Meanfield approach to random Apollonian packing
Abstract
We revisit the scaling properties of growing spheres randomly seeded in d =2 ,3 , and 4 dimensions using a meanfield 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 ×10^{6} spheres in two, three, and four dimensions.
 Publication:

Physical Review E
 Pub Date:
 March 2023
 DOI:
 10.1103/PhysRevE.107.034129
 arXiv:
 arXiv:2211.07509
 Bibcode:
 2023PhRvE.107c4129A
 Keywords:

 Mathematical Physics;
 Condensed Matter  Soft Condensed Matter
 EPrint:
 11 pages, 8 figures