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The Nonlinear Universe : Chaos, Emergence, Life - Alwyn C. Scott

The Nonlinear Universe

Chaos, Emergence, Life

Hardcover Published: 1st August 2007
ISBN: 9783540341529
Number Of Pages: 364

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Written in Alwyn Scott's inimitable style, one that readers will find both lucid and accessible, this masterwork elucidates the explosion of activity in nonlinear science in recent decades. 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 is essential for understanding the scientific developments of the twenty-first century.

From the reviews:

"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. ... The book charms with historical and personal vignettes. The bibliography contains 1,087, mostly referenced, entries. ... it is a must read for anyone in or near nonlinear science. Summing Up: Highly recommended. Upper-division undergraduates through researchers/faculty." (J. Mayer, CHOICE, Vol. 45 (9), 2008)

"Alwyn Scott (1931-2007) completed this summary of his life's study in December 2006 ... . This history book wonderfully summarizes ideas that were so important to him in a way that is largely accessible to `general readers who would understand science and for university undergraduates who would become researchers in or teachers of science.' It also displays his humanity, charm, and broad-reaching interests and knowledge." (Robert E. O'Malley, SIAM Review, Vol. 50 (2), 2008)

Introductionp. 1
What Is Nonlinear Science?p. 4
An Explosion of Activityp. 9
Causes of the Revolutionp. 13
Chaosp. 19
The Three-Body Problemp. 20
Poincare's Instructive Mistakep. 21
The Lorenz Attractorp. 23
Other Irregular Curvesp. 25
The KAM Theoremp. 30
More Early Discoveries of Low-Dimensional Chaosp. 34
Is There Chaos in the Solar System?p. 36
Solitonsp. 43
Russell's Solitary Wavesp. 43
The Inverse Scattering Methodp. 46
The Nonlinear Schrodinger Equationp. 50
The Sine-Gordon Equationp. 51
Nonlinear Latticesp. 56
Some General Commentsp. 58
Nerve Pulses and Reaction-Diffusion Systemsp. 63
Nerve-Pulse Velocityp. 63
Simple Nerve Modelsp. 69
Reaction Diffusion in Higher Dimensionsp. 72
The Unity of Nonlinear Sciencep. 79
The Provinces of Nonlinearityp. 79
Solitons and Reaction Diffusionp. 80
The KAM Theoremp. 83
Chaosp. 84
Reaction Diffusion and Chaosp. 85
Metatheories of Nonlinear Sciencep. 86
Cybernetics (C)p. 86
Mathematical Biology (MB)p. 88
General Systems Theory (GST)p. 93
Nonequilibrium Statistical Mechanics (NSM)p. 94
Catastrophe Theory (CT)p. 95
Synergetics (S)p. 96
Complex Adaptive Systems (CAS)p. 97
Interrelations Among the Metatheoriesp. 98
Physical Applications of Nonlinear Theoryp. 101
Theories of Matterp. 101
Mie's Nonlinear Electromagnetismp. 102
De Broglie's Guiding Waves and the Double Solutionp. 106
Skyrmionsp. 107
Point vs. Extended Particlesp. 108
Quantum Theoryp. 110
Quantum Probabilitiesp. 111
Schrodinger's Catp. 112
The EPR Paradoxp. 113
Nonlocality and Quantum Entanglementp. 116
Bell's Inequalityp. 117
Joint Measurabilityp. 119
Many Worlds?p. 120
Nonlinear Quantum Mechanics?p. 121
Quantum Energy Localization and Chaosp. 122
Local Modes in Moleculesp. 122
Quantum Solitonsp. 124
Quantum Inverse Scatteringp. 125
Quantum Chaos?p. 126
Chemical and Biochemical Phenomenap. 127
Molecular Dynamicsp. 127
Energy Localization in Biomoleculesp. 128
Chemical Aggregatesp. 131
Chemical Kineticsp. 132
Condensed-Matter Physicsp. 132
Extrinsic Nonlinearityp. 133
Phase Transitionsp. 133
Supersonic Solitary Wavesp. 135
Discrete Breathersp. 136
Engineering Applicationsp. 138
Nonlinear Mechanical Vibrationsp. 138
Vacuum Tube Electronicsp. 139
Negative and Positive Feedbackp. 140
Frequency-Power Formulasp. 142
Synchronizationp. 142
Nonlinear Diffusionp. 143
Shock Waves and Solitonsp. 145
Electronic Chaosp. 146
Optical Sciencep. 147
Lasersp. 147
Modulational Instabilityp. 149
Solitons on Optical Fibersp. 150
Pump-Probe Spectroscopyp. 150
Fluid Dynamicsp. 152
Supersonic Wavesp. 152
Shock Wavesp. 153
Rayleigh-Benard Cellsp. 155
Plasma Wavesp. 156
Rogue Wavesp. 157
Coronets, Splashes and Antibubblesp. 160
Atmospheric Dynamicsp. 162
Turbulencep. 164
Gravitation and Cosmologyp. 165
General Relativity Theoryp. 166
Nonlinear Cosmic Phenomenap. 170
Black Holesp. 172
Tests of GRTp. 174
A Hierarchy of Universes?p. 177
Nonlinear Biologyp. 181
Nonlinear Biochemistryp. 182
Frohlich Theoryp. 182
Protein Solitonsp. 183
Biological Applications of Protein Solitonsp. 190
DNA Solitons and the Hijackersp. 196
The Coils of Chromatinp. 203
On Growth and Formp. 204
The Physics of Formp. 205
Biological Membranesp. 211
Leonardo's Lawp. 214
Turing Patternsp. 219
Buridan's Ass, Instability and Emergencep. 222
Relational Biologyp. 225
A Clash of Scientific Cultures?p. 226
Physical and Life Sciencesp. 229
Mathematical Biologyp. 229
Collective Phenomenap. 230
Population Dynamicsp. 232
Immense Numbersp. 236
Homogeneous vs. Heterogeneous Setsp. 238
Biological Hierarchiesp. 239
Neurosciencep. 240
Nerve Modelsp. 242
The Multiplex Neuronp. 252
The McCulloch-Pitts Model of the Brainp. 257
Hebb's Cell Assemblyp. 260
Cognitive Hierarchiesp. 274
Reductionism and Lifep. 277
Newton's Legacyp. 277
The Reductive Programp. 278
Supervenience and Physicalismp. 279
Practical Considerationsp. 280
Objections to Reductionismp. 280
Googols of Possibilitiesp. 281
Convoluted Causalityp. 281
Nonlinear Causalityp. 283
Time's Arrowp. 284
Downward Causationp. 284
Open Systemsp. 285
Closed Causal Loops and Open Networksp. 287
Theories of Lifep. 290
Artificial Life vs. Autopoiesisp. 291
Relational Biologyp. 292
Mechanismsp. 293
Complex Systems and Chaotic Emergencep. 296
What Is Life?p. 300
Epiloguep. 303
Phase Spacep. 307
Quantum Theoryp. 315
Referencesp. 321
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9783540341529
ISBN-10: 3540341528
Series: The Frontiers Collection
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 364
Published: 1st August 2007
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 2.46
Weight (kg): 0.79