Abstract:
We study the process of two-dimensional Laplacian growth in the limit of zero-surface tension for cases with a closed interface around a growing bubble (exterior problem with circular geometry). Using the time-dependent conformal map technique we obtain a class of fingerlike solutions that are characterized by a finite number of poles. We find the conditions under which these solutions remain smooth for all times. These solutions allow the description of the system in terms of a finite number of ce:degrees of freedom, at least in the limit of zero-surface tension. We believe that, whenever they remain smooth, they can also be used as a nonlinear basis even when surface tension is included. © 1998 The American Physical Society.
Registro:
Documento: |
Artículo
|
Título: | Dynamics of closed interfaces in two-dimensional Laplacian growth |
Autor: | Ponce Dawson, S.; Mineev-Weinstein, M. |
Filiación: | Departamento de Física, Facultad de Ciencias Exactas y Naturales, University of Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina Complex Systems Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, Mexico
|
Año: | 1998
|
Volumen: | 57
|
Número: | 3
|
Página de inicio: | 3063
|
Página de fin: | 3072
|
DOI: |
http://dx.doi.org/10.1103/PhysRevE.57.3063 |
Título revista: | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|
Título revista abreviado: | Phys Rev E.
|
ISSN: | 1063651X
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1063651X_v57_n3_p3063_PonceDawson |
Referencias:
- Cross, M.C., Hohenberg, P.C., (1993) Rev. Mod. Phys., 65, p. 851. , RMPHAT
- (1988) Dynamics of Curved Fronts, , edited by P. Pelcé, Academic Press, Inc., Boston
- Vicsek, T., (1992) Fractal Growth Phenomena, , World Scientific, Singapore
- Homsy, G.M., (1987) Annu. Rev. Fluid Mech., 19, p. 271. , ARVFA3
- Matsushita, M., Sano, M., Hayakawa, Y., Honjo, H., Sawada, Y., (1984) Phys. Rev. Lett., 53, p. 286. , PRLTAO
- Langer, J.S., (1980) Rev. Mod. Phys., 52, p. 1. , RMPHAT
- Honjo, H., Ohta, S., Matsushita, M., (1986) J. Phys. Soc. Jpn., 55, p. 2487. , JUPSAU
- Lee, K.J., McCormick, W.D., Puyang, Q., Swinney, H.L., (1993) Science, 261, p. 189. , SCIEAS
- Vicsek, T., Cserzo, M., Horváth, V.K., (1990) Physica A, 167, p. 315. , PHYADX
- Saffman, P.G., Taylor, G.I., (1958) Proc. R. Soc. London, Ser. A, 245, p. 312. , PRLAAZ
- Kessler, D.A., Levine, H., (1988) Adv. Phys., 37, p. 255. , and references therein., ADPHAH
- Saffman, P.G., (1959) Q. J. Mech. Appl. Math., 12, p. 146. , QJMMAV
- Howison, S.D., (1986) J. Fluid Mech., 167, p. 439. , JFLSA7
- Bensimon, D., Pelcé, P., (1986) Phys. Rev. A, 33, pp. R4477. , PLRAAN
- Mineev-Weinstein, M., (1990) Physica D, 43, p. 288. , PDNPDT
- Bensimon, D., Kadanoff, L.P., Liang, S., Shraiman, B.I., Tang, C., (1986) Rev. Mod. Phys., 58, p. 977. , RMPHAT
- Dai, W-S., Kadanoff, L.P., Zhou, S.-M., (1991) Phys. Rev. A, 43, p. 6672. , PLRAAN
- Mineev-Weinstein, M., Dawson, S.P., (1994) Phys. Rev. E, 50, pp. R24. , PLEEE8
- Dawson, S.P., Mineev-Weinstein, M., (1994) Physica, 73, p. 373. , PDNPDT
- Siegel, M., Tanveer, S., (1996) Phys. Rev. Lett., 76, p. 419. , PRLTAO
- Siegel, M., Tanveer, S., Dai, W-S., (1996) J. Fluid Mech., 323, p. 201. , JFLSA7
- Mineev-Weinstein, M., Phys. Rev. Lett., , (to be published)
- Paterson, L., (1981) J. Fluid Mech., 113, p. 513. , JFLSA7
- Ablowitz, M.J., Seguar, H., (1981) Solitons and the Inverse Scattering Transform, , SIAM, Philadelphia
- Ercolani, N., Forest, M.G., McLaughlin, D.W., Sinha, A., (1993) J. Nonlinear Sci., 3, p. 393. , JNSCEK
- Polubarinova-Kochina, P.Y., (1945) Dokl. Akad. Nauk SSSR, 47, p. 254. , [C. R.(Dokl.) Acad. Sci. 47, 250 (1945)]; DANKAS
- Galin, L.A., (1945) Dokl. Akad. Nauk SSSR, 47, p. 246. , [C. R. (Dokl.) Acad. Sci. 47, 246 (1945)]. DANKAS
- Richardson, S., (1972) J. Fluid Mech., 56, p. 609. , JFLSA7
- Mineev-Weinstein, M., (1993) Phys. Rev. E, 47, pp. R2241. , PLEEE8
- Mineev-Weinstein, M., (unpublished); Tomé, H., (1989) Phys. Fluids A, 1, p. 224. , PFADEB
- See, e.g., I.S. Gradshtein and I.M. Ryzhik, Table of Integrals, Series and Products (Academic Press, New York, 1980), p. 1120; Foias, C., Nicolaekno, B., Sell, G.R., Temam, R., (1988) J. Math. Pures Appl., 67, p. 197
- Temam, R., (1988) Infinite Dimensional Dynamical Systems in Mechanics and Physics, , Springer-Verlag, New York
- Jolly, M.S., Kevrekidis, I.G., Titi, E.S., (1990) Physica D, 44, p. 38. , PDNPDT
- Aubry, N., Holmes, P., Lumley, J.L., Stone, E., (1988) J. Fluid Mech., 192, p. 115. , JFLSA7
- Thual, O., Frisch, U., Hénon, M., (1985) J. Phys. (France), 46, p. 1485. , JOPQAG
- Kupervasser, O., Olami, Z., Procaccia, I., (1996) Phys. Rev. Lett., 76, p. 146. , PRLTAO
- Olami, Z., Galanti, B., Kupervasser, O., Procaccia, I., (1997) Phys. Rev. E, 67, p. 2649. , PLEEE8
Citas:
---------- APA ----------
Ponce Dawson, S. & Mineev-Weinstein, M.
(1998)
. Dynamics of closed interfaces in two-dimensional Laplacian growth. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 57(3), 3063-3072.
http://dx.doi.org/10.1103/PhysRevE.57.3063---------- CHICAGO ----------
Ponce Dawson, S., Mineev-Weinstein, M.
"Dynamics of closed interfaces in two-dimensional Laplacian growth"
. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics 57, no. 3
(1998) : 3063-3072.
http://dx.doi.org/10.1103/PhysRevE.57.3063---------- MLA ----------
Ponce Dawson, S., Mineev-Weinstein, M.
"Dynamics of closed interfaces in two-dimensional Laplacian growth"
. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 57, no. 3, 1998, pp. 3063-3072.
http://dx.doi.org/10.1103/PhysRevE.57.3063---------- VANCOUVER ----------
Ponce Dawson, S., Mineev-Weinstein, M. Dynamics of closed interfaces in two-dimensional Laplacian growth. Phys Rev E. 1998;57(3):3063-3072.
http://dx.doi.org/10.1103/PhysRevE.57.3063