Dynamics of Spatial Pattern Formation: Cases of Spikes and Droplets

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Sasaki, Yuya
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dynamics; spatial; pattern; spikes; dropets; Mathematics
thesis / dissertation description
This thesis studies the gradient system that forms spatial patterns such that the minimum distances of pairs among various points are maximized in the end. As this problem innately involves singularity issues, an extended system of the gradient system is proposed. Motivated by the spatial pattern suggested by a numerical example, this extended system is applied to a three-point problem and then to a two-point problem in a quotient space of R2 modulo a lattice.