Dynamics of closed interfaces in two-dimensional Laplacian growth

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 57, Issue 3, 1998, Pages 3063-3072

  Ponce Dawson, Silvina ^a   Mineev Weinstein, Mark ^b  

^a UNIVERSIDAD DE BUENOS AIRES   (Argentina)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4243241438     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.3063     Document Type: Article

References (39)

1. M.C. Cross and P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).RMPHAT
2. Dynamics of Curved Fronts, edited by P. Pelcé (Academic Press, Inc., Boston, 1988);
3. T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1992).
4. G.M. Homsy, Annu. Rev. Fluid Mech. 19, 271 (1987).ARVFA3
5. M. Matsushita, M. Sano, Y. Hayakawa, H. Honjo, and Y. Sawada, Phys. Rev. Lett. 53, 286 (1984).PRLTAO
6. J.S. Langer, Rev. Mod. Phys. 52, 1 (1980); RMPHAT
7. H. Honjo, S. Ohta, and M. Matsushita, J. Phys. Soc. Jpn. 55, 2487 (1986).JUPSAU
8. K.J. Lee, W.D. McCormick, Q. Puyang, and H.L. Swinney, Science 261, 189 (1993).SCIEAS
9. T. Vicsek, M. Cserzo, and V.K. Horváth, Physica A 167, 315 (1990).PHYADX
10. P.G. Saffman and G.I. Taylor, Proc. R. Soc. London, Ser. A 245, 312 (1958).PRLAAZ
11. D.A. Kessler and H. Levine, Adv. Phys. 37, 255 (1988), and references therein.ADPHAH
12. P.G. Saffman, Q. J. Mech. Appl. Math. 12, 146 (1959); QJMMAV
13. S.D. Howison, J. Fluid Mech. 167, 439 (1986); JFLSA7
14. D. Bensimon and P. Pelcé, Phys. Rev. A 33, R4477 (1986).PLRAAN
15. M. Mineev-Weinstein, Physica D 43, 288 (1990).PDNPDT
16. D. Bensimon, L.P. Kadanoff, S. Liang, B.I. Shraiman, and C. Tang, Rev. Mod. Phys. 58, 977 (1986).RMPHAT
17. W-S. Dai, L.P. Kadanoff, and S.-M. Zhou, Phys. Rev. A 43, 6672 (1991).PLRAAN
18. M. Mineev-Weinstein and S.P. Dawson, Phys. Rev. E 50, R24 (1994).PLEEE8
19. S.P. Dawson and M. Mineev-Weinstein, Physica 73, 373 (1994).PDNPDT
20. M. Siegel and S. Tanveer, Phys. Rev. Lett. 76, 419 (1996); PRLTAO
21. M. Siegel, S. Tanveer, and W-S. Dai, J. Fluid Mech. 323, 201 (1996).JFLSA7
22. M. Mineev-Weinstein, Phys. Rev. Lett. (to be published).
23. L. Paterson, J. Fluid Mech. 113, 513 (1981).JFLSA7
24. M.J. Ablowitz and H. Seguar, Solitons and the Inverse Scattering Transform (SIAM, Philadelphia, 1981).
25. N. Ercolani, M.G. Forest, D.W. McLaughlin, and A. Sinha, J. Nonlinear Sci. 3, 393 (1993).JNSCEK
26. P.Ya. Polubarinova-Kochina, Dokl. Akad. Nauk SSSR 47, 254 (1945) [C. R.(Dokl.) Acad. Sci. 47, 250 (1945)]; DANKAS
27. L.A. Galin, Dokl. Akad. Nauk SSSR 47, 246 (1945) [C. R. (Dokl.) Acad. Sci. 47, 246 (1945)].DANKAS
28. S. Richardson, J. Fluid Mech. 56, 609 (1972).JFLSA7
29. M. Mineev-Weinstein, Phys. Rev. E 47, R2241 (1993).PLEEE8
30. M. Mineev-Weinstein (unpublished).
31. H. Tomé et al., Phys. Fluids A 1, 224 (1989).PFADEB
32. See, e.g., I.S. Gradshtein and I.M. Ryzhik, Table of Integrals, Series and Products (Academic Press, New York, 1980), p. 1120.
33. C. Foias, B. Nicolaekno, G. R. Sell, and R. Temam, J. Math. Pures Appl. 67, 197 (1988);
34. R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics (Springer-Verlag, New York, 1988);
35. M.S. Jolly, I.G. Kevrekidis, and E.S. Titi, Physica D 44, 38 (1990); PDNPDT
36. N. Aubry, P. Holmes, J.L. Lumley, and E. Stone, J. Fluid Mech. 192, 115 (1988).JFLSA7
37. O. Thual, U. Frisch, and M. Hénon, J. Phys. (France) 46, 1485 (1985); JOPQAG
38. O. Kupervasser, Z. Olami, and I. Procaccia, Phys. Rev. Lett. 76, 146 (1996); PRLTAO
39. Z. Olami, B. Galanti, O. Kupervasser, and I. Procaccia, Phys. Rev. E 67, 2649 (1997). PLEEE8