Related papers: Dense packings of hard circular arcs
This paper addresses the numerical computation of critical angles between two convex cones in finite-dimensional Euclidean spaces. We present a novel approach to computing these critical angles by reducing the problem to finding stationary…
When a single long piece of elastic wire is injected trough channels into a confining two-dimensional cavity, a complex structure of hierarchical loops is formed. In the limit of maximum packing density, these structures are described by…
Massive stars play an important role in the Universe. Unlike low-mass stars, the formation of these objects located at great distances is still unclear. It is expected to be governed by some combination of self-gravity, turbulence, and…
We examine the fluid phase behaviour of the binary mixture of hard superellipses using the scaled particle theory The superellipse is a general two dimensional convex object which can be tuned between circular and rectangular shapes…
We study the intrinsic shape and alignment of isodensities of galaxy cluster halos extracted from the MultiDark MDR1 cosmological simulation. We find that the simulated halos, are extremely prolate on small scales, and increasingly…
The densest local packings of N three-dimensional identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained for selected values of N up to N = 1054. In the predecessor to this paper…
Products and sums of random matrices have seen a rapid development in the past decade due to various analytical techniques available. Two of these are the harmonic analysis approach and the concept of polynomial ensembles. Very recently, it…
The strong lensing events that are observed in compact clusters of galaxies can, both statistically and individually, return important clues about the structural properties of the most massive structures in the Universe. Substantial work is…
Although high-order Maxwell integral equation solvers provide significant advantages in terms of speed and accuracy over corresponding low-order integral methods, their performance significantly degrades in presence of non-smooth…
Within the framework of hierarchical clustering scenarios, we investigate the consequences for the properties of virialized halos of the constraints provided by numerical simulations on the first few correlation functions. Thus, we show…
We present the results of a systematic search for gravitationally-lensed arcs in clusters of galaxies located in the Hubble Space Telescope Wide Field and Planetary Camera 2 data archive. By carefully examining the images of 128 clusters we…
The Kepler conjecture asserts that no packing of congruent balls in three-dimensional Euclidean space has density greater than that of the face-centered cubic packing. The original proof, announced in 1998 and published in 2006, is long and…
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
This paper demonstrates that random, independently chosen equi-dimensional subspaces with a unitarily invariant distribution in a real Hilbert space provide nearly tight, nearly equiangular fusion frames. The angle between a pair of…
This paper studies the computational difficulty of clustering problems that are defined directly on a continuous probability density. Rather than working with finite samples, we assume the density is given as a polynomial and ask whether it…
A shape of a combinatorial polytope is a convex embedding into Euclidean space. We provide necessary and sufficient conditions for a piecewise linear map between two shapes of the same polytope to be a compression (respectively a weak…
Using Monte Carlo simulation, we analyse the behaviour of two-dimensional hard rods in four different types of geometric confinement: (i) a slit pore where the particles are confined between two parallel walls with homeotropic anchoring;…
We studied the geometrical and topological rules underlying the dispositions and the size distribution of non-overlapping, polydisperse circle-packings. We found that the size distribution of circles that densely cover a plane follows the…
Advancements in the synthesis of faceted nanoparticles and colloids have spurred interest in the phase behavior of polyhedral shapes. Regular tetrahedra have attracted particular attention because they prefer local symmetries that are…
We study the entropy of a set of identical hard objects, of general shape, with each object pivoted on the vertices of a d-dimensional regular lattice of lattice spacing a, but can have arbitrary orientations. When the pivoting point is…