We propose a two-dimensional geometrical model that takes into account geometrical effects of frustration in the rearrangement processes in granular systems. In particular we related the microscopic motor of compaction to the need of cooperative rearrangements in order to find a better packing....

We analyze the non-equilibrium relaxation properties of granular materials in the perspective of a cooperative length approach of Adam and Gibbs. The existence of complex geometrical interactions between the grains induces a rough landscape in the structure of the allowable phase space and in...

We consider a Statistical Mechanics approach to granular systems by following the original ideas developed by Edwards. We use the concept of “inherent states”, defined as the stable configurations in the potential energy landscape, introduced in the context of glasses. Under simplifying...

We review the results of a statistical mechanics approach to granular materials and its extension to non-thermal systems in their “inherent states”. We introduce a “tapping” dynamics, based on a dynamics used for real granular matter, which allows to visit the space of the inherent...

We describe compaction and segregation in granular media in terms of microscopic lattice gas models in which the effects of geometric frustration play a crucial role. Then, exploiting the strong connections which appear with glass forming systems, we introduce a simplified master equation, based...

We study the dynamical properties of recently introduced frustrated lattice gas models (IFLG and Tetris) for granular media under gentle shaking. We consider both the case where grains have inter-grain surface interactions other than contact forces and the case where they have not,...

A Monte Carlo cluster dynamics is proposed for the fully frustrated XY model. The energy autocorrelation time results in systematically much smaller ones compared to that obtained with spin-flip Metropolis dynamics although the estimated dynamic critical exponent is not reduced. It is suggested...

The generalization of Kasteleyn and Fortuin clusters formalism is introduced in XY (or more generally O(n)) models. The clusters' geometrical structure may be linked to spin physical properties as correlation functions. To investigate percolative characteristics, the new cluster definition is...

We review the basic ideas which have been developed to characterize geometrically the equilibrium phase transitions. This approach elucidates many concepts like propagation of correlations, upper critical dimensionality, breakdown of hyperscaling, strong universality, and other basic ideas in...

Clusters in frustrated systems are studied in the context of the frustrated percolation model. This model, which contains frustration and connectivity as an essential ingredient, exhibits a large degree of complexity in both static and dynamics. The bond version of the model maps on the spin...