Optimal packing of a finite collection of deformable objects How should space-filling, deformable objects be packed so as to minimize the area of the interfaces between them? In 3D the search for a packing of equal-volume shapes with minimum surface area is known as the Kelvin problem. In 2D the […]
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 […]