相关论文: Electrostatics of two-dimensional structures: exac…

We show that the method used in the Schwarzschild black hole for finding the elementary solution of the electrostatic equation in closed form cannot extend in higher dimensions. By contrast, we prove the existence of static, spherically…

We study the computation of equilibrium points of electrostatic potentials: locations in space where the electrostatic force arising from a collection of charged particles vanishes. This is a novel scenario of optimization in which…

Approximate solutions representing the gravitational-electrostatic balance of two arbitrary point sources in general relativity have led to contradictory arguments in the literature with respect to the condition of balance. Up to the…

Correspondences between the Thomson Problem and atomic electron shell-filling patterns are observed as systematic non-uniformities in the distribution of potential energy necessary to change configurations of $N\le 100$ electrons into…

We propose a finite element method for the numerical simulation of electroconvection of thin liquid crystals. The liquid is located in between two concentric circular electrodes which are either assumed to be of infinite height or slim.…

The spectra of quantum dots of different geometry (``quantum ring'', ``quantum cylinder'', ``spherical square-well'' and ``parabolic confinement'') are studied. The stochastic variational method on correlated Gaussian basis functions and a…

The relativistic two-body problem is considered for spinless particles subject to an external macroscopic electromagnetic field. When this field is made of the monochromatic superposition of two counter-propagating plane waves (and provided…

Inspired by Tokieda's work on mechanical insights in geometry, we explore a hydrostatic approach to classical geometric problems. Using principles of fluid statics, we derive two mathematical results regarding polygons. These results…

We study the electron magnetohydrodynamics (MHD) in two dimensional geometry, which has a rich family of steady states. In an anisotropic resistivity context, we show global in time existence of small smooth solution near a shear type…

The equations of electrostatics are presented in pre-metric form, and it is pointed out that if the origin of the nonlinearity is the constitutive law for the medium then the differential equations themselves remain linear, while the…

Understanding the electrodes' surface morphology influence on the ions' distribution is essential for designing the supercapacitors with enhanced energy density characteristics. We develop a model for the structure of electrolytes near the…

Exact self-consistent particle-like solutions with spherical and/or cylindrical symmetry to the equations governing the interacting system of scalar, electromagnetic and gravitational fields have been obtained. As a particular case it is…

Energies and wave functions of edge states in twodimensional electron gas are evaluated for a finite step potential barrier model. The spectrum, instead of smooth bending of Landau branches in the vicinity of the barrier acquires a steplike…

In this article we present a study of the effects of hydrostatic pressure on the energy levels of a quantum dot with an electron. A quantum dot is modeled using an infinite potential well and a two-dimensional harmonic oscillator and solved…

In this work we investigate in detail, the different regimes of the pioneering work of Chklovskii et al. (1992), which provides an analytical description to model the electrostatics at the edges of a two-dimensional electron gas. We take…

This is a technical document that outlines a calculation of an electrostatic interaction energy between two rods, with charge helices on them, forming a braid. We deal here with screened electrostatics. A general braid geometry is…

We calculate electrostatic potential landscapes for an external probe charge in the presence of a set of metallic islands. Our numerical calculation in three dimensions (3D)uses an efficient grid relaxation technique. The well-known…

When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…

We have found a (dense) basis for the N-representable, two-electron densities, in which all N-representable two-electron densities can be expanded, using positive coefficients. The inverse problem of finding a representative wavefunction,…

We derive a mixed-dimensional 3D-1D formulation of the electrostatic equation in two domains with different dielectric constants to compute, with an affordable computational cost, the electric field and potential in the relevant case of…