Related papers: Analytical potential-density pairs for bars
Particular solutions of the Poisson equation can be constructed via Newtonian potentials, integrals involving the corresponding Green's function which in two-dimensions has a logarithmic singularity. The singularity represents a significant…
The Kuzmin-Toomre family of discs is used to construct potential-density pairs that represent flat ring structures in terms of elementary functions. Systems composed of two concentric flat rings, a central disc surrounded by one ring and a…
Polarized ferrofluids, lipid monolayers and magnetic bubbles form domains with deformable boundaries. Stability analysis of these domains depends on a family of nontrivial integrals. We present a closed form evaluation of these integrals as…
A family of potential-density pairs that represent spherical shells with finite thickness is obtained from the superposition of spheres with finite radii. Other families of shells with infinite thickness with a central hole are obtained by…
We report a simple method to generate potential/surface density pairs in flat axially symmetric finite size disks. Potential/surface density pairs consist of a ``homogeneous'' pair (a closed form expression) corresponding to a uniform disk,…
The study of self-gravitating stellar systems has provided important hints to develop tools of analytical mechanics. In the present contribution we review how to exploit detuned resonant normal forms to extract information on several…
We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. Its generating function is applied to obtain an analytical result for a class of interesting integrals…
An analytical description of polymer melts and their mixtures as liquids of interacting soft colloidal particles is obtained from liquid-state theory. The derived center-of-mass pair correlation functions with no adjustable parameters…
In this paper we present a method of characteristic sets for inversive difference polynomials and apply it to the analysis of systems of quasi-linear algebraic difference equations. We describe characteristic sets and compute difference…
The mathematical theory of integrable Painleve/Toda type systems sheds new light on the behavior of solutions to the Poisson-Boltzmann equation for the potential due to a long rod-like macroion. We investigate here the case of symmetric…
An efficient integral equation based solver is constructed for the electrostatic problem on domains with cuboidal inclusions. It can be used to compute the polarizability of a dielectric cube in a dielectric background medium at virtually…
The interaction between two particles with shape or interaction anisotropy can be modeled using a pairwise potential energy function that depends on their relative position and orientation; however, this function is often challenging to…
We propose a density functional to find the ground state energy and density of interacting particles, where both the density and the pair density can adjust in the presence of an inhomogeneous potential. As a proof of principle we formulate…
We solve the Schr\"odinger-Newton problem of Newtonian gravity coupled to a nonrelativistic scalar particle for solutions with axial symmetry. The gravitational potential is driven by a mass density assumed to be proportional to the…
Special bases of orthogonal polynomials are defined, that are suited to expansions of density and potential perturbations under strict particle number conservation. Particle-hole expansions of the density response to an arbitrary…
A linear density of mass is assumed uniformly distributed along an infinitely long straight line. All possible motions of a test particle are described, under the newtonian logarithmic gravitational potential alone. Those most interesting…
Einstein field equations for anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities.…
We adapt the well known "displace, cut and reflect" method to construct exact solutions of the Einstein-Maxwell equations corresponding to infinitesimally thin disks of matter endowed with dipole magnetic fields, which are entirely…
We review the current status of one dimensional periodic potentials and also present several new results. It is shown that using the formalism of supersymmetric quantum mechanics, one can considerably enlarge the limited class of…
Using a suitable Laguerre basis set that ensures a tridiagonal matrix representation of the reference Hamiltonian, we were able to evaluate in closed form the matrix representation of the associated Hamiltonian for few exactly solvable 2D…