Fluctuations and Order

1. Front Matter

   Pages i-xx

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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

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.

• Nonlinear system
• bifurcation
• blood cell
• clustering
• deterministic chaos
• dynamical systems
• dynamics
• electrophysiology
• mathematics
• physiology
• system
• temperature

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

  Mark Millonas

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