Anisotropic Diffusion-Limited Reactions with Coagulation and Annihilation

A two species reaction-diffusion model, in which particles diffuse on a one-dimensional lattice and annihilate when meeting each other, has been investigated. Mean field equations for general choice of reaction rates have been solved exactly. Cluster mean field approximation of the model is also studied. It is shown that, the general form of large time behavior of one- and two-point functions of the number operators, are determined by the diffusion rates of the two type of sp...

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 discuss the case of pure ballistic annihilation, that is a model in which each particle moves simultaneously at constant speed. We then review ballistic annihilation with superimposed diffusion in one dimension. This model consists of diffusing...

Some models of diffusion-limited reaction processes in one dimension lend themselves to exact analysis. The known approaches yield exact expressions for a limited number of quantities of interest, such as the particle concentration, or the distribution of distances between nearest particles. However, a full characterization of a particle system is only provided by the infinite hierarchy of multiple-point density correlation functions. We derive an exact description of the ful...

We investigate with the help of analytical and numerical methods the reaction A+A->A on a one-dimensional lattice opened at one end and with an input of particles at the other end. We show that if the diffusion rates to the left and to the right are equal, for large x, the particle concentration c(x) behaves like As/x (x measures the distance to the input end). If the diffusion rate in the direction pointing away from the source is larger than the one corresponding to the opp...

We study the kinetics of diffusion-limited coalescence, A+A->A, and annihilation, A+A->0, in random media consisting of disconnected domains of reaction. Examples include excitons fusion and annihilation in porous matrices and along polymer chains. We begin with an exact analysis of A+A->A in a finite segment. This result is applied to coalescence in a random distribution of segment lengths, and the implications for coalescence and annihilation in percolation clusters and oth...

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, with particle-dependent hopping rates, are investigated. In these models (i.e. reaction-diffusion and drop-push systems), we have the case of distinct particles where each particle $A_\alpha$ has its own intrinsic hopping rate $v_{\alpha}$....

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 large times. However, the decay exponent varies continuously as a function of the probability of which particle, the hopping one or the target, survives in the reaction. These results suggest that diffusion-limited reactions subject to dri...

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 isotropic and anisotropic diffusion (hopping with a drift) in 1d. We find that the particle density decays as a power-law for certain choices of the persistence parameter values. In the anisotropic case, on one symmetric line in the parameter s...

We study a two-species reaction-diffusion model where A+A->0, A+B->0 and B+B->0, with annihilation rates lambda0, delta0 > lambda0 and lambda0, respectively. The initial particle configuration is taken to be randomly mixed with mean densities nA(0) > nB(0), and with the two species A and B diffusing with the same diffusion constant. A field-theoretic renormalization group analysis suggests that, contrary to expectation, the large-time density of the minority species decays at...

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 simulations show that starting with an initially random distribution of A's and B's at equal concentration the density decays like t^{-1/3} for long times. This process is thus in a different universality class from the cases without drift or wi...