Related papers: Edwards Statistical Mechanics for Jammed Granular …
A Gamma-distribution based potential energy landscape (PEL) theory has recently been proposed for supercooled liquids and glasses. This new PEL theory introduces a singularity term in the equation of state (EoS) suitable for representing…
We address the statistical mechanics of randomly and permanently crosslinked networks. We develop a theoretical framework (vulcanization theory) which can be used to systematically analyze the correlation between the statistical properties…
Supercooled liquids and dense colloids exhibit anomalous behaviour known as "spatially heterogeneous dynamics" (SHD), which becomes increasingly pronounced with approach to the glass transition. Recently, SHD has been observed in confined…
Stochastic master equations are often used to describe conditional spin squeezing of atomic ensemble, but are limited so far to the systems with few atoms due to the exponentially increased Hilbert space. In this article, we present an…
Soft composite solids are made of inclusions dispersed within soft matrices. They are ubiquitous in nature and form the basis of many biological tissues. In the field of materials science, synthetic soft composites are promising candidates…
Dense particle packings acquire rigidity through a nonequilibrium jamming transition commonly observed in materials from emulsions to sandpiles. We describe athermal packings and their observed geometric phase transitions using fully…
A theory for jammed granular materials is developed with the aid of a nonequilibrium steady-state distribution function. The approximate nonequilibrium steady-state distribution function is explicitly given in the weak dissipation regime by…
Stochastic mechanics (SM), as proposed by Edward Nelson and others in the 20th century, aims to reconstruct quantum mechanics (QM) from a more fundamental theory of classical point particles interacting with a classical-like ether, where…
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
The Edwards hypothesis of ergodicity of blocked configurations for gently tapped granular materials is tested for abstract models of spin systems on random graphs and spin chains with kinetic constraints. The tapping dynamics is modeled by…
All ensembles of statistical mechanics are equivalent in the sense that they give the equivalent thermodynamic functions in the thermodynamic limit. However, when investigating microscopic structures in the first-order phase transition…
This review describes the diversity of jammed configurations attainable by frictionless convex nonoverlapping (hard) particles in Euclidean spaces and for that purpose it stresses individual-packing geometric analysis. A fundamental feature…
We investigate the existence of random close and random loose packing limits in two-dimensional packings of monodisperse hard disks. A statistical mechanics approach-- based on several approximations to predict the probability distribution…
Several mean-field theories predict that Hessian matrices of amorphous solids can be written by using the random matrix in the limit of the large spatial dimensions $d\to\infty$. Motivated by these results, we here propose a way to map a…
Granular materials, such as sand or grain, exhibit many structural and dynamic characteristics similar to those observed in molecular systems, despite temperature playing no role in their properties. This has led to an effort to develop a…
We discuss the statistical mechanics of granular matter and derive several significant results. First, we show that, contrary to common belief, the volume and stress ensembles are inter-dependent, necessitating the use of both. We use the…
Numerous soft materials jam into an amorphous solid at high packing fraction. This non-equilibrium phase transition is best understood in the context of a model system in which particles repel elastically when they overlap. Recently,…
The ideal glass, a disordered system of particles with zero configurational entropy, cannot be realized through thermal processes. Nevertheless, we present a method for constructing ideal jammed packings of soft spheres, and thus the zero…
Some general dynamical properties of models for compaction of granular media based on master equations are analyzed. In particular, a one-dimensional lattice model with short-ranged dynamical constraints is considered. The stationary state…
We introduce a general method to merge multidimensional equations of state (EoSs) by combining them in a two-fluid equilibrium statistical mixture in the grand canonical ensemble. The merged grand potential density $\omega$ is built…