Related papers: Asymptotics of solutions in nA+nB->C reaction Diff…
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,…
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…
The behaviour is investigated of solutions to a diffusion equation on the real line with nonlocal and singular reaction term, i.e., given by a Dirac source or sink at the origin. It gives a simplified representation of for example a control…
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…
We consider the trapping reaction A + B -> B in space dimension d<=2. By formally eliminating the B particles from the problem we derive an effective dynamics for the A particles from which the survival probability of a given A particle and…
We study front propagation in the reversible reaction-diffusion system A + A <-> A on a 1-d lattice. Extending the idea of leading particle in studying the motion of the front we write a master equation in the stochastically moving frame…
We show that the chemical reactions of the model systems of A+A->0 and A+B->0 when performed on scale-free networks exhibit drastically different behavior as compared to the same reactions in normal spaces. The exponents characterizing the…
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…
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…
We introduce a model of three-species two-particle diffusion-limited reactions A+B -> A or B, B+C -> B or C, and C+A -> C or A, with three persistence parameters (survival probabilities in reaction) of the hopping particle. We consider…
Diffusion-limited reaction A+A->inert with anisotropic hopping on the d=1 lattice, is solved exactly for a simultaneous updating, discrete time-step dynamics. Diffusion-dominated processes slow down as the anisotropy increases. For large…
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…
The phenomenon of burst nucleation in solution, in which a period of apparent chemical inactivity is followed by a sudden and explosive growth of nucleated particles from a solute species, has been given a widely accepted qualitative…
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…
We study asymptotic properties of the system of interacting diffusion particles on the real line which transfer a mass [arXiv:1408.0628]. The system is a natural generalization of the coalescing Brownian motions. The main difference is that…
In this paper we study nonnegative, measure valued solutions of the initial value problem for one-dimensional drift-diffusion equations when the nonlinear diffusion is governed by an increasing $C^1$ function $\beta$ with $\lim_{r\to…
There are two types $i=1,2$ of particles on the line $R$, with $N_{i}$ particles of type $i$. Each particle of type $i$ moves with constant velocity $v_{i}$. Moreover, any particle of type $i=1,2$ jumps to any particle of type $j=1,2$ with…
We look for similarity transformations which yield mappings between different one-dimensional reaction-diffusion processes. In this way results obtained for special systems can be generalized to equivalent reaction-diffusion models. The…
Noncolliding diffusion processes reported in the present paper are $N$-particle systems of diffusion processes in one-dimension, which are conditioned so that all particles start from the origin and never collide with each other in a finite…
The behavior of a confined spherical symmetric anomalous fluid under high external pressure was studied with Molecular Dynamics simulations. The fluid is modeled by a ore-softened potential with two characteristic length scales, which in…