相关论文: A variational formulation of electrodynamics with …

In this paper we present the formulation of relativistic electrodynamics (independent of the reference frame and of the chosen system of coordinates in it) that uses the Faraday bivector field F. This formulation with F field is a…

This paper revisits the geometric foundations of electromagnetic theory, by studying Faraday's concept of field lines. We introduce "covariant electromagnetic field lines," a novel construct that extends traditional field line concepts to a…

We present a new derivation of the expressions for momentum and energy of a relativistic particle. In contrast to the procedures commonly adopted in textbooks, the one suggested here requires only the knowledge of the composition law for…

We consider the bifurcation problem $u'' + \lambda u = N(u)$ with two point boundary conditions where $N(u)$ is a general nonlinear term which may also depend on the eigenvalue $\lambda$. We give a variational characterization of the…

We have studied the motion of antihydrogen atoms in electric and magnetic fields of arbitrary orientation. Our aim was to find an exact model of external (centre-of-charge) and internal dynamics which would allow us to describe antihydrogen…

This work studies time-dependent electromagnetic scattering from obstacles whose interaction with the wave is fully determined by a nonlinear boundary condition. In particular, the boundary condition studied in this work enforces a power…

The equations of electrostatics are presented in pre-metric form, and it is pointed out that if the origin of the nonlinearity is the constitutive law for the medium then the differential equations themselves remain linear, while the…

Continuum electrodynamics is an axiomatic formal theory based on the macroscopic Maxwell equations and the constitutive relations. We apply the formal theory to a thermodynamically closed system consisting of an antireflection coated block…

We propose a finite element discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, we derive a finite element method that arises from a…

Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. In a previous work Yahalom & Lynden-Bell introduced a simpler Eulerian variational principles from which all the…

General relativistic quantum dynamics of twisted (vortex) Dirac particles is constructed. The Hamiltonian and equations of motion in the Foldy-Wouthuysen representation are derived for a twisted relativistic electron in arbitrary electric…

We develop a calculus of variations for functionals which are defined on a set of non differentiable curves. We first extend the classical differential calculus in a quantum calculus, which allows us to define a complex operator, called the…

A modified system of equations of electrodynamics has been obtained. Beside the Lagrangian one an alternative gauge-like formalism has been developed to introduce the toroid moment contributions in the equations obtained. The two potential…

We have derived a variational principle that defines the nonequilibrium steady-state transport across a correlated impurity mimicking, e.g., a quantum dot coupled to biased leads. This variational principle has been specialized to a…

Let $1 \leq m \leq n$ be two integers and $\Omega \Subset \C^n$ a bounded $m$-hyperconvex domain in $\C^n$. Using a variational approach, we prove the existence of the first eigenvalue and an associated eigenfunction which is…

We extend topologically massive electrodynamics, both by adding a higher derivative action to cast the entire three-term model in Chern-Simons (CS) form, and by embedding it in an AdS background. It can then be written as the sum of two CS…

Electromagnetic radiation from an uncharged spin 1/2 particle with an anomalous magnetic moment moving in the classical electromagnetic external field originates from quantum spin-flip transitions. Although this process has a purely quantum…

Based on the requirement of covariance, we propose a new approach for generalizing fractional calculus in multi-dimensional space. As a first application we calculate an approximation for the ground state energy of the fractional…

In the framework of metric-free electrodynamics, we start with a {\em linear} spacetime relation between the excitation 2-form $H = ({\cal D}, {\cal H})$ and the field strength 2-form $F = ({E,B})$. This linear relation is constrained by…

We combine Taub's and Ray's variational approaches to relativistic hydrodynamics of perfect fluids into another simple formulation.