Presentation on theme: "QUIZ Which of these convection patterns is non-Boussinesq?"— Presentation transcript:
QUIZ Which of these convection patterns is non-Boussinesq?
Homological Characterization Of Convection Patterns Kapilanjan Krishan Marcio Gameiro Michael Schatz Konstantin Mischaikow School of Physics School of Mathematics Georgia Institute of Technology Supported by: DOE, DARPA, NSF
Patterns and Drug Delivery Caffeine in Polyurethane Matrix D. Saylor et al., (U.S. Food and Drug Administration)
Patterns and Strength of Materials Maximal Principal Stresses in Alumina E. Fuller et al., (NIST)
Patterns and Convection Camera Light Source Reduced Rayleigh number =(T-T c )/ T c =0.125 Convection cell
Spiral Defect Chaos
Homology Using algebra to determine topology Simplicial Cubical Representations
Time ~ 10 3 Number of connected components Hot flow vs. Cold flow
Time ~ 10 3 Percentage of connected components Hot flow vs. Cold flow
Convergence to Attractor Frequency of occurrence cold 0 : Number of cold flow components ( ~1 )
Entropy Joint Probability P( hot 0, cold 0, hot 1, cold 1 ) Entropy (- P i log P i ) Bifurcations?
Entropy vs epsilon Entropy=8.3Entropy=7.9 Entropy=8.9
Space-Time Topology 1-D Gray-Scott model Space Time Time Series—First Betti number Exhbits Chaos
Summary Homology characterizes complex patterns Underlying symmetries detected in data Alternative measure of boundary effects Detects transitions between complex states Space-time topology may reveal new insights Homology source codes available at: http://www.math.gatech.edu/~chomp