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非线性物理学导论

非线性物理学导论

作者:( )Lui Lam著

出版社:世界图书出版公司北京公司

出版时间:1999-11-01

ISBN:9787506214650

定价:¥67.00

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内容简介
  A revolution occurred quietly in teh development of physics-or,more accu-rately,of science-in the last three decades.The revolution touches uponevery discipline in both the natural and social sciences.We are referring to the birth of a new science-nonlinear science-which,for the sake of presenta-tion,may be diveded into six parts:fractals,chaos,pattrn formation,sol-itons,cellular automata,and complex systems.本书为英文版!
作者简介
暂缺《非线性物理学导论》作者简介
目录
     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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