of chemical space for new reactivity, reactions and molecules is limited by the need for separate work-up-separation steps searching for molecules rather than reactivity. Herein we present a system that can autonomously evaluate chemical reactivity within a network of 64 possible reaction combinations and aims for new reactivity, rather than a predefined set of targets. The robotic system combines chemical handling, in-line spectroscopy and real-time feedback and analysis with an algorithm that is able to distinguish and select the most reactive pathways, generating a reaction selection index (RSI) without need for separate work-up or purification steps. This allows the automatic navigation of a chemical network, leading to previously unreported molecules while needing only to do a fraction of the total possible reactions without any prior knowledge of the chemistry. We show the RSI correlates with reactivity and is able to search chemical space using the most reactive pathways.

A cellular automata approach to chemical reactions : 1 reaction controlled systems

NARCIS (Netherlands)

Korte, de A.C.J.; Brouwers, H.J.H.

2013-01-01

A direct link between the chemical reaction controlled (shrinking core) model and cellular automata, to study the dissolution of particles, is derived in this paper. Previous research on first and second order reactions is based on the concentration of the reactant. The present paper describes the

Simulation of square wave voltammetry of three electrode reactions coupled by two reversible chemical reactions

OpenAIRE

Lovrić, Milivoj

2017-01-01

Three fast and reversible electrode reactions that are connected by two reversible chemical reactions that are permanently in the equilibrium are analysed theoretically for square wave voltammetry. The dependence of peak potentials on the dimensionless equilibrium constants of chemical reactions is calculated. The influence of the basic thermodynamic parameters on the square wave voltammetric responses is analysed.

Versatile Dual Photoresponsive System for Precise Control of Chemical Reactions.

Science.gov (United States)

Xu, Can; Bing, Wei; Wang, Faming; Ren, Jinsong; Qu, Xiaogang

2017-08-22

A versatile method for photoregulation of chemical reactions was developed through a combination of near-infrared (NIR) and ultraviolet (UV) light sensitive materials. This regulatory effect was achieved through photoresponsive modulation of reaction temperature and pH values, two prominent factors influencing reaction kinetics. Photothermal nanomaterial graphene oxide (GO) and photobase reagent malachite green carbinol base (MGCB) were selected for temperature and pH regulation, respectively. Using nanocatalyst- and enzyme-mediated chemical reactions as model systems, we demonstrated the feasibility and high efficiency of this method. In addition, a photoresponsive, multifunctional "Band-aid"-like hydrogel platform was presented for programmable wound healing. Overall, this simple, efficient, and reversible system was found to be effective for controlling a wide variety of chemical reactions. Our work may provide a method for remote and sustainable control over chemical reactions for industrial and biomedical applications.

Modelling Chemical Reasoning to Predict and Invent Reactions.

Science.gov (United States)

Segler, Marwin H S; Waller, Mark P

2017-05-02

The ability to reason beyond established knowledge allows organic chemists to solve synthetic problems and invent novel transformations. Herein, we propose a model that mimics chemical reasoning, and formalises reaction prediction as finding missing links in a knowledge graph. We have constructed a knowledge graph containing 14.4 million molecules and 8.2 million binary reactions, which represents the bulk of all chemical reactions ever published in the scientific literature. Our model outperforms a rule-based expert system in the reaction prediction task for 180 000 randomly selected binary reactions. The data-driven model generalises even beyond known reaction types, and is thus capable of effectively (re-)discovering novel transformations (even including transition metal-catalysed reactions). Our model enables computers to infer hypotheses about reactivity and reactions by only considering the intrinsic local structure of the graph and because each single reaction prediction is typically achieved in a sub-second time frame, the model can be used as a high-throughput generator of reaction hypotheses for reaction discovery. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Chemical diffusion on solid surfaces. Final report

International Nuclear Information System (INIS)

Hudson, J.B.

1980-12-01

The techniques of surface science have been applied to the problem of the measurement of the surface diffusion rate of an adsorbed species over the surface of a chemically dissimilar material. Studies were carried out for hydrogen and nitrogen adatoms on a Ni(100) surface and for silver adatoms on a sapphire surface. Positive results were obtained only for the case of nitrogen on Ni(100). In this system the diffusivity is characterized by the expression D = D 0 exp (/sup -ΔH//RT), with D 0 = 0.25 cm 2 /sec and ΔH = 28kcal/mol

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

Science.gov (United States)

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

2011-01-01

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

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

Directory of Open Access Journals (Sweden)

Louis D Weise

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

Chemical dynamics in the gas phase: Time-dependent quantum mechanics of chemical reactions

Energy Technology Data Exchange (ETDEWEB)

Gray, S.K. [Argonne National Laboratory, IL (United States)

1993-12-01

A major goal of this research is to obtain an understanding of the molecular reaction dynamics of three and four atom chemical reactions using numerically accurate quantum dynamics. This work involves: (i) the development and/or improvement of accurate quantum mechanical methods for the calculation and analysis of the properties of chemical reactions (e.g., rate constants and product distributions), and (ii) the determination of accurate dynamical results for selected chemical systems, which allow one to compare directly with experiment, determine the reliability of the underlying potential energy surfaces, and test the validity of approximate theories. This research emphasizes the use of recently developed time-dependent quantum mechanical methods, i.e. wave packet methods.

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.

A network dynamics approach to chemical reaction networks

Science.gov (United States)

van der Schaft, A. J.; Rao, S.; Jayawardhana, B.

2016-04-01

A treatment of a chemical reaction network theory is given from the perspective of nonlinear network dynamics, in particular of consensus dynamics. By starting from the complex-balanced assumption, the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a very simple derivation of a number of key results in the chemical reaction network theory, and which directly relates to the thermodynamics and port-Hamiltonian formulation of the system. Central in this formulation is the definition of a balanced Laplacian matrix on the graph of chemical complexes together with a resulting fundamental inequality. This immediately leads to the characterisation of the set of equilibria and their stability. Furthermore, the assumption of complex balancedness is revisited from the point of view of Kirchhoff's matrix tree theorem. Both the form of the dynamics and the deduced behaviour are very similar to consensus dynamics, and provide additional perspectives to the latter. Finally, using the classical idea of extending the graph of chemical complexes by a 'zero' complex, a complete steady-state stability analysis of mass action kinetics reaction networks with constant inflows and mass action kinetics outflows is given, and a unified framework is provided for structure-preserving model reduction of this important class of open reaction networks.

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...

Non-equilibrium effects in high temperature chemical reactions

Science.gov (United States)

Johnson, Richard E.

1987-01-01

Reaction rate data were collected for chemical reactions occurring at high temperatures during reentry of space vehicles. The principle of detailed balancing is used in modeling kinetics of chemical reactions at high temperatures. Although this principle does not hold for certain transient or incubation times in the initial phase of the reaction, it does seem to be valid for the rates of internal energy transitions that occur within molecules and atoms. That is, for every rate of transition within the internal energy states of atoms or molecules, there is an inverse rate that is related through an equilibrium expression involving the energy difference of the transition.

Diffusion-controlled reactions modeling in Geant4-DNA

Czech Academy of Sciences Publication Activity Database

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

2014-01-01

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

Mathematical aspects of reacting and diffusing systems

CERN Document Server

Fife, Paul C

1979-01-01

Modeling and analyzing the dynamics of chemical mixtures by means of differ- tial equations is one of the prime concerns of chemical engineering theorists. These equations often take the form of systems of nonlinear parabolic partial d- ferential equations, or reaction-diffusion equations, when there is diffusion of chemical substances involved. A good overview of this endeavor can be had by re- ing the two volumes by R. Aris (1975), who himself was one of the main contributors to the theory. Enthusiasm for the models developed has been shared by parts of the mathematical community, and these models have, in fact, provided motivation for some beautiful mathematical results. There are analogies between chemical reactors and certain biological systems. One such analogy is rather obvious: a single living organism is a dynamic structure built of molecules and ions, many of which react and diffuse. Other analogies are less obvious; for example, the electric potential of a membrane can diffuse like a chemical, and ...

The Electronic Flux in Chemical Reactions. Insights on the Mechanism of the Maillard Reaction

Science.gov (United States)

Flores, Patricio; Gutiérrez-Oliva, Soledad; Herrera, Bárbara; Silva, Eduardo; Toro-Labbé, Alejandro

2007-11-01

The electronic transfer that occurs during a chemical process is analysed in term of a new concept, the electronic flux, that allows characterizing the regions along the reaction coordinate where electron transfer is actually taking place. The electron flux is quantified through the variation of the electronic chemical potential with respect to the reaction coordinate and is used, together with the reaction force, to shed light on reaction mechanism of the Schiff base formation in the Maillard reaction. By partitioning the reaction coordinate in regions in which different process might be taking place, electronic reordering associated to polarization and transfer has been identified and found to be localized at specific transition state regions where most bond forming and breaking occur.

Modular verification of chemical reaction network encodings via serializability analysis

Science.gov (United States)

Lakin, Matthew R.; Stefanovic, Darko; Phillips, Andrew

2015-01-01

Chemical reaction networks are a powerful means of specifying the intended behaviour of synthetic biochemical systems. A high-level formal specification, expressed as a chemical reaction network, may be compiled into a lower-level encoding, which can be directly implemented in wet chemistry and may itself be expressed as a chemical reaction network. Here we present conditions under which a lower-level encoding correctly emulates the sequential dynamics of a high-level chemical reaction network. We require that encodings are transactional, such that their execution is divided by a “commit reaction” that irreversibly separates the reactant-consuming phase of the encoding from the product-generating phase. We also impose restrictions on the sharing of species between reaction encodings, based on a notion of “extra tolerance”, which defines species that may be shared between encodings without enabling unwanted reactions. Our notion of correctness is serializability of interleaved reaction encodings, and if all reaction encodings satisfy our correctness properties then we can infer that the global dynamics of the system are correct. This allows us to infer correctness of any system constructed using verified encodings. As an example, we show how this approach may be used to verify two- and four-domain DNA strand displacement encodings of chemical reaction networks, and we generalize our result to the limit where the populations of helper species are unlimited. PMID:27325906

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

KAUST Repository

Desvillettes, Laurent; Fellner, Klemens

2008-01-01

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

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.

Fast chemical reaction in two-dimensional Navier-Stokes flow: initial regime.

Science.gov (United States)

Ait-Chaalal, Farid; Bourqui, Michel S; Bartello, Peter

2012-04-01

This paper studies an infinitely fast bimolecular chemical reaction in a two-dimensional biperiodic Navier-Stokes flow. The reactants in stoichiometric quantities are initially segregated by infinite gradients. The focus is placed on the initial stage of the reaction characterized by a well-defined one-dimensional material contact line between the reactants. Particular attention is given to the effect of the diffusion κ of the reactants. This study is an idealized framework for isentropic mixing in the lower stratosphere and is motivated by the need to better understand the effect of resolution on stratospheric chemistry in climate-chemistry models. Adopting a Lagrangian straining theory approach, we relate theoretically the ensemble mean of the length of the contact line, of the gradients along it, and of the modulus of the time derivative of the space-average reactant concentrations (here called the chemical speed) to the joint probability density function of the finite-time Lyapunov exponent λ with two times τ and τ[over ̃]. The time 1/λ measures the stretching time scale of a Lagrangian parcel on a chaotic orbit up to a finite time t, while τ measures it in the recent past before t, and τ[over ̃] in the early part of the trajectory. We show that the chemical speed scales like κ(1/2) and that its time evolution is determined by rare large events in the finite-time Lyapunov exponent distribution. The case of smooth initial gradients is also discussed. The theoretical results are tested with an ensemble of direct numerical simulations (DNSs) using a pseudospectral model.

