Related papers: Ballistic annihilation with superimposed diffusion…
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 kinetics of the annihilation process, $A+A\to 0$, with ballistic particle motion is investigated when the distribution of particle velocities is {\it discrete}. This discreteness is the source of many intriguing phenomena. In the mean…
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 propose a model for diffusion-limited annihilation of two species, $A+B\to A$ or $B$, where the motion of the particles is subject to a drift. For equal initial concentrations of the two species, the density follows a power-law decay for…
We consider a system of annihilating particles where particles start from the points of a Poisson process on either the full-line or positive half-line and move at constant i.i.d. speeds until collision. When two particles collide, they…
We consider the asymptotic behavior of the (one dimensional) two-species annihilation reaction A + B --> 0, where both species have a uniform drift in the same direction and like species have a hard core exclusion. Extensive numerical…
The behavior of the single-species reaction process $A+A\to O$ is examined near an impenetrable boundary, representing the flask containing the reactants. Two types of dynamics are considered for the reactants: diffusive and ballistic…
We consider a one-dimensional model consisting of an assembly of two-velocity particles moving freely between collisions. When two particles meet, they instantaneously annihilate each other and disappear from the system. Moreover each…
Infinitely many particles of two types ("plus" and "minus") jump randomly along the one-dimensional lattice $\mathbf{Z}_{\varepsilon}=\varepsilon\mathbf{Z}$. Annihillations occur when two particles of different time occupy the same site.…
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…
We consider ballistic annihilation, a model for chemical reactions first introduced in the 1980's physics literature. In this particle system, initial locations are given by a renewal process on the line, motions are ballistic - i.e. each…
The kinetics of single-species annihilation, $A+A\to 0$, is investigated in which each particle has a fixed velocity which may be either $\pm v$ with equal probability, and a finite diffusivity. In one dimension, the interplay between…
An exactly solvable reaction-diffusion model consisting of first-class particles in the presence of a single second-class particle is introduced on a one-dimensional lattice with periodic boundary condition. The number of first-class…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
We consider the diffusion-controlled annihilation dynamics $A+B\to 0$ with equal species diffusivities in the system where an island of particles $A$ is surrounded by the uniform sea of particles $B$. We show that once the initial number of…
Recently it has been shown that the transition of the 1+1-dimensional annihilation-fission process 2X->3X, 2X->0 exhibits an unusual type of nonequilibrium critical behavior. The phenomenological properties of critical clusters are…
Extensive simulations are performed of the diffusion-limited reaction A$+$B$\to 0$ in one dimension, with initially separated reagents. The reaction rate profile, and the probability distributions of the separation and midpoint of the…
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…
We study diffusion-controlled two-species annihilation with a finite number of particles. In this stochastic process, particles move diffusively, and when two particles of opposite type come into contact, the two annihilate. We focus on the…
The reaction process $A+B->C$ is modelled for ballistic reactants on an infinite line with particle velocities $v_A=c$ and $v_B=-c$ and initially segregated conditions, i.e. all A particles to the left and all B particles to the right of…