publication . Article . 2005

Anisotropic diffusion limited aggregation in three dimensions : universality and nonuniversality

Nicholas R. Goold; Ellák Somfai; Robin C. Ball;
Open Access English
  • Published: 01 Sep 2005
  • Publisher: American Physical Society
  • Country: United Kingdom
We explore the macroscopic consequences of lattice anisotropy for diffusion limited aggregation (DLA) in three dimensions. Simple cubic and bcc lattice growths are shown to approach universal asymptotic states in a coherent fashion, and the approach is accelerated by the use of noise reduction. These states are strikingly anisotropic dendrites with a rich hierarchy of structure. For growth on an fcc lattice, our data suggest at least two stable fixed points of anisotropy, one matching the bcc case. Hexagonal growths, favoring six planar and two polar directions, appear to approach a line of asymptotic states with continuously tunable polar anisotropy. The more p...
free text keywords: QD, Statistics and Probability, Statistical and Nonlinear Physics, Condensed Matter Physics, Anisotropy, Diffusion-limited aggregation, Physics, Random walk, Fixed point, Cubic crystal system, Lattice (order), Snowflake, Anisotropic diffusion
Related Organizations
32 references, page 1 of 3

1Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom 2Universiteit Leiden, Instituut-Lorentz, PO Box 9506, 2300 RA Leiden, The Netherlands (Dated: February 2, 2008)

[1] T. A. Witten and L. M. Sander, Phys. Rev. Lett. 47, 1400 (1981).

[2] M. Plischke and Z. R´acz, Phys. Rev. Lett. 53, 415 (1984).

[3] A. Coniglio and M. Zannetti, Physica A 163, 325 (1990).

[4] E. Somfai, L. M. Sander, and R. C. Ball, Phys. Rev. Lett. 83, 5523 (1999).

[5] C. Amitrano, Phys. Rev. A 39, 6618 (1989).

[6] M. H. Jensen, J. Mathiesen, and I. Procaccia, Phys. Rev. E 67, 042402 (2003).

[7] E. Somfai, N. R. Goold, R. C. Ball, J. P. Devita, and L. M. Sander, Phys. Rev. E 70, 051403 (2004).

[8] J. S. Langer, Rev. Mod. Phys. 52, 1 (1980).

[9] W. W. Mullins and R. F. Sekerka, J. Appl. Phys. 34, 323 (1963).

[10] J. Nittmann, G. Daccord, and H. E. Stanley, Nature 314, 141 (1985).

[11] M. Matsushita, M. Sano, Y. Hayakawa, H. Honjo, and Y. Sawada, Phys. Rev. Lett. 53, 286 (1984).

[12] R. M. Brady and R. C. Ball, Nature 309, 225 (1984).

[13] L. Niemeyer, L. Pietronero, and H. J. Wiesmann, Phys. Rev. Lett. 52, 1033 (1984).

[14] J. Nittman and H. E. Stanley, J. Phys. A: Math. Gen. 20, L1185 (1987).

32 references, page 1 of 3
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue