Related papers: Numerical calculation of granular entropy
To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer…
The time decay of fully discrete finite-volume approximations of porous-medium and fast-diffusion equations with Neumann or periodic boundary conditions is proved in the entropy sense. The algebraic or exponential decay rates are computed…
By means of identical cubic elements, we generate a partition of a volume in which a particle-based cosmological simulation is carried out. In each cubic element, we determine the gas particles with a normalized density greater than an…
The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states $W(N)$ depends on the size $N$ of the system. Here we propose a scaling expansion of…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
The standard definition of particle number fluctuations based on point-like particles neglects the excluded volume effect. This leads to a large and systematic finite-size scaling and an unphysical surface term in the isothermal…
Studies on random packing of bidispersive particles have shown that such systems can capture the underlying behavior of more complex phenomena found in physics and materials engineering. In industry, bidispersive particles are used to allow…
There are a finite number of distinct mechanically stable (MS) packings in model granular systems composed of frictionless spherical grains. For typical packing-generation protocols employed in experimental and numerical studies, the…
In this paper, we demonstrate the efficiency of simulations via direct computation of the partition function under various macroscopic conditions, such as different temperatures or volumes. The method can compute partition functions by…
The concept of entropy connects the number of possible configurations with the number of variables in large stochastic systems. Independent or weakly interacting variables render the number of configurations scale exponentially with the…
We present a numerical simulation of a granular material using hydrodynamic equations. We show that, in the absence of external forces, such a system phase-separates into high density and low density regions. We show that this separation is…
Random packings of objects of a particular shape are ubiquitous in science and engineering. However, such jammed matter states have eluded any systematic theoretical treatment due to the strong positional and orientational correlations…
Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. They involve physics beyond the reach of equilibrium statistical…
The experiments conducted by various scientific groups indicate that, in dense two-dimensional systems of elongated particles subjected to vibration, the pattern formation is possible. Computer simulations have evidenced that the random…
We have performed a numerical simulation of a two-dimensional Eden model with random-size particles. In the present model, the particle radii are generated from a Gaussian distribution with mean $\mu$ and standard deviation $\sigma$. First,…
We consider a generic system composed of a fixed number of particles distributed over a finite number of energy levels. We make only general assumptions about system's properties and the entropy. System's constraints other than fixed number…
The entropies of molecules in solution are routinely calculated using gas phase formulae. It is assumed that, because implicit solvation models are fitted to reproduce free energies, this is sufficient for modeling reactions in solution.…
If a collection of identical particles is poured into a container, different shapes will fill to different densities. But what is the shape that fills a container as close as possible to a pre-specified, desired density? We demonstrate a…
We study the computational complexity of certain integrable quantum theories in 1+1 dimensions. We formalize a model of quantum computation based on these theories. In this model, distinguishable particles start out with known momenta and…
Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…