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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. doi:10.1103/PhysRevLett.83.5523
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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: |
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| Date of first compliant deposit: | 1 August 2016 | ||||
| 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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