Related papers: Charged line segments and ellipsoidal equipotentia…
Electrical double layer (EDL) is formed when an electrode is in contact with an electrolyte solution, and is widely used in biophysics, electrochemistry, polymer solution and energy storage. Poisson-Boltzmann (PB) coupled equations provides…
We investigate the electrostatic equilibria of N discrete charges of size 1/N on a two dimensional conductor (domain). We study the distribution of the charges on symmetric domains including the ellipse, the hypotrochoid and various regular…
We investigate the properties of a static, cylindrically symmetric Majumdar-Papapetrou-type solution of Einstein-Maxwell equations. We locate its singularities, establish its algebraic type, find its asymptotic properties and weak-field…
We consider a pair of driver/witness electron bunches propagating in an ionized gas background a configuration similar to the one produced in a capillary discharge where a plasma oscillation has been excited by a driving pulse. We assume as…
The remarkable geometries of ellipsoidal equipotentials and their associated gradient fields, as produced by uniformly charged straight-line segments, are discussed at an elementary level, motivated by recent treatments intended for…
We study the electric field around a continuous one-dimensional loop of static charge, under the assumption that the charge is distributed uniformly along the loop. For rectangular or stadium-shaped loops in the plane, we find that the…
We study the effect of any uneven voltage distribution on two close cylindrical conductors with parallel axes that are slightly shifted in the radial and by any length in the axial direction. The investigation is especially motivated by…
The uniform acceleration of a point charge moving along a stationary worldline, which emits constant radiated power was investigated. A classification of motion of a particle along stationary worldlines into six types is made. The angular…
We review a model for a solid electrolyte derived under thermodynamics principles. We non-dimensionalise and scale the model to identify small parameters, where we identify a scaling that controls the width of the space-charge layer in the…
We discuss an elementary problem in electrostatics: What does the charge distribution look like for a free charge on a strictly one-dimensional wire of finite length? To the best of our knowledge this question has so far not been discussed…
This paper considers the distribution of charge over the surface of a conductor, and specifically the old rule-of-thumb that charge accumulates near sharp points and more generally in regions of high curvature. The discussion is almost…
This paper presents the approximate analytical solutions to the longitudinal space charge (LSC) impedances of a round beam with uniform transverse distribution and sinusoidal line density modulations under two boundary conditions: (a)…
In this work we study a charged particle in the presence of both a continuous distribution of disclinations and a continuous distribution of edge dislocations in the framework of the geometrical theory of defects. We obtain the self-energy…
It was recently shown by the authors that a semilinear elliptic equation can be represented as an infinite-dimensional dynamical system in terms of boundary data on a shrinking one-parameter family of domains. The resulting system is…
We study the electrostatics of a thin, finite-length conducting cylindrical shell held at constant potential V0. Exploiting axial symmetry, we recast the problem as a one-dimensional singular integral equation for the axial surface-charge…
We solve the nonlinear Poisson-Boltzmann equation for two parallel and likely charged plates both inside a symmetric elecrolyte, and inside a 2 : 1 asymmetric electrolyte, in terms of Weierstrass elliptic functions. From these solutions we…
1. Introduction 2. Charged chains at infinite dilution - asymptotic properties 2.1 Definition of the model and Flory-like calculation 2.2 Variational approaches 2.3 Renormalization group calculations 2.4 Screening of electrostatic…
We consider an interaction of charged bodies under the following simplified conditions: the distribution of charge over each body is stable; the interaction of bodies is governed by electrical forces only. Physically, these assumptions can…
The goal of this paper is to study the electrostatic field due to an arbitrary charge distribution on a dielectric layer in a dielectric-loaded rectangular waveguide. In order to obtain this electrostatic field, the potential due to a point…
Two-dimensional (2D) electronic materials are of significant technological interest due to their exceptional properties and broad applicability in engineering. The transition from nanoscale physics, that dictates their stable…