Iterated conformal dynamics and Laplacian growth

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 65, Issue 4, 2002, Pages

  Barra, Felipe ^a   Davidovitch, Benny ^a,b   Procaccia, Itamar ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b EXXONMOBIL UPSTREAM RESEARCH COMPANY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION LIMITED AGGREGATES (DLA); FRACTAL DIMENSION (FD); ITERATED CONFORMAL DYNAMICS; LAPLACIAN GROWTH;

AGGREGATES; BOUNDARY CONDITIONS; DIFFUSION; PHASE DIAGRAMS; PROBABILITY; RANDOM PROCESSES;

FRACTALS;

EID: 41349111842     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.046144     Document Type: Article

References (26)

1. See for example, L. Paterson, Phys. Rev. Lett. 52, 1621 (1984); L. M. Sander, Nature (London) 322, 789 (1986); J. Nittmann and H. E. Stanley, ibid. 321, 663 (1986); H. E. Stanley, in Fractals and Disordered Systems, edited by A. Bunde and S. Havlin (Springer-Verlag, Berlin, 1991).
2. See for example, L. Paterson, Phys. Rev. Lett. 52, 1621 (1984); L. M. Sander, Nature (London) 322, 789 (1986); J. Nittmann and H. E. Stanley, ibid. 321, 663 (1986); H. E. Stanley, in Fractals and Disordered Systems, edited by A. Bunde and S. Havlin (Springer-Verlag, Berlin, 1991).
3. See for example, L. Paterson, Phys. Rev. Lett. 52, 1621 (1984); L. M. Sander, Nature (London) 322, 789 (1986); J. Nittmann and H. E. Stanley, ibid. 321, 663 (1986); H. E. Stanley, in Fractals and Disordered Systems, edited by A. Bunde and S. Havlin (Springer-Verlag, Berlin, 1991).
4. See for example, L. Paterson, Phys. Rev. Lett. 52, 1621 (1984); L. M. Sander, Nature (London) 322, 789 (1986); J. Nittmann and H. E. Stanley, ibid. 321, 663 (1986); H. E. Stanley, in Fractals and Disordered Systems, edited by A. Bunde and S. Havlin (Springer-Verlag, Berlin, 1991).
5. P. O. Saffman and G. I. Taylor, Proc. R. Soc. London, Ser. A 245, 312 (1958).
6. B. Shraiman and D. Bensimon, Phys. Rev. A 30, 2840 (1984); S. D. Howison, J. Fluid Mech. 167, 439 (1986).
7. B. Shraiman and D. Bensimon, Phys. Rev. A 30, 2840 (1984); S. D. Howison, J. Fluid Mech. 167, 439 (1986).
8. T. A. Witten and L. M. Sander, Phys. Rev. Lett. 47, 1400 (1981).
9. D. Bensimon, L. P. Kadanoff, S. Liang, B. I. Shraiman, and C. Tang, Rev. Mod. Phys. 58, 977 (1986); S. Tanveer, Philos. Trans. R. Soc. London, Ser. A 343, 155 (1993), and references therein.
10. D. Bensimon, L. P. Kadanoff, S. Liang, B. I. Shraiman, and C. Tang, Rev. Mod. Phys. 58, 977 (1986); S. Tanveer, Philos. Trans. R. Soc. London, Ser. A 343, 155 (1993), and references therein.
11. F. Barra, B. Davidovitch, A. Levermann, and I. Procaccia, Phys. Rev. Lett. 87, 134501 (2001).
12. M. B. Hastings and L. S. Levitov, Physica D 116, 244 (1998).
13. B. Davidovitch, H. G. E. Hentschel, Z. Olami, I. Procaccia, L. M. Sander, and E. Somfai, Phys. Rev. E 59, 1368 (1999).
14. B. Davidovitch, M. J. Feigenbaum, H. G. E. Hentschel, and I. Procaccia, Phys. Rev. E 62, 1706 (2000).
15. P. Meakin and J. M. Deutch, J. Chem. Phys. 80, 2115 (1984).
16. U. Uwaha and Y. Saito, Phys. Rev. A 40, 4716 (1989).
17. K. Moriaty, J. Machta, and R. Greenlaw, Phys. Rev. E 55, 6211 (1997).
18. M. G. Stepanov and L. S. Levitov, Phys. Rev. E 63, 061102 (2001).
19. B. Davidovitch and I. Procaccia, Phys. Rev. Lett. 85, 3608 (2000).
20. B. Davidovitch, A. Levermann, and I. Procaccia, Phys. Rev. E 62, R5919 (2000).
21. E. Ben-Jacob, R. Godbey, N. D. Goldenfeld, J. Koplik, H. Levine, T. Mueller, and L. M. Sander, Phys. Rev. Lett. 55, 1315 (1985); J. D. Chen, Exp. Fluids 5, 363 (1987); A. Arneódo, Y. Couder, G. Grasseau, V. Hakim, and M. Rabaud, Phys. Rev. Lett. 63, 984 (1989).
22. E. Ben-Jacob, R. Godbey, N. D. Goldenfeld, J. Koplik, H. Levine, T. Mueller, and L. M. Sander, Phys. Rev. Lett. 55, 1315 (1985); J. D. Chen, Exp. Fluids 5, 363 (1987); A. Arneódo, Y. Couder, G. Grasseau, V. Hakim, and M. Rabaud, Phys. Rev. Lett. 63, 984 (1989).
23. E. Ben-Jacob, R. Godbey, N. D. Goldenfeld, J. Koplik, H. Levine, T. Mueller, and L. M. Sander, Phys. Rev. Lett. 55, 1315 (1985); J. D. Chen, Exp. Fluids 5, 363 (1987); A. Arneódo, Y. Couder, G. Grasseau, V. Hakim, and M. Rabaud, Phys. Rev. Lett. 63, 984 (1989).
24. W.-S. Dai, L. P. Kadanoff, and S.-M. Zhou, Phys. Rev. A 43, 6672 (1991).
25. T. C. Halsey, Phys. Rev. Lett. 72, 1228 (1994).
26. M. B. Hastings, Phys. Rev. E 55, 135 (1997).