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

NARCIS (Netherlands)

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

2011-01-01

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

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.

Stochastic thermodynamics and entropy production of chemical reaction systems

Science.gov (United States)

Tomé, Tânia; de Oliveira, Mário J.

2018-06-01

We investigate the nonequilibrium stationary states of systems consisting of chemical reactions among molecules of several chemical species. To this end, we introduce and develop a stochastic formulation of nonequilibrium thermodynamics of chemical reaction systems based on a master equation defined on the space of microscopic chemical states and on appropriate definitions of entropy and entropy production. The system is in contact with a heat reservoir and is placed out of equilibrium by the contact with particle reservoirs. In our approach, the fluxes of various types, such as the heat and particle fluxes, play a fundamental role in characterizing the nonequilibrium chemical state. We show that the rate of entropy production in the stationary nonequilibrium state is a bilinear form in the affinities and the fluxes of reaction, which are expressed in terms of rate constants and transition rates, respectively. We also show how the description in terms of microscopic states can be reduced to a description in terms of the numbers of particles of each species, from which follows the chemical master equation. As an example, we calculate the rate of entropy production of the first and second Schlögl reaction models.

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.

Scattering theory and chemical reactions

International Nuclear Information System (INIS)

Kuppermann, A.

1988-01-01

In this course, scattering theory and chemical reactions are presented including scattering of one particle by a potential, n-particle systems, colinear triatomic molecules and the study of reactive scattering for 3-dimensional triatomic systems. (A.C.A.S.) [pt

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.

Oxygen Chemical Diffusion Coefficients of (Pu,Am)O2 Fuels

International Nuclear Information System (INIS)

Watanabe, M.; Kato, M.; Matsumoto, T.

2015-01-01

Minor actinide (MA)-bearing MOX fuels have been developed as candidate fuels which are used in fast neutron spectrum cores such as sodium-cooled fast reactor (SFR) cores and experimental accelerator driven system (ADS) cores. Americium (Am) which is one of the MA elements significantly affects basic properties. It is known that Am content causes oxygen potential to increase and that influences irradiation behaviour such as fuel-cladding chemical interaction (FCCI) and chemical state of fission products. However, the effects of Am content on changes of basic properties are not clear. In this work, the oxygen chemical diffusion coefficients were calculated from measured data and the relationship between oxygen diffusion and oxygen potential of (Pu,Am)O 2-x was discussed. (authors)

On the Complexity of Reconstructing Chemical Reaction Networks

DEFF Research Database (Denmark)

Fagerberg, Rolf; Flamm, Christoph; Merkle, Daniel

2013-01-01

The analysis of the structure of chemical reaction networks is crucial for a better understanding of chemical processes. Such networks are well described as hypergraphs. However, due to the available methods, analyses regarding network properties are typically made on standard graphs derived from...... the full hypergraph description, e.g. on the so-called species and reaction graphs. However, a reconstruction of the underlying hypergraph from these graphs is not necessarily unique. In this paper, we address the problem of reconstructing a hypergraph from its species and reaction graph and show NP...

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

Science.gov (United States)

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

2018-04-01

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

Reaction Mechanism Generator: Automatic construction of chemical kinetic mechanisms

Science.gov (United States)

Gao, Connie W.; Allen, Joshua W.; Green, William H.; West, Richard H.

2016-06-01

Reaction Mechanism Generator (RMG) constructs kinetic models composed of elementary chemical reaction steps using a general understanding of how molecules react. Species thermochemistry is estimated through Benson group additivity and reaction rate coefficients are estimated using a database of known rate rules and reaction templates. At its core, RMG relies on two fundamental data structures: graphs and trees. Graphs are used to represent chemical structures, and trees are used to represent thermodynamic and kinetic data. Models are generated using a rate-based algorithm which excludes species from the model based on reaction fluxes. RMG can generate reaction mechanisms for species involving carbon, hydrogen, oxygen, sulfur, and nitrogen. It also has capabilities for estimating transport and solvation properties, and it automatically computes pressure-dependent rate coefficients and identifies chemically-activated reaction paths. RMG is an object-oriented program written in Python, which provides a stable, robust programming architecture for developing an extensible and modular code base with a large suite of unit tests. Computationally intensive functions are cythonized for speed improvements.

Free Convection Heat and Mass Transfer MHD Flow in a Vertical Channel in the Presence of Chemical Reaction

Directory of Open Access Journals (Sweden)

R. N. Barik

2013-09-01

Full Text Available An analysis is made to study the effects of diffusion-thermo and chemical reaction on fully developed laminar MHD flow of electrically conducting viscous incompressible fluid in a vertical channel formed by two vertical parallel plates was taken into consideration with uniform temperature and concentration. The analytical solution by Laplace transform technique of partial differential equations is used to obtain the expressions for the velocity, temperature and concentration. It is interesting to note that during the course of computation, the transient solution at large time coincides with steady state solution derived separately and the diffusion-thermo effect creates an anomalous situation in temperature and velocity profiles for small Prandtl numbers. The study is restricted to only destructive reaction and non-conducting case cannot be derived as a particular case still it is quite interesting and more realistic than the earlier one.

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).

The Theory of Thermodynamics for Chemical Reactions in Dispersed Heterogeneous Systems

Science.gov (United States)

Yongqiang; Baojiao; Jianfeng

1997-07-01

In this paper, the expressions of Gibbs energy change, enthalpy change, entropy change, and equilibrium constant for chemical reactions in dispersed heterogeneous systems are derived using classical thermodynamics theory. The thermodynamical relations for the same reaction system between the dispersed and the block state are also derived. The effects of degree of dispersion on thermodynamical properties, reaction directions, and chemical equilibria are discussed. The results show that the present equation of thermodynamics for chemical reactions is only a special case of the above-mentioned formulas and that the effect of the dispersity of a heterogeneous system on the chemical reaction obeys the Le Chatelier principle of movement of equilibria.

Laser-induced chemical vapor deposition reactions

International Nuclear Information System (INIS)

Teslenko, V.V.

1990-01-01

The results of investigation of chemical reactions of deposition of different substances from the gas phase when using the energy of pulse quasicontinuous and continuous radiation of lasers in the wave length interval from 0.193 to 10.6 μm are generalized. Main attetion is paid to deposition of inorganic substances including nonmetals (C, Si, Ge and others), metals (Cu, Au, Zn, Cd, Al, Cr, Mo, W, Ni) and some simple compounds. Experimental data on the effect of laser radiation parameters and reagent nature (hydrides, halogenides, carbonyls, alkyl organometallic compounds and others) on the deposition rate and deposit composition are described in detail. Specific features of laser-chemical reactions of deposition and prospects of their application are considered

Chemical reactions directed Peptide self-assembly.

Science.gov (United States)

Rasale, Dnyaneshwar B; Das, Apurba K

2015-05-13

Fabrication of self-assembled nanostructures is one of the important aspects in nanoscience and nanotechnology. The study of self-assembled soft materials remains an area of interest due to their potential applications in biomedicine. The versatile properties of soft materials can be tuned using a bottom up approach of small molecules. Peptide based self-assembly has significant impact in biology because of its unique features such as biocompatibility, straight peptide chain and the presence of different side chain functionality. These unique features explore peptides in various self-assembly process. In this review, we briefly introduce chemical reaction-mediated peptide self-assembly. Herein, we have emphasised enzymes, native chemical ligation and photochemical reactions in the exploration of peptide self-assembly.

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.

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.

Supersonic molecular beam experiments on surface chemical reactions.

Science.gov (United States)

Okada, Michio

2014-10-01

The interaction of a molecule and a surface is important in various fields, and in particular in complex systems like biomaterials and their related chemistry. However, the detailed understanding of the elementary steps in the surface chemistry, for example, stereodynamics, is still insufficient even for simple model systems. In this Personal Account, I review our recent studies of chemical reactions on single-crystalline Cu and Si surfaces induced by hyperthermal oxygen molecular beams and by oriented molecular beams, respectively. Studies of oxide formation on Cu induced by hyperthermal molecular beams demonstrate a significant role of the translational energy of the incident molecules. The use of hyperthermal molecular beams enables us to open up new chemical reaction paths specific for the hyperthermal energy region, and to develop new methods for the fabrication of thin films. On the other hand, oriented molecular beams also demonstrate the possibility of understanding surface chemical reactions in detail by varying the orientation of the incident molecules. The steric effects found on Si surfaces hint at new ways of material fabrication on Si surfaces. Controlling the initial conditions of incoming molecules is a powerful tool for finely monitoring the elementary step of the surface chemical reactions and creating new materials on surfaces. Copyright © 2014 The Chemical Society of Japan and Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Surface chemical reactions induced by molecules electronically-excited in the gas

DEFF Research Database (Denmark)

Petrunin, Victor V.

2011-01-01

and alignment are taking place, guiding all the molecules towards the intersections with the ground state PES, where transitions to the ground state PES will occur with minimum energy dissipation. The accumulated kinetic energy may be used to overcome the chemical reaction barrier. While recombination chemical...... be readily produced. Products of chemical adsorption and/or chemical reactions induced within adsorbates are aggregated on the surface and observed by light scattering. We will demonstrate how pressure and spectral dependencies of the chemical outcomes, polarization of the light and interference of two laser...... beams inducing the reaction can be used to distinguish the new process we try to investigate from chemical reactions induced by photoexcitation within adsorbed molecules and/or gas phase photolysis....

Calculation of the energetics of chemical reactions

Energy Technology Data Exchange (ETDEWEB)

Dunning, T.H. Jr.; Harding, L.B.; Shepard, R.L.; Harrison, R.J.

1988-01-01

To calculate the energetics of chemical reactions we must solve the electronic Schroedinger equation for the molecular conformations of importance for the reactive encounter. Substantial changes occur in the electronic structure of a molecular system as the reaction progresses from reactants through the transition state to products. To describe these changes, our approach includes the following three elements: the use of multiconfiguration self-consistent field wave functions to provide a consistent zero-order description of the electronic structure of the reactants, transition state, and products; the use of configuration interaction techniques to describe electron correlation effects needed to provide quantitative predictions of the reaction energetics; and the use of large, optimized basis sets to provide the flexibility needed to describe the variations in the electronic distributions. With this approach we are able to study reactions involving as many as 5--6 atoms with errors of just a few kcal/mol in the predicted reaction energetics. Predictions to chemical accuracy, i.e., to 1 kcal/mol or less, are not yet feasible, although continuing improvements in both the theoretical methodology and computer technology suggest that this will soon be possible, at least for reactions involving small polyatomic species. 4 figs.

Lagrangian descriptors of driven chemical reaction manifolds.

Science.gov (United States)

Craven, Galen T; Junginger, Andrej; Hernandez, Rigoberto

2017-08-01

The persistence of a transition state structure in systems driven by time-dependent environments allows the application of modern reaction rate theories to solution-phase and nonequilibrium chemical reactions. However, identifying this structure is problematic in driven systems and has been limited by theories built on series expansion about a saddle point. Recently, it has been shown that to obtain formally exact rates for reactions in thermal environments, a transition state trajectory must be constructed. Here, using optimized Lagrangian descriptors [G. T. Craven and R. Hernandez, Phys. Rev. Lett. 115, 148301 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.148301], we obtain this so-called distinguished trajectory and the associated moving reaction manifolds on model energy surfaces subject to various driving and dissipative conditions. In particular, we demonstrate that this is exact for harmonic barriers in one dimension and this verification gives impetus to the application of Lagrangian descriptor-based methods in diverse classes of chemical reactions. The development of these objects is paramount in the theory of reaction dynamics as the transition state structure and its underlying network of manifolds directly dictate reactivity and selectivity.

