The Frontiers Collection

The Nonlinear Universe

Chaos, Emergence, Life

Bearbeitet von Alwyn C Scott

1. Auflage 2007. Buch. xiv, 364 S. Hardcover ISBN 978 3 540 34152 9 Format (B x L): 15,5 x 23,5 cm Gewicht: 764 g

Weitere Fachgebiete > Mathematik > Numerik und Wissenschaftliches Rechnen > Angewandte Mathematik, Mathematische Modelle Zu Inhaltsverzeichnis

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Abbott, E. 104 artificial life 291–292, 298 Ablowitz, M. 15, 16, 51 Ashby, W.R. 87 acoustics, nonlinear 50 Aspect, A. 118 actin 191 associative cortex 266, 267 action spectra 183 Asteroid Belt 41 action–angle variable 30 astrology 2 Adler, F.R. 216 Atmanspacher, H. 273 ADP 183, 193 atmospheric dynamics 162–164 Adrian, E.D. 64, 139 ATP hydrolysis 129, 183, 189–191, 193 Agassiz, L. 14 attention 262 Ahlborn, B. 91, 210, 229 switching 273 AIGO 169 Aubry, S. 136 Airy, G. 45, 59, 61 Austin, R. 189 Alexander, D. 188, 190 autopoiesis 95, 292 Alfv´en, H. 156 axiomatization 288 Alfv´en wave 156 axon 144, 192, 245, 253 all-or-nothing principle 64, 139, 253, excitor motor 218 256 giant 64–66, 88, 144, 218, 241, 243, Allee effect 233 248, 249, 256 Allee, W. 232 HH 68 allopoiesis 292 Hodgkin–Huxley 68, 243–244 amide-I mode 129, 130, 184, 188, 189 motor 248 amino acid 131, 185 axonal tree 252, 258 Anderson localization 190 Anderson, C. 105 Baade, W. 172 Anderson, P. 281 Bacillus megaterium 183, 186 antibubble 161, 162 B¨acklund transformation 58 antikink 53, 55, 84, 197 B¨acklund, A. 58 Archaeopteryx 210 backward-wave oscillator 13 Aristarchus of Samos 2 balkanization 15, 77, 288 Aristotelian cosmology 166, 171 ball lightning 157, 289 Aristotelian dynamics 82 Banerjee, A. 201 Aristotelian limit 82, 83 Bar-Natan, D. 160 Aristotle 2–4, 82, 152, 222, 277 Bardeen, J. 143 on causality 5–6, 277, 282 Barone, A. 146 Arnol’d, V. 30 Barthes, M. 186 arrow of time 39, 284 Barwise, J. 223 Arthur Rylah Institute 235 base-rotator model 200 366 Index basin of attraction 285, 310 Bloembergen, N. 15 Basov, N. 147 blood vessels 215 Bateson, G. 87 Bode, H. 141 Bazin, H. 45, 61 Bode, J. 38 Belinski, V. 170 Bohm, D. 106, 117 bell shape 205 Bohr, N. 40, 111, 114, 115, 126, 315 Bell Telephone Laboratories 140, 150, Bohr–Einstein debate 113–116, 119 315 Bohr–Sommerfeld quantum theory 23 Bell’s inequality 117–120 Bolton, C. 174 Bell, J. 117 Boltzmann’s H-theorem 33 Belousov, B. 72, 182 Boltzmann, L. 312 Belousov–Zhabotinsky reaction 73, Bond, G. 36 74, 132, 232, 243 Born, M. 40, 104, 105, 127, 317 Belousov–Zhabotinsky wave 95 Born–Oppenheimer approximation B´enard, H. 155 128 B´enard–Marangoni convection 155 Bose–Einstein condensate 133, 182 Benedict, R. 181, 276 Boulding, K. 93 Bengtsson, H.-U. 216 boundary condition 6, 282 Benjamin, T.B. 149 Bour, E. 58 Benjamin–Feir instability 149 Boussinesq, J. 45, 61 benzene 122, 123, 143 bow wave 153 Bergson, H. 209, 279 Brahe, T. 3 Bernoulli, D. 59 brain 112, 143, 238, 240–276 Bernoulli, J. 20, 59 ambiguous perception 264 Bernstein, J. 63, 242 experiential response 268 Betyaev, S. 161 Hopfield model 270, 271 Beurle, R. 250 language learning 264 Bianchi, L. 58 learning environment 265 bifurcation 28, 215–217 McCulloch–Pitts model 257–260 diagram 29, 96 positive feedback 288 Bigio, I. 185, 200 research 241 biochemical phenomena 127–132, robustness 263 182–203 sensory deprivation 267 biological membrane 211–214 stabilized image 265 biological oscillator 230 Braitenberg, V. 264 biology, nonlinear 181–276 branching exponent 214, 217, 219, 255 bion 54 Brans, C. 176 Birge, R. 122 Brans–Dicke theory 176 Birge–Sponer relation 122, 131, 151, Brattain, W. 143 186 Bray, W. 72 Birkhoff, G.D. 23, 43, 163 breather 55, 84 Bishop, A. 49, 201 discrete 136–137 Bishop, G. 91 in mica 137 black hole 168, 170, 172–174, 177, 297 mass 109 black soap film 211 moving 54 Black, H.S. 140, 223 stationary 54 Bloch-wall dynamics 16 Brillouin, L. 170, 174, 175 Blodgett, K. 132 British coastline 25–27, 40 Index 367

