Related papers: A Percolating Hard Sphere Model
We consider Poisson's equation on the $n$-dimensional sphere in the situation where the inhomogeneous term has zero integral. Using a number of classical and modern hypergeometric identities, we integrate this equation to produce the form…
We discuss how the kernel convolution approach can be used to accurately approximate the spatial covariance model on a sphere using spherical distances between points. A detailed derivation of the required formulas is provided. The proposed…
We analyze the critical connectivity of systems of penetrable $d$-dimensional spheres having size distributions in terms of weighed random geometrical graphs, in which vertex coordinates correspond to random positions of the sphere centers…
We devote this paper to the issue of existence of pulsating travelling front solutions for spatially periodic heterogeneous reaction-diffusion equations in arbitrary dimension, in both bistable and more general multistable frameworks. In…
We consider the unrestricted problem of two mutually attracting rigid bodies, an uniform sphere (or a point mass) and an axially symmetric body. We present a global, geometric approach for finding all relative equilibria (stationary…
In this exploratory article, we present a constructive method for scattering points on the surface of $d$ dimensional spheres which we believe is new and of interest. Indeed, the problem of uniformly distributing points on spheres is an…
A direct analog of Hadamard's three-circle theorem is obtained for harmonic functions (in weighted L^2-norm) in case of (n-1)-dimensional non-concentric spheres in R^n. The result extends the concentric case to correlated non-concentric,…
Uniformly distributed point sets on the unit sphere with and without symmetry constraints have been found useful in many scientific and engineering applications. Here, a novel variant of the Thomson problem is proposed and formulated as an…
This article is covered by the article arxiv.1012.0925 We study intersection of two polyhedral spheres without self-intersections in 3-space. We find necessary and sufficient conditions on sequences x = x_1,x_2,...,x_n, y = y_1,y_2,...,y_n…
Is there a translation-bounded measure whose diffraction is spherically symmetric and concentrated on a single sphere? This note constructively answers this question of Strungaru in the affirmative.
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…
In [EH89, Theorem 1] Ekeland-Hofer prove that for a centrally symmetric, restricted contact type hypersurface in R^{2n} and for any global, centrally symmetric Hamiltonian perturbation there exists a leaf-wise intersection point. In this…
We give a geometrically exact treatment of percolation through voids around assemblies of randomly placed impermeable barrier particles, introducing a computationally inexpensive approach to finding critical barrier density thresholds…
Let $\Sigma$ be a compact immersed stable capillary hypersurface in a wedge bounded by two hyperplanes in $\mathbb R^{n+1}$. Suppose that $\Sigma$ meets those two hyperplanes in constant contact angles and is disjoint from the edge of the…
The problem of finding a point in the intersection of closed sets can be solved by the method of alternating projections and its variants. It was shown in earlier papers that for convex sets, the strategy of using quadratic programming (QP)…
A generalized version of a well-known problem of D. G. Kendall states that the zero cell of a stationary Poisson hyperplane tessellation in ${\mathbb{R}}^d$, under the condition that it has large volume, approximates with high probability a…
The program of understanding Shape Theory layer by layer topologically and geometrically -- proposed in Part I -- is now addressed for 4 points in 1-$d$. Topological shape space graphs are far more complex here, whereas metric shape spaces…
We show that spheres in all dimensions $\geq3$ can be deformed to have diameter larger than the distance between any pair of antipodal points. This answers a question of Yurii Nikonorov.
We present a method to obtain upper bounds on covering numbers. As applications of this method, we reprove and generalize results of Rogers on economically covering Euclidean $n$-space with translates of a convex body, or more generally,…
The situation of the decay of the metastable phase on the several types of heterogeneous centers is described analytically. The total number of heterogeneous centers is supposed to be equal for different types. This description decomposes…