Title: Exact coherent structures in spatiotemporal chaos: 

 From qualitative description to quantitative predictions

Date: Tuesday November 3, 2015

Time: 3:00 PM

Room: N110, Howey Physics Building

Thesis Advisor: Predrag Cvitanovic

Abstract:

The term spatiotemporal chaos refers to physical phenomena that exhibit irregular oscillations in both space and time. Examples of such phenomena range from cardiac dynamics to fluid turbulence, where the motion is described by nonlinear partial differential equations. It is well known from the studies of low dimensional chaotic systems that the state space, the space of solutions to the governing dynamical equations, is shaped by the invariant sets such as equilibria, periodic orbits, and invariant tori. State space of partial differential equations is infinite dimensional, nevertheless, recent computational advancements allow us to find their invariant solutions numerically. In this thesis, we try to elucidate the chaotic dynamics of nonlinear partial

differential equations by studying their exactly coherent solutions and invariant manifolds. Specifically, we investigate the Kuramoto-Sivashinsky equation, which describes the velocity of a flame front, and the Navier-Stokes equations for an incompressible fluid in a circular pipe. We argue with examples that this approach can lead to a theory of turbulence with predictive power.

Thesis committee:

Predrag Cvitanovic (Advisor, School of Physics)

Roman Grigoriev (School of Physics)

Ahmet Turgay Uzer (School of Physics)

Michael Schatz (School of Physics)

Wilfrid Gangbo (School of Mathematics)