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Cover image for The nonlinear universe : chaos, emergence, life
Title:
The nonlinear universe : chaos, emergence, life
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Series:
The frontiers collection
Publication Information:
New York, NY : Springer, 2007
Physical Description:
xvi, 364 p. : ill. ; 25 cm.
ISBN:
9783540341529

9783540341536
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30000010179569 Q172.5.C45 S36 2007 Open Access Book Book
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Summary

Summary

It has been suggested that the big questions of science are answered - that science has entered a "twilight age" where all the important knowledge is known and only the details need mopping up. And yet, the unprecedented progress in science and technology in the twentieth century has raised qu- tions that weren't conceived of a century ago. This book argues that, far from being nearlycomplete, the storyof sciencehas many morechapters,yet unwritten. With the perspective of the century's advance, it's as if we have climbed a mountain and can see just how much broader the story is. Instead of asking how an apple falls from a tree, as Isaac Newton did in the17thcentury,wecannowask:Whatisthefundamentalnatureofanapple (matter)? How does an apple (biological organism) form and grow? Whence came the breeze that blew it loose (meteorology)? What in a physical sense (synaptic ?rings) was the idea that Newton had, and how did it form? A new approach to science that can answer such questions has sprung up in the past 30 years. This approach - known as nonlinear science-ismore than a new ?eld. Put simply, it is the recognition that throughout nature, the whole is greater than the sum of the parts. Unexpected things happen.


Author Notes

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.


Reviews 1

Choice Review

The author makes the central claim that "the concepts of nonlinear science comprise a Kuhnian revolution which will have profound implications for scientific research in the present century." Alwyn, now deceased (formerly, Univ. of Arizona), supports that assertion with erudition, a plethora of examples, insightful discourses on existing work, and philosophical discussions. The book begins with an engaging outline of the history of nonlinear science, followed by chapters on its main aspects, namely, chaos, solitons, and reaction-diffusion systems. Thirteen chapters in "Physical Applications of Nonlinear Theory" and "Nonlinear Biology" constitute the major part of the work. Although such sections as, say, "Quantum Solitons," "Plasma Waves," and "Nonlinear Cosmic Phenomena" are straightforward explications--if, at times, too arcane for the nonspecialist--topics such as "Protein Solitons" and "Population Dynamics" sometimes lead to polemics. The final section, "Reductionism and Life," is an impassioned argument that "nonlinear science is where to seek answers to the remaining riddles of biology." The book charms with historical and personal vignettes. The bibliography contains 1,087, mostly referenced, entries. It suffers from the absence of an index and glossary of the innumerable acronyms. Nevertheless, it is a must read for anyone in or near nonlinear science. Summing Up: Highly recommended. Upper-division undergraduates through researchers/faculty. J. Mayer emeritus, Lebanon Valley College


