Related papers: Electrostatic potential of a uniformly charged dis…
The electrostatic potential of any test charge distribution in Schwarzschild space with boundary values is derived. We calculate the Green's function, generalize the second Green's identity for p-forms and find the general solution.…
This is a survey of the electrostatic potentials produced by charged straight-line segments, in various numbers of spatial dimensions, with comparisons between uniformly charged segments and those having non-uniform linear charge…
An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations modeling ion transport through membrane channels. The differential equations are recast as integral equations using Green's 3rd identity…
We evaluate the electrostatic potential and the electrostatic field created by a point charge and an arbitrarly oriented electrical dipole placed near a grounded perfectly conducting sphere. Induced surface charge distributions as well 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…
The problem of diffraction of an electromagnetic plane wave by a perfectly conducting circular disk and its complementary problem, diffraction by a circular hole in an infinite conducting plate, are rigorously solved using the method of the…
The formal basis for fully relativistic Korringa-Kohn-Rostoker (KKR) or multiple scattering calculations for the electronic Green function in case of a general potential is discussed. Simple criteria are given to identify situations that…
We analytically calculate the correlation potential of a test ion near a \emph{strongly} charged plate inside a dilute $m:-n$ electrolyte. We do this by calculating the electrostatic Green's function in the presence of a nonlinear…
The problem of a spin 1 charged particle with electromagnetic polarizability, obeying a generalized 15-component quantum mechanical equation, is investigated in presence of the external Coulomb potential. With the use of the Wigner's…
We develop a general theory of electric polarization induced by inhomogeneity in crystals. We show that contributions to polarization can be classified in powers of the gradient of the order parameter. The zeroth order contribution reduces…
A new model for calculating the Casimir-Lifshitz force per unit length for two dielectric rods is proposed, based on the Green function method of classical electrodynamics and the Lorentz model for permittivity.
It is shown that Maxwell equations for electromagnetic fields generated by the uniformly accelerated charge could be reduced to the Laplace equation (in {\L}obaczewski geometry) for a single scalar potential. The full solution of this…
A methodology for calculating the contribution of charged defects to the configurational free energy of an ionic crystal is introduced. The temperature-independent Wang-Landau Monte Carlo technique is applied to a simple model of a solid…
In the present work we discuss how to address the solution of electrostatic problems, in professional cycle, using Green's functions and the Poisson's equation. By using this procedure, it was possible to verify its relation with the method…
The main problem in theoretical analysis of structures with strong confinement is the fact that standard mathematical tools: differential equations and Fourier's transformations are no longer applicable. In this paper we have demonstrated…
The disorder averaged single-particle Green's function of electrons subject to a time-dependent random potential with long-range spatial correlations is calculated by means of bosonization in arbitrary dimensions. For static disorder our…
Any polyhedron accommodates a type of potential theoretic skeleton called a mother body. The study of such mother bodies was originally from Mathematical Physics, initiated by Zidarov and developed by Bj\"{o}rn Gustafson and Makoto Sakai.…
The one dimensional Dirac equation with a rational potential is reducible to an ordinary differential equation with a Riccati-like coefficient. Its integrability can be studied with the help of differential Galois theory, although the…
An analytical study of the charged particle dynamics in the presence of an elliptically polarized electromagnetic wave and a uniform axial magnetic field, is presented. It is found that for $g\omega_{0}/ \omega' = \pm 1$, maximum energy…
We study the problem of finding a point of maximal electrostatic potential inside an arbitrary triangle with homogeneous surface charge distribution. In this article we derive several synthetic and analytic relations for its location in the…