STATISTICAL AND NONLINEAR PHYSICS.

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Series Preface Volume Preface Contents About the Editor-in-Chief About the Volume Editor Contributors Statistical and Nonlinear Physics: Introduction Complex Systems and Emergent Phenomena Glossary Definition of the Subject Introduction Equilibrium Averages The Two-Dimensional XY-Model Lack of Ordering in Two Dimensions Vortex Unbinding The Spin Wave Stiffness The KT Transition The Vortex Unbinding Transition in Other Systems Non-Equilibrium Systems 1/f Fluctuations: A Langevin Approach Transport by Diffusion Self-Organized Structure Formation: Ant Trails Summary and Future Directions Acknowledgments Bibliography Polymer Physics Glossary Definition of the Subject Introduction Single Polymer Chain Physics Ideal Non-interacting Chains Self-Interacting Chains: Excluded Volume The Role of Electrostatic Charge Equilibrium Properties of Many-Chain Fluids Semi-dilute Solutions Complex Topology Polymers and Gelation Dynamics of Polymeric Fluids Single Chain Dynamics Polymer Dynamics with Hydrodynamics Entangled Polymer Dynamics Nonlinear Flow of Polymeric Fluids Multiphase Polymeric Fluids Polymer Blends Block Copolymers Future Directions Bibliography Primary Literature Books and Reviews Chaotic Dynamics in Nonequilibrium Statistical Mechanics Glossary Definition of the Subject Introduction The Roles of Ergodicity and Mixing for the Approach to Thermodynamic Equilibrium Ergodic Systems Mixing Systems What Is the Relevance of These Notions for Statistical Mechanics? Integrable, Pseudo-Chaotic, and Chaotic Systems Anosov and Anosov-Like Systems; the Chaotic Hypothesis Fractal Dimensions Applications of Dynamical Systems Theory to Non-equilibrium Statistical Mechanics Microscopic Dynamical Quantities and Macroscopic Transport Coefficients The Escape-Rate Formulae for Transport Coefficients Transport Coefficients and Phase-Space Contraction in Gaussian Thermostatted Systems Ruelle-Pollicott Resonances and Irreversible Processes Fractal Forms in Diffusion and a Dimension Formula Entropy Production in Non-equilibrium, Hamiltonian Systems Kinetic Theory Methods for Analytical Calculations of Lyapunov Spectra Entropy Production in Systems with Gaussian Thermostats and the Cohen-Gallavotti Fluctuation Theorem Discussion Future Directions Acknowledgments Bibliography Primary Literature Books and Reviews Monte Carlo Simulations in Statistical Physics Glossary Definition of the Subject Introduction The Metropolis Importance Sampling Algorithm as a Tool in Classical Equilibrium Statistical Mechanics The Dynamic Interpretation of Monte Carlo Simulation and Application to Study Dynamic Processes Overcoming the Limitations of Finite Size Extensions to Quantum Statistical Mechanics Future Directions Bibliography Nonlinear Fluid Flow, Pattern Formation, Mixing, and Turbulence Glossary Definition Introduction and Theoretical Background Specific Examples of Patterns in Fluid Flows Taylor-Couette Flow Rayleigh-Bénard Convection Bénard-Marangoni Convection Transport and Mixing Manifolds, Lobes, and Transport Barriers Pattern Formation in Reaction-Diffusion and Advection-Reaction-Diffusion Systems Burning Invariant Manifolds and Reaction Fronts Other Examples of Pattern-Forming Systems Future Directions Bibliography Primary Literature Books and Reviews Fluid Dynamics in Clouds Glossary Why Study Clouds Definition of the Subject Microphysics Without Thermodynamics Microphysics with Thermodynamics Thermodynamics of Phase-Change Interactions of Particle Inertia, Thermodynamics, and Buoyancy-Driven Flow Cumulus Clouds: Phase-Change+Buoyancy+Turbulence Mammatus Clouds: Phase-Change + Particle Settling + Buoyancy Droplets in Clouds, Redux: Particle Inertia+Turbulence+Phase-Change Conclusion and Future Directions Acknowledgments Bibliography Collective Transport and Depinning Glossary Definition of the Subject Introduction Elastic Manifolds and Impurity Pinning Elasticity, Order, and Symmetry Breaking Elastic Manifolds in a Disordered Potential Rugged Energy Landscape, Critical Dimension, and the Pinning Length Driven Depinning, Critical Properties, and Scaling The Driven Depinning Transition Continuum