非线性物理学导论 azw3 网盘 高速 下载地址大全 免费

网络（路）分析问题详解，ISBN：9787506214650，作者：（美）范·沃坎伯格（Van Valkenluig M.E.）原著；程元文译著

Contents Preface 1 Introduction LuiLam 1.1 A Quiet Revolution 1.2 Nonlinearity 1.3 Nonlinear Science 1.3.1 Fractals 1.3.2 Chaos 1.3.3 Pattem Fonnation 1.3.4 Solitons 1.3.5 Cellular Automata 1.3.6 Complex Systems 1.4 Remarks References Part I Fractals and Multifractals 2 Fractals and Diffusive Growth Thomas C. Halsey 2.1 Percolation 2.2 Diffusion-Limited Aggregation 2.3 Electrostatic Analogy 2.4 Physical Applications ofDLA 2.4.1 Electrodeposition with Secondary Current Distribution 2.4.2 Diffusive Electrodeposition Problems References 3 Multifractality Thomas C. Halsey 3.1 Defimtionof(q)and f(a) 3.2 SystematicDefinitionofT(q) 3.3 The Two-Scale Cantor Set 3.3.1 Limiting Cases 3.3.2 Stirling Formula andf(a) 3.4 Multifractal Correlations 3.4.1 Operator Product Expansion and Multifractality 3.4.2 Correlations oflso-flt Sets 3.5 Numerical Measurements of f(a) 3.6 Ensemble Averaging and (q) Problems References 4 Scaling Arguments and Diffusive Growth Thomas C. Halsey 4.1 The Information Dimension 4.2 The Turkevich-Scher Scaling Relation 4.3 The Electrostatic Scaling Relation 4.4 Scaling ofNegative Moments 4.5 Conclusions Problems References Part II Chaos and Randomness 5 Introduction to Dynamical Systems Stephen G. Eubank and J. Doyne Farmer 5.1 Introduction 5.2 Detenninism Versus Random Processes 5.3 ScopeofPartII 5.4 Deterministic Dynamical Systems and State Space 5.5 Classification 5.5.1 PropertiesofDynamical Systems 5.5.2 A BriefTaxonomy ofDynamical Systems Models 5.5.3 The Relationship Between Maps and Flows 5.6 Dissipative Versus Conservative Dynamical Systems 5.7 Stability 5.7.1 Lmearization 5.7.2 TheSpectrumofLyapunovExponents 5.7.3 InvariantSets 5.7.4 Attractors 5.7.5 Regular Attractors 5.7.6 ReviewofStability 5.8 Bifurcations 5.9 Chaos 5.9.1 Binary Shift Map 5.9.2 Chaos in Flows 5.9.3 The Rossler Attractor 5.9.4 The Lorenz Attractor 5.9.5 Stable and Unstable Manifolds 5.10 Homoclinic Tangle 5.10.1 Chaos in Higher Dimensions 5.10.2 Bifurcations Between Chaotic Attractors Problems References 6 Probability, Random Processes, and the Statistfcal Description ofDynanucs Stephen G. EubankandJ. Doyne Farmer 6.1 Nondeterminism in Dynamics 6.2 Measure and Probability 6.2.1 Estimating a Density Function from Data 6.3 Nondetenninistic Dynamics 6.4 Averaging 6.4.1 Stationarity 6.4.2 Time Averages and Ensemble Averages 6.4.3 Mixing 6.5 Characterization ofDistributions 6.5.1 Moments 6.5.2 Entropy and Infonnation 6.6 Fractals, Dimension, and the Uncertainty Exponent 6.6.1 Pointwise Dimension 6.6.2 Information Dimension 6.6.3 Fractal Dimension 6.6.4 Generalized Dimensions 6.6.5 Estimating Dimension from Data 6.6.6 Embedding Dimension 6.6.7 Fat Fractals 6.6.8 Lyapunov Dimension 6.6.9 Metric Entropy 6.6.10 Pesin's Identity 6.7 Dimensions, Lyapunov Exponents, and Metric Entropy in the Presence ofNoise Problems References 7 Modeling Chaotic Systems Stephen G. Eubank and J. Doyne Farmer 7.1 Chaos and Prediction 7.2 State Space Reconstruction 7.2.1 Derivative Coordinates 7.2.2 Delay Coordinates 7.2.3 Broomhead and King Coordinates 7.2.4 Reconstruction as Optimal Encoding 7.3 Modeling Chaotic Dynamics 7.3.1 Choosing an Appropriate Model 7.3.2 OrderofApproximation 7.3.3 ScalingofErrors 7.4 System Characterization 7.5 Noise Reduction 7.5.1 Shadowing 7.5.2 Optimal Solution ofShadowing Problem with Euclidean Nonn 7.5.3 Numerical Results 7.5.4 Statistical Noise Reduction 7.5.5 Limits to Noise Reduction Problems References Part III Pattero Formation and Disorderly Growth 8 Phenomenology of Growth Leonard M. Sander 8.1 Aggregation: Pattems and Fractals Far from Equilibrium 8.2 Natural Systems 8.2.1 Ballistic Growth 8.2.2 Diffusion-Limited Growth 8.2.3 GrowthofColloidsandAerosols Problems References 9 Models and Applications Leonard M. Sander 9.1 Ballistic Growth 9.1.1 Simulations and Scaling 9.1.2 Continuum Models 9.2 Diffusion-Limited Growth 9.2.1 Simulations and Scaling 9.2.2 The