Granular Statistical Mechanics: Bridging Between Statics and Dynamics

A first-principles statistical mechanics is formulated for slow dense granular fluids, where prolonged intergranular contacts vitiate collision theory. The contacts are regarded as virtual particles, exchanged during the dynamics between different structure types.
These types, characterised by different mean coordination numbers, have different contact potentials, which are analogous to chemical potentials of reacting chemical species.
Significantly, this formalism converges to the connectivity-based static statistical mechanics when the motion stops, thus bridging between static and dynamic granular mechanics.

The theory is illustrated on a sheared granular system. Expectation values are derived for the mean and variance of the coordination number distribution, as well as a relation between the contact potentials and the shear rate.

References:

Blumenfeld et al., Phys. Rev. Lett. 116, 148001 (2016).
Blumenfeld et al., Phys. Rev. Lett., 119, 039802 (2017).
Amitai and Blumenfeld, Phys. Rev. E 95, 052905 (2017).
Blumenfeld, http://arxiv.org/abs/1603.02015.
<!--![endif]---->