Related papers: Two-Potential Formalism for Numerical Solution of …
New Lagrangians, depending on the field strengths and the electric and magnetic sources are found, which lead to the Maxwell equations. One new feature is that the equations of motion are obtained by varying the Lagrangian with respect to…
With regard to the toroid contributions, a modified system of equations of electrodynamics moving continuous media has been obtained. Alternative formalisms to introduce the toroid moment contributions in the equations of electromagnetism…
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 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…
The problems considered refer to the material equations of electric- and magnetoelectric induction. Some contradictions found in fundamental studies on classical electrodynamics have been explained. The notion magnetoelectric induction has…
The purpose of this article is twofold. On one hand, we rigorously derive the Newton--Maxwell equation in the Coulomb gauge from first principles of quantum electrodynamics in agreement with the formal Bohr's correspondence principle of…
The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. Tey are reviewed in the work presented. It is drawing the attention on the following aspects. EM-field has in general case quaternion…
Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure…
The electromagnetic fields of the hybrid modes of an optical fiber are reformulated using bi-complex mathematics, which leads to simpler expressions relative to those found with the widely used, conventional complex formulation. Generalized…
We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…
In this paper, we discuss the Maxwell equations in terms of differential forms, both in the 3-dimensional space and in the 4-dimensional space-time manifold. Further, we view the classical electrodynamics as the curvature of a line bundle,…
A flux-splitting method is proposed for the hyperbolic-equation system (HES) of magnetized electron fluids in quasi-neutral plasmas. The numerical fluxes are split into four categories, which are computed by using an upwind method which…
In differential-form representation, the Maxwell equations are represented by simple differential relations between the electromagnetic two-forms and source three-forms while the electromagnetic medium is defined through a constitutive…
In the present paper it is shown that the Maxwell theory can be finely represented in the matrix form of Dirac's equation, if the Dirac wave function is identified with the electromagnetic wave by defined way. It seems to us, that such…
We develop a general methodology for numerical computations of electromagnetic (EM) fields and forces in matter, based on solving the macroscopic Maxwell's equations in real space and adopting the Maxwell Stress Tensor formalism. Our…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…
It was shown recently that the constraints on the initial data for Einstein's equations may be posed as an evolutionary problem [9]. In one of the proposed two methods the constraints can be replaced by a first order symmetrizable…
Future developments of lighter, more compact and powerful motors-driven by environmental and sustainability considerations in the transportation industry-involve higher stresses, currents and electromagnetic fields. Strong couplings between…
In plasma simulations, where the speed of light divided by a characteristic length is at a much higher frequency than other relevant parameters in the underlying system, such as the plasma frequency, implicit methods begin to play an…
In this work, a new integral equation (IE) based formulation is proposed using vector and scalar potentials for electromagnetic scattering. The new integral equations feature decoupled vector and scalar potentials that satisfy Lorentz…