Transport Properties of a Kinetic Model for Chemical Reactions without Barriers

International Nuclear Information System (INIS)

Alves, Giselle M.; Kremer, Gilberto M.; Soares, Ana Jacinta

2011-01-01

A kinetic model of the Boltzmann equation for chemical reactions without energy barrier is considered here with the aim of evaluating the reaction rate and characterizing the transport coefficient of shear viscosity for the reactive system. The Chapman-Enskog solution of the Boltzmann equation is used to compute the chemical reaction effects, in a flow regime for which the reaction process is close to the final equilibrium state. Some numerical results are provided illustrating that the considered chemical reaction without energy barrier can induce an appreciable influence on the reaction rate and on the transport coefficient of shear viscosity.

Diffusion in crushed rock and in bentonite clay

International Nuclear Information System (INIS)

Olin, M.

1994-04-01

Diffusion theories for porous media with sorption are reviewed to serve as a basis for considering diffusion in simple systems like sand of crushed rock. A Fickian diffusion and linear sorption model is solved both by analytical Laplance transform and Green's function methods and by numerical methods, and then applied to small-scale experiments for Finnish low- and medium-level operating waste repositories. The main properties of bentonite are reviewed. The hydraulic conductivity of compacted bentonite is so low that the major transport mechanism is diffusion. A Fickian diffusion and linear sorption model is applied to bentonite. The main component of bentonite, montmorillonite, has a high ion-exchange capacity and thus, transport in bentonite consists of interactive chemical and diffusion phenomena. A chemical equilibrium model, CHEQ, is developed for ion-exchange reactions in bentonite water systems. CHEQ is applied to some bentonite experiments with success, especially for monovalent ions. The fitted log-binding constants for sodium exchange with potassium, magnesium, and calcium were 0.27, 1.50, and 2.10, respectively. A coupled chemical and diffusion model, CHEQDIFF, is developed to take account of diffusion in pore water, surface diffusion and ion-exchange reactions. The model is applied to the same experiments as CHEQ, and validation is partly successful. In the diffusion case, the above-mentioned values for binding constants are used. The apparent diffusion (both anions and cations) and surface diffusion (only for cations) constants used are 3.0*10 -11 m 2 /s and 6.0*10 -12 m 2 /s, respectively, but these values are questionable, as experimental results good enough for fitting are not available. (orig.). (74 refs., 27 figs., 12 tabs.)

Single-molecule chemical reactions on DNA origami

DEFF Research Database (Denmark)

Voigt, Niels Vinther; Tørring, Thomas; Rotaru, Alexandru

2010-01-01

as templates for building materials with new functional properties. Relatively large nanocomponents such as nanoparticles and biomolecules can also be integrated into DNA nanostructures and imaged. Here, we show that chemical reactions with single molecules can be performed and imaged at a local position...... on a DNA origami scaffold by atomic force microscopy. The high yields and chemoselectivities of successive cleavage and bond-forming reactions observed in these experiments demonstrate the feasibility of post-assembly chemical modification of DNA nanostructures and their potential use as locally......DNA nanotechnology and particularly DNA origami, in which long, single-stranded DNA molecules are folded into predetermined shapes, can be used to form complex self-assembled nanostructures. Although DNA itself has limited chemical, optical or electronic functionality, DNA nanostructures can serve...

Chemical consequences of nuclear transformations

International Nuclear Information System (INIS)

Collins, C.H.; Lancas, F.M.; Andrade, J.C. de; Collins, K.E.

1979-01-01

The recombination processes of chemical bonds in liquid phase, after being split by nuclear transformations, include hot and diffuse reactions. Both processes probably occur by different mechanisms. The direct substitution process as well as processes which involve atoms, ions or other fragments retained in 'cages' formed by surrounding molecules, are processes not sensitive to the presence of a sequestering agent. The diffuse reactions whose fragments escaped from the 'cage' involve reactions with any reactive species found in the medium. (Author) [pt

Nonequilibrium thermodynamics and a fluctuation theorem for individual reaction steps in a chemical reaction network

International Nuclear Information System (INIS)

Pal, Krishnendu; Das, Biswajit; Banerjee, Kinshuk; Gangopadhyay, Gautam

2015-01-01

We have introduced an approach to nonequilibrium thermodynamics of an open chemical reaction network in terms of the propensities of the individual elementary reactions and the corresponding reverse reactions. The method is a microscopic formulation of the dissipation function in terms of the relative entropy or Kullback-Leibler distance which is based on the analogy of phase space trajectory with the path of elementary reactions in a network of chemical process. We have introduced here a fluctuation theorem valid for each opposite pair of elementary reactions which is useful in determining the contribution of each sub-reaction on the nonequilibrium thermodynamics of overall reaction. The methodology is applied to an oligomeric enzyme kinetics at a chemiostatic condition that leads the reaction to a nonequilibrium steady state for which we have estimated how each step of the reaction is energy driven or entropy driven to contribute to the overall reaction. (paper)

Molecular dynamics simulation of a chemical reaction

International Nuclear Information System (INIS)

Gorecki, J.; Gryko, J.

1988-06-01

Molecular dynamics is used to study the chemical reaction A+A→B+B. It is shown that the reaction rate constant follows the Arrhenius law both for Lennard-Jones and hard sphere interaction potentials between substrate particles. A. For the denser systems the reaction rate is proportional to the value of the radial distribution function at the contact point of two hard spheres. 10 refs, 4 figs

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.

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

Chemical reactions at CdS heterojunctions with CuInSe{sub 2}

Energy Technology Data Exchange (ETDEWEB)

Aquino, Angel; Rockett, Angus [Department of Materials Science and Engineering, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801 (United States)

2013-03-15

The stability of the CdS/CuInSe{sub 2} (CIS) heterojunction is critical to understanding the projected lifetime of CIS devices and the effect of processing conditions on the nanoscale chemistry of the heterojunction. This article reports the results of annealing heterojunctions between CdS deposited by chemical bath deposition and single crystal and polycrystalline CIS films between 200 and 500 Degree-Sign C for 10 to 150 min. No atomic movement was observed by secondary ion mass spectrometry at temperatures of 300 Degree-Sign C and below. At 400 Degree-Sign C even for the shortest time studied, Cu and In were found throughout the region initially consisting of CdS only and Cd was found to have moved into the CIS. In the polycrystal, annealing at 500 Degree-Sign C resulted in movement of Cd throughout the CIS layer. No time dependence was observed in the 400 and 500 Degree-Sign C anneals indicating that a reaction had occurred forming a compound that was in thermodynamic equilibrium with the remaining CIS. Diffusion turns on rapidly between 300 and 400 Degree-Sign C, indicating a high activation energy for atomic movement ({approx}2.4 eV). The onset of diffusion is consistent with the onset of Cu diffusion in CIS.

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.

Chemical boundary layers in CVD II. Reversible reactions

NARCIS (Netherlands)

Croon, de M.H.J.M.; Giling, L.J.

1990-01-01

In addition to irreversible reactions, which were treated in part I, reversible reactions in the gas phase have beenstudied using the concept of the chemical boundary layer. The analysis is given for the situations in which either the forwardor the back reaction is dominant. Two conceptual models

Molecular codes in biological and chemical reaction networks.

Directory of Open Access Journals (Sweden)

Dennis Görlich

Full Text Available Shannon's theory of communication has been very successfully applied for the analysis of biological information. However, the theory neglects semantic and pragmatic aspects and thus cannot directly be applied to distinguish between (bio- chemical systems able to process "meaningful" information from those that do not. Here, we present a formal method to assess a system's semantic capacity by analyzing a reaction network's capability to implement molecular codes. We analyzed models of chemical systems (martian atmosphere chemistry and various combustion chemistries, biochemical systems (gene expression, gene translation, and phosphorylation signaling cascades, an artificial chemistry, and random reaction networks. Our study suggests that different chemical systems possess different semantic capacities. No semantic capacity was found in the model of the martian atmosphere chemistry, the studied combustion chemistries, and highly connected random networks, i.e. with these chemistries molecular codes cannot be implemented. High semantic capacity was found in the studied biochemical systems and in random reaction networks where the number of second order reactions is twice the number of species. We conclude that our approach can be applied to evaluate the information processing capabilities of a chemical system and may thus be a useful tool to understand the origin and evolution of meaningful information, e.g. in the context of the origin of life.

Measurement of oxygen chemical diffusion in PuO{sub 2-x} and analysis of oxygen diffusion in PuO{sub 2-x} and (Pu,U)O{sub 2-x}

Energy Technology Data Exchange (ETDEWEB)

Kato, Masato; Uchida, Teppei [Advanced Nuclear System Research and Development Directorate, Japan Atomic Energy Agency, 4-33 Muramatsu, Tokai-mura, Ibaraki 319-1194 (Japan); Sunaoshi, Takeo [Inspection Development Company Ltd., 4-33 Muramatsu, Tokai-mura, Ibaraki 319-1194 (Japan)

2013-02-15

Oxygen chemical diffusion in PuO{sub 2-x} was investigated in the temperature range of 1473-1873 K by thermogravimetry as functions of oxygen-to-metal (O/M) ratios and temperatures. The oxygen chemical diffusion coefficients, D were determined assuming that the reduction curves were dominated by a diffusion process. The O/M ratio and Pu content dependence on the chemical diffusion coefficients were evaluated. The chemical diffusion coefficient had its minimum value at around O/M=1.98 and decreased with increasing Pu content in (U,Pu)O{sub 2-x}. The self-diffusion coefficients were evaluated. A model for describing the relationship among O/M ratio, oxygen chemical diffusion, and self-diffusion was proposed based on defect chemistry. (copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

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.

Chemical Demonstrations with Consumer Chemicals: The Black and White Reaction

Science.gov (United States)

Wright, Stephen W.

2002-01-01

A color-change reaction is described in which two colorless solutions are combined to afford a black mixture. Two more colorless solutions are combined to afford a white mixture. The black and white mixtures are then combined to afford a clear, colorless solution. The reaction uses chemicals that are readily available on the retail market: vitamin C, tincture of iodine, vinegar, ammonia, bleach, Epsom salt, and laundry starch.

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.

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.

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.

Global dynamics of a reaction-diffusion system

Directory of Open Access Journals (Sweden)

Yuncheng You

2011-02-01

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

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

Science.gov (United States)

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

2017-03-01

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

Modeling Electric Double-Layers Including Chemical Reaction Effects

DEFF Research Database (Denmark)

Paz-Garcia, Juan Manuel; Johannesson, Björn; Ottosen, Lisbeth M.

2014-01-01

A physicochemical and numerical model for the transient formation of an electric double-layer between an electrolyte and a chemically-active flat surface is presented, based on a finite elements integration of the nonlinear Nernst-Planck-Poisson model including chemical reactions. The model works...... for symmetric and asymmetric multi-species electrolytes and is not limited to a range of surface potentials. Numerical simulations are presented, for the case of a CaCO3 electrolyte solution in contact with a surface with rate-controlled protonation/deprotonation reactions. The surface charge and potential...... are determined by the surface reactions, and therefore they depends on the bulk solution composition and concentration...

Dynamic phase transition in diffusion-limited reactions

International Nuclear Information System (INIS)

Tauber, U.C.