Table of Contents

1 Introductionp. 1
1.1 What Is Nonlinear Science?p. 4
1.2 An Explosion of Activityp. 9
1.3 Causes of the Revolutionp. 13
2 Chaosp. 19
2.1 The Three-Body Problemp. 20
2.2 Poincare's Instructive Mistakep. 21
2.3 The Lorenz Attractorp. 23
2.4 Other Irregular Curvesp. 25
2.5 The KAM Theoremp. 30
2.6 More Early Discoveries of Low-Dimensional Chaosp. 34
2.7 Is There Chaos in the Solar System?p. 36
3 Solitonsp. 43
3.1 Russell's Solitary Wavesp. 43
3.2 The Inverse Scattering Methodp. 46
3.3 The Nonlinear Schrodinger Equationp. 50
3.4 The Sine-Gordon Equationp. 51
3.5 Nonlinear Latticesp. 56
3.6 Some General Commentsp. 58
4 Nerve Pulses and Reaction-Diffusion Systemsp. 63
4.1 Nerve-Pulse Velocityp. 63
4.2 Simple Nerve Modelsp. 69
4.3 Reaction Diffusion in Higher Dimensionsp. 72
5 The Unity of Nonlinear Sciencep. 79
5.1 The Provinces of Nonlinearityp. 79
5.1.1 Solitons and Reaction Diffusionp. 80
5.1.2 The KAM Theoremp. 83
5.1.3 Chaosp. 84
5.1.4 Reaction Diffusion and Chaosp. 85
5.2 Metatheories of Nonlinear Sciencep. 86
5.2.1 Cybernetics (C)p. 86
5.2.2 Mathematical Biology (MB)p. 88
5.2.3 General Systems Theory (GST)p. 93
5.2.4 Nonequilibrium Statistical Mechanics (NSM)p. 94
5.2.5 Catastrophe Theory (CT)p. 95
5.2.6 Synergetics (S)p. 96
5.2.7 Complex Adaptive Systems (CAS)p. 97
5.3 Interrelations Among the Metatheoriesp. 98
6 Physical Applications of Nonlinear Theoryp. 101
6.1 Theories of Matterp. 101
6.1.1 Mie's Nonlinear Electromagnetismp. 102
6.1.2 De Broglie's Guiding Waves and the Double Solutionp. 106
6.1.3 Skyrmionsp. 107
6.1.4 Point vs. Extended Particlesp. 108
6.2 Quantum Theoryp. 110
6.2.1 Quantum Probabilitiesp. 111
6.2.2 Schrodinger's Catp. 112
6.2.3 The EPR Paradoxp. 113
6.2.4 Nonlocality and Quantum Entanglementp. 116
6.2.5 Bell's Inequalityp. 117
6.2.6 Joint Measurabilityp. 119
6.2.7 Many Worlds?p. 120
6.2.8 Nonlinear Quantum Mechanics?p. 121
6.3 Quantum Energy Localization and Chaosp. 122
6.3.1 Local Modes in Moleculesp. 122
6.3.2 Quantum Solitonsp. 124
6.3.3 Quantum Inverse Scatteringp. 125
6.3.4 Quantum Chaos?p. 126
6.4 Chemical and Biochemical Phenomenap. 127
6.4.1 Molecular Dynamicsp. 127
6.4.2 Energy Localization in Biomoleculesp. 128
6.4.3 Chemical Aggregatesp. 131
6.4.4 Chemical Kineticsp. 132
6.5 Condensed-Matter Physicsp. 132
6.5.1 Extrinsic Nonlinearityp. 133
6.5.2 Phase Transitionsp. 133
6.5.3 Supersonic Solitary Wavesp. 135
6.5.4 Discrete Breathersp. 136
6.6 Engineering Applicationsp. 138
6.6.1 Nonlinear Mechanical Vibrationsp. 138
6.6.2 Vacuum Tube Electronicsp. 139
6.6.3 Negative and Positive Feedbackp. 140
6.6.4 Frequency-Power Formulasp. 142
6.6.5 Synchronizationp. 142
6.6.6 Nonlinear Diffusionp. 143
6.6.7 Shock Waves and Solitonsp. 145
6.6.8 Electronic Chaosp. 146
6.7 Optical Sciencep. 147
6.7.1 Lasersp. 147
6.7.2 Modulational Instabilityp. 149
6.7.3 Solitons on Optical Fibersp. 150
6.7.4 Pump-Probe Spectroscopyp. 150
6.8 Fluid Dynamicsp. 152
6.8.1 Supersonic Wavesp. 152
6.8.2 Shock Wavesp. 153
6.8.3 Rayleigh-Benard Cellsp. 155
6.8.4 Plasma Wavesp. 156
6.8.5 Rogue Wavesp. 157
6.8.6 Coronets, Splashes and Antibubblesp. 160
6.8.7 Atmospheric Dynamicsp. 162
6.8.8 Turbulencep. 164
6.9 Gravitation and Cosmologyp. 165
6.9.1 General Relativity Theoryp. 166
6.9.2 Nonlinear Cosmic Phenomenap. 170
6.9.3 Black Holesp. 172
6.9.4 Tests of GRTp. 174
6.9.5 A Hierarchy of Universes?p. 177
7 Nonlinear Biologyp. 181
7.1 Nonlinear Biochemistryp. 182
7.1.1 Frohlich Theoryp. 182
7.1.2 Protein Solitonsp. 183
7.1.3 Biological Applications of Protein Solitonsp. 190
7.1.4 DNA Solitons and the Hijackersp. 196
7.1.5 The Coils of Chromatinp. 203
7.2 On Growth and Formp. 204
7.2.1 The Physics of Formp. 205
7.2.2 Biological Membranesp. 211
7.2.3 Leonardo's Lawp. 214
7.2.4 Turing Patternsp. 219
7.2.5 Buridan's Ass, Instability and Emergencep. 222
7.2.6 Relational Biologyp. 225
7.2.7 A Clash of Scientific Cultures?p. 226
7.3 Physical and Life Sciencesp. 229
7.3.1 Mathematical Biologyp. 229
7.3.2 Collective Phenomenap. 230
7.3.3 Population Dynamicsp. 232
7.3.4 Immense Numbersp. 236
7.3.5 Homogeneous vs. Heterogeneous Setsp. 238
7.3.6 Biological Hierarchiesp. 239
7.4 Neurosciencep. 240
7.4.1 Nerve Modelsp. 242
7.4.2 The Multiplex Neuronp. 252
7.4.3 The McCulloch-Pitts Model of the Brainp. 257
7.4.4 Hebb's Cell Assemblyp. 260
7.4.5 Cognitive Hierarchiesp. 274
8 Reductionism and Lifep. 277
8.1 Newton's Legacyp. 277
8.1.1 The Reductive Programp. 278
8.1.2 Supervenience and Physicalismp. 279
8.1.3 Practical Considerationsp. 280
8.2 Objections to Reductionismp. 280
8.2.1 Googols of Possibilitiesp. 281
8.2.2 Convoluted Causalityp. 281
8.2.3 Nonlinear Causalityp. 283
8.2.4 Time's Arrowp. 284
8.2.5 Downward Causationp. 284
8.2.6 Open Systemsp. 285
8.2.7 Closed Causal Loops and Open Networksp. 287
8.3 Theories of Lifep. 290
8.3.1 Artificial Life vs. Autopoiesisp. 291
8.3.2 Relational Biologyp. 292
8.3.3 Mechanismsp. 293
8.3.4 Complex Systems and Chaotic Emergencep. 296
8.3.5 What Is Life?p. 300
9 Epiloguep. 303
A Phase Spacep. 307
B Quantum Theoryp. 315
Referencesp. 321
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