Model of the Manifold Dynamics Critical Properties and Scaling Laws Numerical Results for the Critical Exponents Analytical Treatments of the Depinning Transition and Universality Mean-Field Theory Functional Renormalization Group Contact Line Depinning Self-Organized Criticality Interface Depinning in Anisotropic Medium Easy and Hard Directions of Depinning A Lattice Automaton Quenched KPZ Equation Future Directions Bibliography Primary Literature Books and Reviews Disordered Elastic Media Glossary Definition of the Subject Introduction Static Properties of Disordered Elastic Media Interfaces and Basic Concepts Periodic Systems and Bragg Glass Pinning and Dynamics General Description of the Dynamics Depinning High Velocity Phase Small Applied Force and Creep Motion Future Directions Bibliography Primary Literature Books and Reviews Physics of Jerky Motion in Slowly Driven Magnetic and Earthquake Fault Systems Glossary Definition of the Subject Introduction Global Statistics and Power Law Scaling Models Models for Barkhausen Noise in Magnets The Random Field Ising Model (RFIM) Simple Models for Inhomogeneous Earthquake Faults The Ben-Zion and Rice Model Dynamic Weakening Dynamic Strengthening Related General Continuum Equations of Motion Monotonic Models Non-monotonic Models Theoretical Results The Universality Class of the BZR Model Results on the Monotonic Version of the Model General Results: Depinning Transition More Realistic Driving of a Fault Moment Rate Shapes for Monotonic Models Non-monotonic Models Mode Switching Results on Aftershocks Mapping to Single-Interface Magnet Model Summary Phase Diagram Conclusions Future Directions Acknowledgments Bibliography Primary Literature Flexible Mechanical Structures and Their Topologically Protected Deformations Glossary Introduction Rigidity Linearization Periodic Structures Spatially Varying Modes Topological Boundary Modes of Maxwell Lattices Topological Invariants in Higher Dimensions Alternate Formulations Origami Continuum Systems Conclusion Bibliography Glasses and Aging, A Statistical Mechanics Perspective on Glossary Definition of the Subject Phenomenology Basic Facts Static and Dynamic Correlation Functions Taxonomy of ``Glasses´´ in Science Colloidal Glass Transition Jamming Transition Granular Glass Transition Active Glasses Random Pinning Glass Transition Ultrastable Glasses Other Glasses in Physics, and Beyond Numerical Simulations Dynamic Heterogeneity Existence of Spatiotemporal Dynamic Fluctuations Multipoint Correlation Functions Nonlinear Response Function Theory of the Glass Transition Random First-Order Transition Theory Mean-Field Models and a Zest of Replica Theory Liquids and Glasses in Infinite Dimensions Random First-Order Transitions Heterogeneous Disorder and Mapping to the Random, Field Ising Model Renormalization Group for the Glass Transition Free Volume, Defects, and Facilitated Models Lattice Gases Free Volume, Dynamic Criticality Defects: Connection with Hamiltonian Dynamics Models Connection with Other Perspectives Geometric Frustration, Avoided Criticality, and Locally Preferred Structures Geometric Frustration Coulomb Frustrated Theories Locally Preferred Structures Mean-Field Theory of the Amorphous Phase Mean-Field Glassy Phase Diagrams Jamming Vibrational Properties Rheology New Computational Methods The Swap Monte-Carlo Method Franz-Parisi Potential Point-to-Set Lengthscale s-Ensemble and Large Deviations Machine Learning Developments Aging and Off-Equilibrium Dynamics Why Aging? Memory and Rejuvenation Effects Mean-Field Aging and Effective Temperatures Beyond Mean-Field: Real Space Beyond Mean-Field: Energy Landscape Driven Glassy Materials Future Directions Acknowledgments Bibliography Stress Localization in Soft Particulate Gels Glossary Definition of the Subject Introduction Source of Mechanical Heterogeneities and Frozen-in Stresses: Microscopic Forces and Gelation Processes Origin of Elastic Modulus and Emergence of Rigidity Stress Localization at Rest and Under Shear Future Directions Acknowledgments References Nonlinear Mechanics of Colloidal Gels: Creep, Fatigue, and Shear-Induced Yielding Glossary Definition of the Subject Introduction: From