Somfai, Ellák, Sander, Leonard M. (Leonard Michael) and Ball, Robin (1999) Scaling and crossovers in diffusion limited aggregation. Physical Review Letters, Vol.83 (No.26). pp. 5523-5526. doi:10.1103/PhysRevLett.83.5523

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Abstract

We discuss the scaling of characteristic lengths in diffusion limited aggregation clusters in light of recent developments using conformal maps. We are led-to the:conjecture that the apparently anomalous scaling of lengths is due to one slow crossover. This is supported by an analytical argument for the scaling of the penetration depth of newly arrived random walkers, and by numerical evidence on the Laurent coefficients which uniquely determine each cluster. We find common crossover behavior for the squares of the characteristic lengths and the penetration depth of the form N-2/D(alpha + beta N-phi) With phi in the range -0.3 +/- 0.1 suggesting that there is a single: dominant correction to scaling.

Item Type:	Journal Article
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, Random walks (Mathematics)
Journal or Publication Title:	Physical Review Letters
Publisher:	American Physical Society
ISSN:	0031-9007
Official Date:	27 December 1999
Dates:	Date Event 27 December 1999 Published
Volume:	Vol.83
Number:	No.26
Number of Pages:	4
Page Range:	pp. 5523-5526
DOI:	10.1103/PhysRevLett.83.5523
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	United States. Dept. of Energy, Isaac Newton Institute for Mathematical Sciences
Grant number:	DEFG-02-95ER-45546 (DOE)

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