相关论文: Towards a unified description of knotted light

In this chapter, we review the Ra\~{n}ada field line solutions of Maxwell's equations in the vacuum, which describe a topologically non-trivial electromagnetic field, as well as their relation with the knot theory. Also, we present a…

In this note we have further developed the study of topologically non-trivial solutions of vacuum electrodynamics. We have discovered a novel method of generating such solutions by applying conformal transformations with complex parameters…

The aims of this letter are three-fold: First is to show that nonlinear generalizations of electrodynamics support various types of knotted solutions in vacuum. The solutions are universal in the sense that they do not depend on the…

In this small note we ask several questions which are relevant to the construction of the self-consistent neutrino theory of light. The previous confusions in such attempts are explained in the more detailed publication.

Many papers have been published over the years that either conjecture or even (claim to) prove the universality of the form of Maxwell's equations. We present yet another derivation of Maxwell's equations and discuss the conclusions…

This paper is a concise introduction to virtual knot theory, coupled with a list of research problems in this field.

The gravitational field of an idealized plane-wave solution of the Maxwell equations can be described in closed form. After discussing this particular solution of the Einstein-Maxwell equations, the motion of neutral test particles, which…

Knotted solutions to electromagnetism and fluid dynamics are investigated, based on relations we find between the two subjects. We can write fluid dynamics in electromagnetism language, but only on an initial surface, or for linear…

We present a new range of solutions of the Maxwell equations in vacuum in which the topology of the field lines is that of the whole torus knots set. Knotted electromagnetic fields are solutions of the Maxwell equations in vacuum in which…

Knotted fields enrich a variety of physical phenomena, ranging from fluid flows, electromagnetic fields, to textures of ordered media. Maxwell's electrostatic equations, whose vacuum solution is mathematically known as a harmonic field,…

The idea of monotonicity (or positive-definiteness in the linear case) is shown to be the central theme of the solution theories associated with problems of mathematical physics. A "grand unified" setting is surveyed covering a…

At a first glance, the problem of illuminating the boundary of a convex body by external light sources and the problem of covering a convex body by its smaller positive homothetic copies appear to be quite different. They are in fact two…

The unification of gravity to the other forces has been a major problem for most of the last century. I use a modification to Newtonian gravitation to extract the strong and weak nuclear coupling constants. Some of the possible implications…

The complex relationship between Einstein's second postulate and the Maxwell electromagnetic theory is elucidated. A simple deduction of the main results of the Ignatowski approach to the theory of relativity is given. The peculiar status…

We construct a family of exact solutions to Maxwell's equations in which the points of zero intensity form knotted lines topologically equivalent to a given but arbitrary algebraic link. These lines of zero intensity, more commonly referred…

The aim of this chapter is to make a review of the recent results using the Enclosure Method on inverse obstacle problems governed by the wave equation and the Maxwell system in time domain. We also describe some of unsolved problems…

A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.

This article shows the relations between the electricity, magnetism, gravity and mechanics by presenting an existing hidden structure in the Maxwell equations. This hidden structure allows to discover the classical physic from a new point…

The existence of twisted light may be inferred from modern quantum concepts and experimental data. These waves possess energy, impulse and angular momentum. However, the Maxwell's four-dimensional theory of electromagnetism does not imply…

We investigate the cylindrical class of Newman Tamburino equations in the presence of an aligned Maxwell field. After obtaining a complete integration of the field equations we look at the possible vacuum limits and we examine the…