Related papers: N-sphere chord length distribution
In this note, we study the Gehring link problem in the round sphere, which motives our study of the width of a band in positively curved manifolds. Using the same idea, we are able to get a sphere theorem for hypersurface in in the round…
We establish a comprehensive probability theory for coherent transport of random waves through arbitrary linear media. The transmissivity distribution for random coherent waves is a fundamental B-spline with knots at the transmission…
A flexible model is developed for multivariate generalized spherical distributions, i.e. ones with level sets that are star shaped. To work in dimension above 2 requires tools from computational geometry and multivariate numerical…
A geometry-based density functional theory is presented for mixtures of hard spheres, hard needles and hard platelets; both the needles and the platelets are taken to be of vanishing thickness. Geometrical weight functions that are…
We consider an extremal problem for subsets of high-dimensional spheres that can be thought of as an extension of the classical isoperimetric problem on the sphere. Let $A$ be a subset of the $(m-1)$-dimensional sphere $\mathbb{S}^{m-1}$,…
We present an integral density method for calculating the multifractal dimension spectrum for the nucleon distribution in atomic nuclei. This method is then applied to analyze the non-uniformity of the density distribution in several…
We consider a 2D ballistic and quasi-ballistic structures with spin-orbit-related splitting of the electron spectrum. The ballistic region is attached to the leads with a voltage applied between them. We calculate the edge spin density…
Self-diffusion of a sphere in a network of rods is analyzed theoretically. Hydrodynamic interactions are taken into account according to the model of Dhont et al., under the assumption that $\ka << 1$ and $\bar{a}/L<<1$, where $1/\kappa$ is…
The propagation of SH waves in a solid containing a screen of line-like scatterers is investigated. When the scatterers are uniformly distributed, the amplitudes of the coherent waves inside and outside the screen are evaluated in closed…
We analyze the spectrum of collective modes in a superconductor in which pairing is mediated by long-range nematic fluctuations. Previous experimental and theoretical studies have found that the superconducting gap in such a system is…
We prove the following three statements: 1) Let $(A, \bar A)$ be a partition of the spherical surface $S^n$ into two measurable sets. Let $st_A$ and $st_{\bar A}$ be their measure density functions of distance. Then $|st_A - st_{\bar A}|$…
We consider the statistical analysis of data on high-dimensional spheres and shape spaces. The work is of particular relevance to applications where high-dimensional data are available--a commonly encountered situation in many disciplines.…
A coarse grained model for flexible polymers end-grafted to repulsive spherical nanoparticles is studied for various chain lengths and grafting densities under good solvent conditions, by Molecular Dynamics methods and density functional…
We consider temperate distributions on Euclidean spaces with uniformly discrete support and locally finite spectrum. We find conditions on coefficients of distributions under which they are finite sum of derivatives of generalized lattice…
When modeling directional data, that is, unit-norm multivariate vectors, a first natural question is to ask whether the directions are uniformly distributed or, on the contrary, whether there exist modes of variation significantly different…
An N-body hybrid simulation, integrating both massive and tracer particles, of a Galactic disk is used to study the stellar phase space distribution or velocity distributions in different local neighborhoods. Pattern speeds identified in…
Droplets of electrolyte solutions in an insulating medium are ubiquitous in nature. The net charges of these droplets are normally nonzero, and they fluctuate. However, a theory on the probability distribution function for the net charge of…
We theoretically determine the probability distribution function of the net field of the random planar structure of dipoles which represent polarized particles. At small surface concentrations c of the point dipoles this distribution is…
Each free homotopy class of directed closed curves on a surface with boundary can be described by a cyclic reduced word in the generators of the fundamental group and their inverses. The word length is the number of letters of the cyclic…
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…