Statistical description of static granular systems in the arch ensemble

D. SLOBINSKY; L. PUGNALONI

LA PLATA

Conferencia; Pan-American Advanced Studies Institute (PASI) on Frontiers in Particulate Media: From Fundamentals to Applications; 2014

Pan-American Advanced Studies Institute

We propose a statistical framework to calculate the equilibrium macroscopic properties of static granular systems based on counting microscopic congurations in terms of arches. This arch ensemble exposes why previous attempts of using statistical mechanics partially failed. Using the arch ensemble, we obtain the exact density of states for a model of a granular assembly and calculate the arch size distribution, coordination number, and volume fluctuations; which show good agreement with simulation results of tapped two-dimensional systems. The model has a limiting case where it reduces to the analytically solved Bowles-Ashwin model for quasi-two-dimensional columns of frictionless disks. Interestingly, the arch ensemble is amenable of Monte Carlo type simulations such as the Wang-Landau sampling, which opens the way for a range of granular models to be studied via ensemble theory and the results contrasted against experiments.