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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
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Searching... | 30000010179569 | Q172.5.C45 S36 2007 | Open Access Book | Book | Searching... |
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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 Introduction | p. 1 |
1.1 What Is Nonlinear Science? | p. 4 |
1.2 An Explosion of Activity | p. 9 |
1.3 Causes of the Revolution | p. 13 |
2 Chaos | p. 19 |
2.1 The Three-Body Problem | p. 20 |
2.2 Poincare's Instructive Mistake | p. 21 |
2.3 The Lorenz Attractor | p. 23 |
2.4 Other Irregular Curves | p. 25 |
2.5 The KAM Theorem | p. 30 |
2.6 More Early Discoveries of Low-Dimensional Chaos | p. 34 |
2.7 Is There Chaos in the Solar System? | p. 36 |
3 Solitons | p. 43 |
3.1 Russell's Solitary Waves | p. 43 |
3.2 The Inverse Scattering Method | p. 46 |
3.3 The Nonlinear Schrodinger Equation | p. 50 |
3.4 The Sine-Gordon Equation | p. 51 |
3.5 Nonlinear Lattices | p. 56 |
3.6 Some General Comments | p. 58 |
4 Nerve Pulses and Reaction-Diffusion Systems | p. 63 |
4.1 Nerve-Pulse Velocity | p. 63 |
4.2 Simple Nerve Models | p. 69 |
4.3 Reaction Diffusion in Higher Dimensions | p. 72 |
5 The Unity of Nonlinear Science | p. 79 |
5.1 The Provinces of Nonlinearity | p. 79 |
5.1.1 Solitons and Reaction Diffusion | p. 80 |
5.1.2 The KAM Theorem | p. 83 |
5.1.3 Chaos | p. 84 |
5.1.4 Reaction Diffusion and Chaos | p. 85 |
5.2 Metatheories of Nonlinear Science | p. 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 Metatheories | p. 98 |
6 Physical Applications of Nonlinear Theory | p. 101 |
6.1 Theories of Matter | p. 101 |
6.1.1 Mie's Nonlinear Electromagnetism | p. 102 |
6.1.2 De Broglie's Guiding Waves and the Double Solution | p. 106 |
6.1.3 Skyrmions | p. 107 |
6.1.4 Point vs. Extended Particles | p. 108 |
6.2 Quantum Theory | p. 110 |
6.2.1 Quantum Probabilities | p. 111 |
6.2.2 Schrodinger's Cat | p. 112 |
6.2.3 The EPR Paradox | p. 113 |
6.2.4 Nonlocality and Quantum Entanglement | p. 116 |
6.2.5 Bell's Inequality | p. 117 |
6.2.6 Joint Measurability | p. 119 |
6.2.7 Many Worlds? | p. 120 |
6.2.8 Nonlinear Quantum Mechanics? | p. 121 |
6.3 Quantum Energy Localization and Chaos | p. 122 |
6.3.1 Local Modes in Molecules | p. 122 |
6.3.2 Quantum Solitons | p. 124 |
6.3.3 Quantum Inverse Scattering | p. 125 |
6.3.4 Quantum Chaos? | p. 126 |
6.4 Chemical and Biochemical Phenomena | p. 127 |
6.4.1 Molecular Dynamics | p. 127 |
6.4.2 Energy Localization in Biomolecules | p. 128 |
6.4.3 Chemical Aggregates | p. 131 |
6.4.4 Chemical Kinetics | p. 132 |
6.5 Condensed-Matter Physics | p. 132 |
6.5.1 Extrinsic Nonlinearity | p. 133 |
6.5.2 Phase Transitions | p. 133 |
6.5.3 Supersonic Solitary Waves | p. 135 |
6.5.4 Discrete Breathers | p. 136 |
6.6 Engineering Applications | p. 138 |
6.6.1 Nonlinear Mechanical Vibrations | p. 138 |
