Survival probability of a diffusing particle constrained by two moving, absorbing boundaries

Abstract

We calculate the exact asymptotic survival probability, Q, of a one-dimensional Brownian particle, initially located located at the point x in (-L,L), in the presence of two moving absorbing boundaries located at \pm(L+ct). The result is Q(y,λ) = \sum_{n=-\infty}^\infty (-1)^n \cosh(ny) \exp(-n^2λ), where y=cx/D, λ= cL/D and D is the diffusion constant of the particle. The results may be extended to the case where the absorbing boundaries have different speeds. As an application, we compute the asymptotic survival probability for the trapping reaction A + B -> B, for evanescent traps with a long decay time.

Major typo in abstract corrected, plus minor typos in main text

References in corpus (6)

• Exact Asymptotics for One-Dimensional Diffusion with Mobile Traps
• Pascal Principle for Diffusion-Controlled Trapping Reactions
• Formal Solution of a Class of Reaction-Diffusion Models: Reduction to a Single-Particle Problem
• The target problem with evanescent subdiffusive traps
• Survival Probability of a Ballistic Tracer Particle in the Presence of Diffusing Traps
• Approach to Asymptotic Behaviour in the Dynamics of the Trapping Reaction

Cited by in corpus (7)

• Persistence and First-Passage Properties in Non-equilibrium Systems
• The survival probability of a branching random walk in presence of an absorbing wall
• Non-crossing Brownian paths and Dyson Brownian motion under a moving boundary
• Brownian motion in time-dependent logarithmic potential: Exact results for dynamics and first-passage properties
• Survival of a diffusing particle in an expanding cage
• Sign-changes as a universal concept in first-passage time calculations
• Diffusion of particles in an expanding sphere with an absorbing boundary