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Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…

Pattern Formation and Solitons · Physics 2021-05-14 Andrew L. Krause , Václav Klika , Philip K. Maini , Denis Headon , Eamonn A. Gaffney

We study the pairwise annihilation process $A+A\to$ inert of a number of random walkers, which originally are localized in a small region in space. The size of the colony and the typical distance between particles increases with time and,…

Statistical Mechanics · Physics 2007-05-23 Georg Foltin , Karin A. Dahmen , Nadav M. Shnerb

We investigate a fast-reaction--diffusion system modelling the effect of autotoxicity on plant-growth dynamics, in which the fast-reaction terms are based on the dichotomy between healthy and exposed roots depending on the toxicity. The…

Analysis of PDEs · Mathematics 2024-08-13 Jeff Morgan , Cinzia Soresina , Bao Quoc Tang , Bao-Ngoc Tran

By considering the master equation of the totally asymmetric exclusion process on a one-dimensional lattice and using two types of boundary conditions (i.e. interactions), two new families of the multi-species reaction-diffusion processes,…

Statistical Mechanics · Physics 2013-01-15 Yaghoob Naimi , Frinaz Roshani

The close similarity between the hierarchies of multiple-point correlation functions for the diffusion-limited coalescence and annihilation processes has caused some recent confusion, raising doubts as to whether such hierarchies uniquely…

Statistical Mechanics · Physics 2009-11-10 Eric Brunet , Daniel ben-Avraham

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

Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating problems of pattern robustness and selection, in addition to more realistic…

Pattern Formation and Solitons · Physics 2023-01-18 Andrew L. Krause , Eamonn A. Gaffney , Benjamin J. Walker

The single-species reaction-diffusion process $A+A\to O$ is examined in the presence of an uncorrelated, quenched random velocity field. Utilising a field-theoretic approach, we find that in two dimensions and below the density decay is…

Statistical Mechanics · Physics 2009-10-31 M. J. E. Richardson , John Cardy

One-dimensional reaction-diffusion systems are mapped through a similarity transformation onto integrable (and a priori non-stochastic) quantum chains. Time-dependent properties of these chemical models can then be found exactly. The…

Statistical Mechanics · Physics 2009-10-28 Malte Henkel , Enzo Orlandini , Jaime Santos

Using field-theoretic renormalization group methods the long-time behaviour of the A+B -> 0 annihilation reaction with equal initial densities n_A(0) = n_B(0) = n_0 in a quenched random velocity field is studied. At every point (x, y) of a…

Condensed Matter · Physics 2009-10-28 K. Oerding

We develop an effective numerical method of studying large-time properties of reversible reaction-diffusion systems of type A + B <-> C with initially separated reactants. Using it we find that there are three types of asymptotic reaction…

Statistical Mechanics · Physics 2009-11-10 Zbigniew Koza

We consider a reaction-diffusion process with retardation. The particles, immersed in traps initially, remain inactive until another particle is annihilated spontaneously with a rate $\lambda$ at a certain point $\vec x$. In that case the…

Statistical Mechanics · Physics 2015-06-25 Michael Schulz , Steffen Trimper , Knud Zabrocki

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 $d\leq 2$ the $B$ particle density decays with…

Statistical Mechanics · Physics 2020-02-10 Benjamin Vollmayr-Lee , Jack Hanson , R. Scott McIsaac , Joshua D. Hellerick

We consider the reaction zone that grows between separated regions of diffusing species $A$ and $B$ that react according to $mA+nB\to 0$, within the framework of the mean-fieldlike reaction-diffusion equations. For distances from the centre…

Condensed Matter · Physics 2009-10-22 Stephen Cornell , Zbigniew Koza , Michel Droz

We investigate the A+B=0 bimolecular chemical reaction taking place in low-dimensional spaces when the mobilities of the two reacting species are not equal. While the case of different reactant mobilities has been previously reported as not…

Statistical Mechanics · Physics 2015-06-11 Panos Argyrakis , Raoul Kopelman

We study the reaction-diffusion process $A+B\to \emptyset$ with injection of each species at opposite boundaries of a one-dimensional lattice and bulk driving of each species in opposing directions with a hardcore interaction. The system…

Statistical Mechanics · Physics 2009-10-28 M. J. E. Richardson , M. R. Evans

This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusion processes with killing on $[0,\infty)$. We obtain criteria for the exponential convergence to a unique quasi-stationary distribution in total…

Probability · Mathematics 2017-02-12 Nicolas Champagnat , Denis Villemonais

The trend to equilibrium for reaction-diffusion systems modelling chemical reaction networks is investigated, in the case when reaction processes happen on subsets of the domain. We prove the convergence to equilibrium by directly showing…

Analysis of PDEs · Mathematics 2024-12-17 Laurent Desvillettes , Kim Dang Phung , Bao Quoc Tang

We discuss a reaction-diffusion model in one dimension subjected to an external driving force. Each lattice site may be occupied by at most one particle. The particles hop with asymmetric rates (the sum of which is one) to the right or left…

Condensed Matter · Physics 2016-08-31 Jaime E. Santos , Gunter M. Schutz , Robin B. Stinchcombe

Diffusion is often accompanied by a reaction or sorption which can induce temperature inhomogeneities. Monte Carlo simulations of Lennard-Jones atoms in zeolite NaCaA are reported with a hot zone presumed to be created by a reaction. Our…

Statistical Mechanics · Physics 2019-05-15 A. V. Anil Kumar , S. Yashonath , G. Ananthakrishna