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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 ISSN 1063-651X.
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Official URL: http://dx.doi.org/10.1103/PhysRevE.67.021401
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 | ||||
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Subjects: | Q Science > QC Physics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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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 (Creative Commons) | ||||
Date of first compliant deposit: | 1 August 2016 | ||||
Date of first compliant Open Access: | 1 August 2016 | ||||
Funder: | European Commission (EC) | ||||
Grant number: | HPMF-CT-2000-00800 (EC) |
Data sourced from Thomson Reuters' Web of Knowledge
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