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Fluctuations and Order

The New Synthesis

  • Book
  • © 1996

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Editors:
  1. Mark Millonas

    1. The James Franck Institute, University of Chicago, Chicago, USA

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Part of the book series: Institute for Nonlinear Science (INLS)

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About this book

The volume that you have before you is the result of a growing realization that fluctuations in nonequilibrium systems playa much more important role than was 1 first believed. It has become clear that in nonequilibrium systems noise plays an active, one might even say a creative, role in processes involving self-organization, pattern formation, and coherence, as well as in biological information processing, energy transduction, and functionality. Now is not the time for a comprehensive summary of these new ideas, and I am certainly not the person to attempt such a thing. Rather, this short introductory essay (and the book as a whole) is an attempt to describe where we are at present and how the viewpoint that has evolved in the last decade or so differs from those of past decades. Fluctuations arise either because of the coupling of a particular system to an ex­ ternal unknown or "unknowable" system or because the particular description we are using is only a coarse-grained description which on some level is an approxima­ tion. We describe the unpredictable and random deviations from our deterministic equations of motion as noise or fluctuations. A nonequilibrium system is one in which there is a net flow of energy. There are, as I see it, four basic levels of sophistication, or paradigms, con­ cerning fluctuations in nature. At the lowest level of sophistication, there is an implicit assumption that noise is negligible: the deterministic paradigm.

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Table of contents (26 chapters)

  1. Front Matter

    Pages i-xx
    Download chapter PDF

  2. State-Dependent Noise and Interface Propagation

    • Rolf Landauer
    Pages 1-9

  3. Stochastic Resonance and Its Precursors

    • M. I. Dykman, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, N. D. Stein, N. G. Stocks
    Pages 11-33

  4. Generation of Higher Harmonics in Noisy Nonlinear Systems

    • P. Jung, R. Bartussek
    Pages 35-52

  5. Noise-Induced Linearization and Delinearization

    • N. G. Stocks, N. D. Stein, H. E. Short, R. Mannella, D. G. Luchinsky, P. V. E. McClintock et al.
    Pages 53-67

  6. The Effect of Chaos on a Mean First-Passage Time

    • L. E. Reichl, P. Alpatov
    Pages 69-80

  7. Noise-Induced Sensitivity to Initial Conditions

    • Emil Simiu, Michael Frey
    Pages 81-90

  8. Stabilization Through Fluctuations in Chaotic Systems

    • Michail Zak, Alexander Zak, Ronald Meyers
    Pages 91-107

  9. The Weak-Noise Characteristic Boundary Exit Problem: Old and New Results

    • R. S. Maier, D. L. Stein
    Pages 109-119

  10. Some Novel Features of Nonequilibrium Systems

    • Mark I. Dykman, Mark M. Millonas, Vadim N. Smelyanskiy
    Pages 121-137

  11. Using Path-Integral Methods to Calculate Noise-Induced Escape Rates in Bistable Systems: The Case of Quasi-Monochromatic Noise

    • S. J. B. Einchcomb, A. J. McKane
    Pages 139-154

  12. Noise-Facilitated Critical Behavior in Thermal Ignition of Energetic Media

    • J. R. Leith
    Pages 155-169

  13. The Hierarchies of Nonclassical Regimes for Diffusion-Limited Binary Reactions

    • Katja Lindenberg, Panos Argyrakis, Raoul Kopelman
    Pages 171-203

  14. Scale Invariance in Epitaxial Growth

    • D. D. Vvedensky, A. Zangwill, C. N. Luse, C. Ratsch, P. Šmilauer, M. R. Wilby
    Pages 205-223

  15. Toward a Theory of Growing Surfaces: Mapping Two-Dimensional Laplacian Growth Onto Hamiltonian Dynamics and Statistics

    • Raphael Blumenfeld
    Pages 225-237

  16. Noise, Fractal Growth, and Exact Integrability in Nonequilibrium Pattern Formation

    • Mark B. Mineev-Weinstein
    Pages 239-257

  17. Order by Disorder and Topology in Frustrated Magnetic Systems

    • E. F. Shender, P. C. W. Holdsworth
    Pages 259-279

  18. Noise-Induced Abnormal Growth

    • L. Lam, M. C. Veinott, D. A. Ratoff, R. D. Pochy
    Pages 281-292

  19. Clustering of Active Walkers: Phase Transition from Local Interactions

    • Frank Schweitzer, Lutz Schimansky-Geier
    Pages 293-305

  20. Brownian Combustion Engines

    • Marcelo O. Magnasco
    Pages 307-320
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Editors and Affiliations

  • The James Franck Institute, University of Chicago, Chicago, USA

    Mark Millonas

Bibliographic Information

  • Book Title: Fluctuations and Order

  • Book Subtitle: The New Synthesis

  • Editors: Mark Millonas

  • Series Title: Institute for Nonlinear Science

  • DOI: https://doi.org/10.1007/978-1-4612-3992-5

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1996

  • Hardcover ISBN: 978-0-387-94602-3Published: 08 March 1996

  • Softcover ISBN: 978-1-4612-8463-5Published: 17 September 2011

  • eBook ISBN: 978-1-4612-3992-5Published: 06 December 2012

  • Series ISSN: 1431-4673

  • Edition Number: 1

  • Number of Pages: XX, 456

  • Topics: Complex Systems, Statistical Physics and Dynamical Systems

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