Abstract:
We study a piecewise linear version of a one-component, two-dimensional bistable reaction-diffusion system subjected to partially reflecting boundary conditions, with the aim of analyzing the structural stability of its stationary patterns. Dirichlet and Neumann boundary conditions are included as limiting cases. We find a critical line in the space of the parameters which divides different dynamical behaviors. That critical line merges as the locus of the coalescence of metastable and unstable nonuniform structures.
Registro:
Documento: |
Artículo
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Título: | Boundary effects on the structural stability of stationary patterns in a bistable reaction-diffusion system |
Autor: | Izús, G.G.; Reyes De Rueda, J.; Borzi, C.H. |
Filiación: | Departamento de Física, Fac. de Ciencias Exactas Y Naturales, Univ. Nacional de Mar del Plata, Deán Funes 3350, (7600) Mar del Plata, Argentina MONDITEC S.A., Olazabal 1927, (1428) Buenos Aires, Argentina
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Palabras clave: | Albedo BCs; Hot-spot model; Non-equilibrium potential; Reaction-diffusion; Structural stability |
Año: | 1998
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Volumen: | 90
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Número: | 1-2
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Página de inicio: | 103
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Página de fin: | 117
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Título revista: | Journal of Statistical Physics
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Título revista abreviado: | J. Stat. Phys.
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ISSN: | 00224715
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224715_v90_n1-2_p103_Izus |
Referencias:
- Nicolis, G., Prigogine, I., (1976) Self-Organization in Nonequilibrium Systems, , Wiley, New York
- Fife, P.C., (1979) Mathematical Aspects of Reacting and Diffusing Systems, , Springer-Verlag, Berlin
- Fife, P.C., Current topics in reaction-diffusion systems (1984) Nonequilibrium Cooperative Phenomena in Physics and Related Fields, , M. G. Velarde, ed. Plenum Press, New York
- Cross, M.C., Hohenberg, P.C., (1993) Rev. Mod. Phys., 65, p. 851
- Meron, E., (1992) Phys. Rep., 218, p. 1
- Nicolis, G., Erneux, T., Herschkowitz-Kaufman, M., Pattern formation in reacting and diffusing systems (1978) Advances in Chemical Physics, 38. , I. Prigogine and S. Rice, eds. Wiley, New York
- Mikhailov, A.S., (1990) Foundations of Synergetics I, , Springer-Verlag, Berlin
- Murray, J.D., (1985) Mathematical Biology, , Springer-Verlag, Berlin
- Wio, H.S., (1994) An Introduction to Stochastic Processes and Nonequilibrium Statistical Physics, , World Scientific, Singapore
- Schat, C., Wio, H.S., (1992) Physica A, 180, p. 295
- Hassan, S.A., Kuperman, M.N., Wio, H.S., Zanette, D.H., (1994) Physica A, 206, p. 380
- Hassan, S.A., Zanette, D.H., Wio, H.S., (1994) J. Phys. A, 27, p. 5129
- Zanette, D., Wio, H., Deza, R., (1995) Phys. Rev. E, 52, p. 129
- Wio, H.S., Izús, G., Ramírez, O., Deza, R., Borzi, C., (1993) J. Phys. A:Math. Gen., 26, p. 4281
- Izús, G., Deza, R., Ramírez, O., Wio, H., Zanette, D., Borzi, C., (1995) Phys. Rev. E, 52, p. 129
- Izús, G., Wio, H., De Reyes Rueda, J., Ramírez, O., Deza, R., (1996) Int. J. Mod. Phys. B, 10, p. 1273
- Izús, G., Deza, R., Wio, H., Borzi, C., (1997) Phys. Rev. E, 55, p. 4005
