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

Abstract

Fisher waves have been studied recently in the specific case of diffusion-limited reversible coalescence, A+A<-->A, 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.

5 pages, 2 figures, Revtex, submitted to Physics Letters A

Cited by in corpus (15)

• Front propagation into unstable states
• Effects of Fluctuations on Propagating Fronts
• Microscopic structure of travelling wave solutions in a class of stochastic interacting particle systems
• A Method of Intervals for the Study of Diffusion-Limited Annihilation, A + A --> 0
• Ecological Invasion, Roughened Fronts, and a Competitor's Extreme Advance: Integrating Stochastic Spatial-Growth Models
• An exactly soluble noisy traveling wave equation appearing in the problem of directed polymers in a random medium
• Reaction fronts in stochastic exclusion models with three-site interactions
• Emergence of pulled fronts in fermionic microscopic particle models
• Inhomogeneous Steady States of Diffusion-Limited Coalescence, A+A<-->A
• Branching Brownian motion with selection
• Front Propagation and Diffusion in the A <--> A + A Hard-core Reaction on a Chain
• Generalized von Smoluchowski model of reaction rates, with reacting particles and a mobile trap
• Velocity and diffusion coefficient of $A+A\leftrightarrow A$ reaction fronts in one dimension
• Fluctuating Fronts as Correlated Extreme Value Problems: An Example of Gaussian Statistics
• Phase transitions in a reaction-diffusion model on a line with boundaries