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The late time asymptotics of the physical solutions to the Lorentz-Dirac equation in the electromagnetic external fields of simple configurations -- the constant homogeneous field, the linearly polarized plane wave (in particular, the…
General linear electrodynamics allow for an arbitrary linear constitutive relation between the field strength two-form and induction two-form density if crucial hyperbolicity and energy conditions are satisfied, which render the theory…
We analytically derive a rigorous expression for the relative impedance ratio between two photonic structures based on their electromagnetic interaction. Our approach generalizes the physical meaning of the impedance to a measure for the…
We study the complete electrode model boundary condition for second order elliptic PDE. A specific case of this is the PDE describing the electrostatic potential for a conductive body into which current is injected through electrodes that…
We study differential equations, describing interaction of electromagnetic field with moving sidebars and surfaces, coming from integral electrodynamics laws. It is shown that differential equations contain but the such features of…
Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite…
We describe theoretically ``electrolubrication'' in liquid mixtures, the phenomenon where an electric field applied transverse to the confining surfaces leads to concentration gradients that alter the flow profile significantly. When the…
Plane-wave reflection and refraction at an interface with a double wire medium is considered. The problem of additional boundary conditions (ABC) in application to wire media is discussed and an ABC-free approach, known in the solid state…
We present the first application of phase field modeling to electrochemistry. A free energy functional that includes the electrostatic effect of charged particles leads to rich interactions between concentration, electrostatic potential,…
We generalize the Bergman-Milton spectral representation, originally derived for a two-component composite, to extract the spectral density function for the effective dielectric constant of a graded composite. This work has been motivated…
An ideal conductor electrode in contact with a semi-infinite two-dimensional two-component plasma in an external potential is considered. The model is mapped onto an integrable sine-Gordon theory with Dirichlet boundary conditions. The…
The Schr\"odinger equation is solved for the wave function of an electron moving in a superposition of external constant and uniform electric and magnetic fields at an arbitrary angle between the field directions. The changing of the…
The paper shows the relationship between the major wave equations in quantum mechanics and electromagnetism, such as Schroedinger's equation, Dirac's equation and the Maxwell equations. It is shown that they can be derived in a striking…
Lipid membrane with freely exposed edge is regarded as smooth surface with curved boundary. Exterior differential forms are introduced to describe the surface and the boundary curve. The total free energy is defined as the sum of Helfrich's…
We present a general theory for the contribution from contact electrification to the work necessary to separate two solid bodies. The theory depends on the surface charge density correlation function, which we deduce from Kelvin Force…
The dihedral contact angles between interfaces in three-fluid-phase equilibria must be continuous functions of the bulk thermodynamic fields. This general argument, which we propose, predicts a nonwetting gap in the phase diagram,…
The electric permittivities and magnetic permeabilities for a relativistic electron gas are calculated from quantum electrodynamics at finite temperature and density as functions of temperature, chemical potential, frequency, and…
In the so-called Child-Langmuir law, established since 1911, an electron beam is formed linking two electrodes, which are assumed to be two parallel plates of area $A$, separated to a finite distance $D.$ When $% D\ll \sqrt{A},$…
A kinetic theory is developed to describe radiating electrons whose motion is governed by the Lorentz-Dirac equation. This gives rise to a generalized Vlasov equation coupled to an equation for the evolution of the physical submanifold of…
A generalization of the Einstein equation is considered for complex line elements. Several second order semilinear partial differential equations are derived from it as semilinear field equations in uniform and isotropic spaces. The…