Response properties in a model for granular matter

TL;DR

This paper studies how granular materials respond to different driving procedures using the Random Tetris Model, highlighting the importance of inhomogeneities, history, and driving in understanding their behavior.

Contribution

It introduces a detailed analysis of response properties in a granular model, emphasizing the role of spatial inhomogeneities and history in compaction dynamics.

Findings

Inhomogeneities significantly affect response measurements.

History and driving procedures influence compaction behavior.

Spatial structures emerge during compaction, impacting response properties.

Abstract

We investigate the response properties of granular media in the framework of the so-called {\em Random Tetris Model}. We monitor, for different driving procedures, several quantities: the evolution of the density and of the density profiles, the ageing properties through the two-times correlation functions and the two-times mean-square distance between the potential energies, the response function defined in terms of the difference in the potential energies of two replica driven in two slightly different ways. We focus in particular on the role played by the spatial inhomogeneities (structures) spontaneously emerging during the compaction process, the history of the sample and the driving procedure. It turns out that none of these ingredients can be neglected for the correct interpretation of the experimental or numerical data. We discuss the problem of the optimization of the compaction process and we comment on the validity of our results for the description of granular materials in a thermodynamic framework.