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We characterize diffusion matrices that yield a $L^{\infty}$ convergence rate of $\mathcal{O}(\varepsilon^2)$ in the theory of periodic homogenization of linear elliptic equations in nondivergence-form. Such type-$\varepsilon^2$ diffusion…
The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of exponential type orbitals introduced by the author. Three-center overlap integrals of appearing in these relations…
The mesoscopic field theory for ionic systems [A. Ciach and G. Stell, J. Mol. Liq. 87, 255 (2000)] is extended to the system with charged boundaries. A very simple expression for the excess grand potential functional of the charge density…
The electroosmotic transfer (ratio of velocity of liquid to electric current density) and conductivity of disperse system were calculated as functions of volume fraction of disperse particles. The considered model of electric double layer…
We study the distribution of point charges in a straight conductive needle and the electric field created by them. Starting from the bead model with $n$ point charges on the needle, we show the existence and uniqueness of an equilibrium…
This work explores the use of joint density-functional theory, a new form of density-functional theory for the ab initio description of electronic systems in thermodynamic equilibrium with a liquid environment, to describe electrochemical…
In the past two decades, geometric phases have provided a powerful new way of looking at quantum mechanical systems, manifesting themselves in subtle but observable ways. Here, we use them to define a versatile function ("distribution of…
A closed form of the electrostatic potential of a homogeneously charged cube is derived by integration. The exact result is compared with multipole expansions for the exterior and interior of the cube. The electrostatic potential of a…
An effective pair potential for systems of uniformly charged lamellar colloids in the presence of an electrolytic solution of microscopic co- and counterions is derived. The charge distribution on the discs is expressed as a collection of…
We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors…
The problem of the charged-particle motion in crossed electric and magnetic fields is investigated, and the validity of the guiding-center representation is assessed in comparison with the exact particle dynamics. While the magnetic field…
This paper reports a numerical study of complex classical trajectories of a particle in an elliptic potential. This study of doubly-periodic potentials is a natural sequel to earlier work on complex classical trajectories in trigonometric…
A new kinetic instability which results in formation of charge density waves is proposed. The instability is of a purely classical nature. A spatial period of arising space-charge and field configuration is inversely proportional to…
There are observational and theoretical indications that both the visible (stars) and the dark matter density distributions in elliptical galaxies increase significantly up to the galactic center. I present here some analytical results…
We consider two point-like charges in electrostatic interaction between them within the framework of a nonlinear model, associated with QED, that provides finiteness of their field energy. We find the common field of the two charges in a…
We use covariance and dimensional analysis to find expressions for the discontinuity of the potential and normal electric field across a flat surface with multipolar charge surface density in vacuum.
An exact incompressible quantum liquid is constructed at the filling factor $1/m^2$ in square lattice. It supports deconfined fractionally charged excitation. At the filling factor $1/m^2$, the excitation has fractional charge $\pm e/m^2$,…
We study spherical, charged and self--similar distributions of matter in the diffusion approximation. We propose a simple, dynamic but physically meaningful solution. For such a solution we obtain a model in which the distribution becomes…
Three-dimensional Einstein gravity coupled to zero, one and two forms is solved in terms of a polyhomogeneous asymptotic expansion, generalising stationary black string solutions. From first order terms we obtain, in closed form, a new…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…