Spatial Organization in the Reaction A + B --> inert for Particles with a Drift

We describe the spatial structure of particles in 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. For the case of equal initial concentration, at long times, there are three relevant length scales: the typical distance between similar (neighboring) particles, the typical distance between dissimilar (neighboring) particles, and the typical size of a cluster of one type of particles. These length scales are found to be generically different than that found for particles without a drift.Comment: 10 pp of gzipped uuencoded postscrip

Exact solutions for a mean-field Abelian sandpile

We introduce a model for a sandpile, with N sites, critical height N and each site connected to every other site. It is thus a mean-field model in the spin-glass sense. We find an exact solution for the steady state probability distribution of avalanche sizes, and discuss its asymptotics for large N.Comment: 10 pages, LaTe

Two-Species Annihilation with Drift: A Model with Continuous Concentration-Decay Exponents

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 drift do not fall into a limited number of universality classes.Comment: 10 pages, tex, 3 figures, also available upon reques

Self Organization and a Dynamical Transition in Traffic Flow Models

A simple model that describes traffic flow in two dimensions is studied. A sharp {\it jamming transition } is found that separates between the low density dynamical phase in which all cars move at maximal speed and the high density jammed phase in which they are all stuck. Self organization effects in both phases are studied and discussed.Comment: 6 pages, 4 figure

Time-dependent correlation functions in a one-dimensional asymmetric exclusion process

We study a one-dimensional anisotropic exclusion process describing particles injected at the origin, moving to the right on a chain of $L$ sites and being removed at the (right) boundary. We construct the steady state and compute the density profile, exact expressions for all equal-time n-point density correlation functions and the time-dependent two-point function in the steady state as functions of the injection and absorption rates. We determine the phase diagram of the model and compare our results with predictions from dynamical scaling and discuss some conjectures for other exclusion models.Comment: LATEX-file, 32 pages, Weizmann preprint WIS/93/01/Jan-P

Kinetics of A+B--->0 with Driven Diffusive Motion

We study the kinetics of two-species annihilation, A+B--->0, when all particles undergo strictly biased motion in the same direction and with an excluded volume repulsion between same species particles. It was recently shown that the density in this system decays as t^{-1/3}, compared to t^{-1/4} density decay in A+B--->0 with isotropic diffusion and either with or without the hard-core repulsion. We suggest a relatively simple explanation for this t^{-1/3} decay based on the Burgers equation. Related properties associated with the asymptotic distribution of reactants can also be accounted for within this Burgers equation description.Comment: 11 pages, plain Tex, 8 figures. Hardcopy of figures available on request from S

Anisotropic Diffusion-Limited Reactions with Coagulation and Annihilation

One-dimensional reaction-diffusion models A+A -> 0, A+A -> A, and $A+B -> 0, where in the latter case like particles coagulate on encounters and move as clusters, are solved exactly with anisotropic hopping rates and assuming synchronous dynamics. Asymptotic large-time results for particle densities are derived and discussed in the framework of universality.Comment: 13 pages in plain Te

Effect of a columnar defect on the shape of slow-combustion fronts

We report experimental results for the behavior of slow-combustion fronts in the presence of a columnar defect with excess or reduced driving, and compare them with those of mean-field theory. We also compare them with simulation results for an analogous problem of driven flow of particles with hard-core repulsion (ASEP) and a single defect bond with a different hopping probability. The difference in the shape of the front profiles for excess vs. reduced driving in the defect, clearly demonstrates the existence of a KPZ-type of nonlinear term in the effective evolution equation for the slow-combustion fronts. We also find that slow-combustion fronts display a faceted form for large enough excess driving, and that there is a corresponding increase then in the average front speed. This increase in the average front speed disappears at a non-zero excess driving in agreement with the simulated behavior of the ASEP model.Comment: 7 pages, 7 figure

Two-way traffic flow: exactly solvable model of traffic jam

We study completely asymmetric 2-channel exclusion processes in 1 dimension. It describes a two-way traffic flow with cars moving in opposite directions. The interchannel interaction makes cars slow down in the vicinity of approaching cars in other lane. Particularly, we consider in detail the system with a finite density of cars on one lane and a single car on the other one. When the interchannel interaction reaches a critical value, traffic jam occurs, which turns out to be of first order phase transition. We derive exact expressions for the average velocities, the current, the density profile and the $k$- point density correlation functions. We also obtain the exact probability of two cars in one lane being distance $R$ apart, provided there is a finite density of cars on the other lane, and show the two cars form a weakly bound state in the jammed phase.Comment: 17 pages, Latex, ioplppt.sty, 11 ps figure

Asymptotic behavior of A + B --> inert for particles with a drift

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 with drift in different directions for the different species.Comment: LaTeX, 6pp including 3 figures in LaTeX picture mod