Related papers: Random Loose Packing in Granular Matter
We investigate what kind of images lie in the high-density regions of diffusion models. We introduce a theoretical mode-tracking process capable of pinpointing the exact mode of the denoising distribution, and we propose a practical…
Based on experiments of the compaction of granular materials under periodic shear of a packing of glass beads, a minimal model for the dynamics of the packing density as a function of time is proposed. First, a random ``energy landscape''…
We report experimental measurements of density waves in granular materials flowing down in a capillary tube. The density wave regime occurs at intermediate flow rates between a low density free fall regime and a high compactness slower…
We investigate the two-dimensional packing of extremely prolate (aspect ratio $\alpha=L/D>10$) granular materials, comparing experiments with Monte-Carlo simulations. The average packing fraction of particles with aspect ratio $\alpha=12$…
We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding…
We review results about the density of typical lattices in $R^n.$ They state that such density is of the order of $2^{-n}.$ We then obtain similar results for random packings in $R^n$: after taking suitably a fraction $\nu$ of a typical…
In this paper, we study the fully developed gravity-driven flow of granular materials between two inclined planes. We assume that the granular materials can be represented by a modified form of the second-grade fluid where the viscosity…
We provide a two dimensional deformation model to describe how soft squishy circular particles respond to external forces and collisions. This model involves formulating mathematical equations and algorithms for the shape of a deformed…
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…
The flow and deposition of polydisperse granular materials is simulated through the Magnetic Diffusion Limited Aggregation (MDLA) model. The random walk undergone by an entity in the MDLA model is modified such that the trajectories are…
In dense, static, polydisperse granular media under isotropic pressure, the probability density and the correlations of particle-wall contact forces are studied. Furthermore, the probability density functions of the populations of pressures…
The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 60's. This problem finds applications…
In general, the distribution of residuals cannot be obtained explicitly. We give an asymptotic formula for the density of Pearson residuals in continuous generalized linear models corrected to order $n^{-1}$, where $n$ is the sample size.…
We study the oscillations and conversions of relativistic neutrinos propagating in matter of variable density using the wave packet formalism. We show how the oscillation and coherence lengths are modified in comparison with the case of…
The dynamics of individual colloidal particles in random potential energy landscapes were investigated experimentally and by Monte Carlo simulations. The value of the potential at each point in the two-dimensional energy landscape follows a…
Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function of the particle arises from a kernel smoothing, and is associated with an…
We present here the preliminary results obtained for two experiments on randomly agitated granular assemblies using a novel way of shaking. First we discuss the transport properties of a 2D model system undergoing classical shaking that…
We introduce a simple family of models for representing the dark matter in galaxies. The potential and phase space distribution function are all elementary, while the density is cusped. The models are all hypervirial, that is, the virial…
We present a numerical study of a two dimensional granular medium consisting of hard inelastic disks. The evolution of the medium throughout a cooling process is monitored. Two different types of instabilities (shearing and clustering…
Several generalizations of the relativistic models of Burgers equations have recently been established and developed on different spacetime geometries. In this work, we take into account the de Sitter spacetime geometry, introduce our…