Topological Analysis of Patterns

Patterns;Topology;Homology

Gameiro, Marcio Fuzeto ; Mathematics

University:Georgia Institute of Technology

Department:Mathematics

关键词: Patterns;    Topology;    Homology;   

Others  :  https://smartech.gatech.edu/bitstream/1853/7207/1/gameiro_marcio_f_200508_phd.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

We use computational homology to characterize the geometry of complicatedtime-dependent patterns. Homology provides very basic topological (geometrical)information 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.