Topological and Geometrical Random Walks on Bidisperse Random Sphere Packings

TL;DR

This paper investigates the properties of topological and geometrical random walks on contact graphs derived from bidisperse sphere packings, revealing a linear relationship between walk steps and Euclidean length.

Contribution

It introduces a novel analysis of random walks on contact graphs of bidisperse sphere packings, linking walk metrics to edge length probabilities.

Findings

Linear relationship between steps and Euclidean length of walks

Proportionality constant derived from edge length probabilities

Insights applicable to pharmaceutical science contact networks

Abstract

Motivated by a problem arising from pharmaceutical science [B. Baeumer et al., Discr. Contin. Dyn. Sys. B 12], we study random walks on the contact graph of a bidisperse random sphere packing. For a random walk on the unweighted graph that terminates in a specified target set, we compare the number of steps and the total euclidean length of the walk. We find a linear relationship between the two metrics with a proportionality constant that can be calculated from the edge length probabilities of the contact graph.