Past Event: Oden Institute Seminar

Schrödinger’s Smoke

Albert Chern, Applied and Computational Mathematics, Caltech.

Abstract

Nearly inviscid incompressible fluids has been a challenging study in analysis and numerical simulation. We introduce a new framework for describing incompressible fluids. In it, the fluid state is represented by a wavefunction evolving under the Schrödinger equation subject to incompressibility constraints. The underlying dynamics satisfies the Euler equation modified with a Landau-Lifshitz force. The latter not only regularizes the singular nature of the Euler equation, but also ensures that dynamics due to thin vortical structures are faithfully reproduced. This enables robust simulation of intricate phenomena such as vortical wakes and interacting vortex filaments, even on modestly sized grids. The numerical algorithms for time evolution are exceedingly simple. In the talk I will also discuss the underlying theory which reveals fascinating relations between the Clebsch variables in classical fluids, spins in quantum mechanics, Landau-Lifshitz theory of ferromagnetic material, and the geometry of the 3-sphere. This is a joint work with Peter Schröder from Caltech, and Felix Knöppel, Steffen Weißmann, Ulrich Pinkall from TU Berlin. Bio: Albert Chern is PhD candidate in Applied and Computational Mathematics at Caltech. Research interest: Fluid Dynamics, Computational Math, Discrete Differential Geometry, Computer Graphics.