Related papers: Image Charges Re-Imagined
The problem of the equilibrium state of the charged many-particle system above dielectric surface is formulated.We consider the case of the presence of the external attractive pressing field and the case of its absence. The equilibrium…
In an external constant magnetic field, so strong that the electron Larmour length is much shorter than its Compton length, we consider the modification of the Coulomb potential of a point charge owing to the vacuum polarization. We…
The double-layer potential plays an important role in solving boundary value problems for elliptic equations. All the fundamental solutions of the generalized bi-axially symmetric Helmholtz equation were known, and only for the first one…
The problem of two coupled scalar fields, one with mass much lighter than the other is analysed by means of Wilson's renormalization group approach. Coupled equations for the potential and the wave function renormalization are obtained by…
The objective of electrical impedance tomography is to reconstruct the internal conductivity of a physical body based on measurements of current and potential at a finite number of electrodes attached to its boundary. Although the…
This article describes a method devised for efficient evaluation of arbitrary static magnetic and electric fields in a source free region needed for long time tracking of charged particles. Field values given on the boundary of the region…
We develop a fast method for computing the electrostatic energy and forces for a collection of charges in doubly-periodic slabs with jumps in the dielectric permittivity at the slab boundaries. Our method achieves spectral accuracy by using…
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…
In this work, we estimate the effect of photoinduced screening breakdown of the Coulomb potential mediated by plasmons. In contrast to previous studies, we consider the contribution from the divergence of renormalized inverse electron…
We study the force between two circular electrodes in different configurations. A formula analogous to Kelvin's formula for the spheres is given in the case of equal disks held at the same potential and when one plate is earthed. An…
Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space method, the shifted inverse power method, and the polynomial…
Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary…
In this article, we develop the theory of weighted $L^2$ Sobolev spaces on unbounded domains in $\mathbb R^n$. As an application, we establish the elliptic theory for elliptic operators and prove trace and extension results analogous to the…
The possibility of the existence of magnetic charges is one of the greatest unsolved issues of the physics of this century. The concept of magnetic monopoles has at least two attractive features: (i) Electric and magnetic fields can be…
The evaluation of the electrostatic potential is fundamental to the study of condensed phase systems. We discuss the calculation of the relevant lattice summations by Ewald-type techniques. A model charge density is introduced, that cancels…
The formulation of the Lifshitz formula in terms of real frequencies is reconsidered for half spaces described by the plasma model. It is shown that besides the surface modes (for the TM polarization), and the photonic modes, also waveguide…
Our recent arXiv preprints have described the experimental evidence for the universal occurrence of short circuit photocurrents on illumination of solid state surfaces by strongly absorbed light. A likely mechanism has been proposed based…
We consider a slightly subcritical elliptic system with Dirichlet boundary conditions and a non-power nonlinearity in a bounded smooth domain. For this problem, standard compact embeddings cannot be used to guarantee the existence of…
In this paper, we give probabilistic interpretations of both, the forward and the inverse problem of electrical impedance tomography with possibly anisotropic, merely measurable conductivities: Using the theory of symmetric Dirichlet…
Existence of the magnetic monopole is compatible with the fundamental laws of nature, however, this illusive particle has yet to be detected experimentally. In this work, we show that an electric charge near the topological surface state…