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• W1964000285 abstract "1 State-Dependent Noise and Interface Propagation.- 1.1 Introduction.- 1.2 The Blowtorch Theorem.- 1.3 Kink Motion.- 1.4 Temperature Inhomogeneity and Kink Motion.- 1.5 Conclusion.- 1.6 References.- 2 Stochastic Resonance and Its Precursors.- 2.1 Introduction.- 2.2 A Historical Overview.- 2.2.1 Ice-Ages Prelude.- 2.2.2 Stochastic Resonance in a Ring Laser.- 2.3 Linear-Response Theory.- 2.4 Precursors of Stochastic Resonance in Condensed Matter Physics.- 2.5 Stochastic Resonance in Periodically Driven Systems.- 2.6 Conclusions.- 2.7 Acknowledgments.- 2.8 References.- 3 Generation of Higher Harmonics in Noisy Nonlinear Systems.- 3.1 Introduction.- 3.2 Linear and Nonlinear Response of a Noisy Nonlinear System, General Theory.- 3.2.1 Linear Response Function.- 3.2.2 Nonlinear Response: Generation of Higher Harmonics.- 3.3 Noise-Induced Effects in the Generation of Higher Harmonics.- 3.3.1 Hopping-Induced Higher Harmonics Generation.- 3.3.2 Higher Harmonics Generation in Continuous Systems.- 3.4 Conclusions.- 3.5 Acknowledgments.- 3.6 References.- 4 Noise-Induced Linearization and Delinearization.- 4.1 Introduction.- 4.2 Physical Basis of Noise-Induced Linearization and Delinearization.- 4.3 Noise-Induced Linearization in an Overdamped Bistable System.- 4.4 Noise-Induced Delinearization in an Underdamped Monostable System.- 4.5 Conclusion.- 4.6 Acknowledgments.- 4.7 References.- 5 The Effect of Chaos on a Mean First-Passage Time.- 5.1 Introduction.- 5.2 Periodically Driven Rotor.- 5.3 The Hamiltonian.- 5.4 Mean First-Passage Time.- 5.5 Conclusions.- 5.6 Acknowledgments.- 5.7 References.- 6 Noise-Induced Sensitivity to Initial Conditions.- 6.1 Introduction.- 6.2 One-Degree-of-Freedom Systems.- 6.2.1 Dynamical Systems and the GMF.- 6.2.2 Additive Gaussian Noise.- 6.2.3 Other Forms of Noise.- 6.2.4 Average Flux Factor.- 6.2.5 Probability of Exit from a Safe Region.- 6.3 Mean Time Between Peaks-Brundsen-Holmes Oscillator.- 6.4 Higher-Degree-of-Freedom Systems.- 6.4.1 Slowly Varying Oscillators.- 6.4.2 A Spatially Extended System.- 6.5 Conclusions.- 6.6 Acknowledgment.- 6.7 References.- 7 Stabilization Through Fluctuations in Chaotic Systems.- 7.1 Introduction.- 7.2 Background.- 7.3 Chaos in Fast-Oscillating Frame of Reference.- 7.4 Closure of Reynolds-Type Equations Using the Stabilization Principle.- 7.5 Stable Representation of Chaotic Attractors.- 7.6 Acknowledgments.- 7.7 References.- 8 The Weak-Noise Characteristic Boundary Exit Problem: Old and New Results.- 8.1 Acknowledgments.- 8.2 References.- 9 Some Novel Features of Nonequilibrium Systems.- 9.1 References.- 10 Using Path-Integral Methods to Calculate Noise-Induced Escape Rates in Bistable Systems: The Case of Quasi-Monochromatic Noise.- 10.1 References.- 11 Noise-Facilitated Critical Behavior in Thermal Ignition of Energetic Media.- 11.1 Introduction and Review of Model Equations.- 11.2 Deterministic Model Equations for Thermal Ignition of Energetic Media.- 11.3 Stochastic Model Equations for Thermal Ignition of Energetic Media.- 11.4 Some Experimental Results and Discussion.- 11.5 Conclusions.- 11.6 References.- 12 The Hierarchies of Nonclassical Regimes for Diffusion-Limited Binary Reactions.- 12.1 Introduction.- 12.2 Initial Conditions and Difference Equation.