Statistical mechanics as guidance for particle-based computational methods

IG Tejada and R Jimenez, ENGINEERING COMPUTATIONS, 30, 301-316 (2013).

DOI: 10.1108/02644401311304908

Purpose - The purpose of this paper is to show that there are some underlying principles of granular media that can be derived from statistical mechanics and that could be useful when considered in the context of computer simulations. Design/methodology/approach - The fundamentals of statistical mechanics are presented and they are revised in order to set up a suitable approach for jammed static granular media. After a conceptual discussion about the entropy of granular matter, some specific statistical mechanics approaches that have been used for granular media are reviewed. Finally, a numerical simulation, conducted using an open source molecular dynamics,code, is included as an illustrative example. Findings - It is shown qualitatively how statistical mechanics can be used to analytically compute the expected statistical distribution of some quantities in numerical simulations. Research limitations/implications - The computation of entropy from histograms and the establishment of the constraints of the ensembles in simulations are still open issues. Practical implications - Considering the entropy could set up new computational techniques. Initial arrangements could be analyzed in terms of their probability of occurrence and of their "distance" to the most probable state. Originality/value - The paper includes the distribution of the mean force-moment tensor component of a fast cyclic quasi isotropic compression process of a simple granular media. Results show how the system tends to an equilibrium state.

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