Related papers: Knotted solutions, from electromagnetism to fluid …
This paper explores the quantum-fluid correspondence in a charged relativistic fluid with intrinsic spin. We begin by examining the nonrelativistic case, showing that the inclusion of spin introduces a quantum correction to the classical…
Electromagnetic waves, solving the full set of Maxwell equations in vacuum, are numerically computed. These waves occupy a fixed bounded region of the three dimensional space, topologically equivalent to a toroid. Thus, their fluid dynamics…
We identify that for a broad range of parameters a variant of the soliton solution of the one-dimensional non-linear Schr\"{odinger} equation, the {\it breather}, is distinct when one studies the associated space curve (or soliton surface),…
We employ the relationship between contact structures and Beltrami fields derived in part I of this series to construct steady nonsingular solutions to the Euler equations on a Riemannian $S^3$ whose flowlines trace out closed curves of all…
We develop a covariant formalism to study nonlinear perturbations of dissipative and interacting relativistic fluids. We derive nonlinear evolution equations for various covectors defined as linear combinations of the spatial gradients of…
A classical problem for the two-dimensional Euler flow for an incompressible fluid confined to a smooth domain. is that of finding regular solutions with highly concentrated vorticities around $N$ moving {\em vortices}. The formal dynamic…
Closed nonrelativistic (nonretarded) theory of conservative and dissipative electromagnetic forces and heat exchange between moving particles (nanoprobes) and a surface (flat and cylindrical) is reviewed. The formalism is based on methods…
The problem of two stiff fluids (energy density = pressure) moving radially in spherical symmetry is treated. The metric ansatz is chosen spherically symmetric, conformally static with a multiplicative separation of variables. The first…
The paper considers the nonlinear electrodynamics type model and its relation with relativistic hydrodynamics with no dissipation (including string and membrane hydrodynamics). We are able to convert arbitrary flux of fluid to the family of…
The coupling of the electromagnetic field to gravity is an age-old problem. Presently, there is a resurgence of interest in it, mainly for two reasons: (i) Experimental investigations are under way with ever increasing precision, be it in…
Exact self-consistent particle-like solutions with spherical and/or cylindrical symmetry to the equations governing the interacting system of scalar, electromagnetic and gravitational fields have been obtained. As a particular case it is…
A computational fluid dynamics methodology for the simulation of electromagnetic interactions in compressible reacting flows has been formulated. The developed code, named EMI, is based on the SENGA Direct Numerical Simulation (DNS)…
We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is…
We introduce and examine a collection of unusual electromagnetic disturbances. Each of these is an exact, monochromatic solution of Maxwell's equations in free space with looped electric and magnetic field lines of finite extent and a…
We investigate the trajectories of point charges in the background of finite-action vacuum solutions of Maxwell's equations known as knot solutions. More specifically, we work with a basis of electromagnetic knots generated by the so-called…
We study exact solutions of nonlinear electrodynamics coupled to three-dimensional gravity with torsion. We show that in any static and spherically symmetric configuration, at least one component of the electromagnetic field has to vanish.…
Making use of the equivalence between paraxial wave equation and two-dimensional Schr\"odinger equation, Gaussian beams of monochromatic light, possessing knotted nodal structures are obtained in an analytical way. These beams belong to the…
It is shown that the set of equations known as Maxwell's equations perfectly describe two very different systems: (1) the usual electromagnetic phenomena in vacuum or in the matter and (2) the deformation of isotropic solid lattices,…
We construct a new family of null solutions to Maxwell's equations in free space whose field lines encode all torus knots and links. The evolution of these null fields, analogous to a compressible flow along the Poynting vector that is both…
This fluid dynamics video shows "knotted" vortices in real fluids.