Knotted solutions, from electromagnetism to fluid dynamics

Abstract

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 perturbations, and we use this map to find knotted fluid solutions, as well as new electromagnetic solutions. We find that knotted solutions of Maxwell electromagnetism are also solutions of more general nonlinear theories, like Born-Infeld, and including ones which contain quantum corrections from couplings with other modes, like Euler-Heisenberg and string theory DBI. Null configurations in electromagnetism can be described as a null pressureless fluid, and from this map we can find null fluid knotted solutions. A type of nonrelativistic reduction of the relativistic fluid equations is described, which allows us to find also solutions of the (nonrelativistic) Euler's equations.

36 pages, 3 figures

References in corpus (14)

• Heisenberg-Euler Effective Lagrangians : Basics and Extensions
• Effective field theory for hydrodynamics: thermodynamics, and the derivative expansion
• Tying knots in light fields
• The quantum mechanics of perfect fluids
• Vortex knots in a Bose-Einstein condensate
• More on Heisenberg's model for high energy nucleon-nucleon scattering
• Linked and knotted beams of light, conservation of helicity and the flow of null electromagnetic fields
• New knotted solutions of Maxwell's equations
• A Universe Without Dark Energy: Cosmic Acceleration from Dark Matter-Baryon Interactions
• Electromagnetic Torus Knots
• Knotted solutions for linear and nonlinear theories: electromagnetism and fluid dynamics
• Fuzzy Killing Spinors and Supersymmetric D4 action on the Fuzzy 2-sphere from the ABJM Model
• Nonlinear electrodynamics is skilled with knots
• DBI scalar field theory for QGP hydrodynamics

Cited by in corpus (13)

• Galactic Dynamics in General Relativity: the Role of Gravitomagnetism
• Scalar field as a null dust
• On the existence of the field line solutions of the Einstein-Maxwell equations
• Fluid-electromagnetic helicities and knotted solutions of the fluid-electromagnetic equations
• Finsler Geometries from Topological Electromagnetism
• Nonlinear dynamics of a charged particle in a strong non-null knot wave background
• CSBIon -- a charged soliton of the 3-dimensional CS + BI Abelian gauge theory
• Hopfion solutions in gravity and a null fluid/gravity conjecture
• Lagrangian formulation, generalizations and quantization of null Maxwell's knots
• Gravitoelectromagnetic knot fields
• Coupling ModMax theory precursor with scalars, and BIon-type solutions
• Gauge theories for fluids in 2+1 dimensions through master actions
• Knots and the Maxwell Equations