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The generalized Graetz problem refers to stationary convection-diffusion in uni-directional flows. In this contribution we demonstrate the ana-lyticity of generalized Graetz solutions associated with layered domains: either cylindrical…
It is shown that geometric optical description of electromagnetic wave with account of its polarization in curved space-time can be obtained straightforwardly from the classical variational principle for electromagnetic field. For this end…
A forgotten experiment by Andr\'e Blondel (1914) proves, as held on the basis of theoretical arguments in a previous paper, that the time variation of the magnetic flux is not the cause of the induced $emf$: the physical agent is instead…
In the first part of this paper we review the fundamental difference between the usual transformations of the three-dimensional (3D) vectors of the electric field $\mathbf{E}$, the magnetic field $\mathbf{B}$, the polarization $\mathbf{P}$,…
The generalized Maxwell equations with arbitrary gauge parameter are considered in the $11\times 11$-matrix form. The gauge invariance of such a model is broken due to the presence of a scalar field. The canonical and symmetrical Belinfante…
Modern undergraduate textbooks in electricity and magnetism typically focus on a force representation of electrodynamics with an emphasis on Maxwell's Equations and the Lorentz Force Law. The vector potential $\mathbf{A}$ and scalar…
Motivated by obtaining a consistent mathematical description for the radiation reaction of point charged particles in linear classical electrodynamics, a theory of generalized higher order tensors and differential forms is introduced. The…
We present an analysis of the vacuum Einstein equations for a recently proposed extension of the Kerr-Schild ansatz that includes a spacelike vector field as well as the usual Kerr-Schild null vector. We show that many, although not all, of…
In this paper, we give the covariant formulation of second gradient electrodynamics, which is a generalized electrodynamics of second order including derivatives of higher order. The relativistic form of the field equations, the…
The fact that electromagnetic effects propagate at the speed of light suggests how the Lorenz-gauge scalar and vector potentials of a uniformly moving point charge must be modified when the charge was initially at rest and then set suddenly…
A new scheme of field quantization is proposed. Instead of associating with different frequencies different oscillators we begin with a single oscillator that can exist in a superposition of different frequencies. The idea is applied to the…
We prove a HVZ theorem for a general class of no-pair Hamiltonians describing an atom or positively charged ion with several electrons in the presence of a classical external magnetic field. Moreover, we show that there exist infinitely…
A procedure for solving the Maxwell equations in vacuum, under the additional requirement that both scalar invariants are equal to zero, is presented. Such a field is usually called a null electromagnetic field. Based on the complex Euler…
The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's…
We propose a generic, phenomenological approach to modifying the dispersion of gravitational waves, independent of corrections to the generation mechanism. This model-independent approach encapsulates all previously proposed…
The photon behavior in an arbitrary superposition of constant magnetic and electric fields is considered on most general grounds basing on the first principles like Lorentz- gauge- charge- and parity-invariance. We make model- and…
Application of the generalized continuity equation reveals that the drift current in conductors is equivalent to a negative diffusion current. A phenomenological model of conductivity is developed using the generalized continuity equations.…
We proposed a gravitation theory based on an analogy with electrodynamics on the basis of a vector field. For the first time, to calculate the basic gravitational effects in the framework of a vector theory of gravity, we use a Lagrangian…
Electron transfer coupled to a collective vibronic degree of freedom is studied in strongly condensed phase and at lower temperatures where quantum fluctuations are essential. Based on an exact representation of the reduced density matrix…
Two sets of spatially differential formulas of Lenz law on electromagnetic inductance are presented. They are a cut-magnetic flux induced voltage, which instantaneously results from cutting magnetic flux as a conductor moving with respect…