Title: A Computational Geometry Approach for an Ensemble-based Topological Entropy Calculation in Two and Three Dimensions
Short Abstract: We will explore the single motivating issue of my graduate career: How to best extract meaningful information inherent to highly dynamic and chaotic fluid flows from limited amounts of data. Namely, I will present my efforts combining existing topological techniques with tools from computational geometry to compute mixing rates from potentially-sparse sets of system trajectories. A new algorithm in 2D will be introduced and verified on both theoretical and experimental data. Lastly, with a generalization to 3D, I present the first algorithm for quantifying 3D complexity requiring no knowledge of the governing equations.