The nonlinear universe : chaos, emergence, life / Alwyn C. Scott.

Format:

Book

Author/Creator:

Scott, Alwyn, 1931-2007.

Series:

Frontiers collection

The frontiers collection, 1612-3018

Language:

English

Subjects (All):

Chaotic behavior in systems.

Nonlinear theories--Forecasting.

Nonlinear theories.

Research--Forecasting.

Research.

Twenty-first century.

Forecasting.

Physical Description:

xvi, 364 pages : illustrations ; 25 cm.

Edition:

First edition.

Place of Publication:

Berlin ; New York : Springer, [2007]

Summary:

Written in Alwyn Scott??'s inimitable style?? lucid and accessible?? The Nonlinear Universe surveys and explores the explosion of activity in nonlinear science that began in the 1970s and 1980s and continues today. The book explains the wide-ranging implications of nonlinear phenomena for future developments in many areas of modern science, including mathematics, physics, engineering, chemistry, biology, and neuroscience. Arguably as important as quantum theory, modern nonlinear science?? and an appreciation of its implications?? is essential for understanding scientific developments of the twenty-first century.

Contents:

1.1 What Is Nonlinear Science? 4

1.2 An Explosion of Activity 9

1.3 Causes of the Revolution 13

2 Chaos 19

2.1 The Three-Body Problem 20

2.2 Poincare's Instructive Mistake 21

2.3 The Lorenz Attractor 23

2.4 Other Irregular Curves 25

2.5 The KAM Theorem 30

2.6 More Early Discoveries of Low-Dimensional Chaos 34

2.7 Is There Chaos in the Solar System? 36

3 Solitons 43

3.1 Russell's Solitary Waves 43

3.2 The Inverse Scattering Method 46

3.3 The Nonlinear Schrodinger Equation 50

3.4 The Sine-Gordon Equation 51

3.5 Nonlinear Lattices 56

3.6 Some General Comments 58

4 Nerve Pulses and Reaction-Diffusion Systems 63

4.1 Nerve-Pulse Velocity 63

4.2 Simple Nerve Models 69

4.3 Reaction Diffusion in Higher Dimensions 72

5 The Unity of Nonlinear Science 79

5.1 The Provinces of Nonlinearity 79

5.1.1 Solitons and Reaction Diffusion 80

5.1.2 The KAM Theorem 83

5.1.3 Chaos 84

5.1.4 Reaction Diffusion and Chaos 85

5.2 Metatheories of Nonlinear Science 86

5.2.1 Cybernetics (C) 86

5.2.2 Mathematical Biology (MB) 88

5.2.3 General Systems Theory (GST) 93

5.2.4 Nonequilibrium Statistical Mechanics (NSM) 94

5.2.5 Catastrophe Theory (CT) 95

5.2.6 Synergetics (S) 96

5.2.7 Complex Adaptive Systems (CAS) 97

5.3 Interrelations Among the Metatheories 98

6 Physical Applications of Nonlinear Theory 101

6.1 Theories of Matter 101

6.1.1 Mie's Nonlinear Electromagnetism 102

6.1.2 De Broglie's Guiding Waves and the Double Solution 106

6.1.3 Skyrmions 107

6.1.4 Point vs. Extended Particles 108

6.2 Quantum Theory 110

6.2.1 Quantum Probabilities 111

6.2.2 Schrodinger's Cat 112

6.2.3 The EPR Paradox 113

6.2.4 Nonlocality and Quantum Entanglement 116

6.2.5 Bell's Inequality 117

6.2.6 Joint Measurability 119

6.2.7 Many Worlds? 120

6.2.8 Nonlinear Quantum Mechanics? 121

6.3 Quantum Energy Localization and Chaos 122

