Shape and selfsimilarity of diffusion-limited aggregation clusters
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.
KeywordsSeed Particle Angular Moment Growth Rule Viscous Finger Measured Exponent
Unable to display preview. Download preview PDF.
- Argoul, F., Arneodo, A., Elezgaray, J., Grasseau, G., Murenzi, R., Phys. Rev. A41, 5537Google Scholar
- Ball, R.C., Brady, R.M. (1985): J. Phys. A 18, L809Google Scholar
- Kolb, M. (1984): J. PHysique Lett. 46, L631Google Scholar
- Kolb, M. (1987): J. Phys. A 20, L285Google Scholar
- Lam, C.H., Kaufman, H., Mandelbrot, B.B. (1995): J. Phys. A 28, L213Google Scholar
- Mandelbrot, B.B., Vespignani, A., Kaufman, H. (1995): MRS (USA) Symp. Proc. Vol. 367, p. 73Google Scholar
- Meakin, P. (1985): J. Phys. A 18, L661Google Scholar
- Meakin, P. (1988): “Phase Transitions and Critical Phenomena”, Vol. 12, p. 336, C. Domb and J.L. Lebowitz (Eds.) Academic, LondonGoogle Scholar
- Wen, W., Lu, K. (1997): Phys. Rev. E55, R2100Google Scholar