Memory in aged granular media

– Stimulated by recent experimental results, we simulate " temperature "-cycling experiments in a model for the compaction of granular media. We report on the existence of two types of memory effects: short-term dependence on the history of the sample, and long-term memory for highly compact (aged) systems. A natural interpretation of these results is provided by the analysis of the density heterogeneities. The study of the rheology of granular media represents nowadays an important chapter in the more general context of the so-called soft condensed matter [1]. The general questions one is interested in concern the response behaviour of a generic granular medium submitted to an external perturbation. In this spirit it has been recognized that the response of such systems depends in a non-trivial way on the mechanical properties of the grains composing the medium, on the boundary conditions, on the driving procedure (the way to inject energy to perturb the system) and, last but not the least, on the past history of the system, e.g. on the procedures the system has undergone until the moment we study it. In this context the similarities between granular media and the phenomenology of glassy systems have been exploited. One of the main results has been to recognize that in a compaction procedure, where a certain system increases its density if shaken or tapped, a granular medium displays ageing [2] and its properties, e.g. the two-times correlation function, depend on the time where one performs the measurement[3, 4], i.e. on the age of the system. The analogy with glassy systems has mainly allowed to export tools and techniques from one field to the other. Typical experiments on glassy systems consists in monitoring the effect of changes imposed to the external temperature on the macroscopic observables [5]. Translated in the framework of granular matter, i.e. of a non-thermal system, this means to analyse the effect of changes in the driving procedure, e.g. in the tapping amplitude Γ, which, in a typical compaction experiment, represents the control-parameter.