Related papers: In a search for a shape maximizing packing fractio…
We study the packing of a large number of congruent and non--overlapping circles inside a regular polygon. We have devised efficient algorithms that allow one to generate configurations of $N$ densely packed circles inside a regular polygon…
Random sequential adsorption is an irreversible surface deposition of extended objects. In systems with continuous degrees of freedom coverage follows a power law, theta(t) = theta_J - c t^{-alpha}, where the exponent alpha depends on the…
This chapter introduces the use of X-ray absorption spectroscopy (XAS) in studying the local electronic and atomic structure of high-entropy materials. The element selectivity of XAS makes it particularly suitable to address the challenges…
Particle shape is a key to the space-filling and strength properties of granular matter. We consider a shape parameter $\eta$ describing the degree of distortion from a perfectly spherical shape. Encompassing most specific shape…
Predicting theoretically the highest density, which a disordered packing of discs can achieve, has been a long-standing unresolved problem. Such predictions are hindered by two difficulties - the dependence of the density on the packing…
Predicting the densest random disc packing fraction is an unsolved paradigm problem relevant to a number of disciplines and technologies. One difficulty is that it is ill-defined without setting a criterion for the disorder. Another is that…
Raman spectroscopy stands as a cornerstone technique for probing collective excitations and emergent quantum phases in solids. While polarization-resolved Raman scattering has been widely used to extract symmetry information of eigenmodes,…
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…
Dense, disordered packings of particles are useful models of low-temperature amorphous phases of matter, biological systems, granular media, and colloidal systems. The study of dense packings of nonspherical particles enables one to…
We investigate the problem of density estimation on the unit circle and the unit sphere from a computational perspective. Our primary goal is to develop new density estimators that are both rate-optimal and computationally efficient for…
In this paper I will approach the computation of the maximum density of regular lattices in large dimensions using a statistical mechanics approach. The starting point will be some theorems of Roger, which are virtually unknown in the…
We introduce a novel two-step approach for estimating a probability density function (pdf) given its samples, with the second and important step coming from a geometric formulation. The procedure involves obtaining an initial estimate of…
Dense hard-particle packings are intimately related to the structure of low-temperature phases of matter and are useful models of heterogeneous materials and granular media. Most studies of the densest packings in three dimensions have…
The structural study of entanglement in multipartite systems is hindered by the lack of necessary and sufficient operational criteria able to discriminate among the various entanglement properties of a given mixed state. Here, we pursue a…
Dense packings composed of irregular polyhedral particles are investigated by numerical simulations under quasistatic triaxial compression. The Contact Dynamics method is used for this investigation with 40 000 particles. The effect of…
The massive cost of 3D acquisition calls for methods to reduce the number of receivers by designing optimal receiver sampling masks. Recent studies on 2D seismic showed that maximizing the spectral gap of the subsampling mask leads to…
We construct the densest known two-dimensional packings of superdisks in the plane whose shapes are defined by |x^(2p) + y^(2p)| <= 1, which contains both convex-shaped particles (p > 0.5, with the circular-disk case p = 1) and…
The density profile of simulated dark matter structures is fairly well-established, and several explanations for its characteristics have been put forward. In contrast, the radial variation of the velocity anisotropy has still not been…
The isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics [Song \emph{et al.}, Nature (London) {\bf 453}, 629 (2008)] is generalized to arbitrary dimension $d$ using a liquid-state description. The…
We reveal the fractal nature of patterns arising in random sequential adsorption of particles with continuum power-law size distribution, $P(R)\sim R^{\alpha-1}$, $R \le R_{\rm max}$. We find that the patterns become more and more ordered…