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Diffusion-controlled growth : theory and closure approximations

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Ball, Robin and Somfai, Ellák (2003) Diffusion-controlled growth : theory and closure approximations. Physical Review E, Vol.67 (No.2). doi:10.1103/PhysRevE.67.021401

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Official URL: http://dx.doi.org/10.1103/PhysRevE.67.021401

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Abstract

We expand upon a new theoretical framework for diffusion-limited aggregation and associated dielectric breakdown models in two dimensions [R. C. Ball and E. Somfai, Phys. Rev. Lett. 89, 135503 (2002)]. Key steps are understanding how these models interrelate when the ultraviolet cut-off strategy is changed, the analogy with turbulence, and the use of logarithmic field variables. Within the simplest, Gaussian, truncation of mode-mode coupling, all properties can be calculated. The agreement with prior knowledge from simulations is encouraging, and a new superuniversality of the tip scaling exponent is discussed. We find angular resonances relatable to the cone angle theory, and we are led to predict a new screening transition in the DBM at large eta.

Item Type: Journal Article
Subjects: Q Science > QC Physics
Divisions: Faculty of Science > Physics
Library of Congress Subject Headings (LCSH): Aggregation (Chemistry) -- Mathematical models, Diffusion, Breakdown (Electricity)
Journal or Publication Title: Physical Review E
Publisher: American Physical Society
ISSN: 1063-651X
Official Date: 13 February 2003
Dates:
DateEvent
13 February 2003Published
Volume: Vol.67
Number: No.2
Number of Pages: 11
DOI: 10.1103/PhysRevE.67.021401
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
Funder: European Commission (EC)
Grant number: HPMF-CT-2000-00800 (EC)

Data sourced from Thomson Reuters' Web of Knowledge

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