2002-01-01

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

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

Science.gov (United States)

Schwarz, Karsten; Rieger, Heiko

2013-03-01

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

Emergency Evacuation of Hazardous Chemical Accidents Based on Diffusion Simulation

OpenAIRE

Jiang-Hua Zhang; Hai-Yue Liu; Rui Zhu; Yang Liu

2017-01-01

The recent rapid development of information technology, such as sensing technology, communications technology, and database, allows us to use simulation experiments for analyzing serious accidents caused by hazardous chemicals. Due to the toxicity and diffusion of hazardous chemicals, these accidents often lead to not only severe consequences and economic losses, but also traffic jams at the same time. Emergency evacuation after hazardous chemical accidents is an effective means to reduce the...

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/.

Non-allergic cutaneous reactions in airborne chemical sensitivity--a population based study

DEFF Research Database (Denmark)

Berg, Nikolaj Drimer; Linneberg, Allan; Thyssen, Jacob Pontoppidan

2011-01-01

the relationship between cutaneous reactions from patch testing and self-reported severity of chemical sensitivity to common airborne chemicals. A total of 3460 individuals participating in a general health examination, Health 2006, were patch tested with allergens from the European standard series and screened...... for chemical sensitivity with a standardised questionnaire dividing the participants into four severity groups of chemical sensitivity. Both allergic and non-allergic cutaneous reactions--defined as irritative, follicular, or doubtful allergic reactions--were analysed in relationship with severity of chemical...... most severe groups of self-reported sensitivity to airborne chemicals. When adjusting for confounding, associations were weakened, and only non-allergic cutaneous reactions were significantly associated with individuals most severely affected by inhalation of airborne chemicals (odds ratio = 2.5, p = 0...

Reaction diffusion voronoi diagrams: from sensors data to computing

Czech Academy of Sciences Publication Activity Database

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

2015-01-01

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

Communication: Control of chemical reactions using electric field gradients

Energy Technology Data Exchange (ETDEWEB)

Deshmukh, Shivaraj D.; Tsori, Yoav, E-mail: tsori@bgu.ac.il [Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel)

2016-05-21

We examine theoretically a new idea for spatial and temporal control of chemical reactions. When chemical reactions take place in a mixture of solvents, an external electric field can alter the local mixture composition, thereby accelerating or decelerating the rate of reaction. The spatial distribution of electric field strength can be non-trivial and depends on the arrangement of the electrodes producing it. In the absence of electric field, the mixture is homogeneous and the reaction takes place uniformly in the reactor volume. When an electric field is applied, the solvents separate and the reactants are concentrated in the same phase or separate to different phases, depending on their relative miscibility in the solvents, and this can have a large effect on the kinetics of the reaction. This method could provide an alternative way to control runaway reactions and to increase the reaction rate without using catalysts.

Communication: Control of chemical reactions using electric field gradients.

Science.gov (United States)

Deshmukh, Shivaraj D; Tsori, Yoav

2016-05-21

We examine theoretically a new idea for spatial and temporal control of chemical reactions. When chemical reactions take place in a mixture of solvents, an external electric field can alter the local mixture composition, thereby accelerating or decelerating the rate of reaction. The spatial distribution of electric field strength can be non-trivial and depends on the arrangement of the electrodes producing it. In the absence of electric field, the mixture is homogeneous and the reaction takes place uniformly in the reactor volume. When an electric field is applied, the solvents separate and the reactants are concentrated in the same phase or separate to different phases, depending on their relative miscibility in the solvents, and this can have a large effect on the kinetics of the reaction. This method could provide an alternative way to control runaway reactions and to increase the reaction rate without using catalysts.

Development of Green and Sustainable Chemical Reactions

DEFF Research Database (Denmark)

Taarning, Esben

Abstract This thesis entitled Development of Green and Sustainable Chemical Reactions is divided into six chapters involving topics and projects related to green and sustainable chemistry. The chapters can be read independently, however a few concepts and some background information is introduced...... as well as the possibility for establishing a renewable chemical industry is discussed. The development of a procedure for using unsaturated aldehydes as olefin synthons in the Diels- Alder reaction is described in chapter three. This procedure affords good yields of the desired Diels- Alder adducts...... in chapter one and two which can be helpful to know when reading the subsequent chapters. The first chapter is an introduction into the fundamentals of green and sustainable chemistry. The second chapter gives an overview of some of the most promising methods to produce value added chemicals from biomass...

A coupled model between mechanical deformation and chemical diffusion: An explanation for the preservation of chemical zonation in plagioclase at high temperatures

Science.gov (United States)

Zhong, Xin; Vrijmoed, Johannes; Moulas, Evangelos; Tajcmanová, Lucie

2016-04-01

Compositional zoning in metamorphic minerals have been generally recognized as an important geological feature to decipher the metamorphic history of rocks. The observed chemical zoning of, e.g. garnet, is commonly interpreted as disequilibrium between the fractionated inner core and the surrounding matrix. However, chemically zoned minerals were also observed in high grade rocks (T>800 degree C) where the duration of metamorphic processes was independently dated to take several Ma. This implies that temperature may not be the only factor that controls diffusion timescales, and grain scale pressure variation was proposed to be a complementary factor that may significantly contribute to the formation and preservation of chemical zoning in high temperature metamorphic minerals [Tajcmanová 2013, 2015]. Here, a coupled model is developed to simulate viscous deformation and chemical diffusion. The numerical approach considers the conservation of mass, momentum, and a constitutive relation developed from equilibrium thermodynamics. A compressible viscoelastic rheology is applied, which associates the volumetric change triggered by deformation and diffusion to a change of pressure. The numerical model is applied to the chemically zoned plagioclase rim described by [Tajcmanová 2014]. The diffusion process operating during the plagioclase rim formation can lead to a development of a pressure gradient. Such a pressure gradient, if maintained during ongoing viscous relaxation, can lead to the preservation of the observed chemical zonation in minerals. An important dimensionless number, the Deborah number, is defined as the ratio between the Maxwell viscoelastic relaxation time and the characteristic diffusion time. It characterizes the relative influence between the maintenance of grain scale pressure variation and chemical diffusion. Two extreme regimes are shown: the mechanically-controlled regime (high Deborah number) and diffusion-controlled regime (low Deborah number

Analysis of activation energy in Couette-Poiseuille flow of nanofluid in the presence of chemical reaction and convective boundary conditions

Science.gov (United States)

Zeeshan, A.; Shehzad, N.; Ellahi, R.

2018-03-01

The motivation of the current article is to explore the energy activation in MHD radiative Couette-Poiseuille flow nanofluid in horizontal channel with convective boundary conditions. The mathematical model of Buongiorno [1] effectively describes the current flow analysis. Additionally, the impact of chemical reaction is also taken in account. The governing flow equations are simplified with the help of boundary layer approximations. Non-linear coupled equations for momentum, energy and mass transfer are tackled with analytical (HAM) technique. The influence of dimensionless convergence parameter like Brownian motion parameter, radiation parameter, buoyancy ratio parameter, dimensionless activation energy, thermophoresis parameter, temperature difference parameter, dimensionless reaction rate, Schmidt number, Brinkman number, Biot number and convection diffusion parameter on velocity, temperature and concentration profiles are discussed graphically and in tabular form. From the results, it is elaborate that the nanoparticle concentration is directly proportional to the chemical reaction with activation energy and the performance of Brownian motion on nanoparticle concentration gives reverse pattern to that of thermophoresis parameter.

Evolution of density profiles for reaction-diffusion processes

International Nuclear Information System (INIS)

Ondarza-Rovira, R.

1990-01-01

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

Enrichment: CRISLA [chemical reaction by isotope selective activation] aims to reduce costs

International Nuclear Information System (INIS)

Eerkens, J.W.

1989-01-01

Every year, more than $3 billion is spent on enriching uranium. CRISLA (Chemical Reaction by Isotope Selective Activation) uses a laser-catalyzed chemical reaction which, its proponents claim, could substantially reduce these costs. In CRISLA, an infrared CO laser illuminates the intracavity reaction cell (IC) at a frequency tuned to excite primarily UF 6 . When UF 6 and co-reactant RX are passed through the IC, the tuned laser photons preferentially enhance the reaction of UF 6 with RX ten-thousand-fold over the thermal reaction rate. Thus the laser serves as an activator and the chemical energy for separation is largely chemical. (author)

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.

Interplay between inhibited transport and reaction in nanoporous materials

Energy Technology Data Exchange (ETDEWEB)

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

2013-01-01

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

Chemical modeling of irreversible reactions in nuclear waste-water-rock systems

International Nuclear Information System (INIS)

Wolery, T.J.

1981-02-01

Chemical models of aqueous geochemical systems are usually built on the concept of thermodynamic equilibrium. Though many elementary reactions in a geochemical system may be close to equilibrium, others may not be. Chemical models of aqueous fluids should take into account that many aqueous redox reactions are among the latter. The behavior of redox reactions may critically affect migration of certain radionuclides, especially the actinides. In addition, the progress of reaction in geochemical systems requires thermodynamic driving forces associated with elementary reactions not at equilibrium, which are termed irreversible reactions. Both static chemical models of fluids and dynamic models of reacting systems have been applied to a wide spectrum of problems in water-rock interactions. Potential applications in nuclear waste disposal range from problems in geochemical aspects of site evaluation to those of waste-water-rock interactions. However, much further work in the laboratory and the field will be required to develop and verify such applications of chemical modeling

Effect of chemical reaction on unsteady MHD free convective two ...

African Journals Online (AJOL)

The effect of flow parameters on the coefficient of skin friction, Nusselt number and Sherwood number are also tabulated and discussed appropriately. It was observed that the increase in chemical reaction coefficient/parameter suppresses both velocity and concentration profiles. Keywords: Chemical Reaction, MHD, ...

Non-allergic cutaneous reactions in airborne chemical sensitivity--a population based study.

Science.gov (United States)

Berg, Nikolaj Drimer; Linneberg, Allan; Thyssen, Jacob Pontoppidan; Dirksen, Asger; Elberling, Jesper

2011-06-01

Multiple chemical sensitivity (MCS) is characterised by adverse effects due to exposure to low levels of chemical substances. The aetiology is unknown, but chemical related respiratory symptoms have been found associated with positive patch test. The purpose of this study was to investigate the relationship between cutaneous reactions from patch testing and self-reported severity of chemical sensitivity to common airborne chemicals. A total of 3460 individuals participating in a general health examination, Health 2006, were patch tested with allergens from the European standard series and screened for chemical sensitivity with a standardised questionnaire dividing the participants into four severity groups of chemical sensitivity. Both allergic and non-allergic cutaneous reactions--defined as irritative, follicular, or doubtful allergic reactions--were analysed in relationship with severity of chemical sensitivity. Associations were controlled for the possible confounding effects of sex, age, asthma, eczema, atopic dermatitis, psychological and social factors, and smoking habits. In unadjusted analyses we found associations between allergic and non-allergic cutaneous reactions on patch testing and the two most severe groups of self-reported sensitivity to airborne chemicals. When adjusting for confounding, associations were weakened, and only non-allergic cutaneous reactions were significantly associated with individuals most severely affected by inhalation of airborne chemicals (odds ratio = 2.5, p = 0.006). Our results suggest that individuals with self-reported chemical sensitivity show increased non-allergic cutaneous reactions based on day 2 readings of patch tests. Copyright © 2011 Elsevier GmbH. All rights reserved.

