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Related papers: Reaction-Diffusion Processes with Nonlinear Diffus…

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Reaction-diffusion equations appear in biology and chemistry, and combine linear diffusion with different kind of reaction terms. Some of them are remarkable from the mathematical point of view, since they admit families of travelling waves…

Analysis of PDEs · Mathematics 2019-01-14 Alessandro Audrito

We study diffusion-reaction processes on periodic square planar lattices and simple cubic (sc) lattices. Considered first is a single diffusing reactant undergoing an irreversible reaction upon first encounter with a stationary co-reactant…

Statistical Mechanics · Physics 2018-08-22 E. Abad , T. Abil , A. Santos , J. J. Kozak

We simulate reaction-diffusion processes with discrete fields. We use a novel algorithm to simulate different autocatalytic processes with trace densities. Anderson localization with a diffusive potential is studied. A reaction-diffusion…

Condensed Matter · Physics 2009-09-25 Eldad Bettelheim , Benny Lehmann

We study the 1D kinetics of diffusion-limited coalescence and annihilation with back reactions and different kinds of particle input. By considering the changes in occupation and parity of a given interval, we derive sets of hierarchical…

Statistical Mechanics · Physics 2009-11-07 E. Abad , T. Masser , D. ben-Avraham

We focus on the spreading properties of solutions of monostable equations with fast diffusion. The nonlinear reaction term involves a weak Allee effect, which tends to slow down the propagation. We complete the picture of [3] by studying…

Analysis of PDEs · Mathematics 2018-09-20 Matthieu Alfaro , Thomas Giletti

This paper is concerned with the transient dynamics described by the solutions of the reaction-diffusion equations in which the reaction term consists of a combination of a superlinear power-law absorption and a time-independent point…

Analysis of PDEs · Mathematics 2015-11-10 Peter V. Gordon , Cyrill B. Muratov

Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…

Analysis of PDEs · Mathematics 2013-05-24 William R. Holmes

In this work, we consider a diffusive two-species d-dimensional model and study it in great details. Two types of particles, with hard-core, diffuse symmetrically and cross each other. For arbitrary dimensions, we obtain the exact density,…

Statistical Mechanics · Physics 2009-11-07 M. Mobilia , P. -A. Bares

We study a family of interacting particle systems with annihilating and coalescing reactions. Two types of particles are interspersed throughout a transitive unimodular graph. Both types diffuse as simple random walks with possibly…

Probability · Mathematics 2025-11-04 Sungwon Ahn , Matthew Junge , Hanbaek Lyu , Lily Reeves , Jacob Richey , David Sivakoff

In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…

Dynamical Systems · Mathematics 2018-01-11 Wakil Sarfaraz , Anotida Madzvamuse

We study the steady state of a stochastic particle system on a two-dimensional lattice, with particle influx, diffusion and desorption, and the formation of a dimer when particles meet. Surface processes are thermally activated, with…

Statistical Mechanics · Physics 2015-05-30 A. Wolff , I. Lohmar , J. Krug , O. Biham

We consider reaction diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions. Under reasonable hypotheses, we establish the existence of component wise…

Analysis of PDEs · Mathematics 2020-05-05 Vandana Sharma

In this article we study a reaction diffusion system with $m$ unknown concentration. The non-linearity in our study comes from an underlying reversible chemical reaction and triangular in nature. Our objective is to understand the large…

Analysis of PDEs · Mathematics 2024-11-15 Saumyajit Das , Harsha Hutridurga

A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…

Materials Science · Physics 2008-09-04 Lynda Amirouche , Mathis Plapp

We study the kinetics of diffusion-limited coalescence, A+A->A, and annihilation, A+A->0, in random media consisting of disconnected domains of reaction. Examples include excitons fusion and annihilation in porous matrices and along polymer…

Statistical Mechanics · Physics 2009-10-31 Catalin Mandache , Daniel ben-Avraham

We establish the existence of solutions to a class of non-linear stochastic differential equation of reaction-diffusion type in an infinite-dimensional space, with diffusion corresponding to a given transition kernel. The solution obtained…

Probability · Mathematics 2021-08-10 Conrado da Costa , Bernardo Freitas Paulo da Costa , Daniel Valesin

We examine the long-time behaviour of A+B \to 0 reaction-diffusion systems with initially separated species A and B. All of our analysis is carried out for arbitrary (positive) values of the diffusion constant D_A of particles A and initial…

Statistical Mechanics · Physics 2015-06-25 Zbigniew Koza

The aim of this work is to study the effect of diffusion on the stability of the equilibria in a general two-components reaction-diffusion system with Neumann boundary conditions in the space of continuous functions. As by product, we…

Analysis of PDEs · Mathematics 2023-12-19 Francisco J. Vielma-Leal , Miguel A. D. R. Palma , Miguel Montenegro-Concha

We investigate the kinetics of many-species systems with aggregation of similar species clusters and annihilation of opposite species clusters. We find that the interplay between aggregation and annihilation leads to rich kinetic behaviors…

Condensed Matter · Physics 2009-10-28 E. Ben-Naim , P. L. Krapivsky

We investigate the long-time evolution of branching diffusion processes (starting with a single particle) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of the branching. We analyze the…

Probability · Mathematics 2012-07-03 Leonid Koralov , Stanislav Molchanov