Related papers: Image charges revisited: a closed form solution
We revisit the image charge method for the Green's function problem of the Poisson-Boltzmann equation for a dielectric sphere immersed in ionic solutions. Using finite Mellin transformation, we represent the reaction potential due to a…
We discuss the grounded, equipotential ellipse in two-dimensional electrostatics to illustrate different ways of extending the domain of the potential and placing image charges such that homogeneous boundary conditions are satisfied. In…
Equations describing the complete series of image charges for a system of conducting spheres are presented. The method of image charges, originally described by J. C. Maxwell in 1873, has been and continues to be a useful method for solving…
A new class of exact solutions of the Einstein-Maxwell system is found in closed form. This is achieved by choosing a generalised form for one of the gravitational potentials and a particular form for the electric field intensity. For…
We have performed self-consistent calculations of the nonlinear screening of a point charge Z in a two-dimensional electron gas using a density functional theory method. We find that the screened potential for a Z=1 charge supports a bound…
We record what is known about the closed forms for various Bessel function moments arising in quantum field theory, condensed matter theory and other parts of mathematical physics. More generally, we develop formulae for integrals of…
We investigate the effect of a constant threshold correction to a general non-extreme, static, spherically symmetric, electrically charged black hole solution of the dilatonic Einstein-Maxwell Lagrangian, with an arbitrary coupling $\beta$…
We introduce and motivate the method of effective charges, and consider how to implement an all-orders resummation of large kinematical logarithms in this formalism. Fits for QCD \Lambda and power corrections are performed for the e+e-…
In this article we build a metric for a classical general relativistic electron model with QED corrections. We calculate the stress-energy tensor for the radiative corrections to the Coulomb potential in both the near-field and far-field…
Using a proper gauge condition the static spherically symmetric solutions of Einstein-Maxwell equations with charged point source at the center are derived. It is shown that the solutions of the field equations are a three-parameter family…
An image system for a point charge outside a dielectric sphere is presented for all complex values of relative permittivity $\epsilon=\epsilon'+i\epsilon''$. The standard image integral solution of a point charge outside a dielectric sphere…
We derive analytical expressions for external fields of a relativistic bunch of charged particles with a circular and an elliptical cross section under different boundary conditions and interaction of the fields with an accelerator…
Spherical Bessel functions appear commonly in many areas of physics wherein there is both translation and rotation invariance, and often integrals over products of several arise. Thus, analytic evaluation of such integrals with different…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
Multiple elliptic integrals related to the generalized Clebsch-Gordan (CG) integral are of importance in many areas in physics and special functions theory. Zhou has introduced and applied Legendre function-based techniques to prove…
This work extends the results of [Garde and Hyv\"onen, Math. Comp. 91:1925-1953] on series reversion for Calder\'on's problem to the case of realistic electrode measurements, with both the internal admittivity of the investigated body and…
We reexamine and extend a group of solutions in series of Bessel functions for a limiting case of the confluent Heun equation and, then, apply such solutions to the one-dimensional Schr\"odinger equation with an inverted quasi-exactly…
In this paper, we generalize the Schwarzschild-Melvin solution within Einstein-Maxwell-dilaton theories to include non-null scalar charges, while remaining embedded in a magnetic or electric field \textit{\`a la Melvin}. We then use this…
We find a new class of exact solutions to the Einstein-Maxwell equations which can be used to model the interior of charged relativistic objects. These solutions can be written in terms of special functions in general; for particular…
We analyze the vacuum expectation values of conserved charges in two dimensional integrable theories. We study the situations when the ground-state can be described by a single integral equation with a finite support: the thermodynamic…