On Uniform Decay of the Entropy for Reaction–Diffusion Systems

KAUST Repository

Mielke, Alexander

2014-09-10

This work provides entropy decay estimates for classes of nonlinear reaction–diffusion systems modeling reversible chemical reactions under the detailed-balance condition. We obtain explicit bounds for the exponential decay of the relative logarithmic entropy, being based essentially on the application of the Log-Sobolev estimate and a convexification argument only, making it quite robust to model variations. An important feature of our analysis is the interaction of the two different dissipative mechanisms: pure diffusion, forcing the system asymptotically to the homogeneous state, and pure reaction, forcing the solution to the (possibly inhomogeneous) chemical equilibrium. Only the interaction of both mechanisms provides the convergence to the homogeneous equilibrium. Moreover, we introduce two generalizations of the main result: (i) vanishing diffusion constants in some chemical components and (ii) usage of different entropy functionals. We provide a few examples to highlight the usability of our approach and shortly discuss possible further applications and open questions.

Raman Spectral Determination of Chemical Reaction Rate Characteristics

Science.gov (United States)

Balakhnina, I. A.; Brandt, N. N.; Mankova, A. A.; Chikishev, A. Yu.; Shpachenko, I. G.

2017-09-01

The feasibility of using Raman spectroscopy to determine chemical reaction rates and activation energies has been demonstrated for the saponification of ethyl acetate. The temperature dependence of the reaction rate was found in the range from 15 to 45°C.

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

Directory of Open Access Journals (Sweden)

Said Kouachi

2001-10-01

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

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.

Quantum chemical approach to estimating the thermodynamics of metabolic reactions.

Science.gov (United States)

Jinich, Adrian; Rappoport, Dmitrij; Dunn, Ian; Sanchez-Lengeling, Benjamin; Olivares-Amaya, Roberto; Noor, Elad; Even, Arren Bar; Aspuru-Guzik, Alán

2014-11-12

Thermodynamics plays an increasingly important role in modeling and engineering metabolism. We present the first nonempirical computational method for estimating standard Gibbs reaction energies of metabolic reactions based on quantum chemistry, which can help fill in the gaps in the existing thermodynamic data. When applied to a test set of reactions from core metabolism, the quantum chemical approach is comparable in accuracy to group contribution methods for isomerization and group transfer reactions and for reactions not including multiply charged anions. The errors in standard Gibbs reaction energy estimates are correlated with the charges of the participating molecules. The quantum chemical approach is amenable to systematic improvements and holds potential for providing thermodynamic data for all of metabolism.

Conservation-dissipation structure of chemical reaction systems.

Science.gov (United States)

Yong, Wen-An

2012-12-01

In this Brief Report, we show that balanced chemical reaction systems governed by the law of mass action have an elegant conservation-dissipation structure. From this structure a number of important conclusions can be easily deduced. In particular, with the help of this structure we can rigorously justify the classical partial equilibrium approximation in chemical kinetics.

On the solutions of fractional reaction-diffusion equations

Directory of Open Access Journals (Sweden)

Jagdev Singh

2013-05-01

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

Systematic trends in photonic reagent induced reactions in a homologous chemical family.

Science.gov (United States)

Tibbetts, Katharine Moore; Xing, Xi; Rabitz, Herschel

2013-08-29

The growing use of ultrafast laser pulses to induce chemical reactions prompts consideration of these pulses as "photonic reagents" in analogy to chemical reagents. This work explores the prospect that photonic reagents may affect systematic trends in dissociative ionization reactions of a homologous family of halomethanes, much as systematic outcomes are often observed for reactions between homologous families of chemical reagents and chemical substrates. The experiments in this work with photonic reagents of varying pulse energy and linear spectral chirp reveal systematic correlations between observable ion yields and the following set of natural variables describing the substrate molecules: the ionization energy of the parent molecule, the appearance energy of each fragment ion, and the relative strength of carbon-halogen bonds in molecules containing two different halogens. The results suggest that reactions induced by photonic reagents exhibit systematic behavior analogous to that observed in reactions driven by chemical reagents, which provides a basis to consider empirical "rules" for predicting the outcomes of photonic reagent induced reactions.

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

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

Science.gov (United States)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

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

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

International Nuclear Information System (INIS)

Indekeu, Joseph O; Smets, Ruben

2017-01-01

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

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.

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.

Thermo effect of chemical reaction in irreversible electrochemical systems

International Nuclear Information System (INIS)

Tran Vinh Quy; Nguyen Tang

1989-01-01

From first law of thermodynamics the expressions of statistical calculation of 'Fundamental' and 'Thermo-chemical' thermal effects are obtained. Besides, method of calculation of thermal effect of chemical reactions in non-equilibrium electro-chemical systems is accurately discussed. (author). 7 refs

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.

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

NARCIS (Netherlands)

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

2016-01-01

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

Formal modeling of a system of chemical reactions under uncertainty.

Science.gov (United States)

Ghosh, Krishnendu; Schlipf, John

2014-10-01

We describe a novel formalism representing a system of chemical reactions, with imprecise rates of reactions and concentrations of chemicals, and describe a model reduction method, pruning, based on the chemical properties. We present two algorithms, midpoint approximation and interval approximation, for construction of efficient model abstractions with uncertainty in data. We evaluate computational feasibility by posing queries in computation tree logic (CTL) on a prototype of extracellular-signal-regulated kinase (ERK) pathway.

Computational prediction of chemical reactions: current status and outlook.

Science.gov (United States)

Engkvist, Ola; Norrby, Per-Ola; Selmi, Nidhal; Lam, Yu-Hong; Peng, Zhengwei; Sherer, Edward C; Amberg, Willi; Erhard, Thomas; Smyth, Lynette A

2018-06-01

Over the past few decades, various computational methods have become increasingly important for discovering and developing novel drugs. Computational prediction of chemical reactions is a key part of an efficient drug discovery process. In this review, we discuss important parts of this field, with a focus on utilizing reaction data to build predictive models, the existing programs for synthesis prediction, and usage of quantum mechanics and molecular mechanics (QM/MM) to explore chemical reactions. We also outline potential future developments with an emphasis on pre-competitive collaboration opportunities. Copyright © 2018 Elsevier Ltd. All rights reserved.

Electronic dissipation processes during chemical reactions on surfaces

CERN Document Server

Stella, Kevin

2012-01-01

Hauptbeschreibung Every day in our life is larded with a huge number of chemical reactions on surfaces. Some reactions occur immediately, for others an activation energy has to be supplied. Thus it happens that though a reaction should thermodynamically run off, it is kinetically hindered. Meaning the partners react only to the thermodynamically more stable product state within a mentionable time if the activation energy of the reaction is supplied. With the help of catalysts the activation energy of a reaction can be lowered. Such catalytic processes on surfaces are widely used in industry. A

Dynamic transition in the structure of an energetic crystal during chemical reactions at shock front prior to detonation.

Science.gov (United States)

Nomura, Ken-Ichi; Kalia, Rajiv K; Nakano, Aiichiro; Vashishta, Priya; van Duin, Adri C T; Goddard, William A

2007-10-05

Mechanical stimuli in energetic materials initiate chemical reactions at shock fronts prior to detonation. Shock sensitivity measurements provide widely varying results, and quantum-mechanical calculations are unable to handle systems large enough to describe shock structure. Recent developments in reactive force-field molecular dynamics (ReaxFF-MD) combined with advances in parallel computing have paved the way to accurately simulate reaction pathways along with the structure of shock fronts. Our multimillion-atom ReaxFF-MD simulations of l,3,5-trinitro-l,3,5-triazine (RDX) reveal that detonation is preceded by a transition from a diffuse shock front with well-ordered molecular dipoles behind it to a disordered dipole distribution behind a sharp front.

Sintering with a chemical reaction as applied to uranium monocarbide

International Nuclear Information System (INIS)

Accary, A.; Caillat, R.

1960-01-01

The present paper provides a survey of different investigations whose aim was the preparation and fabrication of uranium monocarbide for nuclear use. If a chemical reaction takes place in the sample during the sintering operation, it may be expected that the atom rearrangements involved in this reaction should favour the sintering process and thereby lower the temperature needed to yield a body of a given density. With this hypothesis in mind, the following methods have been studied: - Sintering of U-C mixtures; - Sintering of UO 2 -C mixtures; - Hot pressing of U-C mixtures; - Extrusion of U-C mixtures. To generalize our result, it could be said that a chemical reaction does not lead to high densification, if one depends on a simple contact between discrete particles. On the contrary, a chemical reaction can help sintering if, as our hot pressing experiments shows, the densification can be achieved prior to the reaction. (author) [fr

Reaction path analysis of sodium-water reaction phenomena in support of chemical reaction model development

International Nuclear Information System (INIS)

Kikuchi, Shin; Ohshima, Hiroyuki; Hashimoto, Kenro

2011-01-01

Computational study of the sodium-water reaction at the gas (water) - liquid (sodium) interface has been carried out using ab initio (first-principle) method. A possible reaction channel has been identified for the stepwise OH bond dissociations of a single water molecule. The energetics including the binding energy of a water molecule to the sodium surface, the activation energies of the bond cleavages, and the reaction energies, have been evaluated, and the rate constants of the first and second OH bond-breakings have been compared. The results are used as the basis for constructing the chemical reaction model used in a multi-dimensional sodium-water reaction code, SERAPHIM, being developed by JAEA toward the safety assessment of the steam generator (SG) in a sodium-cooled fast reactor (SFR). (author)

An Application of Equivalence Transformations to Reaction Diffusion Equations

Directory of Open Access Journals (Sweden)

Mariano Torrisi

2015-10-01

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

Multiple Scale Reaction-Diffusion-Advection Problems with Moving Fronts

Science.gov (United States)

Nefedov, Nikolay

2016-06-01

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

Minimum Energy Pathways for Chemical Reactions

Science.gov (United States)

Walch, S. P.; Langhoff, S. R. (Technical Monitor)

1995-01-01

Computed potential energy surfaces are often required for computation of such parameters as rate constants as a function of temperature, product branching ratios, and other detailed properties. We have found that computation of the stationary points/reaction pathways using CASSCF/derivative methods, followed by use of the internally contracted CI method to obtain accurate energetics, gives useful results for a number of chemically important systems. The talk will focus on a number of applications to reactions leading to NOx and soot formation in hydrocarbon combustion.

Theoretical studies of chemical reaction dynamics

Energy Technology Data Exchange (ETDEWEB)

Schatz, G.C. [Argonne National Laboratory, IL (United States)

1993-12-01

This collaborative program with the Theoretical Chemistry Group at Argonne involves theoretical studies of gas phase chemical reactions and related energy transfer and photodissociation processes. Many of the reactions studied are of direct relevance to combustion; others are selected they provide important examples of special dynamical processes, or are of relevance to experimental measurements. Both classical trajectory and quantum reactive scattering methods are used for these studies, and the types of information determined range from thermal rate constants to state to state differential cross sections.

A Data-Driven Sparse-Learning Approach to Model Reduction in Chemical Reaction Networks

OpenAIRE

Harirchi, Farshad; Khalil, Omar A.; Liu, Sijia; Elvati, Paolo; Violi, Angela; Hero, Alfred O.

2017-01-01

In this paper, we propose an optimization-based sparse learning approach to identify the set of most influential reactions in a chemical reaction network. This reduced set of reactions is then employed to construct a reduced chemical reaction mechanism, which is relevant to chemical interaction network modeling. The problem of identifying influential reactions is first formulated as a mixed-integer quadratic program, and then a relaxation method is leveraged to reduce the computational comple...

Inward propagating chemical waves in Taylor vortices.

