Fisher Waves in the Diffusion-Limited Coalescence Process A+A<-->A

Fisher waves have been studied recently in the specific case of diffusion-limited reversible coalescence, A+AA, on the line. An exact analysis of the particles concentration showed that waves propagate from a stable region to an unstable region at constant speed, just as in Fisher's "mean-field" theory; but also that the wave front fails to retain its initial shape and instead it broadens with time. Our present analysis encompasses the full hierarchy of multiple-point density correlation functions, and thus it provides a complete exact description of the same system. We find that as the wave propagates, the particles in the stable phase remain distributed exactly as in their initial (equilibrium) state. On the other hand, the leading particle---the one at the edge of the wave---advances as a biased random walk, rather than simply linearly with time. Thus the shape of the wave remains actually constant, but it is the "noisy" propagation of the wave's edge that causes its apparent broadening.Comment: 5 pages, 2 figures, Revtex, submitted to Physics Letters

Large Scale Simulations of Two-Species Annihilation, A+B->0, with Drift

We present results of computer simulations of the diffusion-limited reaction process A+B->0, on the line, under extreme drift conditions, for lattices of up to 2^{27} sites, and where the process proceeds to completion (no particles left). These enormous simulations are made possible by the renormalized reaction-cell method (RRC). Our results allow us to resolve an existing controversy about the rate of growth of domain sizes, and about corrections to scaling of the concentration decay.Comment: 13 pages, RevTeX, Submitted to Physics Letters

On the Google-Fame of Scientists and Other Populations

We study the fame distribution of scientists and other social groups as measured by the number of Google hits garnered by individuals in the population. Past studies have found that the fame distribution decays either in power-law [arXiv:cond-mat/0310049] or exponential [Europhys. Lett., 67, (4) 511-516 (2004)] fashion, depending on whether individuals in the social group in question enjoy true fame or not. In our present study we examine critically Google counts as well as the methods of data analysis. While the previous findings are corroborated in our present study, we find that, in most situations, the data available does not allow for sharp conclusions.Comment: 6 pages, 1 figure, to appear in the proceedings of the 8th Granada seminar on Computational Physic

Entropy production in nonequilibrium steady states: A different approach and an exactly solvable canonical model

We discuss entropy production in nonequilibrium steady states by focusing on paths obtained by sampling at regular (small) intervals, instead of sampling on each change of the system's state. This allows us to study directly entropy production in systems with microscopic irreversibility, for the first time. The two sampling methods are equivalent, otherwise, and the fluctuation theorem holds also for the novel paths. We focus on a fully irreversible three-state loop, as a canonical model of microscopic irreversibility, finding its entropy distribution, rate of entropy pr oduction, and large deviation function in closed analytical form, and showing that the widely observed kink in the large deviation function arises solely f rom microscopic irreversibility.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

Compact directed percolation with movable partial reflectors

We study a version of compact directed percolation (CDP) in one dimension in which occupation of a site for the first time requires that a "mine" or antiparticle be eliminated. This process is analogous to the variant of directed percolation with a long-time memory, proposed by Grassberger, Chate and Rousseau [Phys. Rev. E 55, 2488 (1997)] in order to understand spreading at a critical point involving an infinite number of absorbing configurations. The problem is equivalent to that of a pair of random walkers in the presence of movable partial reflectors. The walkers, which are unbiased, start one lattice spacing apart, and annihilate on their first contact. Each time one of the walkers tries to visit a new site, it is reflected (with probability r) back to its previous position, while the reflector is simultaneously pushed one step away from the walker. Iteration of the discrete-time evolution equation for the probability distribution yields the survival probability S(t). We find that S(t) \sim t^{-delta}, with delta varying continuously between 1/2 and 1.160 as the reflection probability varies between 0 and 1.Comment: 12 pages, 4 figure

Diffusion-Limited One-Species Reactions in the Bethe Lattice

We study the kinetics of diffusion-limited coalescence, A+A-->A, and annihilation, A+A-->0, in the Bethe lattice of coordination number z. Correlations build up over time so that the probability to find a particle next to another varies from \rho^2 (\rho is the particle density), initially, when the particles are uncorrelated, to [(z-2)/z]\rho^2, in the long-time asymptotic limit. As a result, the particle density decays inversely proportional to time, \rho ~ 1/kt, but at a rate k that slowly decreases to an asymptotic constant value.Comment: To be published in JPCM, special issue on Kinetics of Chemical Reaction