Related papers: Planck's Other Quanta: Corpuscular Electrodiffusio…
A previously-established model of steady one-dimensional two-ion electrodiffusion across a liquid junction is reconsidered. It involves three coupled first-order nonlinear ordinary differential equations, and has the second-order Painlev\'e…
The Maxwell equations in the presence of sources are first derived without making use of the potentials and the Hamilton-Jacobi equation for classical electrodynamics is written down. The manifestly gauge invariant theory is then quantized…
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…
The drift and diffusion of a cloud of ions in a fluid are distorted by an inhomogeneous electric field. If the electric field carries the center of the distribution in a straight line and the field configuration is suitably symmetric, the…
Addition formulae of trigonometric and elliptic functions are used to generate B\"acklund transformations together with their connecting quadrilateral equations. As a result we obtain periodic solutions for a number of multidimensionally…
Electron gases in metals are described as quantum charged Newtonian viscous fluids experiencing Ohmic Darcy friction on the solid lattice ions as well. The dispersion relation of the electron acoustic waves is derived, which shows the…
Molecular conduction operating in dielectric solvent environments are often described using kinetic rates based on Marcus theory of electron transfer at a molecule-metal electrode interface. However, the successive nature of charge transfer…
The B\"{a}cklund transformation for the three-level Maxwell-Bloch equation is presented in the matrix potential formalism. By applying the B\"{a}cklund transformation to a constant electric field background, we obtain a general solution for…
We compute electromagnetic fields created by a relativistic charged spin-half particle in empty space at distances comparable to the particle Compton wavelength. The particle is described as a wave packet evolving according to the Dirac…
Classical thermodynamics and statistical mechanics describe systems in which nothing interacts with nothing. Even the highly refined theory of simple fluids does not deal very well with electrical interactions, boundary conditions, or…
The assumption is made that only transversely polarized photons are needed for a correct description of Quantum Electrodynamics. A simple mathematical transformation is used to introduce new field operators which satisfy the full Maxwell…
A quantum kinetic equation is obtained for an inhomogeneous solid having arbitrary gradient concentration and chemical potential. We find, starting from nonequilibrium statistical operator, a new equation to describe atom migration in solid…
We combine Maxwell's equations with Eulers's equation, related to a velocity field of an immaterial fluid, where the density of mass is replaced by a charge density. We come out with a differential system able to describe a relevant…
A classical description of the dynamics of a dissipative charged-particle fluid in a quadrupole-like device is developed. It is shown that the set of the classical fluid equations contains the same information as a complex function…
Starting from the Boltzmann-Enskog kinetic equations, the charge transport equation for bidisperse granular flows with contact electrification is derived with separate mean velocities, total kinetic energies, charges and charge variances…
The equations governing one-dimensional, steady-state electrodiffusion are considered when there are arbitrarily many mobile ionic species present, in any number of valence classes, possibly also with a uniform distribution of fixed…
In the context of Born-Infeld electrodynamics, the electromagnetic fields interact with each other via their non-linear couplings. A calculation will be performed where an incoming electromagnetic plane wave scatters off a Coulomb Field in…
B\"acklund transformations (BTs) are traditionally regarded as a tool for integrating nonlinear partial differential equations (PDEs). Their use has been recently extended, however, to problems such as the construction of recursion…
Clairin's method of obtaining B\"{a}cklund transformations is applied to Einstein's field equations for the interior of a uniformly rotating stationary axisymmetric perfect fluid. It is shown that for arbitrary pressure $p$ and mass density…
When an electrically charged system is subjected to the action of an electromagnetic field, it responds by generating an electrical current. In the case of a multicomponent plasma other effects, the so called cross effects, influence the…