6.6.2 Vacuum Tube Electronics | p. 139 |
6.6.3 Negative and Positive Feedback | p. 140 |
6.6.4 Frequency-Power Formulas | p. 142 |
6.6.5 Synchronization | p. 142 |
6.6.6 Nonlinear Diffusion | p. 143 |
6.6.7 Shock Waves and Solitons | p. 145 |
6.6.8 Electronic Chaos | p. 146 |
6.7 Optical Science | p. 147 |
6.7.1 Lasers | p. 147 |
6.7.2 Modulational Instability | p. 149 |
6.7.3 Solitons on Optical Fibers | p. 150 |
6.7.4 Pump-Probe Spectroscopy | p. 150 |
6.8 Fluid Dynamics | p. 152 |
6.8.1 Supersonic Waves | p. 152 |
6.8.2 Shock Waves | p. 153 |
6.8.3 Rayleigh-Benard Cells | p. 155 |
6.8.4 Plasma Waves | p. 156 |
6.8.5 Rogue Waves | p. 157 |
6.8.6 Coronets, Splashes and Antibubbles | p. 160 |
6.8.7 Atmospheric Dynamics | p. 162 |
6.8.8 Turbulence | p. 164 |
6.9 Gravitation and Cosmology | p. 165 |
6.9.1 General Relativity Theory | p. 166 |
6.9.2 Nonlinear Cosmic Phenomena | p. 170 |
6.9.3 Black Holes | p. 172 |
6.9.4 Tests of GRT | p. 174 |
6.9.5 A Hierarchy of Universes? | p. 177 |
7 Nonlinear Biology | p. 181 |
7.1 Nonlinear Biochemistry | p. 182 |
7.1.1 Frohlich Theory | p. 182 |
7.1.2 Protein Solitons | p. 183 |
7.1.3 Biological Applications of Protein Solitons | p. 190 |
7.1.4 DNA Solitons and the Hijackers | p. 196 |
7.1.5 The Coils of Chromatin | p. 203 |
7.2 On Growth and Form | p. 204 |
7.2.1 The Physics of Form | p. 205 |
7.2.2 Biological Membranes | p. 211 |
7.2.3 Leonardo's Law | p. 214 |
7.2.4 Turing Patterns | p. 219 |
7.2.5 Buridan's Ass, Instability and Emergence | p. 222 |
7.2.6 Relational Biology | p. 225 |
7.2.7 A Clash of Scientific Cultures? | p. 226 |
7.3 Physical and Life Sciences | p. 229 |
7.3.1 Mathematical Biology | p. 229 |
7.3.2 Collective Phenomena | p. 230 |
7.3.3 Population Dynamics | p. 232 |
7.3.4 Immense Numbers | p. 236 |
7.3.5 Homogeneous vs. Heterogeneous Sets | p. 238 |
7.3.6 Biological Hierarchies | p. 239 |
7.4 Neuroscience | p. 240 |
7.4.1 Nerve Models | p. 242 |
7.4.2 The Multiplex Neuron | p. 252 |
7.4.3 The McCulloch-Pitts Model of the Brain | p. 257 |
7.4.4 Hebb's Cell Assembly | p. 260 |
7.4.5 Cognitive Hierarchies | p. 274 |
8 Reductionism and Life | p. 277 |
8.1 Newton's Legacy | p. 277 |
8.1.1 The Reductive Program | p. 278 |
8.1.2 Supervenience and Physicalism | p. 279 |
8.1.3 Practical Considerations | p. 280 |
8.2 Objections to Reductionism | p. 280 |
8.2.1 Googols of Possibilities | p. 281 |
8.2.2 Convoluted Causality | p. 281 |
8.2.3 Nonlinear Causality | p. 283 |
8.2.4 Time's Arrow | p. 284 |
8.2.5 Downward Causation | p. 284 |
8.2.6 Open Systems | p. 285 |
8.2.7 Closed Causal Loops and Open Networks | p. 287 |
8.3 Theories of Life | p. 290 |
8.3.1 Artificial Life vs. Autopoiesis | p. 291 |
8.3.2 Relational Biology | p. 292 |
8.3.3 Mechanisms | p. 293 |
8.3.4 Complex Systems and Chaotic Emergence | p. 296 |
8.3.5 What Is Life? | p. 300 |
9 Epilogue | p. 303 |
A Phase Space | p. 307 |
B Quantum Theory | p. 315 |
References | p. 321 |