Diffusion-limited aggregation: A continuum mean field model

作者: A. B. Ryabov , E. B. Postnikov , A. Yu. Loskutov

DOI: 10.1134/1.2047790

关键词:

摘要: Mean field theory is used as a basis for new approach to analyzing fractal pattern formation by diffusion-limited aggregation. A coarse time scale introduced take into account the discrete nature of DLA clusters. system equations derived and solved numerically determine dimension density cluster function distance from its center. The results obtained are in good agreement with direct numerical simulations.

参考文章(19)
Matthew B. Hastings, RENORMALIZATION THEORY OF STOCHASTIC GROWTH Physical Review E. ,vol. 55, pp. 135- 152 ,(1997) , 10.1103/PHYSREVE.55.135
Kaoru Ohno, Katsuhiko Kikuchi, Hiroshi Yasuhara, Continuous mean-field theory of the diffusion-limited-aggregation model Physical Review A. ,vol. 46, pp. 3400- 3404 ,(1992) , 10.1103/PHYSREVA.46.3400
R. Ball, M. Nauenberg, T. A. Witten, Diffusion-controlled aggregation in the continuum approximation Physical Review A. ,vol. 29, pp. 2017- 2020 ,(1984) , 10.1103/PHYSREVA.29.2017
T. A. Witten, L. M. Sander, Diffusion-limited aggregation, a kinetic critical phenomenon Physical Review Letters. ,vol. 47, pp. 1400- 1403 ,(1981) , 10.1103/PHYSREVLETT.47.1400
A. Erzan, L. Pietronero, A. Vespignani, The fixed-scale transformation approach to fractal growth Reviews of Modern Physics. ,vol. 67, pp. 545- 604 ,(1995) , 10.1103/REVMODPHYS.67.545
Ellák Somfai, Robin C. Ball, Jason P. DeVita, Leonard M. Sander, Diffusion-limited aggregation in channel geometry. Physical Review E. ,vol. 68, pp. 020401- ,(2003) , 10.1103/PHYSREVE.68.020401
A. Loskutov, D. Andrievsky, V. Ivanov, K. Vasiliev, A. Ryabov, Fractal growth of rotating DLA‐clusters Macromolecular Symposia. ,vol. 160, pp. 239- 248 ,(2000) , 10.1002/1521-3900(200010)160:1<239::AID-MASY239>3.0.CO;2-Q
Carl Evertsz, Self-affine nature of dielectric-breakdown model clusters in a cylinder. Physical Review A. ,vol. 41, pp. 1830- 1842 ,(1990) , 10.1103/PHYSREVA.41.1830
Paul Meakin, Progress in DLA research Physica D: Nonlinear Phenomena. ,vol. 86, pp. 104- 112 ,(1995) , 10.1016/0167-2789(95)00092-I
Herbert Levine, Yuhai Tu, Mean-field diffusion-limited aggregation in radial geometries Physical Review A. ,vol. 45, pp. 1053- 1057 ,(1992) , 10.1103/PHYSREVA.45.1053