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Statistical topology of cellular networks in two and three dimensions

J. K. Mason*

E. A. Lazar† and R. D. MacPherson‡

D. J. Srolovitz§

  • Lawrence Livermore National Laboratory, Livermore, California 94550, USA

  • School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540, USA

  • Depts. of Materials Science and Engineering & Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

  • *mason47@llnl.gov
  • †lazar@math.ias.edu
  • ‡rdm@math.ias.edu
  • §srol@ihpc.a-star.edu.sg
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Phys. Rev. E 86, 051128 – Published 26 November, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.051128

Abstract

Cellular networks may be found in a variety of natural contexts, from soap foams to biological tissues to grain boundaries in a polycrystal, and the characterization of these structures is therefore a subject of interest to a range of disciplines. An approach to describe the topology of a cellular network in two and three dimensions is presented. This allows for the quantification of a variety of features of the cellular network, including a quantification of topological disorder and a robust measure of the statistical similarity or difference of a set of structures. The results of this analysis are presented for numerous simulated systems including the Poisson-Voronoi and the steady-state grain growth structures in two and three dimensions.

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Phys. Rev. E 86, 051128– Published 26 November, 2012
  • Received 12 September 2012
Article part of CHORUS

©2012 American Physical Society

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