Related papers: Unexplored aspects of a variational principle in e…
We formulate variation principle for force-free magnetosphere of an inclined pulsar: ${\cal E} +{\bf \Omega}\cdot {\bf M}$ ($\cal E$, ${\bf M}$ are electromagnetic energy and angular momentum, ${\bf \Omega}$ is the angular velocity of a…
Electric field plays an important role in ferroelectric phase transition. There have been numerous phase field formulations attempting to account for electrostatic interactions subject to different boundary conditions. In this paper, we…
This paper deals with the problem of a point-like charged source under the influence of the external electromagnetic field in terms of perturbation theory for GR equations. It is obtained that GR, in contrast with the classical…
A variational theory is developed to study electrolyte solutions, composed of interacting point-like ions in a solvent, in the presence of dielectric discontinuities and charges at the boundaries. Three important and non-linear…
The article presents an alternative approach to the definition of vector electrodynamic potential and its properties. It is shown that generally it has vortical and potential components. The system of differential equations of generalized…
A dynamic diffraction theory is developed for describing electron diffraction by dielectric crystals in a strong electromagnetic field. It is shown that additional diffraction maxima arise in an electromagnetic field, their intensity…
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 variational formulation of electrodynamics using de Rham even and odd differential forms. Our formulation relies on a variational principle more complete than the Hamilton principle and thus leads to field equations with…
It is a matter of common knowledge that the field of gravitation influences the propagation of light, but the question to which extent electromagnetic fields do something similar is not completely answered. The birefringence caused by…
We present a new variational principle for linking models of beams and deformable solids, providing also its mathematical analysis. Despite the apparent differences between the two types of governing equations, it will be shown that the…
Long-ranged electrostatic interactions in electrolytes modify their contact angles on charged substrates in a scale and geometry dependent manner. For angles measured at scales smaller than the typical Debye screening length, the wetting…
It is common practice to take for granted the equality (up to the constant $\varepsilon_0$) of the electric displacement ($\bf{D}$) and electric ($\bf{E}$) field vectors in vacuum. The same happens with the magnetic field ($\bf{H}$) and the…
Electrostatic forces play many important roles in molecular biology, but are hard to model due to the complicated interactions between biomolecules and the surrounding solvent, a fluid composed of water and dissolved ions. Continuum model…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
A geometrical approach to calculate the electric field due to a uniformly charged rod is presented. The result is surprisingly simple and elegant. Using pure geometrical quantities like length and angle, the direction of the electric field…
It is shown that when the well-known minimal complementary energy variational principle in linear elastostatics is written in a different form with the strain tensor as an independent variable and the constitutive relation as one of the…
The Dirichlet Principle is an approach to solving the Dirichlet problem by means of a Dirichlet energy integral. It is part of the folklore of mathematics that the genesis of this argument was motivated by physical analogy involving…
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…
The dispersion relation of vertically oscillating fluid surfaces has been a subject extensively studied in the past, as well as surface instabilities produced by electrohydrodynamic (EHD) waves in similar configurations. In the present work…
Several features of electrostatics of point charged particles in a weak, homogeneous, gravitational field are discussed using the Rindler metric to model the gravitational field. Some previously known results are obtained by simpler and…