Size-topology correlations in disk packings

Terminal bidispersity in order-disorder transitions

Research output: Contribution to journalArticle

Abstract

In random packings or tilings, the size distribution of individual elements (domains) and the statistics of numbers of neighbours of those domains are strongly correlated. In the case of circular disks forming a random packing in the plane, it has long been known empirically that a certain critical amount of bidispersity avoids crystallization of the packing. We demonstrate how the formalism of a simplified granocentric model allows for an analytical computation of the sizetopology correlation as a function of both size ratio and frequency of small disks. The results, obtained without free parameters, are in excellent agreement with the empirical findings of packing simulations concerning critical (terminal) bidispersity. It is also shown that, at equal size variance, the discrete (bidisperse) disk size distributions induce stronger disorder than continuously polydisperse disks.

Original languageEnglish (US)
Pages (from-to)4018-4029
Number of pages12
JournalPhilosophical Magazine
Volume93
Issue number31-33
DOIs
StatePublished - Apr 8 2013

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topology
disorders
statistics
crystallization
formalism
simulation

Keywords

  • Disorder
  • Foams
  • Granular materials

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Size-topology correlations in disk packings : Terminal bidispersity in order-disorder transitions. / Hilgenfeldt, Sascha.

In: Philosophical Magazine, Vol. 93, No. 31-33, 08.04.2013, p. 4018-4029.

Research output: Contribution to journalArticle

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