Related papers: On the fields due to line segments
The assumption that matter charges and currents could generate fields, which are called, by analogy with electromagnetism, gravitoeletric and gravitomagnetic fields, dates from the origins of General Relativity (GR). On the other hand, the…
Problems involving boundary conditions on corrugated surfaces are relevant to understand nature, since, at some scale, surfaces manifest corrugations that have to be taken into account. In introductory level electromagnetism courses, a very…
Some highlights of the priority in the discovery of the gravitational field equations are given.
A generalization of the Einstein equation is considered for complex line elements. Several second order semilinear partial differential equations are derived from it as semilinear field equations in uniform and isotropic spaces. The…
The solution of some equations involving functional derivatives is given as a series indexed by planar binary trees. The terms of the series are given by an explicit recursive formula. Some algebraic properties of these series are…
This article traces the origins of Kenneth Wilson's conception of effective field theories (EFTs) in the 1960s. I argue that what really made the difference in Wilson's path to his first prototype of EFT are his long-standing pragmatic…
The paper is devoted to vector fields on the spaces R^2 and R^3, their flow and invariants. Attention is plaid on the tensor representations of the group GL(2,R) and on fundamental vector fields. The rotation group on R^3 is generalized to…
Oleg D. Jefimenko's electrodynamics textbook is unique in its approaches to deriving the electric and magnetic fields of arbitrary charge and current distributions and of an arbitrarily moving point charge. However, an uncommon form of the…
We show that a three rank Lanczos type tensor field is an appropriate choice to describe relativistic electromagnetic and gravitational effects. More precisely, we identify the irreducible field-decompositions of this tensor as…
The paper aims to apply the complex-octonions to explore the variable gravitational mass and energy gradient of several particles in the external ultra-strong magnetic fields. J. C. Maxwell was the first to introduce the algebra of…
Carter derived the forms of the metric and the vector potentials of the space-times in which the relativistic Schrodinger equation for the motion of a charged particle separates. Here we show that on each `spheroidal' surface a rotation…
We calculate the electrostatic potential and electric field of a uniformly charged disk everywhere in space. This electrostatic problem was solved long ago, and its gravitational analogue - even earlier. However, it seems that physics…
We describe some instances of the appearance of Chern's mathematical ideas in physics. By means of simple examples, we bring out the geometric and topological ideas which have found application in describing the physical world. These…
Inspired by the prospect of having discretized spaces emerge from random graphs, we construct a collection of simple and explicit exponential random graph models that enjoy, in an appropriate parameter regime, a roughly constant vertex…
Helmholtz decomposition theorem for vector fields is presented usually with too strong restrictions on the fields. Based on the work of Blumenthal of 1905 it is shown that the decomposition of vector fields is not only possible for…
We study estimates of the Green's function in $\mathbb{R}^d$ with $d \ge 2$, for the linear second order elliptic equation in divergence form with variable uniformly elliptic coefficients. In the case $d \ge 3$, we obtain estimates on the…
An approach to the teaching of electromagnetism to senior undergraduate students, designed for overcoming the fragmentation of the theory is described. As usual it starts from the static case, but it is strictly based on Helmholtz theorem…
We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors…
Green's famous essay (Nottingham, 1828), with which he introduced the potential function, was transcribed from its reprint in Crelle's Journal (1850-54), with several typographical corrections and a reference section added. Green starts…
In this note, we provide a important considerations of a familiar topic: the gradient of a vector field. The gradient of a vector field is a common quantity represented in continuum mechanics. However, even for Cartesian coordinate systems,…