137 citations · 584 across the 21 of their papers we have counts for
5 papers · 1 filter
Statistical Topology of Perturbed Two-Dimensional Lattices
Hannes Leipold, Emanuel A. Lazar, Kenneth A. Brakke +1
The Voronoi cell of any atom in a lattice is identical. If atoms are perturbed from their lattice coordinates, then the topologies of the Voronoi cells of the atoms will change. We…
A Topological Framework for Local Structure Analysis in Condensed Matter
Emanuel A. Lazar, Jian Han, David J. Srolovitz
Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems d…
Geometric and topological properties of the canonical grain growth microstructure
Jeremy K. Mason, Emanuel A. Lazar, Robert D. MacPherson +1
Many physical systems can be modeled as large sets of domains "glued" together along boundaries - biological cells meet along cell membranes, soap bubbles meet along thin films, co…
Coarsening in one dimension: invariant and asymptotic states
Emanuel Lazar, Robin Pemantle
We study a coarsening process of one-dimensional cell complexes. We show that if cell boundaries move with velocities proportional to the difference in size of neighboring cells, t…
On fiber diameters of continuous maps
Peter S. Landweber, Emanuel A. Lazar, Neel Patel
We present a surprisingly short proof that for any continuous map , if , then there exists no bound on the diameter of fibers of …