Competition effects in steady-state diffusion-limited reactions: Renormalization group approach

Abstract

We consider the steady-state competition between perfectly absorbing sinks distributed uniformly in a spherical region. An equation for the coarse-grained concentration of diffusing particles inside the region is derived following the renormalization group approach. The total flux of diffusing particles, their coarse-grained concentration, and the characteristic penetration length are found. We then compare our results with so-called mean field approximation, and show that the latter approach cannot correctly describe the coarse-grained concentration in the system under consideration. © 1996 American Institute of Physics.