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Electromechanics in fluids describes the response of the number density to electric fields, and thus provides a powerful means by which to control the behavior of liquids. While continuum approaches have proven successful in describing…
The creation of large scale magnetic fields is studied in an inflationary universe where electrodynamics is assumed to be nonlinear. After inflation ends electrodynamics becomes linear and thus the description of reheating and the…
The paper formulates Maxwell's equations in 4-dimensional Euclidean space by embedding the electromagnetic vector potential in the frame vector $g_0$. Relativistic electrodynamics is the first problem tackled; in spite of using a geometry…
The Schr\"odinger theory of electrons in an external electromagnetic field can be described from the perspective of the individual electron via the `Quantal Newtonian' laws (or differential virial theorems). These laws are in terms of…
We consider a complex covariant form of the macroscopic Maxwell equations, in a moving medium or at rest, following the original ideas of Minkowski. A compact, Lorentz invariant, derivation of the energy-momentum tensor and the…
In the framework of the classical Maxwell-Lorentz electrodynamics the energy conservation law is reconsidered.
We argue that the definition of the thermodynamic work done on a charged particle by a time-dependent electromagnetic field is an open problem, because the particle's Hamiltonian is not gauge-invariant. The solution of this problem demands…
We consider field localizing and concentration of electromagnetic waves governed by the time-harmonic anisotropic Maxwell system in a bounded domain. It is shown that there always exist certain boundary inputs which can generate…
Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to…
This paper presents a brief review of the newly developed \emph{Extended Electrodynamics}. The relativistic and non-relativistic approaches to the extension of Maxwell equations are considered briefly, and the further study is carried out…
Electrically conducting films in a time-varying transverse applied magnetic field are considered. Their behavior is strongly influenced by the self-field of the induced currents, making the electrodynamics nonlocal, and consequently…
In the present work foundations of the law of the energy conservation and the introduction of particles in the classical electrodynamics are discussed. We pay attention to a logic error which takes place at an interpretation of the…
Background fields of electromagnetic and gravitational type emerge in the low kinetic energy limit of any regular Lagrangian system and, in particular, in the corresponding limit of any spacetime theory in which the free motion of test…
We calculate the first order maximal acceleration corrections to the classical electrodynamics of a particle in external electromagnetic fields. These include additional dissipation terms, the presence of a critical electric field, a…
We look at the foundations of electromagnetism in this chapter of the "eletromagnetism" book. For doing this, after some review (constraints on photon mass etc.), we use two approaches. The first one is to formulate a Parametrized…
Based on the derivation of the macroscopic Maxwell's equations by spatial averaging of the microscopic equations, we discuss the electrophysiology of living organs. Other methods of averaging (or homogenization) like the bidomain model are…
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 fully relativistically covariant and manifestly gauge invariant formulation of classical Maxwell electrodynamics is presented, purely in terms of gauge invariant potentials without entailing any gauge fixing. We show that the…
A formulation of quantum electrodynamics is proposed, in which the local law of conservation of electric charge serves as the source of the gauge condition. The equations of motion of the gauge variable and the density of the charge…
We describe the interplay between electric-magnetic duality and higher symmetry in Maxwell theory. When the fine-structure constant is rational, the theory admits non-invertible symmetries which can be realized as composites of…