Related papers: Concentration for One and Two Species One-Dimensio…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
Different branching and annihilating random walk models are investigated by cluster mean-field method and simulations in one and two dimensions. In case of the A -> 2A, 2A -> 0 model the cluster mean-field approximations show diffusion…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
Reaction-diffusion systems, which consist of the reacting particles subject to diffusion process, constitute one of the common examples of non-linear statistical systems. In low space dimensions $d \leq 2$ the usual description by means of…
Reaction-diffusion systems with reversible reactions generically display power-law relaxation towards chemical equilibrium. In this work we investigate through numerical simulations aging processes that characterize the non-equilibrium…
We present an exact mapping between two simple spin models: the Fredrickson-Andersen (FA) model and a model of annihilating random walks with spontaneous creation from the vacuum, A+A <-> 0. We discuss the geometric structure of the mapping…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
In a recent paper, de Freitas et al. [Phys. Rev. E 61, 6330 (2000)] presented simulational results for the critical exponents of the two-species reaction-diffusion system A + B -> 2B and B -> A in dimension d = 1. In particular, the…
In this work, we study a $3\times 3$ triangular reaction-diffusion system. Our main objective is to understand the long time behaviour of solutions to this reaction-diffusion system when there are degeneracies. More precisely, we treat…
The dynamics of a coupled two-component nonequilibrium system is examined by means of continuum field theory representing the corresponding master equation. Particles of species A may perform hopping processes only when particles of…
We study diffusion-limited (on-site) pair annihilation $A+A\to 0$ and (on-site) fusion $A+A\to A$ which we show to be equivalent for arbitrary space-dependent diffusion and reaction rates. For one-dimensional lattices with nearest neighbour…
We consider a single species reaction diffusion system on a two dimensional lattice where the particles $A$ are biased to move towards their nearest neighbours and annihilate as they meet; $A + A \to \emptyset$. Allowing the bias to take…
We consider the coagulation dynamics A+A -> A and A+A <-> A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension. This scenario combines the "anomalous kinetics" and "anomalous diffusion" problems,…
We study diffusion-controlled single-species annihilation with a finite number of particles. In this reaction-diffusion process, each particle undergoes ordinary diffusion, and when two particles meet, they annihilate. We focus on spatial…
Using the Monte Carlo simulation method for bosonic reaction-diffusion systems introduced recently [S.-C. Park, Phys. Rev. E {\bf 72}, 036111 (2005)], one dimensional bosonic models are studied and compared to the corresponding Langevin…
We discuss stationary concentrations of reactants in an A + B -> 0 reaction under subdiffusion and show that they are described by stationary reaction-diffusion equations with a nonlinear diffusion term. We consider stationary profiles of…
In this article we review the problem of reaction annihilation $A+A \rightarrow \emptyset$ on a real lattice in one dimension, where $A$ particles move ballistically in one direction with a discrete set of possible velocities. We first…
The scaling exponent and scaling function for the 1D single species coagulation model $(A+A\rightarrow A)$ are shown to be universal, i.e. they are not influenced by the value of the coagulation rate. They are independent of the initial…
The $A + B\to 0$ diffusion-limited reaction, with equal initial densities $a(0) = b(0) = n_0$, is studied by means of a field-theoretic renormalization group formulation of the problem. For dimension $d > 2$ an effective theory is derived,…
In this paper, we study a parabolic reaction diffusion system with constraints that model biofilm growth. Within a unified framework encompassing multiple numerical schemes, we derive the first general convergence rates for approximating…