Stationary Apollonian Packings

The notion of stationary Apollonian packings in the d -dimensional Euclidean space is introduced as a mathematical formalization of so-called random Apollonian packings and rotational random Apollonian packings, which constitute popular grain packing models in physics. Apart from dealing with issues...

Full description

Saved in:
Bibliographic Details
Published inJournal of statistical physics Vol. 161; no. 1; pp. 35 - 72
Main Authors Hirsch, Christian, Delaney, Gary, Schmidt, Volker
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2015
Springer
Subjects
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
60D05
Growth model
Fractal germ-grain model
28A80
Dense packing
05C70
Continuum percolation
Online AccessGet full text

Cover

More Information
Summary:The notion of stationary Apollonian packings in the d -dimensional Euclidean space is introduced as a mathematical formalization of so-called random Apollonian packings and rotational random Apollonian packings, which constitute popular grain packing models in physics. Apart from dealing with issues of existence and uniqueness in the entire Euclidean space, asymptotic results are provided for the growth durations and it is shown that the packing is space-filling with probability 1, in the sense that the Lebesgue measure of its complement is zero. Finally, the phenomenon is studied that grains arrange in clusters and properties related to percolation are investigated.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-015-1326-6