- 12.2.1 Random and Correlated Initial Conditions.- 12.2.2 Solution of Difference Equations.- 12.2.3 Discretization.- 12.3 Method of Simulations.- 12.4 Kinetic Behavior for Random Initial Conditions.- 12.4.1 Kinetic Regimes.- 12.4.2 Crossovers.- 12.4.3 Comparison With Monte Carlo Simulations.- 12.5 Kinetic Behavior for Correlated Initial Conditions.- 12.5.1 Kinetic Regimes and Crossovers.- 12.5.2 Comparison With Monte Carlo Simulations.- 12.6 Summary.- 12.7 Appendix: Solution of Difference Equations.- 12.8 Appendix: Initial Averages.- 12.9 Acknowledgments.- 12.10 References.- 13 Scale Invariance in Epitaxial Growth.- 13.1 Introduction.- 13.2 The Lattice Model.- 13.3 Scaling in the Submonolayer Regime.- 13.4 Scaling in the Multilayer Regime.- 13.5 Summary and Conclusions.- 13.6 Acknowledgments.- 13.7 References.- 14 Toward a Theory of Growing Surfaces: Mapping Two-Dimensional Laplacian Growth Onto Hamiltonian Dynamics and Statistics.- 14.1 Introduction.- 14.2 Formulation of the Problem and Hamiltonian Dynamics.- 14.3 A Case Study: N-Symmetric Growth.- 14.4 Introduction of Surface Tension.- 14.5 Effects of Noise and a Statistical Formulation of the Theory.- 14.6 Discussion and Concluding Remarks.- 14.7 Acknowledgment.- 14.8 References.- 15 Noise, Fractal Growth, and Exact Integrability in Nonequilibrium Pattern Formation.- 15.1 General Things.- 15.1.1 We Live in a Dissipative and Nonlinear World.- 15.1.2 Dissipation Comes From Averaging of Noise.- 15.1.3 Pattern Formation Results From a Multitude of Instabilities, that is, From a High Sensitivity to Noise.- 15.2 Concrete Things.- 15.2.1 Freezing of a Liquid (Stefan Problem), Solidification in a Supersaturated Solution, Bacterial Growth, Electrodeposition, and Viscous Fingering (Saffman-Taylor Problem).- 15.2.2 Two Dimensions: Laplacian Growth Equation.- 15.2.3 Remarkable Properties of LGE.- 15.2.4 Laplacian Growth on the Lattice.- 15.2.5 Recent Extensions and Elaborations of Results Concerning an Infinite Number of Conservation Laws in These (and Related) Processes.- 15.3 Conclusions and Speculations.- 15.3.1 List of Results.- 15.3.2 List of Possible Connections With Different Branches of Mathematics.- 15.3.3 List of Possible Connections With Different Branches of Physics.- 15.3.4 List of Possible Applications.- 15.4 Acknowledgments.- 15.5 Afterword.- 15.6 References.- 16 Order by Disorder and Topology in Frustrated Magnetic Systems.- 16.1 Introduction.- 16.2 Order by Disorder in a Heisenberg Magnet With One Additional Zero Mode (n0 = 1).- 16.2.1 Order by Quantum Disorder.- 16.3 Order by Thermal Fluctuations.- 16.4 Systems With More Than One Zero Mode.- 16.5 A System With a Macroscopic Number of Zero Modes: The Classical Kagome Antiferromagnet.- 16.5.1 Ground State Manifold and Spin Origami.- 16.6 Selection of Coplanar States by Order by Disorder.- 16.7 Does the Question What Particular Coplanar State Is Selected? Make Sense.- 16.8 An Effective Hamiltonian and Description as a Fluctuating Surface.- 16.9 Magnetic Field Effects.- 16.10 Effect of Spatial Disorder.- 16.11 Quantum Kagome Antiferromagnets.- 16.12 Conclusion.- 16.13 Acknowledgments.- 16.14 References.- 17 Noise-Induced Abnormal Growth.- 17.1 Introduction.- 17.2 A Computer Model.- 17.3 Computer Results.- 17.3.1 Effects of ? and ?.- 17.3.2 Effects of s.- 17.3.3 Effects of L.- 17.4 Discussion.