Reaction spreading on percolating clusters

TL;DR

This paper studies reaction-diffusion processes on two-dimensional percolating structures, revealing power-law behaviors and traveling wave dynamics through numerical and analytical methods.

Contribution

It provides new insights into reaction spreading and front propagation on percolating clusters, combining numerical simulations with analytical estimates.

Findings

Reaction product grows as t^dl, with dl being the connectivity dimension.

A stationary traveling wave forms in percolating channels with computable speed and width.

Front speed is stable and predictable, while front width exhibits power-law fluctuations.

Abstract

Reaction-diffusion processes in two-dimensional percolating structures are investigated. Two different problems are addressed: reaction spreading on a percolating cluster and front propagation through a percolating channel. For reaction spreading, numerical data and analytical estimates show a power-law behavior of the reaction product as M(t) \sim t^dl, where dl is the connectivity dimension. In a percolating channel, a statistically stationary traveling wave develops. The speed and the width of the traveling wave are numerically computed. While the front speed is a low-fluctuating quantity and its behavior can be understood using a simple theoretical argument, the front width is a high-fluctuating quantity showing a power-law behavior as a function of the size of the channel