- Izús, G., Deza, R., Borzi, C., Wio, H., (1997) Physica A, 237, p. 135
- Van Kampen, N.G., (1984) Stochastic Processes in Physics and Chemistry, , North Holland, Amsterdam
- Boddington, T., Gray, P., Wake, C., (1977) Proc. R. Soc. Lond. A, 357, p. 403
- Fedotov, S.P., (1993) Phys. Lett. A, 176, p. 220
- Castest, V., Dulos, E., Boissonade, J., De Keeper, P., (1990) Phys. Rev. Lett., 64, p. 2953
- Ouyang, Q., Swinney, H., Nature, 352, p. 1991
- Nicolis, G., (1995) Introduction to Nonlinear Science, , Cambridge University Press, Cambridge
- Izús, G., Ramírez, O., Deza, R., Wio, H., (1996) J. Chem. Phys., 105, p. 10424
- Ross, B., Lister, J.D., (1977) Phys. Rev. A, 15, p. 1246
- Landauer, R., (1977) Phys. Rev. A, 15, p. 2117
- Bedeaux, D., Mazur, P., Pasmanter, R.A., (1977) Physica A, 86, p. 355
- Bedeaux, D., Mazur, P., (1981) Physica A, 105, p. 1
- Skocpol, W.J., Beasley, M.R., Tinkham, M., (1974) J. Appl. Phys., 45, p. 4054
- Frisch, H.L., Some recent exact solutions of the Fokker Planck equation (1996) Non-Equilibrium Statistical Mechanics in One Dimension, , V. Privman, ed. Cambridge University Press, Cambridge, Chapter XVII
- Frisch, H.L., Privman, V., Nicolis, C., Nicolis, G., (1990) J. Phys. A, 23, p. 1147
- Privman, V., Frisch, H.L., (1991) J. Chem. Phys., 94, p. 8216
- Von Haeften, B., Izús, G., Deza, R., Borzi, C., Phys. Lett. A, , in press
- Scott, A.C., (1975) Rev. Mod. Phys., 47, p. 47
- Graham, R., (1978) Lecture Notes in Physics, 84. , Springer-Verlag, Berlin
- Graham, R., Tel, T., (1990) Phys. Rev. A, 42, p. 4661
- Graham, R., Weak noise limit and nonequilibrium potentials of dissipative dynamical systems (1987) Instabilities and Nonequilibrium Structures, , E. Tirapegui and D. Villarroel, eds. Reidel, Dordrecht
- Kerszberg, M., (1983) Phys. Rev. A, 28, p. 1198
- De La Torre, M., Rehberg, I., (1990) Phys. Rev. A, 42, p. 2096
- Viñals, J., Hernandez-Garcia, E., San Miguel, M., Toral, R., (1991) Phys. Rev. A, 44, p. 1123
- Hernandez-Garcia, E., Viñals, J., Toral, R., San Miguel, M., (1993) Phys. Rev. Lett., 70, p. 3576
- Jung, P., (1993) Phys. Rep., 234, p. 175
Citas:
---------- APA ----------
Izús, G.G., Reyes De Rueda, J. & Borzi, C.H.
(1998)
. Boundary effects on the structural stability of stationary patterns in a bistable reaction-diffusion system. Journal of Statistical Physics, 90(1-2), 103-117.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224715_v90_n1-2_p103_Izus [ ]
---------- CHICAGO ----------
Izús, G.G., Reyes De Rueda, J., Borzi, C.H.
"Boundary effects on the structural stability of stationary patterns in a bistable reaction-diffusion system"
. Journal of Statistical Physics 90, no. 1-2
(1998) : 103-117.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224715_v90_n1-2_p103_Izus [ ]
---------- MLA ----------
Izús, G.G., Reyes De Rueda, J., Borzi, C.H.
"Boundary effects on the structural stability of stationary patterns in a bistable reaction-diffusion system"
. Journal of Statistical Physics, vol. 90, no. 1-2, 1998, pp. 103-117.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224715_v90_n1-2_p103_Izus [ ]
---------- VANCOUVER ----------
Izús, G.G., Reyes De Rueda, J., Borzi, C.H. Boundary effects on the structural stability of stationary patterns in a bistable reaction-diffusion system. J. Stat. Phys. 1998;90(1-2):103-117.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224715_v90_n1-2_p103_Izus [ ]