Related papers: Granular entropy: Explicit calculations for planar…
A method is proposed for the characterisation of the entropy of cellular structures, based on the compactivity concept for granular packings. Hamiltonian-like volume functions are constructed both in two and in three dimensions, enabling…
We first show that the currently accepted statistical mechanics for granular matter is flawed. The reason is that it is based on the volume function, which depends only on a minute fraction of all the structural degrees of freedom and is…
We present numerical simulations that allow us to compute the number of ways in which $N$ particles can pack into a given volume $V$. Our technique modifies the method of Xu et al. (Phys. Rev. Lett. 106, 245502 (2011)) and outperforms…
We attempt to find a function that characterizes gravitational clumping and that increases monotonically as inhomogeneity increases. We choose $S = ln\Omega$ as the candidate ``gravitational entropy'' function, where $\Omega$ is the…
We introduce a "Hamiltonian"-like function, called the volume function, indispensable to describe the ensemble of jammed matter such as granular materials and emulsions from a geometrical point of view. The volume function represents the…
This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…
Microscopic formula to describe the entropy of biomolecular solutions are derived based on the Gibbs formula of entropy, and the generalized Langevin theory combined with the RISM/3D-RISM theory. Two formula are derived: one is concerned…
Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…
Granular matter is comprised of a large number of particles whose collective behavior determines macroscopic properties such as flow and mechanical strength. A comprehensive theory of the properties of granular matter, therefore, requires a…
We describe a maximum entropy approach for computing volumes and counting integer points in polyhedra. To estimate the number of points from a particular set X in R^n in a polyhedron P in R^n, by solving a certain entropy maximization…
Using X-ray tomography, we experimentally investigate granular packings subject to mechanical tapping for three types of beads with different friction coefficients. We validate Edwards volume ensemble in these three-dimensional granular…
It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a…
Thermal fluctuations are not large enough to lead to state changes in granular materials. However, such materials do achieve reproducible bulk properties, suggesting that they are controlled by an underlying statistical mechanics analogous…
We have derived an analytical formulation for estimating the volume of geometries enclosed by implicitly defined surfaces. The novelty of this work is due to two aspects. First we provide a general analytical formulation for all…
The nature of randomness in disordered packings of frictional and frictionless spheres is investigated using theory and simulations of identical spherical grains. The entropy of the packings is defined through the force and volume ensemble…
Fluctuating entropy production is studied for a set of linearly coupled complex fields. The general result is applied to non-equilibrium fluctuating hydrodynamic equations for coarse-grained fields (density, temperature and velocity), in…
A possible approach to the statistical description of granular assemblies starts from Edwards' assumption that all blocked states occupying the same volume are equally probable (S.F. Edwards, R. Oakeshott, Physica A 157, 1080 (1989)). We…
We investigate the nature of randomness in disordered packings of frictional spheres. We calculate the entropy of 3D packings through the force and volume ensemble of jammed matter, a mesoscopic ensemble and numerical simulations using…
Entropy functionals are computed for non-stationary distributions of particles of Lorentz gas and hard disks. The distributions consisting of beams of particles are found to have the largest amount of entropy and entropy increase. The…
We present an implementation in a linear-scaling density-functional theory code of an electronic enthalpy method, which has been found to be natural and efficient for the ab initio calculation of finite systems under hydrostatic pressure.…