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Anisotropic diffusion limited aggregation in three dimensions : universality and nonuniversality

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Goold, Nicholas R., Somfai, Ellák and Ball, R. C.. (2005) Anisotropic diffusion limited aggregation in three dimensions : universality and nonuniversality. Physical Review E, Vol.72 (No.3). ISSN 1539-3755

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Official URL: http://dx.doi.org/10.1103/PhysRevE.72.031403

Abstract

We explore the macroscopic consequences of lattice anisotropy for diffusion limited aggregation (DLA) in three dimensions. Simple cubic and bcc lattice growths are shown to approach universal asymptotic states in a coherent fashion, and the approach is accelerated by the use of noise reduction. These states are strikingly anisotropic dendrites with a rich hierarchy of structure. For growth on an fcc lattice, our data suggest at least two stable fixed points of anisotropy, one matching the bcc case. Hexagonal growths, favoring six planar and two polar directions, appear to approach a line of asymptotic states with continuously tunable polar anisotropy. The more planar of these growths visually resembles real snowflake morphologies. Our simulations use a new and dimension-independent implementation of the DLA model. The algorithm maintains a hierarchy of sphere coverings of the growth, supporting efficient random walks onto the growth by spherical moves. Anisotropy was introduced by restricting growth to certain preferred directions.

Item Type:	Journal Article
Subjects:	Q Science > QD Chemistry
Divisions:	Faculty of Science > Physics
Library of Congress Subject Headings (LCSH):	Aggregation (Chemistry) -- Mathematical models, Anisotropy, Diffusion
Journal or Publication Title:	Physical Review E
Publisher:	American Physical Society
ISSN:	1539-3755
Date:	September 2005
Volume:	Vol.72
Number:	No.3
Number of Pages:	10
Identification Number:	10.1103/PhysRevE.72.031403
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	European Commission (EC), Engineering and Physical Sciences Research Council (EPSRC), Higher Education Funding Council for England (HEFCE)
Grant number:	HPMF-CT-2000-00800 (EC)
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URI:	http://wrap.warwick.ac.uk/id/eprint/34485