Related papers: Variational electrodynamics of Atoms
Gauge-invariant Wigner theory describes the quantum-mechanical evolution of charged particles in the presence of an electromagnetic field in phase space, which is spanned by position and kinetic momentum. This approach is independent of the…
We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic…
We derive from a microscopic Hamiltonian a set of stochastic equations of motion for a system of spinless charged particles in an electromagnetic (EM) field based on a consistent application of a dimensionful 1/c expansion of quantum…
We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of monotone and…
A new modified model of nonlinear arcsin-electrodynamics with two parameters is proposed and analyzed. We obtain the corrections to the Coulomb law. The effect of vacuum birefringence takes place when the external constant magnetic field is…
The theory of Bloch electron dynamics for carriers in homogeneous electric and magnetic fields of arbitrary time dependence is developed in the framework of the Liouville equation. The Wigner distribution function (WDF) is determined from…
Classical electrodynamics can be based on the conservation laws of electric charge and magnetic flux. Both laws are independent of the metric and the linear connection of spacetime. Within the framework of such a premetric electrodynamics…
We consider a Wheeler delayed-choice experiment based on the Mach-Zehnder Interferometer. Since the development of the causal interpretation of relativistic boson fields there have not been any applications for which the equations of motion…
We consider two classes of linear kinetic equations: with constant collision frequency and constant mean free path of gas molecules (i.e., frequency of molecular collisions, proportional to the modulus molecular velocity). Based homogeneous…
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…
We consider a bound system of charged particles moving in an external electromagnetic field, including leading relativistic corrections. The difference from the point particle with a magnetic moment comes from the presence of…
We derive the fully time-dependent solution to a run-and-tumble model for a particle which has tumbling restricted to the boundaries of a one-dimensional interval. This is achieved through a field-theoretic perturbative framework by…
We prove that the electromagnetic fields in dielectric media whose susceptibility follows a fractional power-law dependence in a wide frequency range can be described by differential equations with time derivatives of noninteger order. We…
A nonlinear phase-field model is developed to simulate corrosion damage. The motion of the electrode$-$ electrolyte interface follows the usual kinetic rate theory for chemical reactions based on the Butler-Volmer equation. The model links…
We rigorously construct a variety of orbits for certain delay differential equations, including the electrodynamic equations formulated by Wheeler and Feynman in 1949. These equations involve delays and advances that depend on the…
Electrical machines employing superconductors are attractive solutions in a variety of application domains. Numerical models are powerful and necessary tools to optimize their design and predict their performance. The electromagnetic…
In the present work, we establish space Bounded Variation $(BV)$ regularity of the solution for a non-linear parabolic partial differential equations involving a linear drift term. We study the problem in a bounded domain with mixed…
The gyrokinetic paradigm in the long wavelength regime is reviewed from the perspective of variational averaging (VA). The VA-method represents a third pillar for averaging kinetic equations with highly-oscillatory characteristics, besides…
Relativistic definition of the phase of the electromagnetic field, involving two Lorentz invariants, based on the Riemann-Silberstein vector is adopted to extend our previous study [I. Bialynicki-Birula, Z. Bialynicka-Birula and C. Sliwa,…
In this contribution we present how to obtain explicit state space models in port-Hamiltonian form when a mixed finite element method is applied to a linear mechanical system with non-uniform boundary conditions. The key is to express the…