Scott The Nonlinear Universe

Chaos, Emergence, Life
1. Auflage 2007
ISBN: 978-3-540-34153-6
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 364 Seiten

Reihe: The Frontiers Collection

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.

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.

Autoren/Hrsg.

Scott, Alwyn C.

Inhaltsverzeichnis

1;Preface;7
2;Contents;11
3;1 Introduction;15
3.1;1.1 What Is Nonlinear Science?;18
3.2;1.2 An Explosion of Activity;23
3.3;1.3 Causes of the Revolution;27
4;2 Chaos;33
4.1;2.1 The Three-Body Problem;34
4.2;2.2 Poincar´ e’s Instructive Mistake;35
4.3;2.3 The Lorenz Attractor;37
4.4;2.4 Other Irregular Curves;39
4.5;2.5 The KAM Theorem;44
4.6;2.6 More Early Discoveries of Low-Dimensional Chaos;48
4.7;2.7 Is There Chaos in the Solar System?;50
5;3 Solitons;56
5.1;3.1 Russell’s Solitary Waves;56
5.2;3.2 The Inverse Scattering Method;59
5.3;3.3 The Nonlinear Schr¨ odinger Equation;63
5.4;3.4 The Sine-Gordon Equation;64
5.5;3.5 Nonlinear Lattices;69
5.6;3.6 Some General Comments;71
6;4 Nerve Pulses and Reaction- Diffusion Systems;75
6.1;4.1 Nerve-Pulse Velocity;75
6.2;4.2 Simple Nerve Models;81
6.3;4.3 Reaction Diffusion in Higher Dimensions;84
7;5 The Unity of Nonlinear Science;90
7.1;5.1 The Provinces of Nonlinearity;90
7.2;5.2 Metatheories of Nonlinear Science;97
7.3;5.3 Interrelations Among the Metatheories;109
8;6 Physical Applications of Nonlinear Theory;112
8.1;6.1 Theories of Matter;112
8.2;6.2 Quantum Theory;121
8.3;6.3 Quantum Energy Localization and Chaos;133
8.4;6.4 Chemical and Biochemical Phenomena;138
8.5;6.5 Condensed-Matter Physics;143
8.6;6.6 Engineering Applications;149
8.7;6.7 Optical Science;158
8.8;6.8 Fluid Dynamics;163
8.9;6.9 Gravitation and Cosmology;176
9;7 Nonlinear Biology;191
9.1;7.1 Nonlinear Biochemistry;192
9.2;7.2 On Growth and Form;214
9.3;7.3 Physical and Life Sciences;239
9.4;7.4 Neuroscience;250
10;8 Reductionism and Life;287
10.1;8.1 Newton’s Legacy;287
10.2;8.2 Objections to Reductionism;290
10.3;8.3 Theories of Life;300
11;9 Epilogue;312
12;A Phase Space;315
13;B Quantum Theory;322
14;References;327