Topological Analysis of Patterns

Marcio Gameiro

ISBN 10: 3836459051 / ISBN 13: 9783836459051

Published by VDM Verlag Dr. Müller, 2009

About this Item

nach der Bestellung gedruckt Neuware - Printed after ordering - 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.

Seller Inventory # 9783836459051

Bibliographic Details

• Title: Topological Analysis of Patterns
• Publisher: VDM Verlag Dr. Müller
• Publication Date: 2009
• Language: English
• ISBN 10: 3836459051
• ISBN 13: 9783836459051
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 22W x 15H x 0.6D centimeters 22 centimeters width by 15 centimeters height by 0.6 centimeters depth
• Weight: 171 grams

About this title

Synopsis

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.

About the Author

Marcio Gameiro, Masters in Electrical and Computer Engineering and PhD in Mathematics. Georgia Institute of Technology.