Ball, R. C. and Somfai, Ellák. (2003) Diffusion-controlled growth : theory and closure approximations. Physical Review E, Vol.67 (No.2). ISSN 1063-651X

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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
Date:	13 February 2003
Volume:	Vol.67
Number:	No.2
Number of Pages:	11
Identification Number:	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)
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URI:	http://wrap.warwick.ac.uk/id/eprint/9919

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