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By I. Prigogine (auth.), Professor Dr. Werner Horsthemke, Dilip K. Kondepudi PhD (eds.)

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Read Online or Download Fluctuations and Sensitivity in Nonequilibrium Systems: Proceedings of an International Conference, University of Texas, Austin, Texas, March 12–16, 1984 PDF

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Additional info for Fluctuations and Sensitivity in Nonequilibrium Systems: Proceedings of an International Conference, University of Texas, Austin, Texas, March 12–16, 1984

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Hanggi and H. Thomas, Phys. Reports 88, 207-cI982) and H. Grabert, P. Hanggi and I. Oppenheim, Physica l17A, 300 (1983). R. Landauer, to appear in Self-Organizing Systems: The Emergence of Order, F. E. Yates, D. O. Walter and G. B. , Plenum Press, New York (1984). J. Troe, J. Chem. Phys. 66, 4745 (1977) . R. A. , 284 (1940). J. E. Moyal, J. Roy. Stat is. Soc. (B) 11, 150 (1949). H. J. Kushner, Stochastics 6, 117 (1982). B. Z. B. B. B. 35 23. 24. 25. 26. 27. 36 E. B. Dynkin, "Markov Processes", two volumes (translated from Russian) Springer - Berlin (1963).

Tier and M. Hangel, to appear, Phys. Rev. A (1984). B. J. Matkowsky, Z. Schuss, C. Knessl and C. Tier, to appear, SIAM J. Appl. Math. (1984). S. O. Box 451, Princeton, NJ 08544, USA Recent theories and experiments challenge the applicability of linear stability theory near the onset of buoyancy-dri ven (Rayleigh-B~nard) convection. This stabili ty theory, based on small perturbations of infinite parallel rolls, is found to miss several important features of the convective flow. The reason is that the lateral boundaries have a profound influence on the possible wavenumbers and flow patterns even for the largest cells studied.

The question is then to determine what wavenurnbers are possible in the final stationary state, and how these wavenumbers depend on R, A, and the initial conditions (if there is hysteresis). 40 An alternative way of posing this question -- one that is closer to the theme of this workshop -- is to study the sensitivity of the final stationary state to fluctuations in the initial conditions. We assume that the initial conditions are somehow restricted to evolve only into one-dimensional rolls. For example, an experiment could start with parallel or concentric rolls of varying wavelengths.

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