Related papers: Expressing Maxwell's equations independently of th…
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
We present an educational proposal which aims to illustrate the elegant, refined and coherent physics contained in Thermodynamics, through a path which assigns to the microscopic description of the physical systems a constantly privileged…
A process-theoretic approach to electrodynamics based on persistent Kac-type stochastic processes is developed. Finite-velocity stochastic propagation is taken as primary, while relativistic wave equations arise as emergent descriptions…
We speculate that the universe may be filled with a visco-elastic continuum which may be called aether. Thus, the Maxwell's equations in vacuum are derived by methods of continuum mechanics based on a continuum mechanical model of vacuum…
The present tutorial aims at covering the fundamentals of electromagnetism, in a condensed and clear manner. Some solved and proposed exercises have been included. The reader is assumed to have knowledge of basic electricity, partial…
Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…
A number of physical phenomena are described by nonlinear hyperbolic equations. Presence of discontinuous solutions motivates the necessity of development of reliable numerical methods based on the fundamental mathematical properties of…
A new method to find the propagation equation system governing the scattering of an electromagnetic wave by a nonlinear medium is proposed. The aim is to let the effects appear spontaneously, deleting as far as possible the phenomenological…
A modified Faraday's law of electromagnetic induction in media is put forward.
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
Almost all theories of physics have expressed physical laws by means of differential equations. One can ask: why differential equations? What is special about them? This article addresses these questions and is presented as an inquiry-based…
We present an alternative Eulerian hydrodynamic model for the electromagnetic field in which the discrete vector indices in Maxwell\s equations are replaced by continuous angular freedoms, and develop the corresponding Lagrangian picture in…
It is shown how point charges and point dipoles with finite self-energies can be accomodated into classical electrodynamics. The key idea is the introduction of constitutive relations for the electromagnetic vacuum, which actually mirrors…
Introductory calculus-based physics textbooks state that electromagnetic waves are transverse and list many of their properties, but most such textbooks do not bring forth arguments why this is so. Both physical and theoretical arguments…
A suitable correction of the Maxwell model brings to an enlargement of the space of solutions, allowing for the existence of solitons in vacuum. We review the basic achievements of the theory and discuss some approximation results based on…
A formulation of the Maxwell equations in terms of the split octonions is presented.
Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant…
The illuminating role of differential forms in electromagnetism is seldom discussed in the classroom. It is the aim of this article to bring forth some of the relevant insights that can be learnt from a differential forms approach to E\&M.…
Experience collected in mesoscopic dynamic modeling of externally driven systems indicates absence of potentials that could play role of equilibrium or nonequilibrium thermodynamic potentials yet their thermo-dynamics-like modeling is often…
These lecture notes for the course APM 351 at the University of Toronto are aimed at mathematicians and physicists alike. It is not meant as an introductory course to PDEs, but rather gives an overview of how to view and solve differential…