Related papers: Minimum Energy Problem on the Hypersphere
Obtaining the rest mass of leptons with electric charge minus 1 is pursued by considering the existence of a medium made up of sub-quantum particles, called etherons, having a rest energy at the lowest limit which is possible in the…
Minimizing the so-called "Dirichlet energy" with respect to the domain under a volume constraint is a standard problem in shape optimization which is now well understood. This article is devoted to a prototypal non-linear version of the…
The Casimir-Polder and van der Waals interaction energy of an atom with infinitely thin sphere with finite conductivity is investigated in the framework of the hydrodynamic approach. We put the sphere into spherical cavity inside the…
Optimal packing of spheres in $\mathbb R^d$ is studied by optimization of the energy $E$ (effective conductivity) of composites with ideally conducting spherical inclusions. It is demonstrated that the minimum of $E$ over locations of…
We calculate the electric dipole moment (EDM) for the neutron in the framework of the minimal 3-3-1 model. We assume that the only source of $CP$ violation arises from a complex trilinear coupling constant and two complex vacuum expectation…
In "Classical Electrodynamics" (Jackson) a theorem is proved on the average of an electrostatic or magnetostatic field over a spherical volume. The proof of the theorem is based on an expansion in spherical harmonics and it is useful for…
This survey discusses recent developments in the context of spherical designs and minimal energy point configurations on spheres. The recent solution of the long standing problem of the existence of spherical $t$-designs on $\mathbb{S}^d$…
Using the method of retarded potentials approximate formulas are obtained that describe the electromagnetic field outside the relativistic uniform system in the form of a charged sphere rotating at a constant speed. For the near, middle and…
In the present paper we study the minimization of energy integrals on the sphere with a focus on an interesting clustering phenomenon: for certain types of potentials, optimal measures are discrete or are supported on small sets. In…
The exact solution for a static spherically symmetric field outside a charged point particle is found in a non-linear $U(1)$ gauge theory with a logarithmic Lagrangian. The electromagnetic self-mass is finite, and for a particular relation…
Various properties of the Misner-Sharp spherically symmetric gravitational energy E are established or reviewed. In the Newtonian limit of a perfect fluid, E yields the Newtonian mass to leading order and the Newtonian kinetic and potential…
The Brown-York quasi-local energy of a charged rotating black hole described by the Kerr-Newman metric and enclosed by a fixed-radius surface is computed. No further assumptions on the angular momentum or the radial coordinate in…
We reduce two-body problem to the one-body problem in general case of deformed Heisenberg algebra leading to minimal length.Two-body problems with delta and Coulomb-like interactions are solved exactly. We obtain analytical expression for…
The work investigate a static, isotropic and almost homogeneous Universe containing a real scalar field modeling the Dark-Energy (quintaessence) interacting with pressureless matter. It is argued that the interaction between matter and the…
We consider charged spherically symmetric static solutions of the Einstein-Maxwell equations with a positive cosmological constant $\Lambda$. If $r$ denotes the area radius, $m_g$ and $q$ the gravitational mass and charge of a sphere with…
We consider the Casimir effect for a sphere in front of a plane at finite temperature for scalar and electromagnetic fields and calculate the limiting cases. For small separation we compare the exact results with the corresponding ones…
The problem concerning the form of the electrostatic field potential of the infinite charged metallic plane contacting with the metallic sphere is solved. The distributions of the surface charge densities both on the plane and the sphere…
We show that the energy levels predicted by a 1/N-expansion method for an N-dimensional Hydrogen atom in a spherical potential are always lower than the exact energy levels but monotonically converge towards their exact eigenstates for…
The aim of this paper is to provide a complete analysis of the Coulomb equilibrium problem in the euclidean space $\mathbb{R}^d$, $d\geq2$, associated to the kernel $1/|x|^{d-2}$, with a non-convex external field created by an…
We study the minimizer of the electrostatic Born--Infeld energy \begin{equation*} \int_{\mathbb{R}^n}1-\sqrt{1-|D v|^2}\ dx-\int_{\mathbb{R}^n}\rho v\ dx, \end{equation*} which vanishes at infinity. We show that the minimizer $u$ is…