Related papers: Legendre transforms for electrostatic energies
Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure…
Electromagnetic phenomena can be described by Maxwell equations written for the vectors of electric and magnetic field. Equivalently, electrodynamics can be reformulated in terms of an electromagnetic vector potential. We demonstrate that…
Theories of solvation free energies often involve electrostatic potentials at the position of a solute charge. Simulation calculations that apply cutoffs and periodic boundary conditions based on molecular centers result in center-dependent…
Electric and magnetic current densities are an essential part of electromagnetic theory. The goal of the present paper is to define and investigate stored energies that are valid for structures that can support both electric and magnetic…
This note is a geometric commentary on maximum-entropy proofs. Its purpose is to illustrate the geometric structures involved in such proofs, to explain more in detail why the maximization of the entropy can be turned into the minimization…
The standard model of classical Density Functional Theory for pair potentials consists of a hard-sphere functional plus a mean-field term accounting for long ranged attraction. However, most implementations using sophisticated Fundamental…
Finite-field calculations in periodic insulators are technically and conceptually challenging, due to fundamental problems in defining polarization in extended solids. While significant progress has been made recently with the establishment…
In order to explore electric-field-induced transformations of polarization singularities in the polarization-resolved angular (conoscopic) patterns emerging after deformed helix ferroelectric liquid crystal (DHFLC) cells with subwavelength…
We show that there exists a choice of gauge in which the electromagnetic 4-potential may be written as the difference of two 4-velocity vector fields describing the motion of a two-component space-filling relativistic fluid. Maxwell's…
The dynamics of a charged relativistic particle in electromagnetic field of a rotating magnetized celestial body with the magnetic axis inclined to the axis of rotation is studied. The covariant Lagrangian function in the rotating reference…
A simple mathematical procedure is introduced which allows redefining in an exact way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once…
In this paper, we introduce a new classical fractional particle model incorporating fractional first derivatives. This model represents a natural extension of the standard classical particle with kinetic energy being quadratic in fractional…
Following Brown[1], we construct composite operators for the scalar $\phi^3$ theory in six dimensions using renormalisation group methods with dimensional regularisation. We express bare scalar operators in terms of renormalised composite…
Artstein-Avidan and Milman [Annals of mathematics (2009), (169):661-674] characterized invertible reverse-ordering transforms on the space of lower semi-continuous extended real-valued convex functions as affine deformations of the ordinary…
The electromagnetic fields of the hybrid modes of an optical fiber are reformulated using bi-complex mathematics, which leads to simpler expressions relative to those found with the widely used, conventional complex formulation. Generalized…
It is shown that geometric optical description of electromagnetic wave with account of its polarization in curved space-time can be obtained straightforwardly from the classical variational principle for electromagnetic field. For this end…
This paper offers a pedestrian guide from the fundamental properties of entropy to the axioms of thermodynamics, which are a consequence of the axiom of statistical physics. It also dismantles flawed concepts, such as assigning physical…
Geometric continuum models for fluid lipid membranes are considered using classical field theory, within a covariant variational approach. The approach is cast as a higher-derivative Lagrangian formulation of continuum classical field…
We determine the electrostatic self-force at rest in an arbitrary static metric with cylindrical symmetry in the linear approximation in the Newtonian constant. In linearised Einstein theory, we express it in terms of the components of the…
A recently proposed technique is described that provides improved nearside-farside (NF) decompositions of elastic scattering amplitudes. The technique, involving a new resummation formula for Legendre partial wave series, reduces the…