Measures of order for imperfect two-dimensional patterns
Motivated by patterns with defects in natural and laboratory systems, we develop two quantitative measures of order for imperfect Bravais lattices in the plane. A tool from topological data analysis called persistent homology combined with the sliced Wasserstein distance, a metric on point distributions, are the key components for defining these measures. We also study imperfect hexagonal, square, and rhombic arrangements of nanodots produced by numerical simulations of pattern-forming partial differential equations and apply the measures to study packing on surfaces.
2 Responses
Is this talk recorded somwhere?
Hi Shakeeb – I’m just waiting for Patrick to give me permission to upload the talk. It will be made public eventually.