6.3.1 Local Modes in Molecules 122

6.3.2 Quantum Solitons 124

6.3.3 Quantum Inverse Scattering 125

6.3.4 Quantum Chaos? 126

6.4 Chemical and Biochemical Phenomena 127

6.4.1 Molecular Dynamics 127

6.4.2 Energy Localization in Biomolecules 128

6.4.3 Chemical Aggregates 131

6.4.4 Chemical Kinetics 132

6.5 Condensed-Matter Physics 132

6.5.1 Extrinsic Nonlinearity 133

6.5.2 Phase Transitions 133

6.5.3 Supersonic Solitary Waves 135

6.5.4 Discrete Breathers 136

6.6 Engineering Applications 138

6.6.1 Nonlinear Mechanical Vibrations 138

6.6.2 Vacuum Tube Electronics 139

6.6.3 Negative and Positive Feedback 140

6.6.4 Frequency-Power Formulas 142

6.6.5 Synchronization 142

6.6.6 Nonlinear Diffusion 143

6.6.7 Shock Waves and Solitons 145

6.6.8 Electronic Chaos 146

6.7 Optical Science 147

6.7.1 Lasers 147

6.7.2 Modulational Instability 149

6.7.3 Solitons on Optical Fibers 150

6.7.4 Pump-Probe Spectroscopy 150

6.8 Fluid Dynamics 152

6.8.1 Supersonic Waves 152

6.8.2 Shock Waves 153

6.8.3 Rayleigh-Benard Cells 155

6.8.4 Plasma Waves 156

6.8.5 Rogue Waves 157

6.8.6 Coronets, Splashes and Antibubbles 160

6.8.7 Atmospheric Dynamics 162

6.8.8 Turbulence 164

6.9 Gravitation and Cosmology 165

6.9.1 General Relativity Theory 166

6.9.2 Nonlinear Cosmic Phenomena 170

6.9.3 Black Holes 172

6.9.4 Tests of GRT 174

6.9.5 A Hierarchy of Universes? 177

7 Nonlinear Biology 181

7.1 Nonlinear Biochemistry 182

7.1.1 Frohlich Theory 182

7.1.2 Protein Solitons 183

7.1.3 Biological Applications of Protein Solitons 190

7.1.4 DNA Solitons and the Hijackers 196

7.1.5 The Coils of Chromatin 203

7.2 On Growth and Form 204

7.2.1 The Physics of Form 205

7.2.2 Biological Membranes 211

7.2.3 Leonardo's Law 214

7.2.4 Turing Patterns 219

7.2.5 Buridan's Ass, Instability and Emergence 222

7.2.6 Relational Biology 225

7.2.7 A Clash of Scientific Cultures? 226

7.3 Physical and Life Sciences 229

7.3.1 Mathematical Biology 229

7.3.2 Collective Phenomena 230

7.3.3 Population Dynamics 232

7.3.4 Immense Numbers 236

7.3.5 Homogeneous vs. Heterogeneous Sets 238

7.3.6 Biological Hierarchies 239

7.4 Neuroscience 240

7.4.1 Nerve Models 242

7.4.2 The Multiplex Neuron 252

7.4.3 The McCulloch-Pitts Model of the Brain 257

7.4.4 Hebb's Cell Assembly 260

7.4.5 Cognitive Hierarchies 274

8 Reductionism and Life 277

8.1 Newton's Legacy 277

8.1.1 The Reductive Program 278

8.1.2 Supervenience and Physicalism 279

8.2 Objections to Reductionism 280

8.2.1 Googols of Possibilities 281

8.2.2 Convoluted Causality 281

8.2.3 Nonlinear Causality 283

8.2.4 Time's Arrow 284

8.2.5 Downward Causation 284

8.2.6 Open Systems 285

8.2.7 Closed Causal Loops and Open Networks 287

8.3 Theories of Life 290

8.3.1 Artificial Life vs. Autopoiesis 291

8.3.2 Relational Biology 292

8.3.3 Mechanisms 293

8.3.4 Complex Systems and Chaotic Emergence 296

8.3.5 What Is Life? 300

A Phase Space 307

B Quantum Theory 315.

Notes:

Includes bibliographical references (pages [321]-364).

ISBN:

9783540341529

3540341528

OCLC:

186358816