Related papers: The 5 Electron Case of Thomson's Problem
We propose a new formalism to analyse the extremum structure of scale-invariant effective potentials. The problem is stated in a compact matrix form, used to derive general expressions for the stationary point equation and the mass matrix…
We introduce a practical and efficient approach for calculating the all-electron full potential bandstructure in real space, employing a finite element basis. As an alternative to the k-space method, the method involves the self-consistent…
Let S be a triangulated 2-sphere with fixed triangulation T. We apply the methods of thin position from knot theory to obtain a simple version of the three geodesics theorem for the 2-sphere [5]. In general these three geodesics may be…
We explore BPS quivers for D=5 theories, compactified on a circle and geometrically engineered over local Calabi-Yau 3-folds, for which many of known machineries leading to (refined) indices fail due to the fine-tuning of the…
We present measurements of bias triangles in several biasing configurations. Thorough analysis of the data allows us to present data from all four possible bias configurations on a single plot in chemical potential space. This presentation…
In this study, we present a rigorous analytical proof of the uniqueness of central configurations for the five-body problem, assuming that all five masses are equal and positioned at the vertices of a planar polygon. We consider…
We devise variants of classical nonconforming methods for symmetric elliptic problems. These variants differ from the original ones only by transforming discrete test functions into conforming functions before applying the load functional.…
In the minimal scenario of quantum correlations, two parties can choose from two observables with two possible outcomes each. Probabilities are specified by four marginals and four correlations. The resulting four-dimensional convex body of…
A procedure for constructing bound state potentials is given. We show that, under the natural conditions imposed on a radial eigenvalue problem, the only special cases of the general central potential, which are exactly solvable and have…
In this paper, we study minimization problems among Bravais lattices for finite energy per point. We prove that if a function is completely monotonic, then the triangular lattice minimizes energy per particle among Bravais lattices with…
We derive a formally simple approximate analytical solution to the Poisson-Boltzmann equation for the spherical system via a geometric mapping. Its regime of applicability in the parameter space of the spherical radius and the surface…
Electron-electron correlation forms the basis of difficulties encountered in multi-electron systems. Accurate treatment of the correlation problem is likely to unravel some nice physical properties of matter embedded in this correlation. In…
The Electron Counting Capacitance Standard currently pursued at PTB aims to close the Quantum Metrological Triangle with a final precision of a few parts in 10^7. This paper reports the considerable progress recently achieved with a new…
The author suggests an approach based on the separation of total energy of multielectron systems into the semi-classical Coulomb part and the non-classical additional part. This approach allows on the one hand to simplify calculations and…
We introduce a circular restricted charged three-body problem on the plane. In this model, the gravitational and Coulomb forces, due to the primary bodies, act on a test particle; the net force exerted by some primary body on the test…
The present paper is devoted to studying of minimal parametric fillings of finite metric spaces (a version of optimal connection problem) by methods of Linear Programming. The estimate on the multiplicity of multi-tours appearing in the…
Meyerson's Theorem says that all but at most 2 points of any Jordan loop are vertices of inscribed equilateral triangles. We show that for any Jordan loop there are uncountable many other triangle shapes for which this same result is true.…
We establish the Gaussian Multi-Bubble Conjecture: the least Gaussian-weighted perimeter way to decompose $\mathbb{R}^n$ into $q$ cells of prescribed (positive) Gaussian measure when $2 \leq q \leq n+1$, is to use a "simplicial cluster",…
A generalized vector particle theory with the use of an extended set of Lorentz group irredicible representations, including scalar, two 4-vectors, and antisymmetric 2-rang tensor, is investigated. Initial equations depend upon four complex…
To advance Thomson problem we generalize physical principles suggested by Caspar and Klug (CK) to model icosahedral capsids. Proposed simplest distortions of the CK spherical arrangements yield new-type trial structures very close to the…