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The Poisson-Boltzmann mean-field description of ionic solutions has been successfully used in predicting charge distributions and interactions between charged macromolecules. While the electrostatic model of charged fluids, on which the…
The present paper is a concluding part of the series [N.B. Volkov and A.M. Iskoldsky: 1; 2; [1], [2]]. Here on the basis of the results of the above papers the experiments on the electric explosion in conductors have been discussed and the…
Condensed water on vertical surfaces ultimately leaves the substrate at the lower edge, where accumulated liquid detaches as drops. While droplet growth and surface transport have been extensively studied, this final release step remains…
The wave propagation of edge modes in a superlattice of 2D electron Gases in quantum Hall regime is investigated. After introducing surfaces charge and current densities at the edge, the Maxwell equations are solved for waves running along…
Porous electrodes are widely used in electrochemical systems, where accurately determining electric potentials, particularly overpotentials, is essential for understanding electrode behavior. At the macroscopic scale, porous electrodes are…
A two-scale model is presented to simulate the dynamic ion transport and adsorption processes in porous electrodes used for capacitive deionization (CDI). At the pore scale, the Stokes equation governing water flow in porous CDI electrodes…
We present the theory and implementation of a Poisson-Boltzmann implicit solvation model for electrolyte solutions. This model can be combined with arbitrary electronic structure methods that provide an accurate charge density of the…
The Faddeev equation for three-body scattering at arbitrary energies is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. In its simplest form the Faddeev equation…
We consider the diffusive limit of an unsteady neutron transport equation in a two-dimensional plate with one-speed velocity. We show the solution can be approximated by the sum of interior solution, initial layer, and boundary layer with…
A dispersion-managed optical system with step-wise periodical variation of dispersion is studied in a strong dispersion map limit in the framework of path-averaged Gabitov-Turitsyn equation. The soliton solution is obtained by iterating the…
We study ion condensation onto a patterned surface of alternating charges. The competition between self-energy and ion-surface interactions leads to the formation of ionic crystalline structures at low temperatures. We consider different…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
The problem of the one dimensional electro-diffusion of ions in a strong binary electrolyte is considered. In such a system the solute dissociates completely into two species of ions with unlike charges. The mathematical description…
Experimental observations of thermionic electron emission demonstrate a smooth transition between TL and FSCL regions of the emitted-current-density-versus-temperature (J-T) (Miram) curve and the emitted-current-density-versus-voltage (J-V)…
This paper describes a novel numerical model aiming at solving moving-boundary problems such as free-surface flows or fluid-structure interaction. This model uses a moving-grid technique to solve the Navier--Stokes equations expressed in…
We present a new model to identify natural fluctuations in fluids, allowing us to describe localization phenomena in the transport of electrons, positrons and positronium through non-polar fluids. The theory contains no free parameters and…
The spatio-temporal aspects of the transition to turbulence are considered in the case of a boundary layer flow developing above a flat plate exposed to free-stream turbulence. Combining results on the receptivity to free-stream turbulence…
We study a 1D geometry of a plasma confined between two conducting floating walls with applications to laboratory plasmas. These plasmas are characterized by a quasi-neutral bulk that is joined to the wall by a thin boundary layer called…
A typical graphene heterojunction device can be divided into two classical zones, where the transport is basically diffusive, separated by a "quantum active region" (e.g., a locally gated region), where the charge carriers are scattered…
We solve Poisson's equation by combining a spectral-element method with a mapped infinite-element method. We focus on problems in geostatics and geodynamics, where Earth's gravitational field is determined by Poisson's equation inside the…