- 17.5 Acknowledgments.- 17.6 References.- 18 Clustering of Active Walkers: Phase Transition from Local Interactions.- 18.1 Introduction.- 18.2 Equations of Motion for the Active Walker.- 18.3 Stability Analysis for Homogeneous Distributions.- 18.4 Estimation of an Effective Diffusion Coefficient.- 18.5 Results of Computer Simulations.- 18.6 Conclusions.- 18.7 Acknowledgments.- 18.8 References.- 19 Brownian Combustion Engines.- 19.1 Introduction.- 19.2 The Feynman Ratchet.- 19.3 Forced Ratchets.- 19.4 Forced Thermal Ratchets.- 19.5 Source of Time Correlations.- 19.6 Discussion.- 19.7 Outlook.- 19.8 Acknowledgments.- 19.9 References.- 20 A Depolymerization Ratchet for Intracellular Transport.- 20.1 Introduction.- 20.2 A Model for Intracellular Transport by Microtubule Depolymerization.- 20.3 Discussion.- 20.4 Acknowledgment.- 20.5 References.- 21 Order From Randomness: Spontaneous Firing From Stochastic Properties of Ion Channels.- 21.1 Introduction.- 21.2 Theory.- 21.3 Methods.- 21.4 Results.- 21.5 Discussion.- 21.6 Acknowledgments.- 21.7 References.- 22 Simple Noise-Induced Transitions in Models of Neural Systems.- 22.1 Noise and Bifurcations in the Nervous System.- 22.1.1 Studying Biological Noise Near a Bifurcation.- 22.2 Noise-Induced Transitions in the Pupil Light Reflex.- 22.3 Additive Noise-Induced Transitions in One Dimension?.- 22.4 Sensory Detection Through Noise-Induced Firing.- 22.5 Bursting and Noise in Cold Receptors.- 22.5.1 Summary of the Relevant Electrophysiology.- 22.5.2 Plant's Model With Stochastic Forcing.- 22.6 Conclusion.- 22.7 Acknowledgments.- 22.8 References.- 23 Noise and Nonlinearity in Neuron Modeling.- 23.1 Introduction.- 23.2 Coupled Neurodendrite Processes.- 23.2.1 The Reduced Neuron.- 23.2.2 Stochastic Resonance.- 23.3 Statistical Analysis of Firing Events.- 23.3.1 Bistability and the Interspike Interval Histogram.- 23.3.2 More Experiments: The Crayfish of Missouri and the SNR-ISIH Connection.- 23.3.3 The Perfect Integrator Revisited: All Cats Are Not Grey in the Dark.- 23.4 Concluding Remarks.- 23.5 Acknowledgments.- 23.6 References.- 24 Physiological Singularities Modeled by Nondeterministic Equations of Motion and the Effect of Noise.- 24.1 Introduction.- 24.2 Theory.- 24.3 Methods.- 24.4 Examples.- 24.4.1 Respiratory System.- 24.4.2 Cardiovascular System.- 24.5 Conclusion.- 24.6 Acknowledgments.- 24.7 References.- 25 Temporal Stochasticity Leads to Nondeterministic Chaos in a Model for Blood Cell Production.- 25.1 Introduction.- 25.2 The Dynamics of Blood Cell Production.- 25.3 A Computer Model of the Stem Cell Dynamics.- 25.4 Chaos in Biological Systems.- 25.5 Acknowledgments.- 25.6 References.- 26 Quantum Noise in Gravitation and Cosmology.- 26.1 Introduction.- 26.2 Quantum Noise From the Influence Functional.- 26.3 Fluctuation-Dissipation Relation for Systems With Colored and Multiplicative Noise.- 26.4 Brownian Particle in a Bath of Parametric Oscillators.- 26.4.1 Bogolubov Transformation and Particle Creation.- 26.4.2 Noise and Decoherence.- 26.5 Particle-Field Interaction.- 26.5.1 Accelerated Observer.- 26.5.2 Thermal Radiance in de Sitter Space.- 26.6 Field-Space-time Coupling: Backreaction in Semiclassical Cosmology.- 26.7 Discussion.- 26.8 Acknowledgment.- 26.9 References." @default.
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