Shape and selfsimilarity of diffusion-limited aggregation clusters

Kolb, M.

doi:10.1007/BFb0106848

Shape and selfsimilarity of diffusion-limited aggregation clusters

M. Kolb¹

Conference paper
First Online: 01 January 2007

248 Accesses

Part of the book series: Lecture Notes in Physics ((LNP,volume 519))

Abstract

Diffusion-limited aggregation (DLA) is a paradigm of disordered, diffusion-controlled growth, with experimental applications ranging from viscous fingering to the growth of biological colonies. An important question still under debate are the shape and the fractal properties of the structure in the asymptotic limit. A related issue is the response of shape to various modifications of the elementary growth rules, such as anisotropy and noise.

Standard and modified off-lattice DLA growth rules were investigated by direct simulation. The global characteristics of the angular moments and the outermost tips were analysed in order to test the selfsimilarity of DLA. The results show a slight but distinct deviation from selfsimilarity, consistent with previous geometric investigations of the completed central portion of DLA aggregates. To study the effect of the particle size, a modified version of DLA, in which the monomer size changes with the particle index, has been simulated. The measured exponents characterizing the cluster geometry differ from the standard DLA values.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

References

Argoul, F., Arneodo, A., Grasseau, G., Swinney, H.J. (1988): Phys. Rev. Lett. 61, 2558
Article ADS Google Scholar
Argoul, F., Arneodo, A., Elezgaray, J., Grasseau, G., Murenzi, R., Phys. Rev. A41, 5537
Google Scholar
Arneodo, A., Argoul, F., Muzy, J.F., Tabard, M. (1992): Physica A188, 217
ADS Google Scholar
Ball, R.C., Brady, R.M. (1985): J. Phys. A 18, L809
Google Scholar
Ball, R.C. (1986): Physica 140A, 62
ADS Google Scholar
Barker, P.W., Ball, R. (1990): Phys. Rev. A 42, 6289
ADS Google Scholar
Brener, E., Levine, H., Tu, Y. (1991): Phys. Rev. Lett. 66, 1978
Article ADS Google Scholar
Boularot, H., Albinet, G. (1996): Phys. Rev. E 53, 5106
ADS Google Scholar
Cafiero, R., Pietronero, L, Vespignani, A. (1993): Phys. Rev. Lett. 70, 3939
Article ADS Google Scholar
Coniglio, A. (1993): Physica A200, 165
ADS Google Scholar
Hakanishi, H., Family, F. (1985): Phys. Rev. A32, 3606
ADS Google Scholar
Halsey, T., Leibig, M. (1992): Phys. Rev. A46, 7793
ADS Google Scholar
Jullien, R., Kolb, M., Botet, R. (1984): J. Physique 45, 395
Article Google Scholar
Jarecki, J. (1997): Phys. Rev. E56, 3301
ADS Google Scholar
Kessler, D.A., Koplik, J., Levine, H. (1990): Adv. Phys. 37, 255
Article ADS Google Scholar
Kolb, M. (1984): J. PHysique Lett. 46, L631
Google Scholar
Kolb, M. (1987): J. Phys. A 20, L285
Google Scholar
Lam, C.H., Kaufman, H., Mandelbrot, B.B. (1995): J. Phys. A 28, L213
Google Scholar
Mandelbrot, B.B. (1992): Physica A 191, 95
ADS Google Scholar
Mandelbrot, B.B., Vespignani, A., Kaufman, H. (1995): MRS (USA) Symp. Proc. Vol. 367, p. 73
Google Scholar
Mandelbrot, B.B., Kaufman, H., Vespignani, A., Yekutieli, I. Lam, C.H. (1995): Europhys. Lett. 29, 599
Article ADS Google Scholar
Mandelbrot, B.B., Vespignani, A., Kaufman, H. (1995): Europhys. Lett. 32, 199
Article ADS Google Scholar
Matsushita, M., Sano, M., Hayaskawa, Y., Honjo, H., Sawada, Y. (1984): Phys. Rev. Lett. 53, 286
Article ADS Google Scholar
Meakin, P., Sander, L.M. (1985): Phys. Rev. Lett. 54, 2053
Article ADS Google Scholar
Meakin, P., Vicsek, T. (1985): Phys. Rev. A 32, 685
ADS Google Scholar
Meakin, P. (1985): J. Phys. A 18, L661
Google Scholar
Meakin, P. (1988): “Phase Transitions and Critical Phenomena”, Vol. 12, p. 336, C. Domb and J.L. Lebowitz (Eds.) Academic, London
Google Scholar
Michely, T., Hohage, M., Bott, M., Comsa, G. (1993): Phys. Rev. Lett. 70, 3943
Article ADS Google Scholar
Montag, J.L., Family, F., Vicsek, T. (1985): Phys. Rev. A32, 2558
ADS Google Scholar
Nittmann, J., Daccord, G., Stanley, H.E. (1985): Nature bf 34, 141
Article ADS Google Scholar
Ohgiwari, M., Matsushita, M., Matsuyama, T. (1992): J. Phys. Soc. Jap. 61, 816
Article ADS Google Scholar
Ossadnik, P. (1992): Phys. Rev. A45, 1058
ADS Google Scholar
Ossadnik, P., Lee, J. (1993): J. Phys. A26, 6789
ADS Google Scholar
Plischke, M., Racz, Z. (1984): Phys. Rev. Lett. 53, 415
Article ADS Google Scholar
Roeder, H., Bromann, K., Brune, H., Kern H. (1995): Phys. Rev. Lett. 74, 3217
Article ADS Google Scholar
Turkevitch, L., Scher, H. (1985): Phys. Rev. Lett. 55, 1026
Article ADS MathSciNet Google Scholar
Wang, X., Huang, Y. (1992): Phys. Rev. A46, 5038
ADS Google Scholar
Wen, W., Lu, K. (1997): Phys. Rev. E55, R2100
Google Scholar
Witten, T.A., Sander, L.M. (1981): Phys. Rev. Lett. 47, 1400
Article ADS Google Scholar
Yekutieli, I., Mandelbrot, B.B., Kaufman, H. (1994): J. Phys. A27, 275
ADS MathSciNet Google Scholar

Download references

Author information

Authors and Affiliations

Laboratoire de Chimie Théorique, Ecole Normale Superieure, 46 allée d’Italie, 69364, Lyon Cedex 07, France
M. Kolb

Authors

M. Kolb
View author publications
You can also search for this author in PubMed Google Scholar

Editor information

Andrzej Pękalski Katarzyna Sznajd-Weron

Rights and permissions

Reprints and permissions

Copyright information

About this paper

Cite this paper

Kolb, M. (1999). Shape and selfsimilarity of diffusion-limited aggregation clusters. In: Pękalski, A., Sznajd-Weron, K. (eds) Anomalous Diffusion From Basics to Applications. Lecture Notes in Physics, vol 519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0106848

Download citation

DOI: https://doi.org/10.1007/BFb0106848
Published: 03 May 2007
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65416-2
Online ISBN: 978-3-540-49259-7
eBook Packages: Springer Book Archive

Publish with us

Policies and ethics