Gelation to Rupture in Colloidal Dispersions General Context: The Mechanics of Colloidal Gels A Brief Reminder on Colloidal Gelation Two Illustrations of Colloidal Gel Microstructures A First Approach of Yielding Based on Oscillatory Shear Rheometry Reversible Yielding Versus Irreversible Rupture Carbon Black Gels as Model Materials for ``Reversible´´ Yielding Caseinate Gels as Model Materials for Irreversible Yielding Characterizing Yielding Through Spatially-Resolved Dynamical Measurements Fundamental Questions and Perspectives What Is the Physical Meaning of the Functional Form τf (σ)? How Does Strain-Induced Yielding Compare to Stress-Induced Yielding? Can One Predict the Yielding Scenario from Macroscopic Observables? What Does Strain-Stiffening Tell Us About Yielding? Can We Get a Microscopic Picture of Yielding? Summary and Conclusion Bibliography Statistical Physics of the Yielding Transition Glossary Introduction Elastoplastic Models Mean-Field Descriptions Conclusion and Outlook Bibliography Granular Flows Glossary Definition of the Subject Introduction Granular Fluid and Its Statistical Mechanics Nonequilibrium Statistical Mechanics Liouville Equation and Cooling Stationary Homogeneous State Macroscopic Balance Equations ``Normal´´ States and Hydrodynamics Navier-Stokes Approximation Constitutive Equations Green-Kubo Expressions Navier-Stokes Hydrodynamic Equations Future Directions Acknowledgments Appendix Bibliography Primary Literature Books and Reviews Statistical Mechanics of Clogging Glossary Definition of the Subject Introduction Clogging Clogging as a Stochastic Process Does a Critical Outlet Size Exist? Statistics of Avalanches Dynamical Signatures of Clogging Incipient Clogging Effect of Other Variables Influence of Particles Properties Role of Dynamics on Clogging Arches Unclogging The Weakest Link Arch Breaking Is a History Dependent Process Summary and Discussion Future Directions Bibliography Jamming of Granular Matter Glossary Definition of the Subject Introduction Statistical Framework of Jamming Granular Packings Edward´s Ensemble Force Ensembles Generalized Ensembles Tests of the Stress-Based Ensemble Jamming Phase Diagram Force Fluctuations, Dynamical Heterogeneities, Length and Time Scales in Granular Flows Approaching Jamming Force Distributions, Length and Time Scales in Jammed States Near the Jamming Transition Sheared States Isotropic vs. Anistropic Stress States Isostaticity and Point J Isostaticity and Random Close Packing Isostatic Packings are Marginal Simulations and Theory Experimental Observations Future Directions Bibliography Books and Reviews Rigidity Percolation and Frictional Jamming Glossary Definition of the Subject Introduction Friction in Granular Materials Frictional Contacts Experiments Numerical Models Frictional Jamming Rigidity Percolation Maxwell Constraint Counting Laman´s Theorem The Pebble Game Rigid Clusters and Nature of the Rigidity Transition The Frictional Rigidity Transition Frictional Constraint Counting The Frictional Pebble Game Results for Lattices, Simulated, and Experimental Packings Future Directions Bibliography Cell Biology: Networks, Regulation and Pathways Glossary Definition of the Subject Introduction Biological Networks and Their Building Blocks Genetic Regulatory Networks Protein-Protein Interaction Networks Metabolic Networks Signaling Networks Models of Biological Networks Topological Models Boolean Networks Probabilistic Models Dynamical Systems Stochastic Dynamics Network Properties and Operating Principles Modularity Robustness Noise Dynamics, Attractors, Stability and Large Fluctuations Optimization Principles Evolvability and Designability Future Directions Acknowledgments Bibliography Fluctuation Theorems, Brownian Motors and Thermodynamics of Small Systems Glossary Definition of the Subject Introduction Molecular Motors Non-equilibrium Thermodynamics of Small Systems Non-equilibrium States Microscopic Definitions of Work and Heat The Jarzynski Equality Fluctuation Theorems Experimental Tests and Free Energy Recovery Future Directions Bibliography Primary Literature Books and Reviews Neuronal Dynamics Glossary Definition of the Subject Introduction Types of Modeling