English
Related papers

Related papers: A microscopic approach to nonlinear Reaction-Diffu…

200 papers

We consider a system of reaction-diffusion equations describing the reversible reaction of two species $\mathcal{U}, \mathcal{V}$ forming a third species $\mathcal{W}$ and vice versa according to mass action law kinetics with arbitrary…

Analysis of PDEs · Mathematics 2015-12-29 Klemens Fellner , El-Haj Laamri

The kinetics of the q species pair annihilation reaction (A_i + A_j -> 0 for 1 <= i < j <= q) in d dimensions is studied by means of analytical considerations and Monte Carlo simulations. In the long-time regime the total particle density…

Statistical Mechanics · Physics 2009-11-10 H. J. Hilhorst , O. Deloubriere , M. J. Washenberger , U. C. Tauber

We study the single-species diffusion-annihilation process with a time-dependent reaction rate, lambda(t)=lambda_0 t^-omega. Scaling arguments show that there is a critical value of the decay exponent omega_c(d) separating a…

Statistical Mechanics · Physics 2007-05-23 L. Turban

We investigate the long term behavior in terms of finite dimensional global and exponential attractors, as time goes to infinity, of solutions to a semilinear reaction-diffusion equation on non-smooth domains subject to nonlocal Robin…

Dynamical Systems · Mathematics 2016-07-20 Ciprian G. Gal , Mahamadi Warma

The multi-grid reaction-diffusion master equation (mgRDME) provides a generalization of stochastic compartment-based reaction-diffusion modelling described by the standard reaction-diffusion master equation (RDME). By enabling different…

Quantitative Methods · Quantitative Biology 2024-05-06 Radek Erban , Stefanie Winkelmann

We extend the energetic variational approach so it can be applied to a chemical reaction system with general mass action kinetics. Our approach starts with an energy-dissipation law. We show that the chemical equilibrium is determined by…

Chemical Physics · Physics 2021-01-04 Yiwei Wang , Chun Liu , Pei Liu , Bob Eisenberg

Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special…

Materials Science · Physics 2015-03-17 A. N. Gorban , H. P. Sargsyan , H. A. Wahab

We develop a micromorphic-based approach for finite element stabilization of reaction-convection-diffusion equations, by gradient enhancement of the field of interest via introducing an auxiliary variable. The well-posedness of the…

Mathematical Physics · Physics 2025-10-15 Soheil Firooz , B. Daya Reddy , Paul Steinmann

This paper treats the solvability of a semilinear reaction-diffusion system, which incorporates transport (diffusion) and reaction effects emerging from two separated spatial scales: $x$ - macro and $y$ - micro. The system's origin connects…

Analysis of PDEs · Mathematics 2012-02-10 Tasnim Fatima , Adrian Muntean , Toyohiko Aiki

The validity of two fundamental concepts of classical chemical kinetics - the notion of "Chemical Equilibrium" and the "Law of Mass Action" - are re-examined for reversible \textit{diffusion-limited} reactions (DLR), as exemplified here by…

Statistical Mechanics · Physics 2009-11-10 R. Voituriez , M. Moreau , G. Oshanin

A general phenomenological reaction-diffusion model for flow-induced phase transitions in complex fluids is presented. The model consists of an equation of motion for a nonconserved composition variable, coupled to a Newtonian stress…

Soft Condensed Matter · Physics 2009-11-07 J. L. Goveas , P. D. Olmsted

Q-conditional symmetries (nonclassical symmetries) for a general class of two-component reaction-diffusion systems with constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first type…

Mathematical Physics · Physics 2019-09-17 Roman Cherniha , Vasyl' Davydovych

Fully non-linear equations of motion for dissipative general relativistic multi-fluids can be obtained from an action principle involving the explicit use of lower dimensional matter spaces. More traditional strategies for incorporating…

General Relativity and Quantum Cosmology · Physics 2021-01-13 Thomas Celora , Nils Andersson , Greg L. Comer

In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional…

Chemical Physics · Physics 2019-11-05 Denis S. Grebenkov , Diego Krapf

The purpose of this article is to investigate the emergence of cross-diffusion in the time evolution of two slow-fast species in competition. A class of triangular cross-diffusion system is obtained as the singular limit of a fast…

Analysis of PDEs · Mathematics 2025-06-25 Elisabetta Brocchieri , Lucilla Corrias

Reaction-diffusion models are common in many areas of statistical physics, where they describe the late-time dynamics of chemical reactions. Using a Bose gas representation, which maps the real-time dynamics of the reactants to the…

Statistical Mechanics · Physics 2022-02-25 Johannes Hofmann

In this paper a reaction-diffusion type equation is the starting point for setting up a genuine thermodynamic reduction, i.e. involving a finite number of parameters or collective variables, of the initial system. This program is carried…

Mathematical Physics · Physics 2016-11-17 Franco Cardin , Marco Favretti , Alberto Lovison

We develop a convergent reaction-drift-diffusion master equation (CRDDME) to facilitate the study of reaction processes in which spatial transport is influenced by drift due to one-body potential fields within general domain geometries. The…

Numerical Analysis · Mathematics 2025-01-22 Samuel A. Isaacson , Ying Zhang

We study a p-adic reaction-diffusion system and the associated Turing patterns. We establish an instability criteria and show that the Turing patterns are not classical patterns consisting of alternating domains. Instead of this, a Turing…

Analysis of PDEs · Mathematics 2021-09-07 W. A. Zúñiga-Galindo

In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…

Statistical Mechanics · Physics 2015-05-14 Sven Dorosz , Michel Pleimling