Statistical topology of perturbed two-dimensional lattices

Hannes Leipold, Emanuel A. Lazar, Kenneth A. Brakke, David J. Srolovitz

Research output: Contribution to journalArticlepeer-review


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 consider the distribution of Voronoi cell topologies in two-dimensional perturbed systems. These systems can be thought of as simple models of finite-temperature crystals. We give analytical results for the distribution of Voronoi topologies of points in two-dimensional Bravais lattices under infinitesimal perturbations and present a discussion with numerical results for finite perturbations.

Original languageEnglish
Article number043103
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number4
StatePublished - 13 Apr 2016
Externally publishedYes


  • exact results
  • networks
  • random graphs
  • random/ordered microstructures (theory)
  • stochastic processes (theory)

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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