Reaction-Diffusion Process Driven by a Localized Source: First Passage Properties
arXiv:1111.6207 · doi:10.1103/PhysRevE.85.031124
Abstract
We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We assume that initially only immobile atoms, uniformly distributed throughout the entire space, are present. Diffusing atoms are injected at the origin by a source which is turned on at time t=0. When a diffusing atom collides with an immobile atom, the two atoms form an immobile stable molecule. The region occupied by molecules is asymptotically spherical with radius growing as t^{1/d} in d>=2 dimensions. We investigate the survival probability that a diffusing atom has not become a part of a molecule during the time interval t after its injection and the probability density of such a particle. We show that asymptotically the survival probability (i) saturates in one dimension, (ii) vanishes algebraically with time in two dimensions (with exponent being a function of the dimensionless flux and determined as a zero of a confluent hypergeometric function), and (iii) exhibits a stretched exponential decay in three dimensions.
7 pages; version 2: section IV is re-written, references added, 8 pages (final version)
References in corpus (2)
Cited by in corpus (10)
- On the definition of the domain growth rate constant on a two dimensional substrate
- Reaction-Diffusion Processes with Nonlinear Diffusion
- Scaling theory for two-dimensional single domain growth driven by attachment of diffusing adsorbates
- Optimal recruitment strategies for groups of interacting walkers with leaders
- Stochastic Dynamics of Growing Young Diagrams and Their Limit Shapes
- First-passage-time statistics of a Brownian particle driven by an arbitrary unidimensional potential with a superimposed exponential time-dependent drift
- Aggregation Driven by a Localized Source
- Assortative Exchange Processes
- Diffusion in a fluid flow generated by a source at the apex of a wedge
- Dynamic Space Filling