Boundary effects in reaction-diffusion processes

Details Boundary effects in reaction-diffusion processes Boundary effects in reaction-diffusion processes

1999-02-28

arxiv.org/abs/cond-mat/9903009v1

Phys. Rev. E 59 R4725-R4728 (1999)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.59.R4725

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.

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