Abstract
We review the role of linear instabilities on phase transition processes induced by external spatiotemporal noise. In particular, we present a detailed linear stability analysis of a standard Ginzburg-Landau model with multiplicative noise. The results show the well-known constructive role of fluctuations in this case. The analysis is performed for both non-conserved and conserved dynamics, corresponding to order-disorder and phase separation transitions, respectively.
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References
J. García-Ojalvo, A. Hernández-Machado, and J.M. Sancho, “Effects of external noise on the Swift-Hohenberg equation,” Phys. Rev. Lett. 71, 1542 (1993).
J.M.R. Parrondo, C. Van den Broeck, J. Buceta, and J. de la Rubia, “Noise-induced spatial patterns,” Physica A 224, 153 (1996).
A.A. Zaikin and L. Schimansky-Geier, “Spatial patterns induced by additive noise,” Phys. Rev. E 58, 4355 (1998).
A. Becker and L. Kramer, “Linear stability analysis for bifurcations in spatially extended systems with fluctuating control parameter,” Phys. Rev. Lett. 73, 955 (1994).
J. García-Ojalvo and J.M. Sancho, “External fluctuations in a pattern-forming instability,” Phys. Rev. E 53, 5680 (1996).
C. Van den Broeck, J.M.R. Parrondo, and R. Toral, “Noise-induced nonequilibrium phase transitions,” Phys. Rev. Lett. 73, 3395 (1994).
P. Luque, J. García-Ojalvo, and J.M. Sancho, “Nonequilibrium phase transitions and external noise,” in Fluctuation phenomena: disorder and nonlinearity, edited by A.R. Bishop, S. Jiménez, and L. Vázquez, p. 75 (World Scientific, Singapore, 1995).
C. Van den Broeck, J.M.R. Parrondo, R. Toral, and R. Kawai, “Nonequilibrium phase transitions induced by multiplicative noise,” Phys. Rev. E 55, 4084 (1997).
J. García-Ojalvo, A.M. Lacasta, J.M. Sancho and R. Toral, Europhys. Lett. 42, 125 (1998).
J. García-Ojalvo and J.M. Sancho, Noise in spatially extended systems, Springer Verlag, New York (1999).
J.M. Sancho and J. García-Ojalvo, “Noise-induced order in extended systems: A tutorial,”, this volume.
P.C. Hohenberg and B.I. Halperin, “Theory of dynamic critical phenomena,” Rev. Mod. Phys. 49, 435 (1977).
E.A. Novikov, “Functionals and the random-force method in turbulence theory,” Sov. Phys. JETP 20, 1290 (1965).
M. Ibañes, J. García-Ojalvo, R. Toral, and J.M. Sancho, “Noise-induced phase separation: mean-field results,” Phys. Rev. E 60, 3597 (1999).
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Ibañes, M., García-Ojalvo, J., Toral, R., Sancho, J.M. (2000). Linear Instability Mechanisms of Noise-Induced Phase Transitions. In: Freund, J.A., Pöschel, T. (eds) Stochastic Processes in Physics, Chemistry, and Biology. Lecture Notes in Physics, vol 557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45396-2_23
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DOI: https://doi.org/10.1007/3-540-45396-2_23
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