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 3-dimensional patterns it also provides the number of voids. 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. These techniques allow us to distinguish patterns at different parameter values, to detect complicated dynamics through the computation of positive Lyapunov exponents and entropies, to compare experimental data with numerical simulations, to quantify boundary effects on finite size domains, among other things.

Thèse doctorat : Images et Systèmes : Villeurbanne, INSA : 2005. / Thèse rédigée en anglais. Titre provenant de l'écran-titre. Bibliogr. p. 87-99.

Thesis (Ph. D.)--University of Oregon, 2001. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 98-99). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p3025008.

Thesis (doctoral)--Friedrichs-Universität Halle-Wittenberg, 1912. / Vita. Includes bibliographical references (p. [74]-86).

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (Ph. D.) -- University of Maryland, College Park, 2006. / Includes bibliographical references (leaves 117-119). Also available online.

Thesis (M. Phil.)--University of Hong Kong, 1981.

Not available / text

Not available / text