相关论文: Birthday Inequalities, Repulsion, and Hard Spheres
We develop a model to describe the properties of random assemblies of polydisperse hard spheres. We show that the key features to describe the system are (i) the dependence between the free volume of a sphere and the various coordination…
We study the statistical geometry of random chords on n-dimensional spheres by deriving explicit analytical expressions for the chord length distribution and its associated structural properties. A critical threshold emerges at dimension…
We prove rigidity for hypersurfaces with boundary in the unit $(n+1)$-sphere with scalar curvature bounded below by $n(n-1)$. Under appropriate boundary conditions, the hypersurfaces are shown to be part of the equatorial spheres. The lower…
We review a virial-type estimate which bounds the strength of interaction for a gas of $N$ hard spheres (billiard balls) dispersing into Euclidean space $\mathbb{R}^d$. This type of estimate has been known for decades in the context of…
We study the random variable B(c,n), which counts the number of balls that must be thrown into n equally-sized bins in order to obtain c collisions. The asymptotic expected value of B(1,n) is the well-known $\sqrt{n\pi/2}$ appearing in the…
Using molecular-dynamics simulation, we have calculated the interfacial free energy, \gamma, between a hard-sphere fluid and hard spherical and cylindrical colloidal particles, as functions of the particle radius R and the fluid packing…
A celebrated result of Legendre and Gauss determines which integers can be represented as a sum of three squares, and for those it is typically the case that there are many ways of doing so. These different representations give collections…
We consider density estimators based on the nearest neighbors method applied to discrete point distibutions in spaces of arbitrary dimensionality. If the density is constant, the volume of a hypersphere centered at a random location is…
We compute analytically the joint probability density of eigenvalues and the level spacing statistics for an ensemble of random matrices with interesting features. It is invariant under the standard symmetry groups (orthogonal and unitary)…
We present high resolution 3-D simulations of the planet-disc interaction using smoothed particle hydrodynamics, to investigate the possibility of driving eccentricity growth by this mechanism. For models with a given disc viscosity (\alpha…
We have developed a simulation model to describe particle adsorption to and desorption from liquid interfaces. Using this model we formulate a closed interfacial equation of state for repulsive elastic spheres. The effect of a long-range…
We extend the insertion approach for calculating depletion potentials to the case of non-spherical solutes. Instead of a brute-force calculation we suggest to employ the recently developed curvature expansion of density profiles close to…
A stochastic birth-death competition model for particles with excluded volume is proposed. The particles move, reproduce, and die on a regular lattice. While the death rate is constant, the birth rate is spatially nonlocal and implements…
Computer simulations and theory are used to systematically investigate how the effective force between two big colloidal spheres in a sea of small spheres depends on the basic (big-small and small-small) interactions. The latter are modeled…
We generate non-lattice packings of spheres in up to 22 dimensions using the geometrical constraint satisfaction algorithm RRR. Our aggregated data suggest that it is easy to double the density of Ball's lower bound, and more tentatively,…
We investigate the effects on cosmological clustering statistics of empirical biasing, where the galaxy distribution is a local transformation of the present-day Eulerian density field. The effects of the suppression of galaxy numbers in…
The Euclidean concentration inequality states that, among sets with fixed volume, balls have $r$-neighborhoods of minimal volume for every $r>0$. On an arbitrary set, the deviation of this volume growth from that of a ball is shown to…
We study the sphere packing problem in Euclidean space where we impose additional constraints on the separations of the center points. We prove that any sphere packing in dimension $48$, with spheres of radii $r$, such that no two centers…
Let $P$ be a set of $n$ random points in $R^d$, generated from a probability measure on a $m$-dimensional manifold $M \subset R^d$. In this paper we study the homology of $U(P,r)$ -- the union of $d$-dimensional balls of radius $r$ around…
The Kneser-Poulsen conjecture says that if a finite collection of balls in a Euclidean (spherical or hyperbolic) space is rearranged so that the distance between each pair of centers does not increase, then the volume of the union of these…