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A general recipe proposed elsewhere to define, via Noether theorem, the variation of energy for a natural field theory is applied to Einstein-Maxwell theory. The electromagnetic field is analysed in the geometric framework of natural…
We study the well-posedness theory for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations in a bounded domain. We express the magnetic field in terms of the velocity field and the deformation tensors…
A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…
We present a numerical method for the solution of linear magnetostatic problems in domains with a symmetry direction, including axial and translational symmetry. The approach uses a Fourier series decomposition of the vector potential…
We study invariant random fields of nonlinear multiplicative stochastic heat equations in the weak disorder regime. Under a natural second-moment condition, we show that positive invariant fields are in one-to-one correspondence with…
In the presence of a variable magnetic field, the Weyl pseudodifferential calculus must be modified. The usual modification, based on ``the minimal coupling principle'' at the level of the classical symbols, does not lead to gauge invariant…
A comparison between the two possible variational principles for the study of a free falling spinless particle in a space-time with torsion is noted. It is well known that the autoparallel trajectories can be obtained from a variational…
We derive the covariant equations of motion for Maxwell field theory and electrodynamics in multiscale spacetimes with weighted Laplacian. An effective spacetime-dependent electric charge of geometric origin naturally emerges from the…
Quantum electrodynamics (QED) effects may be included in physical processes of magnetar and pulsar magnetospheres with strong magnetic fields. Involving the quantum corrections, the Maxwell electrodynamics is modified to non-linear…
We present a geometric formulation of classical Cosserat elasticity in which the coframe and rotational connection are treated as independent variational fields. In contrast to conventional metric-based approaches, this formulation makes…
The variational principle for a spherical configuration consisting of a thin spherical dust shell in gravitational field is constructed. The principle is consistent with the boundary-value problem of the corresponding Euler-Lagrange…
This paper presents a set of complete solutions of a nonconvex variational problem with a double-well potential. Based on the canonical duality-triality theory, the associated nonlinear differential equation with either Dirichlet/Neumann or…
When describing elastic deformations of a body sometimes it is worth to take in account elastic spatial dispersion. If spatial dispersion is weak, as usually happens, then it can be reduced to dependence of thermodynamic potential on strain…
It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to…
The governing equations of Maxwell electrodynamics in multi-dimensional spaces are derived from the variational principle of least action which is applied to the action function of the electromagnetic field. The Hamiltonian approach for the…
We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is…
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 our previous article [4] an approach to derive Papapetrou equations for constrained electromagnetic field was demonstrated by use of field variational principles. The aim of current work is to present more universal technique of…
We study differential equations, describing interaction of electromagnetic field with moving sidebars and surfaces, coming from integral electrodynamics laws. It is shown that differential equations contain but the such features of…
The foundations of gyrokinetic theory are reviewed with an emphasis on the applications of Lagrangian and Hamiltonian methods used in the derivation of nonlinear gyrokinetic Vlasov-Maxwell equations. These reduced dynamical equations…