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.
| Identifer | oai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/7207 |
| Date | 19 July 2005 |
| Creators | Gameiro, Marcio Fuzeto |
| Publisher | Georgia Institute of Technology |
| Source Sets | Georgia Tech Electronic Thesis and Dissertation Archive |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
| Format | 6424682 bytes, application/pdf |
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