相关论文: Approximate third integrals for axisymmetric poten…
We present new equilibrium component distribution functions that depend on three analytic integrals in a Stackel potential, and that can be used to model stellar discs of galaxies. These components are generalizations of two-integral ones…
We develop an empirical potential for silicon which represents a considerable improvement over existing models in describing local bonding for bulk defects and disordered phases. The model consists of two- and three-body interactions with…
When using the boundary integral equation method to solve a boundary value problem, the evaluation of the solution near the boundary is challenging to compute because the layer potentials that represent the solution are nearly-singular…
This article is dedicated to research of approximation properties of B-splines and Lagrangian finite elements in Hilbert spaces of functions defined on surfaces in three-dimensional space. Hereinafter the conditions are determined for…
Analytical formulas for some useful three-particles integrals are derived. Many of these integrals include Bessel and/or trigonometric functions of one and two interparticle (relative) coordinates $r_{32}, r_{31}$ and $r_{21}$. The formulas…
We develop new methods for approximating conformal blocks as positive functions times polynomials, with applications to the numerical bootstrap. We argue that to obtain accurate bootstrap bounds, conformal block approximations should…
We present an approach to approximating rapidly the actions in a general triaxial potential. The method is an extension of the axisymmetric approach presented by Binney (2012), and operates by assuming that the true potential is locally…
Using lattice approximations of Euclidean space, we develop a way to approximate stable processes that are represented by stochastic integrals over Euclidean space. Via a stable version of the Lindeberg-Feller Theorem we show that the…
I report a study of the nonstationary one-dimensional Fokker-Planck solutions by means of the strictly isospectral method of supesymmetric quantum mechanics. The main conclusion is that this technique can lead to a space-dependent…
We discuss a novel approach that allows to obtain effective potentials from ab initio trajectories. Our method consists in fitting the weighted radial distribution functions obtained from the ab initio data with the ones obtained from…
A new scheme for constructing approximate effective electron potentials within density-functional theory is proposed. The scheme consists of calculating the effective potential for a series of reference systems, and then using these…
The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients of order three. We prove that this difference equation can be solved in general. Consequently we can find an exact solution to the…
In this work we develop an approach to obtain analytical expressions for potentials in an impenetrable box. It is illustrated through the particular cases of the harmonic oscillator and the Coulomb potential. In this kind of system the…
In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate…
We describe a novel technique that renders theories of $N$ axions tractable, and more generally can be used to efficiently analyze a large class of periodic potentials of arbitrary dimension. Such potentials are complex energy landscapes…
We present an efficient and robust semi-analytical formulation to compute the electric potential due to arbitrary-located point electrodes in three-dimensional cylindrically stratified media, where the radial thickness and the medium…
The problem of evaluating potential integrals on planar triangular elements has been addressed using a polar coordinate decomposition. The resulting formulae are general, exact, easily implemented, and have only one special case, that of a…
Symmetric elliptic integrals, which have been used as replacements for Legendre's integrals in recent integral tables and computer codes, are homogeneous functions of three or four variables. When some of the variables are much larger than…
We present numerical results showing how our recently proposed relativistic three-particle quantization condition can be used in practice. Using the isotropic (generalized $s$-wave) approximation, and keeping only the leading terms in the…
An efficient method is presented for solving axisymmetric, frictionless contact problems between a rigid punch and an elastically non-homogeneous, power-law graded half-space. Provided that the contact area is simply-connected profiles of…