Complex Systems and Biological Physics Seminars

Spatiotemporal tiling of the Kuramoto-Sivashinsky equation.

by Mr Matthew Gudorf (Georgia Tech)

Europe/Stockholm
Fysikum equipment

Fysikum equipment

Description

Motivated by space-time translational invariance, `spatiotemporally chaotic' or `turbulent' flows are recast as a (D+1)-dimensional spatiotemporal theory which treats space and time equally. In this formulation time evolution is replaced by a repertoire of spatiotemporal patterns taking the form of (D+1) dimensional invariant tori. Infinite space-time is then explained by the shadowing of these tori. This is formalized by the development of a (D+1)-dimensional symbolic dynamics whose alphabet is comprised of space-time tori of minimal size. Enumerating these spatiotemporal building blocks enables the construction of all admissible spatiotemporal patterns. These ideas are investigated in the context of the Kuramoto-Sivashinsky equation using new, open source spatiotemporal computational computing package 'orbithunter'. These codes are designed to offer easy access to new spatiotemporal techniques, persistent homology, convolutional neural networks and more.

The talk will be given on zoom https://kth-se.zoom.us/j/61653304385