Studying Fluid Flows with Persistent Homology - Rachel Levanger
Institute for Advanced Study via YouTube
Overview
Syllabus
Intro
DYNAMICS
PATTERNS
2D Kolmogorov Flow
Sublevel Set Persistent Homology
Bottleneck Distance in per
Point Cloud Persistent Homology
Dealing with Multiple Time Scales
Algebraic Stability Theorem for Generalized Interleavings
2D Rayleigh-Bénard Convection : Spiral Defect Chaos
Lyapunov Vectors and SDC
Topological Defects + Canonical Pattern Classification
Critical Point Pairings and Persistent Homology
Persistent Homology Defects
Finding a Correspondence...
Tangled Vines in a Vineyard of Persistence Diagrams
Linear Interpolation vs. Actual Flow
BEYOND PERSISTENCE MODULES
3D Navier-Stokes: Fully-developed Turbulence
Diffusion Maps
Landscape Metric on per
Diffusion Map Embedding of 512 Vorticity Fields
RESULT:Uncovered a New Relationship
Tsurushima Mechanism for HCCI
Landscape l'Speed Profiles
Differentiating Chemical Species by Speed Profile
Reaction Profile: R1
Taught by
Institute for Advanced Study