Boundary effects in reaction-diffusion processes

Abstract

The effects of a boundary on reaction systems are examined in the framework of the general single-species reaction/coalescence process. The boundary naturally represents the reactants' container, but is applicable to exciton dynamics in a doped TMMC crystal. We show that a density excess, which extends into the system diffusively from the boundary, is formed in two dimensions and below. This implies a surprising result for the magnetisation near a fixed spin in the coarsening of the one-dimensional critical Ising model. The universal, dimensionally-dependent functional forms of this density excess are given by an exact solution and the field-theoretic renormalisation group.

References in corpus (4)

• Theory of Branching and Annihilating Random Walks
• Non-Markovian Persistence and Nonequilibrium Critical Dynamics
• Diffusion-limited annihilation in inhomogeneous environments
• Surface Critical Behavior in Systems with Absorbing States

Cited by in corpus (5)

• Phase transitions in autonomous reaction-diffusion systems on a one-dimensional lattice with boundaries
• Surface Critical Behavior in Systems with Non-Equilibrium Phase Transitions
• Dynamical phase transition in one-dimensional kinetic Ising model with nonuniform coupling constants
• One-dimensional kinetic Ising model with nonuniform coupling constants
• Multi-species reaction-diffusion models admitting shock solutions