Science.gov (United States)

Thompson, Barnaby W; Novak, Jan; Wilson, Mark C T; Britton, Melanie M; Taylor, Annette F

2010-04-01

Advection-reaction-diffusion (ARD) waves in the Belousov-Zhabotinsky reaction in steady Taylor-Couette vortices have been visualized using magnetic-resonance imaging and simulated using an adapted Oregonator model. We show how propagating wave behavior depends on the ratio of advective, chemical and diffusive time scales. In simulations, inward propagating spiral flamelets are observed at high Damköhler number (Da). At low Da, the reaction distributes itself over several vortices and then propagates inwards as contracting ring pulses--also observed experimentally.

A network dynamics approach to chemical reaction networks

NARCIS (Netherlands)

van der Schaft, Abraham; Rao, S.; Jayawardhana, B.

2016-01-01

A treatment of chemical reaction network theory is given from the perspective of nonlinear network dynamics, in particular of consensus dynamics. By starting from the complex-balanced assumption the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a

Non-stationary filtration mode during chemical reactions with the gas phase

Science.gov (United States)

Zavialov, Ivan; Konyukhov, Andrey; Negodyaev, Sergey

2015-04-01

An experimental and numerical study of filtration accompanied by chemical reactions between displacing fluid and solid skeleton is considered. Glass balls (400-500 μm in diameter) were placed in 1 cm gap between two glass sheets and were used as model porous medium. The baking soda was added to the glass balls. The 70% solution of acetic acid was used as the displacer. The modeling porous medium was saturated with a mineral oil, and then 70% solution of colored acetic acid was pumped through the medium. The glass balls and a mineral oil have a similar refractive index, so the model porous medium was optically transparent. During the filtration, the gas phase was generated by the chemical reactions between the baking soda and acetic acid, and time-dependent displacement of the chemical reaction front was observed. The front of the chemical reaction was associated with the most intensive gas separation. The front moved, stopped, and then moved again to the area where it had been already. We called this process a secondary oxidation wave. To describe this effect, we added to the balance equations a term associated with the formation and disappearance of phases due to chemical reactions. The equations were supplemented by Darcy's law for multiphase filtration. Nonstationarity front propagation of the chemical reaction in the numerical experiment was observed at Damköhler numbers greater than 100. The mathematical modelling was agreed well with the experimental results.

Study of the diffusion of some emulsions in the human skin by pulsed photoacoustic spectroscopy

International Nuclear Information System (INIS)

Lahjomri, F; Benamar, N; Chatri, E; Leblanc, R M

2003-01-01

We previously used pulsed photoacoustic spectroscopy (PPAS) to quantify sunscreen diffusion into human skin, and suggested a methodology to evaluate the time and the depth diffusion profile. These results were obtained by the analysis of the photoacoustic maximum response signal P max decrease, the time delay t max and the Fourier transform representation of the photoacoustic signal. In this study we present the results obtained for diffusion of four typical emulsions used in sunscreen compositions that show, for the first time, a particular behaviour for one of these emulsions due to a chemical reaction inside the skin during the diffusion process. This result provides a particularly interesting technique through the PPAS, to evaluate in situ the eventual chemical reactions that can occur during drug diffusion into human skin

Strain-induced structural changes and chemical reactions. 1: Thermomechanical and kinetic models

International Nuclear Information System (INIS)

Levitas, V.I.; Nesterenko, V.F.; Meyers, M.A.

1998-01-01

Strain-induced chemical reactions were observed recently (Nesterenko et al) in experiments in the shear band in both Ti-Si and Nb-Si mixtures. Reactions can start in the solid state or after melting of at least one component. One of the aims is to find theoretically whether there are possible macroscopic mechanisms of mechanical intensification of the above and other chemical reactions due to plastic shear in the solid state. Continuum thermodynamical theory of structural changes with an athermal kinetics, which includes martensitic phase transformations, plastic strain-induced chemical reactions and polymorphic transformations, is developed at finite strains. The theory includes kinematics, criterion of structural change and extremum principle for determination of all unknown variable parameters for the case with neglected elastic strains. Thermodynamically consistent kinetic theory of thermally activated structural changes is suggested. The concept of the effective temperature is introduced which takes into account that temperature can vary significantly (on 1,000 K) during the chemical reactions under consideration. The theory will be applied in Part 2 of the paper for the description of chemical reactions in the shear band

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

International Nuclear Information System (INIS)

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

2014-01-01

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

A reaction-based paradigm to model reactive chemical transport in groundwater with general kinetic and equilibrium reactions

International Nuclear Information System (INIS)

Zhang, Fan; Yeh, Gour-Tsyh; Parker, Jack C.; Brooks, Scott C; Pace, Molly; Kim, Young Jin; Jardine, Philip M.; Watson, David B.

2007-01-01

This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M. partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M. species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing NE equilibrium reactions and a set of reactive transport equations of M-NE kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions

A reaction-based paradigm to model reactive chemical transport in groundwater with general kinetic and equilibrium reactions.

Science.gov (United States)

Zhang, Fan; Yeh, Gour-Tsyh; Parker, Jack C; Brooks, Scott C; Pace, Molly N; Kim, Young-Jin; Jardine, Philip M; Watson, David B

2007-06-16

This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing N(E) equilibrium reactions and a set of reactive transport equations of M-N(E) kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions.

BGK-type models in strong reaction and kinetic chemical equilibrium regimes

International Nuclear Information System (INIS)

Monaco, R; Bianchi, M Pandolfi; Soares, A J

2005-01-01

A BGK-type procedure is applied to multi-component gases undergoing chemical reactions of bimolecular type. The relaxation process towards local Maxwellians, depending on mass and numerical densities of each species as well as common velocity and temperature, is investigated in two different cases with respect to chemical regimes. These cases are related to the strong reaction regime characterized by slow reactions, and to the kinetic chemical equilibrium regime where fast reactions take place. The consistency properties of both models are stated in detail. The trend to equilibrium is numerically tested and comparisons for the two regimes are performed within the hydrogen-air and carbon-oxygen reaction mechanism. In the spatial homogeneous case, it is also shown that the thermodynamical equilibrium of the models recovers satisfactorily the asymptotic equilibrium solutions to the reactive Euler equations

Theoretical study of coupling mechanisms between oxygen diffusion, chemical reaction, mechanical stresses in a solid-gas reactive system

International Nuclear Information System (INIS)

Creton, N.; Optasanu, V.; Montesin, T.; Garruchet, S.

2008-01-01

This paper offers a study of oxygen dissolution into a solid, and its consequences on the mechanical behaviour of the material. In fact, mechanical strains strongly influence the oxidation processes and may be, in some materials, responsible for cracking. To realize this study, mechanical considerations are introduced into the classical diffusion laws. Simulations were made for the particular case of uranium dioxide, which undergoes the chemical fragmentation. According to our simulations, the hypothesis of a compression stress field into the oxidised UO 2 compound near the internal interface is consistent with some oxidation mechanisms of oxidation experimentally observed. More generally, this work will be extended to the simulation to an oxide layer growth on a metallic substrate. (authors)

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

International Nuclear Information System (INIS)

Wang Jian; Lu Junguo

2008-01-01

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

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

Directory of Open Access Journals (Sweden)

Demongeot Jacques

2004-06-01

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

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

Science.gov (United States)

Glade, Nicolas; Demongeot, Jacques; Tabony, James

2004-01-01

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

Femtosecond laser control of chemical reaction of carbon monoxide and hydrogen

CSIR Research Space (South Africa)

Du Plessis, A

2010-09-01

Full Text Available Femtosecond laser control of chemical reactions is made possible through the use of pulse-shaping techniques coupled to a learning algorithm feedback loop – teaching the laser pulse to control the chemical reaction. This can result in controllable...

Nanoparticle-triggered in situ catalytic chemical reactions for tumour-specific therapy.

Science.gov (United States)

Lin, Han; Chen, Yu; Shi, Jianlin

2018-03-21

Tumour chemotherapy employs highly cytotoxic chemodrugs, which kill both cancer and normal cells by cellular apoptosis or necrosis non-selectively. Catalysing/triggering the specific chemical reactions only inside tumour tissues can generate abundant and special chemicals and products locally to initiate a series of unique biological and pathologic effects, which may enable tumour-specific theranostic effects to combat cancer without bringing about significant side effects on normal tissues. Nevertheless, chemical reaction-initiated selective tumour therapy strongly depends on the advances in chemistry, materials science, nanotechnology and biomedicine. This emerging cross-disciplinary research area is substantially different from conventional cancer-theranostic modalities in clinics. In response to the fast developments in cancer theranostics based on intratumoural catalytic chemical reactions, this tutorial review summarizes the very-recent research progress in the design and synthesis of representative nanoplatforms with intriguing nanostructures, compositions, physiochemical properties and biological behaviours for versatile catalytic chemical reaction-enabled cancer treatments, mainly by either endogenous tumour microenvironment (TME) triggering or exogenous physical irradiation. These unique intratumoural chemical reactions can be used in tumour-starving therapy, chemodynamic therapy, gas therapy, alleviation of tumour hypoxia, TME-responsive diagnostic imaging and stimuli-responsive drug release, and even externally triggered versatile therapeutics. In particular, the challenges and future developments of such a novel type of cancer-theranostic modality are discussed in detail to understand the future developments and prospects in this research area as far as possible. It is highly expected that this kind of unique tumour-specific therapeutics by triggering specific in situ catalytic chemical reactions inside tumours would provide a novel but efficient

Open complex-balanced mass action chemical reaction networks

NARCIS (Netherlands)

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

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

A chemical reaction in the movie The Ten Commandments

Directory of Open Access Journals (Sweden)

López Pérez, José Pedro;

2012-04-01

Full Text Available The study of natural sciences in the second year of Secondary Education must be complemented with a visit to the laboratory, where experiments should be permormed. The curriculum emphasizes the initial basis of Chemistry and the study of reactions. In this paper we describe a laboratory experience, useful for understanding the concept of chemical change. Also, we present the hypothesis that a chemical reaction was used in the classic movie The Ten Commandments.

Effects of the fluid flows on enzymatic chemical oscillations

Science.gov (United States)

Shklyaev, Oleg; Yashin, Victor; Balazs, Anna

2017-11-01

Chemical oscillations are ubiquitous in nature and have a variety of promising applications. Usually, oscillating chemical systems are analyzed within the context of a reaction-diffusion framework. Here, we examine how fluid flows carrying the reactants can be utilized to modulate the negative feedback loops and time delays that promote chemical oscillations. We consider a model where a chemical reaction network involves two species, X and Y, which undergo transformations catalyzed by respective enzymes immobilized at the bottom wall of a fluid-filled microchamber. The reactions with the enzymes provide a negative feedback in the chemically oscillating system. In particular, the first enzyme, localized on the first patch, promotes production of chemical X, while the second enzyme, immobilized on the second patch, promotes production of chemical Y, which inhibits the production of chemical X. The separation distance between the enzyme-coated patches sets the time delay required for the transportation of X and Y. The chemical transport is significantly enhanced if convective fluxes accompany the diffusive ones. Therefore, the parameter region where oscillations are present is modified. The findings provide guidance to designing micro-scale chemical reactors with improved functionalities.

