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Scaling and crossovers in diffusion limited aggregation

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Somfai, Ellák, Sander, Leonard M. (Leonard Michael) and Ball, R. C.. (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
Date:	27 December 1999
Volume:	Vol.83
Number:	No.26
Number of Pages:	4
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:	[1] T.A. Witten and L.M. Sander, Phys. Rev. Lett, 47, 1400 (1981). [2] P. Meakin, in Phase Transitions and Critical Phenomena, eds. C. Domb and J. L. Lebowitz, Vol.12 (Academic, NY, 1988). [3] M. B. Hastings and L. S. Levitov, Physica D 116, 244 (1998). [4] B. Davidovitch, H. G. E. Hentschel, Z. Olami, I. Procaccia, L. M. Sander, and E. Somfai, Phys. Rev. E 59, 1368 (1999). [5] T. A. Witten and L. M. Sander, Phys. Rev. B 27, 2586 (1983). [6] L. Niemeyer, L. Pietronero and H.J. Wiessmann, Phys. Rev. Lett. 52, 1033 (1984). [7] M. Plischke and Z. R´acz, Phys. Rev. Lett. 53, 415 (1984) [8] P. Meakin and L. M. Sander, Phys. Rev. Lett. 54, 2053 (1985). [9] B. B. Mandelbrot, H. Kaufman, A. Vespignani, I. Yekutieli, and C.-H. Lam, Europhys. Lett. 29, 599 (1995). [10] W. W. Mullins and R. F. Sekerka, J. Appl. Phys. 34, 323 (1963). [11] T.C. Halsey, P. Meakin and I. Procaccia, Phys. Rev. Lett. 56, 854 (1986). [12] This estimate differs from the calculation in Appendix B of Ref. [4] because in that paper \|Z\| in our Eq.6 was implicitly replaced by ro. We believe this to be too crude an approximation. [13] P. W. Barker and R. C. Ball, Phys. Rev. A 42,6289 (1990). [14] R. C. Ball, L. M. Sander, and E. Somfai, to be published.
URI:	http://wrap.warwick.ac.uk/id/eprint/13830