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Diffusion-controlled growth : theory and closure approximations

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Ball, Robin and Somfai, Ellák. (2003) Diffusion-controlled growth : theory and closure approximations. Physical Review E, Vol.67 (No.2). ISSN 1063-651X

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Official URL: http://dx.doi.org/10.1103/PhysRevE.67.021401

Abstract

We expand upon a new theoretical framework for diffusion-limited aggregation and associated dielectric breakdown models in two dimensions [R. C. Ball and E. Somfai, Phys. Rev. Lett. 89, 135503 (2002)]. Key steps are understanding how these models interrelate when the ultraviolet cut-off 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 discussed. We find angular resonances relatable to the cone angle theory, and we are led to predict a new screening transition in the DBM at large eta.

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 E
Publisher:	American Physical Society
ISSN:	1063-651X
Official Date:	13 February 2003
Volume:	Vol.67
Number:	No.2
Number of Pages:	11
Identification Number:	10.1103/PhysRevE.67.021401
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] W. W. Mullins and R. F. Sekerka, J. Appl. Phys. 34, 323 (1963). [2] T. A. Witten and L. M. Sander, Phys. Rev. Lett. 47, 1400 (1981). [3] R. C. Ball, in On Growth and Form, edited by H. E. Stanley and N. Ostrowski (Martinus Nijhoff, Dordrecht, 1986), pp. 69–78. [4] L. Niemeyer, L. Pietronero, and H. J. Wiesmann, Phys. Rev. Lett. 52, 1033 (1984). [5] R. C. Ball and E. Somfai, Phys. Rev. Lett. 89, 135503 (2002), cond-mat/0205660. [6] C. Amitrano, A. Coniglio, P. Meakin, and M. Zannetti, Phys. Rev. B 44, 4974 (1991). [7] T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman, Phys. Rev. A 33, 1141 (1986). [8] M. Plischke and Z. R´acz, Phys. Rev. Lett. 53, 415 (1984). [9] A. Coniglio and M. Zannetti, Physica D 38, 37 (1989). [10] B. B. Mandelbrot, B. Kol, and A. Aharony, Phys. Rev. Lett. 88, 055501 (2002), cond-mat/0109426. [11] P. Meakin and L. M. Sander, Phys. Rev. Lett. 54, 2053 (1985). [12] E. Somfai, L. M. Sander, and R. C. Ball, Phys. Rev. Lett. 83, 5523 (1999), cond-mat/9909040. [13] R. C. Ball, N. E. Bowler, L. M. Sander, and E. Somfai, Phys. Rev. E 66, 026109 (2002), cond-mat/0108252. [14] R. Ball, M. Nauenberg, and T. A. Witten, Phys. Rev. A 29, 2017 (1984). [15] R. C. Ball and T. A. Witten, Phys. Rev. A 29, 2966 (1984). [16] L. A. Turkevich and H. Scher, Phys. Rev. Lett. 55, 1026 (1985). [17] R. C. Ball, Physica A 140, 62 (1986). [18] T. C. Halsey, Phys. Rev. Lett. 59, 2067 (1987). [19] T. C. Halsey and M. Leibig, Phys. Rev. A 46, 7793 (1992). [20] N. G. Makarov, P. Lond. Math. Soc. 51, 369 (1985). [21] B. Shraiman and D. Bensimon, Phys. Rev. A 30, 2840 (1984). [22] J. S. Langer, Rev. Mod. Phys. 52, 1 (1980). [23] F. Barra, B. Davidovitch, A. Levermann, and I. Procaccia, Phys. Rev. Lett. 87, 134501 (2001), condmat/ 0103126. [24] L. M. Sander, P. Ramanlal, and E. Ben-Jacob, Phys. Rev. A 32, 3160 (1985). [25] D. A. Kessler and H. Levine, Phys. Rev. Lett. 86, 4532 (2001). [26] P. W. Barker and R. C. Ball, Phys. Rev. A 42, R6289 (1990). [27] R. Cafiero, L. Pietronero, and A. Vespignani, Phys. Rev. Lett 70, 3939 (1993). [28] R. Kubo, J. Phys. Soc. Japan 17, 1100 (1962). [29] R. C. Ball and O. R. Spivack, J. Phys. A 23, 5295 (1990). [30] M. H. Jensen, A. Levermann, J. Mathiesen, and I. Procaccia, Phys. Rev. E 65, 046109 (2002), condmat/ 0110203. [31] P. Ossadnik, Physica A 176, 454 (1991). [32] E. Somfai, L. M. Sander, and R. C. Ball, (in preparation). [33] A. Sanchez, F. Guinea, L. M. Sander, V. Hakim, and E. Louis, Phys. Rev. E 48, 1296 (1993). [34] M. B. Hastings, Phys. Rev. E 64, 046104 (2001), condmat/ 0104344. [35] T. C. Halsey, Phys. Rev. E 65, 021104 (2002), condmat/ 0105047. [36] M. B. Hastings, Phys. Rev. Lett. 87, 175502 (2001), cond-mat/0103312. [37] D. A. Kessler, Z. Olami, J. Oz, I. Procaccia, E. Somfai, and L. M. Sander, Phys. Rev. E 57, 6913 (1998).
URI:	http://wrap.warwick.ac.uk/id/eprint/9919