Related papers: The Maxwell-Volterra reciprocity law in electrodyn…
We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.
A new term describing interactions between charge and potentials may be added to the right hand side of the Einstein equations. In the proposed term an additional tensor has been introduced containing a charge density, analogous to the…
In the present paper, we introduce a multibasic extension of the Ehrhart theory. We give a multibasic extension of Ehrhart polynomials and Ehrhart series. We also show that an analogue of Ehrhart reciprocity holds for multibasic Ehrhart…
This paper proves a reciprocity formula for modular inverses for non-zero integers and demonstrates some applications of the reciprocity formula in calculating or verifying some modular inverses of specific forms, including the modular…
Author presents mathematical model for acting-on-a-distance attractive and repulsive forces based on propagation of energy waves that produces Newton expression for gravitational and Coulomb expression for electrostatic forces. Model uses…
In the recent decades, it became more and more popular for engineers, physicists, and mathematicians alike to put the Maxwell equations into a generally covariant form. This is particularly useful for understanding the fundamental structure…
The derivation of the Maxwell equations is reproduced whereby magnetic charges are included. This ansatz yields the results: 1) Longitudinal Ampere forces in a differential magnetostatic force law are improbable. Otherwise an electric…
We derive self-reciprocity properties for a number of polyomino generating functions, including several families of column-convex polygons, three-choice polygons and staircase polygons with a staircase hole. In so doing, we establish a…
We use the residue theorem to derive an expression for the number of lattice oints in a dilated n-dimensional tetrahedron with vertices at lattice points on each coordinate axis and the origin. This expression is known as the Ehrhart…
We consider an inverse boundary problem for the dynamical Maxwell's equations. We show that the electric permittivity, conductivity, and magnetic permeability can be uniquely determined locally if there is a strictly convex foliation with…
The Lorentz reciprocal theorem -- that is used to study various transport phenomena in hydrodynamics -- is violated in chiral active fluids that feature odd viscosity with broken time-reversal and parity symmetries. Here we show that the…
A classical general relativistic theory possessing magnetic currents, as well electric ones and admitting massive photons was built up. As the geometric basis serves a space with Weylian non-metricity and torsion. The theory is coordinate…
Maxwell's equations describe the relation of charge and electric force almost perfectly even though electrons and permanent charge were not in his equations, as he wrote them. For Maxwell, all charge depended on electric field. Charge was…
Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a q-deformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the…
The study explores the conformable electromagnetic field theory. The concept of the conformable delta function is introduced. Subsequently, the conformable Maxwell's equations are derived.
We present a method for calculating ab initio interatomic forces which scales quadratically with the size of the system and provides a physically transparent representation of the force in terms of the spatial variation of the electronic…
A general law for electromagnetic induction phenomena is derived from Lorentz force and Maxwell equation connecting electric field and time variation of magnetic field. The derivation provides with a unified mathematical treatment the…
The motion visualization in a structural component was studied for defect detection. Elastic motions were excited by hammer impacts at multiple points and received by an accelerometer at a fixed point. Reciprocity in elastodynamics is only…
Electroosmotic pumping of fluid through a nanopore that traverses an insulating membrane is considered. The density of surface charge on the membrane is assumed uniform, and sufficiently low for the Poisson-Boltzmann equation to be…
In this effort we show that the Legendre reciprocity relations,thermodynamic's essential formal feature, are respected by any entropic functional, even if it is NOT of trace-form nature, as Shannon's is. Further, with reference to the…