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Scaling and crossovers in diffusion limited aggregation

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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. ISSN 0031-9007

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Official URL: http://dx.doi.org/10.1103/PhysRevLett.83.5523

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 > 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:

Page Range:

pp. 5523-5526

Identification Number:

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)

References:

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