Related papers: The solution of complex problems on calculation of…
A new method to calculate the electric field inside a spherical shell with surface charge in terms of solid angle is presented. The integral can be readily carried out without invoking special functions typically used for this classical…
The electron and current density distributions in the close proximity of quantum point contacts (QPCs) are investigated. A three dimensional Poisson equation is solved self-consistently to obtain the electron density and potential profile…
This article describes Monte-Carlo algorithms for charged systems using constrained updates for the electric field. The method is generalized to treat inhomogeneous dielectric media, electrolytes via the Poisson-Boltzmann equation and…
We present the first application of phase field modeling to electrochemistry. A free energy functional that includes the electrostatic effect of charged particles leads to rich interactions between concentration, electrostatic potential,…
This paper presents a simple and effective new numerical scheme for the computation of electrostatic fields exterior to a collection of close-to-touching discs. The method is presented in detail for the two-cylinder case. The key idea is to…
The supersymmetric quantum mechanics of a two-dimensional non-relativistic particle subject to external magnetic and electric fields is studied in a superfield formulation and with the typical non-minimal coupling of (2+1) dimensions. Both…
The charge and potential distributions for insulating particles approaching a substrate with regular insulating structures are studied by particle-in-cell numerical simulations. An elongated particle and substrate with elongated structures…
In this paper the distribution of charged particles is constructed under the approximation of ambipolar diffusion. The results of mathematical modelling in two-dimensional case taking into account the velocities of the system are presented.
Two main approaches in particle-based simulations for modeling a charged surface are using explicit, discrete charges and continuum, uniform charges. It is well-known that these two approaches could lead to substantially distinct ionic…
Theoretically, the electric field becomes infinite at corners of two and three dimensions and edges of three dimensions. Conventional finite-element and boundary element methods do not yield satisfactory results at close proximity to these…
Using techniques from geometry and complex analysis in their simplest form, we present a derivation of electric fields on surfaces with non-trivial topology. A byproduct of this analysis is an intuitive visualization of elliptic functions…
Dielectric interfaces are crucial to the behavior of charged membranes, from graphene to synthetic and biological lipid bilayers. Understanding electrolyte behavior near these interfaces remains a challenge, especially in the case of rough…
In this work, we present an analytical study of the electrostatic potential generated by a charged disk with a surface charge distribution that possesses radial axial symmetry. We express the potential in cylindrical coordinates and apply a…
A numerical method is presented for first-principle simulations of charged colloidal dispersions in electrolyte solutions. Utilizing a smoothed profile for colloid-solvent boundaries, efficient mesoscopic simulations are enabled for…
This paper presents results for the electric field due to a uniformly charged elliptical beam in the region outside the beam.
A better understanding of interfacial mechanisms is needed to improve the performances of electrochemical devices. Yet, simulating an electrode surface at fixed electrolyte composition remains a challenge. Here we apply a finite electric…
The partition function for the random walk of an electrostatic field produced by several static parallel infinite charged planes in which the charge distribution could be either $\pm\sigma$ is obtained. We find the electrostatic energy of…
The electrostatic force is described in this model by the action of electric dipole distributions on charged particles. The individual hypothetical dipoles are propagating at the speed of light in vacuum transferring momentum and energy…
The Inverse problem for an electromagnetic field produced by a dipole is solved. It is assumed that the field of an arbitrary changing dipole is known. Obtained formulae allow calculation of the position and dynamics of the dipole which…
The low-frequency electric microfield distribution in a Coulomb plasma is calculated for various plasma parameters, from weak to strong Coulomb coupling and from zero to strong electron screening. Two methods of numerical calculations are…