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Mobile charge in an electrolytic solution can in principle be represented as the divergence of ionic polarization. After adding explicit solvent polarization a finite volume of electrolyte can then be treated as a composite non-uniform…
Resonant electron interaction with whistler-mode chorus waves is recognized as one of the main drivers of radiation belt dynamics. For moderate wave intensity, this interaction is well described by quasi-linear theory. However, recent…
In multispecies electrolyte solutions, even in the absence of an external electric field, differences in ion diffusivities induce an electric potential and generate additional fluxes for each species. This electro-diffusion process is…
We present a porous electrode model for lithium-ion batteries using Butler--Volmer reaction kinetics. We model lithium concentration in both the solid and fluid phase along with solid and liquid electric potential. Through asymptotic…
The description of a conducting medium in thermal equilibrium, such as an electrolyte solution or a plasma, involves nonlinear electrostatics, a subject rarely discussed in the standard electricity and magnetism textbooks. We consider in…
The development of a bubble plume from a vertical gas-evolving electrode is driven by buoyancy and hydrodynamic bubble dispersion. This canonical fluid mechanics problem is relevant for both thermal and electrochemical processes. We adopt a…
A brief analysis of the physics and effects of electrolytic gas evolution is presented. Aspects considered include bubble nucleation, growth, and detachment, enhancement of mass and heat transfer, and decrease of apparent electrical…
We consider charge transport in nanopores where the dielectric constant inside the nanopore is much greater than in the surrounding material, so that the flux of the electric fields due to the charges is almost entirely confined to the…
We consider stationary and propagating solutions for a Bose-Einstein condensate in a periodic optical potential with an additional confining optical or magnetic potential. Using an effective mass approximation we express the condensate…
Molecular dynamics simulations are used to study the mechanism and kinetics of hydrated electron diffusion. The electron center of mass is found to exhibit Brownian-type behavior with a diffusion coefficient considerably greater than that…
A conditional entropic approach is discussed for nonequilibrium complex systems with a weak correlation between spatiotemporally fluctuating quantities on a large time scale. The weak correlation is found to constitute the fluctuation…
The dispersion curves for the electrons and holes in CsPbI$_3$ in the orthorhombic phase are calculated using the density functional theory (DFT), with the spin-orbit coupling taken into account. The effective masses of the charge carriers…
The steady state of ions diffusion in polymer electrolytes at arbitrary applied voltage is analyzed in the framework of the Nernst-Planck-Poisson equation (NPP). The exact solution of the set of equations is found without the assumption of…
We introduce a simple model of the time evolution of a binary mixture of compressible fluids including the thermal effects. Despite its apparent simplicity, the model is thermodynamically consistent admitting an entropy balance equation. We…
Since its elaboration by Whitham, almost fifty years ago, modulation theory has been known to be closely related to the stability of periodic traveling waves. However, it is only recently that this relationship has been elucidated, and that…
For the field amplitude, a nonlinear integro-differential equation is derived that describes the operation of a Compton FEL in the presence of electron velocity spread typical for modern facilities. Numerical solutions of the equation are…
A hydrodynamic model for determining the electrophoretic speed of a polyelectrolyte through a nanopore is presented. It is assumed that the speed is determined by a balance of electrical and viscous forces arising from within the pore and…
We study the local well-posedness of the solution to a coupled nonlinear elliptic-parabolic system which models electrical discharge in a Micro-Electro-Mechanical System (MEMS). A simple MEMS capacitor device contains two plates acting as…
We propose a model to describe an evolution of a bubble cluster with rupture. In a special case, the equation is reduced to a single parabolic equation with evaporation for the thickness of a liquid layer covering bubbles. We postulate that…
We show existence of small solitary and periodic traveling-wave solutions in Sobolev spaces ${\mathrm{H}^s}$, ${ s > 0 }$, to a class of nonlinear, dispersive evolution equations of the form \begin{equation*} u_t + \left(Lu+ n(u)\right)_x =…