and Theoretical Tools Different Classes of Neurons Models Synapses A Simplified Semi-realistic Description for Single PSCs Network Architecture Theoretical Tools Intrinsic Network Dynamics Irregular Firing at Low Rates Attractors with Inhomogeneously Distributed Activity Dynamics at Various Time Scales Stimulus Driven Dynamics Dynamics During Stimulus Presentation Switching from Asynchronous to Synchronous State Multistability and Working Memory Effect of Long-Term Synaptic Plasticity on Network Dynamics Dynamics and Information Processing: Two Specific Examples Future Directions Bibliography Primary Literature Books and Reviews Dense Active Matter Glossary Why Study Active Matter? Definition of the Subject Experimental Studies Models Numerical Studies Theoretical Studies Comparison with Experiments Conclusion and Future Directions Bibliography Ultracold Atomic Gases: Novel States of Matter Glossary Definition of the Subject Introduction One-Dimensional Lattices Luttinger Liquid of Polarons in One-Dimensional Bose-Fermi Mixtures Commensurate Mixtures of Ultracold Atoms in One Dimension Phase-Locking Transition of Coupled Low-Dimensional Superfluids 2D Superfluids Kibble-Zurek Mechanism Bose-Fermi Mixtures in Two-Dimensional Optical Lattices Renormalization Group Method Phase Diagram and Subdominant Orders Quantum Frustration in Triangular Lattices Conclusions Bibliography Primary Literature Books and Reviews Quantum Chaos Glossary Definition of the Subject Introduction Quantum Chaos: Stationary Aspects Quantum Chaos: Dynamical Aspects Applications of Quantum Chaos Atomic Physics Mesoscopic Solid-State Physics Quantum Information Wave Chaos Future Directions Bibliography Networks: Structure and Dynamics Glossary Definition and Relevance Introduction Structural Properties of Complex Networks Simple Graphs Directed Networks Weighted Networks Dynamics on Complex Networks Robustness and Vulnerability of Complex Networks Spreading Processes and Social Dynamics Searching on Complex Networks Future Directions Bibliography Primary Literature Books and Reviews Centralities in Complex Networks Glossary Why Study Networks? Definition of the Subject Centrality Measures Based on Shortest Paths Centrality Measures Based on Walks Centrality Measures Based on Random Walks Centrality Measures Based on Non-Backtracking Walks Conclusion and Future Directions Acknowledgments Bibliography Optimization Problems and Algorithms from Computer Science Glossary Definition of the Subject Introduction Polymers in a Disordered Environment Many Repulsive Elastic Lines in Random Media Vortex Glasses and Loop Percolation Interfaces and Elastic Manifolds Elastic Manifold Periodic Medium Random Field Ising Model The Spin Glass Problem Two Dimensions, Planar Graph Three Dimensions, Non-planar Graphs Potts Free Energy and Submodular Functions Submodular Functions Minimization of Submodular Function Results Future Directions Bibliography Primary Literature Books and Reviews Statistical Mechanics Approach to Econophysics Glossary Definition of the Subject Historical Introduction Statistical Mechanics of Money Distribution The Boltzmann-Gibbs Distribution of Energy Conservation of Money The Boltzmann-Gibbs Distribution of Money Models with Debt Proportional Money Transfers and Saving Propensity Additive Versus Multiplicative Models Statistical Mechanics of Wealth Distribution Models with a Conserved Commodity Models with Stochastic Growth of Wealth Empirical Data on Money and Wealth Distributions Data and Models for Income Distribution Empirical Data on Income Distribution Theoretical Models of Income Distribution Other Applications of Statistical Physics Economic Temperatures in Different Countries Society as a Binary Alloy Future Directions, Criticism, and Conclusions Future Directions Agents with a Finite Lifespan Agent-Based Simulations of the Two-Class Society Access to Detailed Empirical Data Economies in Transition Relation to Physical Energy Criticism from Economists Awareness of Previous Economics Literature Reliance on Visual Data Analysis Quest for Universality Theoretical Modeling of Money, Wealth, and Income Conclusions Bibliography Primary Literature Books and Reviews Index