Hysteresis in vibrated granular media

TL;DR

This paper analyzes a lattice model for granular media that exhibits hysteresis during compaction cycles, linking its behavior to experimental observations and the dynamics of structural glasses.

Contribution

It introduces a one-dimensional lattice model with dynamical constraints that reproduces hysteresis and reversible-irreversible behavior seen in experiments and glasses.

Findings

Model reproduces hysteresis cycles in granular compaction.

Behavior aligns with experimental reversible-irreversible branches.

Hysteresis explained via the model's dynamical properties and normal solutions.

Abstract

Some general dynamical properties of models for compaction of granular media based on master equations are analyzed. In particular, a one-dimensional lattice model with short-ranged dynamical constraints is considered. The stationary state is consistent with Edward's theory of powders. The system is submitted to processes in which the tapping strength is monotonically increased and decreased. In such processes the behavior of the model resembles the reversible-irreversible branches which have been recently obaserved in experiments. This behavior is understood in terms of the general dynamical properties of the model, and related to the hysteresis cycles exhibited by structural glasses in thermal cycles. The existence of a "normal" solution, i.e., a solution of the master equation which is monotonically approached by all the other solutions, plays a fundamental role in the understanding of the hysteresis effects.