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Ball, R. C. and Somfai, Ellák. (2002) Theory of diffusion controlled growth. Physical Review Letters, Vol.89 (No.13). ISSN 0031-9007
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Official URL: http://dx.doi.org/10.1103/PhysRevLett.89.135503
Abstract
We present a new theoretical framework for diffusion limited aggregation and associated dielectric breakdown models in two dimensions. Key steps are understanding how these models interrelate when the ultraviolet cutoff strategy is changed, the analogy with turbulence and the use of logarithmic field variables. Within the simplest, Gaussian, truncation of mode-mode coupling, all properties can be calculated. The agreement with prior knowledge from simulations is encouraging, and a new superuniversality of the tip scaling exponent is both predicted and confirmed.
| 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, Breakdown (Electricity) |
| Journal or Publication Title: | Physical Review Letters |
| Publisher: | American Physical Society |
| ISSN: | 0031-9007 |
| Date: | 23 September 2002 |
| Volume: | Vol.89 |
| Number: | No.13 |
| Number of Pages: | 4 |
| Identification Number: | 10.1103/PhysRevLett.89.135503 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Open Access |
| Funder: | European Commission (EC) |
| Grant number: | HPMF-CT-2000-00800 (EC) |
| References: | [1] T.A. Witten and L.M. Sander, Phys. Rev. Lett. 47, 1400 (1981). [2] R. C. Ball, in On Growth and Form, edited by H. E. Stanley and N. Ostrowski (Martinus Nijhof, Dordrecht, 1986) pp. 69–78. [3] L. Niemeyer, L. Pietronero and H.J. Wiesmann, Phys. Rev. Lett. 52, 1033 (1984). [4] C. Amitrano, A. Coniglio, P. Meakin and M. Zannetti, Phys.Rev. B 44, 4974 (1991). [5] T.C. Halsey, P. Meakin and I. Procaccia, Phys. Rev. Lett. 56, 854 (1986). [6] M. Plischke and Z. R´acz, Phys. Rev. Lett. 53, 415 (1984). [7] A. Coniglio and M. Zannetti, Physica D 38, 37 (1989). [8] B. B. Mandelbrot, B. Kol, and A. Aharony, Phys. Rev. Lett. 88, 055501 (2002). [9] P. Meakin and L.M. Sander, Phys. Rev. Lett. 54, 2053 (1985) [10] E. Somfai, L.M. Sander and R.C. Ball, Phys. Rev. Lett. 83, 5523 (1999). [11] R.C. Ball, N.E. Bowler, L.M. Sander and E. Somfai, cond-mat/0108252, submitted to Phys. Rev. E. [12] B. Shraiman and D. Bensimon, Phys. Rev. A 30, 2840 (1984). [13] J.S. Langer, Rev. Mod. Phys. 52, 1 (1980). [14] F. Barra, B. Davidovitch, A. Levermann and I. Procaccia, Phys. Rev. Lett. 87, 134501 (2001). [15] W.W. Mullins and R.F. Sekerka, J. Appl. Phys. 34, 323 (1963). [16] P. Ossadnik, Physica A 176, 454 (1991). [17] E. Somfai, R.C. Ball and L.M. Sander, (in preparation). [18] R. Kubo, J. Phys. Soc. Japan 17, 1100 (1962). [19] R.C. Ball and O.R. Spivack, J. Phys. A. (Lond) 23, 5295 (1990). [20] M.H. Jensen, A. Levermann, J. Mathiesen, I. Procaccia, Phys. Rev. E 65, 046109 (2002). [21] N.G. Makarov, P. Lond. Math. Soc. 51, 369 (1985). [22] T.C. Halsey and M. Leibig, Phys. Rev. A 46, 7793 (1992). [23] R.C. Ball, Physica A 140, 62 (1986). |
| URI: | http://wrap.warwick.ac.uk/id/eprint/10565 |
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