Knotted solutions, from electromagnetism to fluid dynamics

From kinetic theory to dissipative fluid dynamics

We present the results of deriving the Israel-Stewart equations of relativistic dissipative fluid dynamics from kinetic theory via Grad’s 14-moment expansion. Working consistently to second order in the Knudsen number, these equations contain several new terms which are absent in previous treatments.

The Dynamics of Knotted Strings Attached to D-Branes

We extend the general solution to the Cauchy problem for the relativistic closed string (Phys. Lett. B404 (1997) 57-65) to the case of open strings attached to Dp-branes, including the cases where the initial data has a knotlike topology. We use this extended solution to derive intrinsic dynamical properties of open and closed relativistic strings attached to Dp-branes. We also study the singul...

Integrable Dynamics of Knotted Vortex Filaments

The dynamics of vortex filaments has provided for almost a century one of the most interesting connections between differential geometry and soliton equations, and an example in which knotted curves arise as solutions of differential equations possessing an infinite family of symmetries and a remarkably rich geometrical structure. These lectures discuss several aspects of the integrable dynamic...

Corrections to Fluid Dynamics

We propose a kinetic model of a fluid in which five macroscopic fields, the mass, energy, and three components of momentum, are conserved. The dynamics is constructed using the methods of statistical dynamics, and results in a discrete-time Markov chain for random fields on a lattice, followed by projection onto the information manifold. In the continuum limit we obtain a non-linear coupled par...

Nonlinear Fluid Dynamics From Gravity