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Petrovskii elliptic systems of linear differential equations given on a closed smooth manifold are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the…
An explicit solution of the stationary one dimensional half-space boundary value problem for the linear Boltzmann equation is presented in the presence of an arbitrarily high constant external field. The collision kernel is assumed to be…
We consider spherically symmetric, asymptotically flat space-times with a collisionless gas as matter model. Many properties of the resulting Vlasov-Einstein system are not yet accessible by purely analytical means. We present a discretized…
The double-layer potential plays an important role in solving boundary value problems for elliptic equations, and in the study of which for a certain equation, the properties of the fundamental solutions of the given equation are used. All…
We demonstrate the role of selectivity variation in the structure of the non-equilibrium extended space-charge using 1D analytic and 2D numerical Poisson-Nernst-Planck models for the electro- diffusive transport of a symmetric electrolyte.…
We are interested in the homogenization of elastic-electric coupling equation, with rapidly oscillating coefficients, in periodically perforated piezoelectric body. We justify the two first terms in the usual asymptotic development of the…
We present a method that gives highly accurate electrostatic potentials for systems where we have periodic boundary conditions in two spatial directions but free boundary conditions in the third direction. These boundary conditions are…
We revisit the problem of the structure and physical properties of electrically charged static spherically symmetric solutions of the Einstein-Maxwell system of equations where the matter model is a polytropic gas. We consider a…
We introduce an accurate non-Hermitian Schr\"odinger-type approximation of Bloch optical equations for two-level systems. This approximation provides a complete description of the excitation, relaxation and decoherence dynamics in both weak…
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…
We consider an osmotic equilibrium between bulk solutions of polyelectrolyte bounded by semipermeable membranes and separated by a thin film of salt-free liquid. Although the membranes are neutral, the counter-ions of the polyelectrolyte…
The electrostatic potential of a highly charged disc (clay platelet) in an electrolyte is investigated in detail. The corresponding non-linear Poisson-Boltzmann (PB) equation is solved numerically, and we show that the far-field behaviour…
Using methods of functional integration, and performing simple Gaussian integrals, I show that an interacting system of electrons can be bosonized in arbitrary dimensions, in terms of the electrostatic potential which mediates the…
Electrochemical devices often consist of multicomponent electrolyte solutions. Two processes influence the overall dynamics of these devices: the formation of electrical double layers and chemical conversion due to redox reactions. However,…
Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one completions of a linear matrix polynomial derived from…
We extend our previous study of surface tension of ionic solutions and apply it to the case of acids (and salts) with strong ion-surface interactions. These ion-surface interactions yield a non-linear boundary condition with an effective…
A simple method of variational calculations of the electronic structure of a two-electron atom/ion, primarily near the nucleus, is proposed. The method as a whole consists of a standard solution of a generalized matrix eigenvalue equation,…
We have found a (dense) basis for the N-representable, two-electron densities, in which all N-representable two-electron densities can be expanded, using positive coefficients. The inverse problem of finding a representative wavefunction,…
The spherical-harmonics expansion is a mathematically rigorous procedure and a powerful tool for the representation of potential energy surfaces of interacting molecular systems, determining their spectroscopic and dynamical properties,…