Related papers: Asymptotics of Reaction-Diffusion Fronts with One …
A diffusion-limited annihilation process, A+B->0, with species initially separated in space is investigated. A heuristic argument suggests the form of the reaction rate in dimensions less or equal to the upper critical dimension $d_c=2$.…
We examine the long time behaviour of A+B->0 reaction diffusion systems with initially segregated species A and B. All of our analysis is carried out for arbitrary (positive) values of the diffusion constants $D_A$, $D_B$, and initial…
We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We assume that initially only immobile atoms, uniformly distributed throughout the entire space, are present. Diffusing atoms are injected at…
We study various combinations of active diffusion with branching, as an extension of standard reaction-diffusion processes. We concentrate on the selection of the asymptotic wavefront speed for thermal run-and-tumble and for thermal active…
We study the asymptotic behaviour of sharp front solutions arising from the nonlinear diffusion equation \theta_t = (D(\theta)\theta_x)_x, where the diffusivity is an exponential function D({\theta}) = D_o exp(\beta\theta). This problem…
We consider the properties of the diffusion controlled reaction A+B->0 in the steady state, where fixed currents of A and B particles are maintained at opposite edges of the system. Using renormalisation group methods, we explicitly…
The empirical velocity of a reaction-diffusion front, propagating into an unstable state, fluctuates because of the shot noises of the reactions and diffusion. Under certain conditions these fluctuations can be described as a diffusion…
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…
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…
We have studied the front propagation in a one dimensional case of combustion by solving numerically an advection-reaction-diffusion equation. The physical model is simplified so that no coupling phenomena are considered and the reacting…
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to…
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…
The position of a reaction front, propagating into a metastable state, fluctuates because of the shot noise of reactions and diffusion. A recent theory [B. Meerson, P.V. Sasorov, and Y. Kaplan, Phys. Rev. E 84, 011147 (2011)] gave a closed…
We consider a reaction-diffusion equation in narrow random channels. We approximate the generalized solution to this equation by the corresponding one on a random graph. By making use of large deviation analysis we study the asymptotic wave…
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…
We study front propagation in the reaction diffusion process $\{A\stackrel{\epsilon}\to2A, A\stackrel {\epsilon_t}\to3A\}$ on a one dimensional (1d) lattice with hard core interaction between the particles. Using the leading particle…
We develop an analytical diffusion-equation-type approximation scheme for the one-dimensional coagulation reaction A+A->A with partial reaction probability on particle encounters which are otherwise hard-core. The new approximation…
Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
We study long-time properties of reversible reaction-diffusion systems of type A + B <-> C by means of perturbation expansion in powers of 1/t (inverse of time). For the case of equal diffusion coefficients we present exact formulas for the…
We study flow-induced enhancement of the speed of pulsating traveling fronts for reaction-diffusion equations, and quenching of reaction by fluid flows. We prove, for periodic flows in two dimensions and any combustion-type reaction, that…