Diffusion in plasma: The Hall effect, compositional waves, and chemical spots

Energy Technology Data Exchange (ETDEWEB)

Urpin, V., E-mail: Vadim.urpin@uv.es [Ioffe Institute of Physics and Technology (Russian Federation)

2017-03-15

Diffusion caused by a combined influence of the electric current and Hall effect is considered, and it is argued that such diffusion can form inhomogeneities of a chemical composition in plasma. The considered mechanism can be responsible for the formation of element spots in laboratory and astrophysical plasmas. This current-driven diffusion can be accompanied by propagation of a particular type of waves in which the impurity number density oscillates alone. These compositional waves exist if the magnetic pressure in plasma is much greater than the gas pressure.

Adsorption and catalysis: The effect of confinement on chemical reactions

International Nuclear Information System (INIS)

Santiso, Erik E.; George, Aaron M.; Turner, C. Heath; Kostov, Milen K.; Gubbins, Keith E.; Buongiorno-Nardelli, Marco; Sliwinska-Bartkowiak, MaIgorzata

2005-01-01

Confinement within porous materials can affect chemical reactions through a host of different effects, including changes in the thermodynamic state of the system due to interactions with the pore walls, selective adsorption, geometrical constraints that affect the reaction mechanism, electronic perturbation due to the substrate, etc. In this work, we present an overview of some of our recent research on some of these effects, on chemical equilibrium, kinetic rates and reaction mechanisms. We also discuss our current and future directions for research in this area

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.

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

Science.gov (United States)

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

2017-07-01

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

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

Directory of Open Access Journals (Sweden)

Shahid Hasnain

2017-07-01

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

Direct single-molecule dynamic detection of chemical reactions.

Science.gov (United States)

Guan, Jianxin; Jia, Chuancheng; Li, Yanwei; Liu, Zitong; Wang, Jinying; Yang, Zhongyue; Gu, Chunhui; Su, Dingkai; Houk, Kendall N; Zhang, Deqing; Guo, Xuefeng

2018-02-01

Single-molecule detection can reveal time trajectories and reaction pathways of individual intermediates/transition states in chemical reactions and biological processes, which is of fundamental importance to elucidate their intrinsic mechanisms. We present a reliable, label-free single-molecule approach that allows us to directly explore the dynamic process of basic chemical reactions at the single-event level by using stable graphene-molecule single-molecule junctions. These junctions are constructed by covalently connecting a single molecule with a 9-fluorenone center to nanogapped graphene electrodes. For the first time, real-time single-molecule electrical measurements unambiguously show reproducible large-amplitude two-level fluctuations that are highly dependent on solvent environments in a nucleophilic addition reaction of hydroxylamine to a carbonyl group. Both theoretical simulations and ensemble experiments prove that this observation originates from the reversible transition between the reactant and a new intermediate state within a time scale of a few microseconds. These investigations open up a new route that is able to be immediately applied to probe fast single-molecule physics or biophysics with high time resolution, making an important contribution to broad fields beyond reaction chemistry.

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.

Chemical diffusion of Cr, Ni and Si in welded joints. II

International Nuclear Information System (INIS)

Kucera, J.; Ciha, K.

1987-01-01

The results are given of a study in chemical diffusion in welded joints P2/A and P3/A. P2 stands for the steel (Fe-17.48 Cr-8.15 Ni-0.14 Si), P3 for (Fe-18.52 Cr-8.20 Ni-1.78 Si) and A for the Fe-Arema. Triadic sandwiche-like samples were diffusion heated at temperatures from 920 to 1170 degC. The concentration distributions N(x,t) of the given elements were measured with microprobe JXA-3A. The evaluation of the experimental data was carried out either by Grube's method, or in some cases by the spline-polynomial method. The evaluated diffusivities D-bar satisfy the Arrhenius relation and yield the standard diffusion characteristics D 0 and H. The diffusivities D-bar of Cr, Ni and Si in P1/A, in P2/A and P3/A welded joints vary with Si content in P1, P2 and P3 alloys, similar to the Cr-51 and Ni-63 self-diffusivities in Fe-18 Cr-12 Ni-X Si steels, and tend to increase with increasing Si content. The values D-bar measured in the vicinity of grain boundaries are higher than the bulk diffusion coefficients. The most rapid diffusant is Si and the slowest one Ni. Thus, the relations D-bar Si :D-bar Cr :D-bar Ni ≅ 6:3:1 (P3/A) and D-bar Si :D-bar Cr :D-bar Ni ≅ 1.7:1.4:1 (P3/A) are valid at 1050 degC. Comparing the results with those published if can be noted that the Cr-51 and Ni-63 self-diffusion in Fe-18 Cr-12 Ni-X Si steels is faster than chemical diffusion of these elements in the said steel welded joints P2/A and P3/A; X varies from 0.14 to 1.98. (author). 7 tabs., 7 figs., 20 refs

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.

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

Science.gov (United States)

Hu, Wenjie; Duan, Yueliang

2018-04-01

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

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

Science.gov (United States)

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

2018-04-01

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

Generalized hydrodynamic treatment of the interplay between restricted transport and catalytic reactions in nanoporous materials.

Science.gov (United States)

Ackerman, David M; Wang, Jing; Evans, James W

2012-06-01

Behavior of catalytic reactions in narrow pores is controlled by a delicate interplay between fluctuations in adsorption-desorption at pore openings, restricted diffusion, and reaction. This behavior is captured by a generalized hydrodynamic formulation of appropriate reaction-diffusion equations (RDE). These RDE incorporate 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 RDE elucidate the nonexponential decay of the steady-state reactant concentration into the pore and the non-mean-field scaling of the reactant penetration depth.

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

Science.gov (United States)

Ernst, Dominique; Köhler, Jürgen; Weiss, Matthias

2014-05-07

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

The Dynamics of Chemical Reactions: Atomistic Visualizations of Organic Reactions, and Homage to van 't Hoff.

Science.gov (United States)

Yang, Zhongyue; Houk, K N

2018-03-15

Jacobus Henricus van 't Hoff was the first Nobel Laureate in Chemistry. He pioneered in the study of chemical dynamics, which referred at that time to chemical kinetics and thermodynamics. The term has evolved in modern times to refer to the exploration of chemical transformations in a time-resolved fashion. Chemical dynamics has been driven by the development of molecular dynamics trajectory simulations, which provide atomic visualization of chemical processes and illuminate how dynamic effects influence chemical reactivity and selectivity. In homage to the legend of van 't Hoff, we review the development of the chemical dynamics of organic reactions, our area of research. We then discuss our trajectory simulations of pericyclic reactions, and our development of dynamic criteria for concerted and stepwise reaction mechanisms. We also describe a method that we call environment-perturbed transition state sampling, which enables trajectory simulations in condensed-media using quantum mechanics and molecular mechanics (QM/MM). We apply the method to reactions in solvent and in enzyme. Jacobus Henricus van 't Hoff (1852, Rotterdam-1911, Berlin) received the Nobel Prize for Chemistry in 1901 "in recognition of the extraordinary services he has rendered by the discovery of the laws of chemical dynamics and osmotic pressure in solutions". van 't Hoff was born the Netherlands, and earned his doctorate in Utrecht in 1874. In 1896 he moved to Berlin, where he was offered a position with more research and less teaching. van 't Hoff is considered one of the founders of physical chemistry. A key step in establishing this new field was the start of Zeitschrift für Physikalische Chemie in 1887. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

International Nuclear Information System (INIS)

Li Zuoan; Li Kelin

2009-01-01

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

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

Science.gov (United States)

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

2018-02-01

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

The chemical evolution of white dwarf atmospheres: Diffusion and accretion

International Nuclear Information System (INIS)

Vauclair, G.; Vauclair, S.; Greenstein, J.L.

1979-01-01

A study of diffusion processes in white dwarfs is presented. We are especially interested in the estimate of the diffusion time scales for C, N, O, Mg, and Ca along the cooling sequence. The effect of the radiative acceleration is important in hot white dwarfs while in cooler ones the thermal diffusion dominates the gravitational settling. In hot white dwarfs, there should be an observable amount of CNO elements unless they have previously left the stars by a selective wind. Observational tests of this result are discussed. The diffusion time scales are always short compared to the evolutionary time scales. It is shown that in both hydrogen and helium envelopes, the convection zone, even at its maximum depth, is not able to bring back to the stellar surface the metals which have previously diffused downwards. The diffusion alone predicts a complete absence of metals in white dwarf atmospheres and envelopes. As metals are observed in white dwarfs, at least at effective temperatures lower than 15,000 K, there must be some mechanism competing with diffusion. We investigate the competition between diffusion and accretion and propose a general scheme for the chemical evolution of white dwarf atmospheres along the cooling sequence. (orig.)

Mass transfer with chemical reaction in multiphase systems

International Nuclear Information System (INIS)

Alper, E.

1983-01-01

These volumes deal with the phenomenon of 'mass transfer with chemical reaction' which is of industrial, biological and physiological importance. In process engineering, it is encountered both in separation processes and in reaction engineering and both aspects are covered here in four sections: introduction; gas-liquid system; liquid-liquid system; and gas-liquid-solid system

Matrix isolation as a tool for studying interstellar chemical reactions

Science.gov (United States)

Ball, David W.; Ortman, Bryan J.; Hauge, Robert H.; Margrave, John L.

1989-01-01

Since the identification of the OH radical as an interstellar species, over 50 molecular species were identified as interstellar denizens. While identification of new species appears straightforward, an explanation for their mechanisms of formation is not. Most astronomers concede that large bodies like interstellar dust grains are necessary for adsorption of molecules and their energies of reactions, but many of the mechanistic steps are unknown and speculative. It is proposed that data from matrix isolation experiments involving the reactions of refractory materials (especially C, Si, and Fe atoms and clusters) with small molecules (mainly H2, H2O, CO, CO2) are particularly applicable to explaining mechanistic details of likely interstellar chemical reactions. In many cases, matrix isolation techniques are the sole method of studying such reactions; also in many cases, complexations and bond rearrangements yield molecules never before observed. The study of these reactions thus provides a logical basis for the mechanisms of interstellar reactions. A list of reactions is presented that would simulate interstellar chemical reactions. These reactions were studied using FTIR-matrix isolation techniques.

A Stefan model for mass transfer in a rotating disk reaction vessel

KAUST Repository

BOHUN, C. S.

2015-01-01

chemical reactions occurring in the bulk. The wide range in the reaction rates of the underlying chemistry allows for a natural decoupling of the problem into a simplified set of weakly coupled convective-reaction-diffusion equations for the slowly reacting

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

Science.gov (United States)

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

2017-12-01

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

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

Science.gov (United States)

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

2018-01-01

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

Quantum dynamics of fast chemical reactions

Energy Technology Data Exchange (ETDEWEB)

Light, J.C. [Univ. of Chicago, IL (United States)

1993-12-01

The aims of this research are to explore, develop, and apply theoretical methods for the evaluation of the dynamics of gas phase collision processes, primarily chemical reactions. The primary theoretical tools developed for this work have been quantum scattering theory, both in time dependent and time independent forms. Over the past several years, the authors have developed and applied methods for the direct quantum evaluation of thermal rate constants, applying these to the evaluation of the hydrogen isotopic exchange reactions, applied wave packet propagation techniques to the dissociation of Rydberg H{sub 3}, incorporated optical potentials into the evaluation of thermal rate constants, evaluated the use of optical potentials for state-to-state reaction probability evaluations, and, most recently, have developed quantum approaches for electronically non-adiabatic reactions which may be applied to simplify calculations of reactive, but electronically adiabatic systems. Evaluation of the thermal rate constants and the dissociation of H{sub 3} were reported last year, and have now been published.

