Numerical study of the force network ensemble

Turning intractable counting into sampling: Computing the configurational entropy of three-dimensional jammed packings

We present a numerical calculation of the total number of disordered jammed configurations Ω of N repulsive, three-dimensional spheres in a fixed volume V. To make these calculations tractable, we increase the computational efficiency of the approach of Xu et al. [Phys. Rev. Lett. 106, 245502 (2011)10.1103/PhysRevLett.106.245502] and Asenjo et al. [Phys. Rev. Lett. 112, 098002 (2014)10.1103/PhysRevLett.112.098002] and we extend the method to allow computation of the configurational entropy as a function of pressure. The approach that we use computes the configurational entropy by sampling the absolute volume of basins of attraction of the stable packings in the potential energy landscape. We find a surprisingly strong correlation between the pressure of a configuration and the volume of its basin of attraction in the potential energy landscape. This relation is well described by a power law. Our methodology to compute the number of minima in the potential energy landscape should be applicable to a wide range of other enumeration problems in statistical physics, string theory, cosmology, and machine learning that aim to find the distribution of the extrema of a scalar cost function that depends on many degrees of freedom.

Regime transitions of granular flow in a shear cell: a micromechanical study

The regime transitions of granular flow in a model shear cell are investigated numerically with a stress-controlled boundary condition. The correlations between the elastically and kinetically scaled stresses and the packing fraction are examined, and two packing fractions (0.58 and 0.50) are identified for the quasistatic to intermediate and intermediate to inertial regime transitions. The profiles and structures of contact networks and force chains among particles in different flow regimes are investigated. It is shown that the connectivity (coordination number) among particles and the homogeneity in the shear flow increase as the system goes through the inertial, intermediate, and then quasistatic regimes, and there is only little variation in the internal structure after the system has entered the quasistatic regime. Short-range force chains start to appear in the inertial regime, which also depend on the magnitude of the shear rate. The percolation of system-spanning force chains through the whole system is a characteristic of the onset of the quasistatic regime, which happens at a packing fraction that is close to the glass transition, i.e., about random loose packing (0.58) but far below the isotropic quasistatic (athermal) jamming packing fraction of random close packing (0.64). The tails of the probability density distribution P(f) of the scaled normal contact forces for the flows in different regimes are quantified by a stretched exponential P(f)=exp(-cf^{n}) with a remarkable finding that n ∼ 1.1 may be a potential demarcation point separating the quasistatic regime and the inertial or intermediate regimes.