Mullins-Sekerka Instability 9.2.3 Orderiy and Disorderiy Growth 9.2.4 Electrochemical Deposition: A Case Study 9.3 Cluster-Cluster Aggregation Appendix: A DLA Program Problems References Part IV SoBtons 10 Integrable Systems LuiLam 10.1 Introduction 10.2 Origin and History of Solitons 10.3 Integrability and Conservation Laws 10.4 Soliton Equations and their Solutions 10.4.1 Korteweg-de Vries Equation 10.4.2 Nonlinear Schrodinger Equation 10.4.3 Smc-Gordon Equation 10.4.4 Kadomtsev-Petviashvili Equation 10.5 MethodsofSolution 10.5.1 Inverse Scattering Method 10.5.2 Bficklund Transformation 10.5.3 Hirota Method 10.5.4 Numerical Method 10.6 Physical Soliton Systems 10.6.1 ShallowWaterWaves 10.6.2 Dislocations in Crystals 10.6.3 Self-FocusingofLight 10.7 Conclusions Problems References 11 Nonintegrable Systems LuiLam 11.1 Introduction 11.2 Nonintegrable Soliton Equations with Hamiltonian Structures 11.2.1 The Equation 11.2.2 Double Sine-Gordon Equation 11.3 Nonlinear Evolution Equations 11.3.1 Fisher Equation 11.3.2 The Damped Equation 11.3.3 The Damped Driven Sine-Gordon Equation 11.4 A Method of Constructing Soliton Equations 11.5 FonnationofSolitons 11.6 Perturbations 11.7 Soliton Statistical Mechanics 11.7.1 TheSystem 11.7.2 The Sine-Gordon System 11.8 Solitons in Condensed Matter 11.8.1 Liquid Crystals 11.8.2 Polyacetylene 11.8.3 Optical Fibers 11.8.4 Magnetic Systems 11.9 Conclusions Problems References Part V Special Topics 12 Cellular Automata and Discrete Physics David E. Hiebeler and Robert Tatar 12.1 Introduction 12.1.1 A Well-Kaown Example: Life 12.1.2 Cellular Automata 12.1.3 The Information Mechanics Group 12.2 Physical Modeling 12.2.1 CA Quasiparticles 12.2.2 Physical Properties from CA Simulations 12.2.3 Diffusion 12.2.4 SoundWaves 12.2.5 Optics 12.2.6 Chemical Reactions 12.3 Hardware 12.4 Current Sources of Literature 12.5 An Outstanding Problem in CA Simulations Problems References 13 Visualization Techniques for Cellular Dynamata Ralph H. Abraham 13.1 Historical Introduction 13.2 Cellular Dynamata 13.2.1 Dynamical Schemes 13.2.2 Complex Dynamical Systems 13.2.3 CD Definitions 13.2.4 CD States 13.2.5 CD Simulation 13.2.6 CD Visualization 13.3 An Example ofZeeman's Method 13.3.1 Zeeman's Heart Model: Standard Cell 13.3.2 Zeeman's Heart Model: Physical Space 13.3.3 Zeeman's Heart Model: Beating 13.4 The Graph Method 13.4.1 The Biased Logistic Scheme 13.4.2 The Logistic/Diffusion Lattice 13.4.3 The Global State Graph 13.5 The Isochron Coloring Method 13.5.1 Isochrons ofa Periodic Attractor 13.5.2 Coloring Strategies 13.6 Conclusions References 14 From Laminar Flow to Turbulence GeoffreyK. Vallis 14.1 Preamble and Basic Ideas 14.1.1 What Is Turbulence? 14.2 From Laminar Flow to Nonlinear Equilibration 14.2.1 A Linear Analysis: The Kelvin-Helmholz Instability 14.2.2 A Weakly Nonlinear Analysis: Landau's Equation 14.3 From Nonlinear Equilibration to Weak Turbulence 14.3.1 The Quasi-Periodic Sequence 14.3.2 The Period Doubling Sequence 14.3.3 The Intermittent Sequence 14.3.4 Fluid Relevance and Experimental Evidence 14.4 Strong Turbulence 14.4.1 Scaling Arguments for Inertial Ranges 14.4.2 Predictability of Strong Turbulence 14.4.3 Renormalizing the Diffusivity 14.5 Remarks References 15 Active Walks: Pattern Formation, Self-Organization, and Complex Systems LuiLam 15.1 Introduction 15.2 Basic Concepts 15.3 Continuum Description 15.4 Computer Models 15.4.1 ASingleWalker 15.4.2 Branching 15.4.3 Multiwalkers and Updating Rules 15.4.4 Track Pattems 15.5 Three Applications 15.5.1 Dielectric Breakdown in a Thin Layer ofLiquid 15.5.2 lon Transport in Glasses 15.5.3 Ant Trails in Food Collection 15.6 Intrinsic Abnormal Growth 15.7 Landscapes and Rough Surfaces 15.7.1 GrooveStates 15.7.2 Localization-Delocalization Transition 15.7.3 Scaling Properties 15.8 FuzzyWalks 15.9 Related Developments and Open Problems 15.10 Conclusions References Appendix: Historical Remarks on Chaos Michael Nauenberg Contributors Index

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