Mean-field approach to random Apollonian packing

Pierre Auclair
Phys. Rev. E 107, 034129 – Published 17 March 2023

Abstract

We revisit the scaling properties of growing spheres randomly seeded in d=2,3, and 4 dimensions using a mean-field approach. We model the insertion probability without assuming a priori a functional form for the radius distribution. The functional form of the insertion probability shows an unprecedented agreement with numerical simulations in d=2,3, and 4 dimensions. We infer from the insertion probability the scaling behavior of the random Apollonian packing and its fractal dimensions. The validity of our model is assessed with sets of 256 simulations each containing 20×106 spheres in two, three, and four dimensions.

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  • Received 18 November 2022
  • Accepted 2 March 2023

DOI:https://doi.org/10.1103/PhysRevE.107.034129

©2023 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsPolymers & Soft MatterStatistical Physics & Thermodynamics

Authors & Affiliations

Pierre Auclair*

  • Cosmology, Universe and Relativity at Louvain (CURL), Institute of Mathematics and Physics, University of Louvain, 2 Chemin du Cyclotron, 1348 Louvain-la-Neuve, Belgium

  • *pierre.auclair@uclouvain.be

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Issue

Vol. 107, Iss. 3 — March 2023

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