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Due to significant computational expense, discrete element method simulations of jammed packings of size-dispersed spheres with size ratios greater than 1:10 have remained elusive, limiting the correspondence between simulations and…
Unraveling the complexities of random packing in three dimensions has long puzzled physicists. While both experiments and simulations consistently show a maximum density of 64 percent for tightly packed random spheres, we still lack an…
We investigate ordering properties of two-dimensional granular materials using several shapes created by welding ball bearings together. Ordered domains form much more easily in two than in three dimensions, even when configurations lack…
We consider random polytopes in the $d$-dimensional Euclidean space that are the convex hulls i.i.d. random points selected according to beta-prime distributions. These distributions are rotationally symmetric, heavy-tailed, and their…
This paper studies the limits of a spatial random field generated by uniformly scattered random sets, as the density $\lambda$ of the sets grows to infinity and the mean volume $\rho$ of the sets tends to zero. Assuming that the volume…
Using random walk simulations we explore diffusive transport through monodisperse sphere packings over a range of packing fractions, $\phi$, in the vicinity of the jamming transition at $\phi_{c}$. Various diffusion properties are computed…
Last years studies have shown that the spatial regularity in the distribution of young stellar population along the spiral arms and rings of galaxies, previously considered to be rare, is a fairly common phenomenon. Spatial regularity has…
We present a systematic investigation of the distribution of normal forces at the boundaries of static packings of spheres. A new method for the efficient construction of large hexagonal-close-packed crystals is introduced and used to study…
We use a hybrid Monte Carlo algorithm to simulate the shaking of spheres at different vibrational amplitudes, and find that spontaneous crystallisation occurs in specific dynamical regimes. Several crystallising transitions are typically…
Diffusion models have shown remarkable empirical success in sampling from rich multi-modal distributions. Their inference relies on numerically solving a certain differential equation. This differential equation cannot be solved in closed…
Motivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are consistent with the static…
Packing problems, even of objects with regular geometries, are in general non-trivial. For few special shapes, the features of crystalline as well as random, irregular two-dimensional (2D) packings are known. The packing of 2D crosses does…
This work analyzes the distribution and size of interparticle gaps arising in an ensemble of hexagonal unit structures in the xy plane when packing disks with a Gaussian distribution of radii with mean (r) and standard deviation $\Delta r$.…
We consider the distribution of cycles in two models of random permutations, that are related to one another. In the first model, cycles receive a weight that depends on their length. The second model deals with permutations of points in…
In "Dense Sphere Packings: A Blueprint for Formal Proofs" Hales proves that for every packing of unit spheres, the density in a ball of radius $r$ is at most $\pi/\sqrt{18}+c/r$ for some constant $c$. When $r$ tends to infinity, this gives…
We present a strategy for estimating the mass per unit length along supercluster-scale filaments that are oriented across the sky, based on mock redshift surveys of 264 filaments from the Millennium simulation. In our fiducial scenario, we…
We consider collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with a random perturbation (i.e. rotational fluctuation). They…
We extend the results previously published on exact packing dimensions of random recursive constructions to include constructions satisfying commonly occurring conditions. We remove the restrictive assumption that the diameter reduction…
Saturated random packing of particles built of two identical, relatively shifted spheres in two and three dimensional flat and homogeneous space was studied numerically using random sequential adsorption algorithm. The shift between centers…
The segment distribution around the center of gravity is derived for unperturbed ring polymers. We show that, although a small difference is observed, the exact distribution can be well approximated by the Gaussian probability distribution…