Analysis and Modeling of Pattern Formation in Biological and Physical Systems

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Lega0075827 The investigator uses numerical simulations and analytictechniques related to amplitude equations to study patternformation dynamics in swimming bacteria, wave number selection ina Swift-Hohenberg equation modeling traveling wave patterns, andtraveling hole solutions of the complex Ginsburg-Landau equation. The broad topics of pattern formation and the behavior ofpatterns are widely important in mathematics and in applicationareas. The investigator studies the conditions under whichcertain equations have solutions that show such patterns, andwhat these patterns say about the underlying physical orbiological problems.