Analysis and Modeling of Pattern Formation in Biological and Physical Systems

研究者使用数值模拟和与振幅方程相关的分析技术来研究游泳细菌的模式信息动力学，在斯威夫特-霍恩伯格方程中建模行波模式的波数选择，以及复杂Ginsburg-Landau方程的行孔解。模式形成和模式行为的广泛主题在数学和应用领域中非常重要。研究者研究在何种条件下某些方程的解显示出这种模式，以及这些模式对潜在的物理或生物问题的说明。

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.