Chemical reaction between single hydrogen atom and graphene

International Nuclear Information System (INIS)

Ito, Atsushi; Nakamura, Hiroaki; Takayama, Arimichi

2007-04-01

We study chemical reaction between a single hydrogen atom and a graphene, which is the elemental reaction between hydrogen and graphitic carbon materials. In the present work, classical molecular dynamics simulation is used with modified Brenner's empirical bond order potential. The three reactions, that is, absorption reaction, reflection reaction and penetration reaction, are observed in our simulation. Reaction rates depend on the incident energy of the hydrogen atom and the graphene temperature. The dependence can be explained by the following mechanisms: (1) The hydrogen atom receives repulsive force by π-electrons in addition to nuclear repulsion. (2) Absorbing the hydrogen atom, the graphene transforms its structure to the 'overhand' configuration such as sp 3 state. (3) The hexagonal hole of the graphene is expanded during the penetration of the hydrogen atom. (author)

Reaction-assisted diffusion bonding of TiAl alloy to steel

Energy Technology Data Exchange (ETDEWEB)

Simões, S., E-mail: ssimoes@fe.up.pt [CEMUC, Department of Metallurgical and Materials Engineering, University of Porto, R. Dr. Roberto Frias, 4200-465 Porto (Portugal); Viana, F. [CEMUC, Department of Metallurgical and Materials Engineering, University of Porto, R. Dr. Roberto Frias, 4200-465 Porto (Portugal); Ramos, A.S.; Vieira, M.T. [CEMUC, Department of Mechanical Engineering, University of Coimbra, R. Luís Reis Santos, 3030-788 Coimbra (Portugal); Vieira, M.F. [CEMUC, Department of Metallurgical and Materials Engineering, University of Porto, R. Dr. Roberto Frias, 4200-465 Porto (Portugal)

2016-03-01

The dissimilar joining of TiAl to AISI 310 stainless steel by a reaction-assisted diffusion bonding process, using Ni/Al nanolayers as an interlayer, was investigated in the present work. The Ni and Al alternated nanolayers were deposited by d.c. magnetron sputtering onto the base materials, with a bilayer thickness of 14 nm. Joining experiments were performed at 800 °C for 60 min with compressive stress of 25 and 50 MPa. The effectiveness of the interlayer on the bonding process was assessed by microstructural characterization of the interface and by mechanical tests. Diffusion bonded joints were characterized by scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), transmission electron microscopy (TEM), high resolution transmission electron microscopy (HRTEM), scanning transmission electron microscopy (STEM) and analyzed by energy dispersive X-ray spectroscopy (EDS) in SEM and TEM and Fast Fourier Transform (FFT). The thickness of the interface region, together with its microstructural and mechanical characteristics, is affected by the use of Ni/Al multilayers; which promote joints with lower hardness values, closer to the values of the base materials, and exhibit higher shear strength. - Highlights: • Dissimilar joining by a reaction-assisted diffusion bonding were studied. • Ni/Al nanolayers allows join TiAl to steel in less demanding processing conditions. • The microstructural and mechanical characterization of the joints were investigated. • The fracture occurring in the TiAl base material attests to the sound joining. • Shear strength value decreases for joints with base materials without nanolayers.

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.

Application of laser diagnostics to sodium-water chemical reaction field

International Nuclear Information System (INIS)

Deguchi, Yoshihiro; Tamura, Kenta; Muranaka, Ryota; Kusano, Koji; Kikuchi, Shin; Kurihara, Akikazu

2013-01-01

In a sodium-cooled fast reactor (SFR), liquid sodium is used as a heat transfer fluid because of its excellent heat transport capability. On the other hand, it has strong chemical reactivity with water vapor. One of the design basis accidents of the SFR is the water leakage into the liquid sodium flow by a breach of heat transfer tubes in a steam generator. Therefore the study on sodium-water chemical reactions is of paramount importance for safety reasons. This study aims to clarify the sodium-water reaction mechanisms using laser diagnostics. The sodium-water counter-flow reactions were measured using laser diagnostics such as laser induced fluorescence, CARS, Raman scattering and photo-fragmentation. The measurement results show that the sodium-water reaction proceeds mainly by the reaction Na + H 2 O → NaOH + H and the main product is NaOH in this reaction. Its forward and backward reaction rates tend to balance with each other and the whole reaction rate reduces as temperature increases. (author)

Quantum indistinguishability in chemical reactions.

Science.gov (United States)

Fisher, Matthew P A; Radzihovsky, Leo

2018-05-15

Quantum indistinguishability plays a crucial role in many low-energy physical phenomena, from quantum fluids to molecular spectroscopy. It is, however, typically ignored in most high-temperature processes, particularly for ionic coordinates, implicitly assumed to be distinguishable, incoherent, and thus well approximated classically. We explore enzymatic chemical reactions involving small symmetric molecules and argue that in many situations a full quantum treatment of collective nuclear degrees of freedom is essential. Supported by several physical arguments, we conjecture a "quantum dynamical selection" (QDS) rule for small symmetric molecules that precludes chemical processes that involve direct transitions from orbitally nonsymmetric molecular states. As we propose and discuss, the implications of the QDS rule include ( i ) a differential chemical reactivity of para- and orthohydrogen, ( ii ) a mechanism for inducing intermolecular quantum entanglement of nuclear spins, ( iii ) a mass-independent isotope fractionation mechanism, ( iv ) an explanation of the enhanced chemical activity of "reactive oxygen species", ( v ) illuminating the importance of ortho-water molecules in modulating the quantum dynamics of liquid water, and ( vi ) providing the critical quantum-to-biochemical linkage in the nuclear spin model of the (putative) quantum brain, among others.

Chemical reactions inside the plasma chamber of the SEAFP reactor plant models

International Nuclear Information System (INIS)

Gay, J.M.; Ebert, E.; Mazille, F.

1995-01-01

Loss of coolant or loss of vacuum accidents may lead to chemical reactions between the protecting materials of the plasma facing components and air or water. A production of energy, reaction products and hydrogen may be induced. The paper defines the operating conditions and chemical reactions and presents the main results from the underlying studies. (orig.)

Chemical Reactions at Surfaces. Final Progress Report

Energy Technology Data Exchange (ETDEWEB)

Freud, Hans-Joachim [Max-Planck-Gesellschaft, Berlin (Germany). Fritz-Haber-Inst.

2003-02-21

The Gordon Research Conference (GRC) on Chemical Reactions at Surfaces was held at Holiday Inn, Ventura, California, 2/16-21/03. Emphasis was placed on current unpublished research and discussion of the future target areas in this field.

Determination of the diffusion coefficient of hydrogen ion in hydrogels.

Science.gov (United States)

Schuszter, Gábor; Gehér-Herczegh, Tünde; Szűcs, Árpád; Tóth, Ágota; Horváth, Dezső

2017-05-17

The role of diffusion in chemical pattern formation has been widely studied due to the great diversity of patterns emerging in reaction-diffusion systems, particularly in H + -autocatalytic reactions where hydrogels are applied to avoid convection. A custom-made conductometric cell is designed to measure the effective diffusion coefficient of a pair of strong electrolytes containing sodium ions or hydrogen ions with a common anion. This together with the individual diffusion coefficient for sodium ions, obtained from PFGSE-NMR spectroscopy, allows the determination of the diffusion coefficient of hydrogen ions in hydrogels. Numerical calculations are also performed to study the behavior of a diffusion-migration model describing ionic diffusion in our system. The method we present for one particular case may be extended for various hydrogels and diffusing ions (such as hydroxide) which are relevant e.g. for the development of pH-regulated self-healing mechanisms and hydrogels used for drug delivery.

Effects of Ramped Wall Temperature on Unsteady Two-Dimensional Flow Past a Vertical Plate with Thermal Radiation and Chemical Reaction

Directory of Open Access Journals (Sweden)

V. Rajesh

2014-08-01

Full Text Available The interaction of free convection with thermal radiation of a viscous incompressible unsteady flow past a vertical plate with ramped wall temperature and mass diffusion is presented here, taking into account the homogeneous chemical reaction of first order. The fluid is gray, absorbing-emitting but non-scattering medium and the Rosseland approximation is used to describe the radiative flux in the energy equation. The dimensionless governing equations are solved using an implicit finite-difference method of the Crank-Nicolson type, which is stable and convergent. The velocity profiles are compared with the available theoretical solution and are found to be in good agreement. Numerical results for the velocity, the temperature, the concentration, the local and average skin friction, the Nusselt number and Sherwood number are shown graphically. This work has wide application in chemical and power engineering and also in the study of vertical air flow into the atmosphere. The present results can be applied to an important class of flows in which the driving force for the flow is provided by combination of the thermal and chemical species diffusion effects.

Chemical Ligation Reactions of Oligonucleotides for Biological and Medicinal Applications.

Science.gov (United States)

Abe, Hiroshi; Kimura, Yasuaki

2018-01-01

Chemical ligation of oligonucleotides (ONs) is the key reaction for various ON-based technologies. We have tried to solve the problems of RNA interference (RNAi) technology by applying ON chemical ligation to RNAi. We designed a new RNAi system, called intracellular buildup RNAi (IBR-RNAi), where the RNA fragments are built up into active small-interference RNA (siRNA) in cells through a chemical ligation reaction. Using the phosphorothioate and iodoacetyl groups as reactive functional groups for the ligation, we achieved RNAi effects without inducing immune responses. Additionally, we developed a new chemical ligation for IBR-RNAi, which affords a more native-like structure in the ligated product. The new ligation method should be useful not only for IBR-RNAi but also for the chemical synthesis of biofunctional ONs.

NATO Advanced Research Workshop on The Theory of Chemical Reaction Dynamics

CERN Document Server

1986-01-01

The calculation of cross sections and rate constants for chemical reactions in the gas phase has long been a major problem in theoretical chemistry. The need for reliable and applicable theories in this field is evident when one considers the significant recent advances that have been made in developing experimental techniques, such as lasers and molecular beams, to probe the microscopic details of chemical reactions. For example, it is now becoming possible to measure cross sections for chemical reactions state selected in the vibrational­ rotational states of both reactants and products. Furthermore, in areas such as atmospheric, combustion and interstellar chemistry, there is an urgent need for reliable reaction rate constant data over a range of temperatures, and this information is often difficult to obtain in experiments. The classical trajectory method can be applied routinely to simple reactions, but this approach neglects important quantum mechanical effects such as tunnelling and resonances. For al...

Impulsive Synchronization of Reaction-Diffusion Neural Networks With Mixed Delays and Its Application to Image Encryption.

Science.gov (United States)

Chen, Wu-Hua; Luo, Shixian; Zheng, Wei Xing

2016-12-01

This paper presents a new impulsive synchronization criterion of two identical reaction-diffusion neural networks with discrete and unbounded distributed delays. The new criterion is established by applying an impulse-time-dependent Lyapunov functional combined with the use of a new type of integral inequality for treating the reaction-diffusion terms. The impulse-time-dependent feature of the proposed Lyapunov functional can capture more hybrid dynamical behaviors of the impulsive reaction-diffusion neural networks than the conventional impulse-time-independent Lyapunov functions/functionals, while the new integral inequality, which is derived from Wirtinger's inequality, overcomes the conservatism introduced by the integral inequality used in the previous results. Numerical examples demonstrate the effectiveness of the proposed method. Later, the developed impulsive synchronization method is applied to build a spatiotemporal chaotic cryptosystem that can transmit an encrypted image. The experimental results verify that the proposed image-encrypting cryptosystem has the advantages of large key space and high security against some traditional attacks.

The effects of a stress field and chemical diffusion on electronic behaviour in InAs/GaAs quantum dots