Related papers: Note on transformation to general curvilinear coor…
The purpose of this effort is to investigate if the use of quaternion mathematics can be used to better model and simulate the electromagnetic fields that occur from moving electromagnetic charges. One observed deficiency with the commonly…
Maxwell's equations are modified to incorporate a scalar field to account for the London's superconductivity. Assuming the electromagnetic field is described by the Klein-Gordon equation, London's equations of superconductivity are then…
In recent years, the $H$ formulation of Maxwell's equation has become the de facto standard for simulating the time-dependent electromagnetic behavior of superconducting applications with commercial software. However, there are cases where…
Complex vector fields with Maxwell, Chern-Simons and Proca terms are minimally coupled to an Abelian gauge field. The consistency of the spectrum is analysed and 1-loop quantum corrections to the self-energy are explicitly computed and…
Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector…
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,…
We devise and analyze hybrid polyhedral methods of arbitrary order for the approximation of div-curl systems on three-dimensional domains featuring non-trivial topology. The div-curl systems we are interested in stem from magnetostatics,…
This paper deals with the modelling of superconducting and resistive wires with a helicoidal symmetry, subjected to an external field and a transport current. Helicoidal structures are three-dimensional, and therefore yield computationally…
In general relativity, Maxwell's equations are embedded in curved spacetime through the minimal prescription, but this could change if strong-gravity modifications are present. We show that with a nonminimal coupling between gravity and a…
Teaching magnetism is one of the most challenging topics at undergraduate level in programmes with scientific background. A basic course includes the description of the magnetic interaction along with empirical results such as the…
In this paper it is exactly proved that the standard transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not relativistically correct transformations. Thence the 3D vectors E and B are not…
Using Maxwell's mental imagery of a tube of fluid motion of an imaginary fluid, we derive his equations $\operatorname{curl} \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$, $\operatorname{curl} \mathbf{H} = \frac{\partial…
In the past five years, there has been considerable research on the collider phenomenology of TeV-scale extra compact dimensions which are universal - i.e. accessible to all the Standard Model fields. We consider in detail a fundamental…
We derive Maxwell equations for electric and magnetic fields in curved spacetime from first principles, relaxing an unnecessary assumption on the structure of the four-potential inherent to the standard approach and thus restoring the full…
The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…
The magnetic flux dynamics of type-II superconductors within the critical state regime is posed in a generalized framework, by using a variational theory supported by well established physical principles. The equivalence between the…
Defining the electric and magnetic field vectors in curved spacetime requires a proper choice of the observer's frame four-vector. Related literature shows that this fundamental issue in physics still needs to be properly resolved. In…
The relation M = mu x B is presented in all elementary courses on electromagnetism but it is usually given just for the simple case of a rectangular wire. We will present a completely general but elementary proof of this relation together…
In curved spacetime, Maxwell's equations can be expressed in forms valid in Minkowski background, with the effect of the metric (gravity) appearing as effective polarizations and magnetizations. The electric and magnetic (EM) fields depend…
Suppose that X is a complex projective variety and L is a pseudo-effective divisor. A numerical reduction map is a quotient of X by all subvarieties along which L is numerically trivial. We construct two variants: the L-trivial reduction…