Slow relaxation due to optimization and restructuring: Solution on a hierarchical lattice

TL;DR

This paper introduces a model for slow relaxation in granular materials, analyzing its behavior on hierarchical lattices, revealing ergodicity breakdown, size effects, and multifractal age distributions.

Contribution

It presents an exact asymptotic renormalization analysis of a new model combining optimization and restructuring, with insights into slow relaxation phenomena.

Findings

Breakdown of ergodicity observed

Unusual size effects in density development

Multifractal properties in age distribution

Abstract

Motivated by the large strain shear of loose granular materials we introduced a model which consists of consecutive optimization and restructuring steps leading to a self organization of a density field. The extensive connections to other models of statistical phyics are discussed. We investigate our model on a hierarchical lattice which allows an exact asymptotic renormalization treatment. A surprisingly close analogy is observed between the simulation results on the regular and the hierarchical lattices. The dynamics is characterized by the breakdown of ergodicity, by unusual system size effects in the development of the average density as well as by the age distribution, the latter showing multifractal properties.