The Real-Space Renormalization Group Applied to Diffusion in Inhomogeneous Media

TL;DR

This paper introduces a real-space renormalization group method to compute effective diffusion constants in inhomogeneous media, facilitating numerical analysis and offering an alternative to singular perturbation techniques.

Contribution

It presents a novel application of real-space renormalization group to diffusion problems in inhomogeneous media, bridging analytical and numerical approaches.

Findings

Effective diffusion constants can be evaluated using the proposed RG method.

The method is compatible with numerical studies of PDEs.

It offers an alternative to singular perturbation techniques.

Abstract

The real-space renormalization group technique is introduced to evaluate the effective diffusion constant for diffusion in inhomogeneous media, which has been obtained by singular perturbation methods. Our method is formulated on a discretized real space and hence it can be easily combined with numerical studies for partial differential equations.