Topological Analysis of Patterns » książka
Topological Analysis of Patterns
ISBN-13: 9783836459051 / Angielski / Miękka / 2009 / 104 str.
We use computational homology to characterize the geometry of complicated time-dependent patterns. Homology provides very basic topological (geometrical) information about the patterns, such as the number of components (pieces) and the number of holes. For three- dimensional patterns it also provides the number of enclosed cavities. We apply these techniques to patterns generated by experiments on spiral defect chaos, as well as to numerically simulated patterns in the Cahn-Hilliard theory of phase separation and on spiral wave patterns in excitable media. Some of the results obtained with these techniques include distinguishing patterns at different parameter values, detecting complicated dynamics through the computation of positive Lyapunov exponents and entropies, comparing experimental and numerically simulated data, and quantifying boundary effects on finite size domains.
We use computational homology to characterize thegeometry of complicated time-dependent patterns. Homologyprovides very basic topological (geometrical) information about thepatterns, such as the number of components (pieces) and the number ofholes. For three-dimensional patterns it also provides the number ofenclosed cavities. We apply these techniques to patterns generated byexperiments on spiral defect chaos, as well as to numericallysimulated patterns in the Cahn-Hilliard theory of phase separation and onspiral wave patterns in excitable media. Some of the results obtained withthese techniques include distinguishing patterns at differentparameter values, detecting complicated dynamics through the computation ofpositive Lyapunov exponents and entropies, comparing experimental andnumerically simulated data, and quantifying boundary effects onfinite size domains.
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