The Nonlinear Universe (eBook)

One of the pioneers in the area, Alwyn Scott entered nonlinear science as a teacher and researcher after completing his doctoral work at MIT in the late 1950s. His research, both experimental and theoretical, has addressed a wide range of topics from nonlinear laser optics to neuroscience. In 1981, Scott was selected as the founding director of the Center for Nonlinear Studies at the Los Alamos National Laboratory. He was also a founding editor of Physica D: Nonlinear Phenomena, the first journal devoted exclusively to the area. His other books include Neuroscience: A Mathematical Primer (Springer, New York) and Nonlinear Science: Emergence and Dynamics of Coherent Structures (Oxford University Press) and he served as editor of the recently published Encyclopedia of Nonlinear Science (Routledge). He completed 'The Nonlinear Universe' shortly before his untimely death in January 2007.

Preface 7
Contents 11
1 Introduction 15
1.1 What Is Nonlinear Science? 18
1.2 An Explosion of Activity 23
1.3 Causes of the Revolution 27
2 Chaos 33
2.1 The Three-Body Problem 34
2.2 Poincar´ e’s Instructive Mistake 35
2.3 The Lorenz Attractor 37
2.4 Other Irregular Curves 39
2.5 The KAM Theorem 44
2.6 More Early Discoveries of Low-Dimensional Chaos 48
2.7 Is There Chaos in the Solar System? 50
3 Solitons 56
3.1 Russell’s Solitary Waves 56
3.2 The Inverse Scattering Method 59
3.3 The Nonlinear Schr¨ odinger Equation 63
3.4 The Sine-Gordon Equation 64
3.5 Nonlinear Lattices 69
3.6 Some General Comments 71
4 Nerve Pulses and Reaction- Diffusion Systems 75
4.1 Nerve-Pulse Velocity 75
4.2 Simple Nerve Models 81
4.3 Reaction Diffusion in Higher Dimensions 84
5 The Unity of Nonlinear Science 90
5.1 The Provinces of Nonlinearity 90
5.2 Metatheories of Nonlinear Science 97
5.3 Interrelations Among the Metatheories 109
6 Physical Applications of Nonlinear Theory 112
6.1 Theories of Matter 112
6.2 Quantum Theory 121
6.3 Quantum Energy Localization and Chaos 133
6.4 Chemical and Biochemical Phenomena 138
6.5 Condensed-Matter Physics 143
6.6 Engineering Applications 149
6.7 Optical Science 158
6.8 Fluid Dynamics 163
6.9 Gravitation and Cosmology 176
7 Nonlinear Biology 191
7.1 Nonlinear Biochemistry 192
7.2 On Growth and Form 214
7.3 Physical and Life Sciences 239
7.4 Neuroscience 250
8 Reductionism and Life 287
8.1 Newton’s Legacy 287
8.2 Objections to Reductionism 290
8.3 Theories of Life 300
9 Epilogue 312
A Phase Space 315
B Quantum Theory 322
References 327