Related papers: A simple method to construct exact density-potenti…
Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials.…
The fundamental measure approach to classical density functional theory has been shown to be a powerful tool to predict various thermodynamic properties of hard-sphere systems. We employ this approach to determine not only one-particle…
We obtain a full asymptotic expansion for orthogonal polynomials with respect to weighted area measure on a Jordan domain $\mathscr{D}$ with real-analytic boundary. The weight is fixed and assumed to be real-analytically smooth and strictly…
Optimized stellarator configurations and their analytical properties are obtained using a near-axis expansion approach. Such configurations are associated with good confinement as the guiding center particle trajectories and neoclassical…
This article tackles the problem of the classification of expansive homeomorphisms of the plane. Necessary and sufficient conditions for a homeomorphism to be conjugate to a linear hyperbolic automorphism will be presented. The techniques…
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field equations sourced by a topological defect, \ie~a singularity of a very specific form, the result is a localised…
We have derived exact axisymmetric solutions of the two-dimensional Lane-Emden equations with rotation. These solutions are intrinsically favored by the differential equations regardless of any adopted boundary conditions and the physical…
We give a method to compute the smooth part of the density of states in a semi-classical expansion, when the Hamiltonian contains a Coulomb potential and non-cartesian coordinates are appropriate. We apply this method to the case of the…
As the generalization of gravitational effects on the point mass systems, we want to study the tidal effect exerted on an extended stellar system using spherical and axisymmetric elliptical models. Considering the Isochrone and Plummer…
A complete and consistent inversion technique is proposed to derive an accurate interaction potential from an effective-range function for a given partial wave in the neutral case. First, the effective-range function is Taylor or Pad\'e…
Topological structures of electromagnetic fields could give access to nontrivial light-matter interactions and additional degrees of freedom for information and energy transfer. A characteristic example of such electromagnetic excitations…
Solitons in one-dimensional parity-time (PT)-symmetric periodic potentials are studied using exponential asymptotics. The new feature of this exponential asymptotics is that, unlike conservative periodic potentials, the inner and outer…
Relativistic thick ring models are constructed using previously found analytical Newtonian potential-density pairs for flat rings and toroidal structures obtained from Kuzmin-Toomre family of discs. In particular, we present systems with…
A new form to construct complex superpotentials that produce real energy spectra in supersymmetric quantum mechanics is presented. This is based on the relation between the nonlinear Ermakov equation and a second order differential equation…
We study dynamical models for elliptical galaxies, deriving the projected kinematic profiles in a form that is valid for general surface-brightness profiles and (spherical) total mass profiles, without the need for any explicit…
We present a simple, closed form expression for the potential of an axisymmetric disk of stars interacting through gravitational potentials of the form $V(r)=-\beta /r+\gamma r/2$, the potential associated with fundamental sources in the…
A transitional layer matching the asymptotically flat exterior of a charged, massive toroidal body to an interior with spatially cylindrical symmetry is described. The changes in the geometry, which by themselves would require an energy…
We use the weighted integral form of spherical Bessel functions, and introduce a new analytical set of complete and biorthogonal potential--density basis functions. The potential and density functions of the new set have finite central…
Polymer self-consistent field theory techniques are used to find radial electron densities and total binding energies for isolated atoms. Quantum particles are modelled as Gaussian threads with ring-polymer architecture in a four…
The phase-space structure of two families of galactic potentials is approximated with a resonant detuned normal form. The normal form series is obtained by a Lie transform of the series expansion around the minimum of the original…