Uninfected random walkers in one dimension

Abstract

We consider a system of unbiased diffusing walkers (A0 <-> 0A) in one dimension with random initial conditions. We investigate numerically the relation between the fraction of walkers, U(t), which have never encountered another walker up to time t, calling such walkers ``uninfected'' and the fraction of sites, P(t), which have never been visited by a diffusing particle. We extend our study to include the A + B -> 0 diffusion-limited reaction in one-dimension, with equal initial densities of A and B particles distributed homogeneously at t=0. We find U(t) \simeq [P(t)]^γ, with γ\simeq 1.39, in both models, though there is evidence that a smaller value of γis required for t -> infinity.

improved data analysis, some new figures

References in corpus (3)

• Persistence in the One-Dimensional A+B -> 0 Reaction-Diffusion Model
• Persistence in One-dimensional Ising Models with Parallel Dynamics
• Fraction of uninfected walkers in the one-dimensional Potts model

Cited by in corpus (6)

• Exact Asymptotics for One-Dimensional Diffusion with Mobile Traps
• Persistence properties of a system of coagulating and annihilating random walkers
• Segregation in diffusion-limited multispecies pair annihilation
• Fraction of uninfected walkers in the one-dimensional Potts model
• Persistence in Cluster--Cluster Aggregation
• Cluster persistence in one-dimensional diffusion--limited cluster--cluster aggregation