Stochastic transport in the presence of spatial disorder: fluctuation-induced corrections to homogenization

TL;DR

This paper studies how spatial disorder and sink strength fluctuations affect particle transport, revealing that extrinsic noise causes long-range correlations and biases the mean concentration profile compared to classical homogenization.

Contribution

It introduces a stochastic homogenization approach that explicitly accounts for sink strength fluctuations and their impact on particle concentration in disordered transport systems.

Findings

Extrinsic noise induces long-range spatial correlations.

Mean concentration is elevated due to sink strength fluctuations.

Classical homogenization can bias the true mean concentration.

Abstract

Motivated by uncertainty quantification in natural transport systems, we investigate an individual-based transport process involving particles undergoing a random walk along a line of point sinks whose strengths are themselves independent random variables. We assume particles are removed from the system via first-order kinetics. We analyse the system using a hierarchy of approaches when the sinks are sparsely distributed, including a stochastic homogenization approximation that yields explicit predictions for the extrinsic disorder in the stationary state due to sink strength fluctuations. The extrinsic noise induces long-range spatial correlations in the particle concentration, unlike fluctuations due to the intrinsic noise alone. Additionally, the mean concentration profile, averaged over both intrinsic and extrinsic noise, is elevated compared with the corresponding profile from a uniform sink distribution, showing that the classical homogenization approximation can be a biased estimator of the true mean.