Approach to Asymptotic Behaviour in the Dynamics of the Trapping Reaction

Abstract

We consider the trapping reaction A + B -> B in space dimension d=1, where the A and B particles have diffusion constants D_A, D_B respectively. We calculate the probability, Q(t), that a given A particle has not yet reacted at time t. Exploiting a recent formulation in which the B particles are eliminated from the problem we find, for t -> \infty, $Q(t)\sim \exp [-(4/\sqrt{\pi })({\rho }^2{D}_{B}t{)}^{1/2}-(C{\rho }^2{D}_{A}t{)}^{1/3}+...]$, where $\rho$ is the density of B particles and $C\propto D_A/D_B$ for $D_A/D_B<<1$.

8 pages, 2 figures; minor changes

References in corpus (6)

• Exact Asymptotics for One-Dimensional Diffusion with Mobile Traps
• Pascal Principle for Diffusion-Controlled Trapping Reactions
• Trapping Reactions with Randomly Moving Traps: Exact Asymptotic Results for Compact Exploration
• Survival probability of a diffusing particle in the presence of Poisson-distributed mobile traps
• Formal Solution of a Class of Reaction-Diffusion Models: Reduction to a Single-Particle Problem
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Cited by in corpus (5)

• Persistence and First-Passage Properties in Non-equilibrium Systems
• Survival probability of a diffusing particle constrained by two moving, absorbing boundaries
• Simulations for trapping reactions with subdiffusive traps and subdiffusive particles
• Spatial fluctuations of a surviving particle in the trapping reaction
• Survival probabilities in the double trapping reaction A +B -> B, B + C -> C