Volume 55, Number 5, September 2001
|Page(s)||679 - 685|
|Section||Condensed matter: structure, mechanical and thermal properties|
|Published online||01 December 2003|
High-dimensional diffusive growth
Center for Nonlinear Studies, MS B258, Los Alamos National
Laboratory Los Alamos, NM 87545, USA
2 Corporate Strategic Research, ExxonMobil Research and Engineering Route 22 East, Annandale, NJ 08801, USA
Corresponding author: firstname.lastname@example.org
Accepted: 14 June 2001
We consider a model of aggregation, both diffusion-limited and ballistic, based on the Cayley tree. Growth is from the leaves of the tree towards the root, leading to non-trivial screening and branch competition effects. The model exhibits a phase transition between ballistic and diffusion-controlled growth, with non-trivial corrections to cluster size at the critical point. Even in the ballistic regime, cluster scaling is controlled by rare events due to the branching structure of the Cayley tree; it is this that enables us to solve the model.
PACS: 61.43.Hv – Fractals; macroscopic aggregates (including diffusion-limited aggregates) / 47.53.+n – Fractals / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EDP Sciences, 2001
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