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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). 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

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:

Date	Event
13 February 2003	Published

Volume:

Vol.67

Number:

No.2

Number of Pages:

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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