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Topological Analysis of Patterns

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We use computational homology to characterize the geometry of complicatedtime-dependent patterns. Homology provides very basic topological geometricalinformation about the patterns, such as thenumber of components pieces andthe number of holes. For 3-dimensional patterns it also provides the number ofvoids. We apply these techniques to patterns generated by experiments on spiraldefect chaos, as well as to numerically simulated patterns in the Cahn-Hilliardtheory of phase separation and on spiral wave patterns in excitable media.These techniques allow us to distinguish patterns at different parameter values,to detect complicated dynamics through the computation of positive Lyapunovexponents and entropies, to compare experimental data with numerical simulations,to quantify boundary effects on finite size domains, among other things.

Georgia Tech Theses and Dissertations - School of Mathematics Theses and Dissertations -

Author: Gameiro, Marcio Fuzeto - -


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