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Diffusion-limited aggregation (DLA) on nonuniform substrates was investigated by computer simulations. The nonuniform substrates are represented by Leath percolations with the occupied probability p . p stands for the degree of nonuniformity and takes values in the range p c ≤ p ≤1, where p c is the threshold of percolation. The DLA cluster grows up on the Leath percolation substrate. The patterns of the DLA clusters appear asymmetrical and nonuniform, and the branches are relatively few for the case that p is close to p c . In addition, the pattern depends on the shape of substrate. As p increases from p c to 1, cluster changes to pure DLA gradually. Correspondingly, the fractal dimension increases from 1.46 to 1.68. Furthermore, the random walks on Leath percolations through the range p c ≤ p ≤1 were examined. Our simulations show the Honda–Toyoki–Matsushita relation is still reasonable for DLA growth in fractional dimensional spaces.
References
- 1 A.-L.Barabasi and H. E.Stanley:Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995). Crossref, Google Scholar
- 2 P.Meakin:Fractals, Scaling and Growth Far From Equilibrium (Cambridge University Press, Cambridge, 1998). Google Scholar
- 3 Fractals and Disordered Systems, ed. A.Bunde and S.Havlin (Springer, Berlin, 1991) and the references therein. Crossref, Google Scholar
- 4 T. A.Witten and L. M.Sander:Phys. Rev. Lett. 47 (1981) 1400; P.Meakin:Phys. Rev. A 27 (1983) 1495. Crossref, Google Scholar
- 5 T.Vicsek:Fractal Growth Phenomena (World Scientific, Singapore, 1992). Crossref, Google Scholar
- 6 Z.-J.Tan, X.-W.Zou, W.-B.Zhang and Z.-Z.Jin:Phys. Rev. E 60 (1999) 6202;Phys. Lett. A 268 (2000) 112;; Phys. Lett. A 282 (2001) 121. Crossref, Google Scholar
- 7 E.Somfai, L. M.Sander and R. C.Ball:Phys. Rev. Lett. 83 (1999) 5523; F.Mallanmace, L.Monsu'Scolaro, A.Romeo and N.Micali:: Phys. Rev. Lett. 82 (1999) 3480. Crossref, Google Scholar
- 8 T.Nagatani and F.Sagues:Phys. Rev. A 43 (1991) 2970; H.Honjo and S.Ohta:Phys. Rev. E 57 (1998) 6202; V. A.Bogoyavlenskiy and N. A.Chernova:: Phys. Rev. E 61 (2000) 5422. Crossref, Google Scholar
- 9 P.Meakin:Phys. Rev. Lett. 51 (1983) 1119; M.Kolb, R.Botet and R.Jullien:: Phys. Rev. Lett. 51 (1983) 1123. Crossref, Google Scholar
- 10 Z.-J.Tan, X.-W.Zou, W.-B.Zhang and Z.-Z.Jin:Phys. Rev. E 62 (2000) 734. Crossref, Google Scholar
- 11 H. J.Herrmann:Phys. Rep. 136 (1986) 153. Crossref, Google Scholar
- 12 H. A.Makse, J. S.Andrade and H. E.Stanley:Phys. Rev. E 61 (2000) 583. Crossref, Google Scholar
- 13 M. A.Knackstedt, M.Sahimi and A. P.Sheppard:Phys. Rev. E 61 (2000) 4920. Crossref, Google Scholar
- 14 K. S.Mendelson:Phys. Rev. E 61 (2000) 2432;; Phys. Rev. E 60 (1999) 6496. Crossref, Google Scholar
- 15 M.Murat and A.Aharony:Phys. Rev. Lett. 57 (1986) 1875. Crossref, Google Scholar
- 16 P.Jensen:Rev. Mod. Phys. 71 (1999) 1695. Crossref, Google Scholar
- 17 A.Ordemann, M.Porto, H. E.Roman and S.Havlin:Phys. Rev. E 63 (2001) 020104. Crossref, Google Scholar
- 18 P. L.Leath:Phys. Rev. B 14 (1976) 5046. Crossref, Google Scholar
- 19 Z.-J.Tan, X.-W.Zou and Z.-Z.Jin:Phys. Rev. E 62 (2000) 8409. Crossref, Google Scholar
- 20 M.Tokuyama and K.Kawasaki:Phys. Lett. A 100 (1984) 337. Crossref, Google Scholar
- 21 M.Muthukumar:Phys. Rev. Lett. 50 (1983) 839. Crossref, Google Scholar
- 22 K.Honda, H.Toyoki and M.Matsushita:J. Phys. Soc. Jpn. 55 (1986) L707. Link, Google Scholar
- 23 M.Eden:Proc. Berkeley Symp. Mathematical Statistics and Probability, ed. J.Neyman (University of California Press, Berkeley, 1961) pp. 223–239, see also in refs. [rf1,rf2,rf3]. Google Scholar
- 24 Z.-J.Tan, X.-W.Zou, W.Zhang and Z.-Z.Jin: to be published. Google Scholar