Analytic study of clustering in shaken granular material using zero-range processes

TL;DR

This paper demonstrates that models of granular clustering under vertical shaking can be understood as zero-range processes, enabling exact derivation of properties like particle distributions, phase diagrams, and clustering times.

Contribution

It establishes a direct correspondence between granular clustering models and zero-range processes, simplifying analysis and deriving key properties exactly.

Findings

Exact particle distribution functions derived

Phase diagram characterized

Characteristic clustering times calculated

Abstract

We show that models used to described granular clustering due to vertical shaking belong to the class of zero-range processes. This correspondence allows us to derive exactly in a very easy and straightforward manner a number of properties of the models like particle distribution functions, phase diagram, and characteristic time of clusterization.