Brody, T. 119 quantum 126–127 Brownian motion 27, 40, 85 research 34, 43 Brunswik, E. 91 spatial 56 Brusselator 132 chaotic trajectory 59, 307 Burgers equation 153, 165, 296 charge-density wave 133 Burgers, J. 165 Chase, P. 276 Buridan, J. 222 chemical aggregate 131–132 butterfly effect 16, 35, 164, 282 chemical garden 208, 209 chemical kinetics 132 Caianiello, E. 88 chemical phenomena 127–132 calcium pump 193, 194 chemical reaction 27 calculus 19 autocatalytic 182, 242 candle 9, 63, 69, 286, 288, 295 chemiosmotic hypothesis 129 Careri, G. 130, 136, 182, 186, 195, 208 Chirikov, B. 23, 33, 37 Carnap, R. 91 Chizmadzhev, Y. 244, 254 Cartwright, M. 35 Chklovskii, D. 218 catastrophe theory 95–97, 99, 208 Christiansen, P. 201 causality 5, 277 chromatin 203 convoluted 281–283 remodelling 203 nonlinear 283 Clarkson University 15 causation closed causal loop 10, 79, 87, 88, 129, downward 284–285, 289, 301 141, 156, 167, 184, 223, 224, 240, upward 284, 301 259, 275, 286–290 cause in biology 87 distal 6 closed causal network 289 efficient 6, 7, 13, 210, 227, 282, 284 cloud formation 156 final 6, 282 cognitive hierarchy 274–276, 297 formal 6, 7, 13, 210, 282 material 5, 282 Cole, K. 64 proximal 6 collective phenomena 230–232, 270 teleological 6 complex adaptive system 97–99 cell 7 complex network 289 dielectric properties 182 complex system 90, 92, 296–300 division 185 complexity 281 membrane 182, 193, 211–214, 242 Compton, A. 89, 243 pyramidal 253 computing power 13 reproduction 289 of neuron 254 cerebellum 253 condensed matter 132–137, 182, 280 Chandrasekhar, S. 172 conformon 190, 191, 195 Changeux, J.-P. 194 Conley, C. 18, 71 chaos 4, 9, 17, 18, 84–87, 122–127, 277 consciousness 278 dissipative 86 constructionist hypothesis 281 dynamical 240 Conway, J. 291 electronic 146 Copernican revolution 1, 3, 8, 14 energy-conserving 83 Copernicus,N. 2,3,36 homoclinic 32 cortical wave 250–252 in Solar System 36–41, 170 cosmic ray 105 low-dimensional 8, 13, 19–41, 55, 79, cosmology 15, 170–171, 177–178 84, 164, 289 Cowan, J. 251 368 Index

Crane, H. 70, 241 dissipation 67, 81, 82, 84, 86, 145, 224, crayfish 218 230 Crick, F. 90, 300 dissipative perturbation 55 critical exponent 135 dissipative structure 95 critical phenomena 135 DNA 7, 90, 290, 300 Cruzeiro, L. 131, 190 hijacking 199, 228 Curie principle 223 soliton 196–203 Curie temperature 134 DNLS equation 124 curved spacetime 166, 170–172 domain wall 53, 133, 134 cybernetics 7, 86–88, 99, 224, 288 Dublin Institute for Advanced Studies Cygnum X-1 174 105, 301 dust devil 162, 163 da Vinci, L. 34, 85, 214 Dalibard, J. 118 Eddington, A. 172, 175 Dante Alighieri 2 Ed´en, P. 216 Darboux, G. 58 Edler, J. 131, 188 Darwin, C. 14, 209 Edwards, G. 197 Dashen, R. 109 Eigen, M. 92, 226, 288 Davis, C. 197 eigenvector 308 Davisson, C. 315 Davydov, A.S. 50, 128, 129, 182, 183, Eilbeck, C. 84, 137, 186 188, 190 Einstein tensor 167 de Broglie, L. 23, 106, 315 Einstein, A. 22, 101, 104, 105, 108, De Forest, L. 139 110, 111, 113–116, 118, 121, 126, de Vaucanson, J. 290, 299 147, 166, 168, 172, 315 de Vries, G. 45, 61 Einstein–Hilbert equations 166, 168, deep water wave 16, 50 171, 173, 177, 297 Deering, W. 217 electromagnetism, nonlinear 102–105 Deimos 37, 170 electron 102, 103, 105, 108, 117 Delbr¨uck, M. 300 Born–Infeld model 105, 171 dendrite 217, 218, 252–257, 282 Mie model 103 dendritic logic 254 spinor field 106 dendritic tree 252, 253, 258 electron–positron creation 105 geometric ratio 253–257 electron–positron decay 53, 117 dependent variable 6 electrophysiology 139, 217, 242, 244, Derrick–Hobart theorem 107 247 Descartes, R. 3, 279, 290 electrostatic interaction 20 developmental biology 222, 226, 227 elementary particle 16, 101–110 DeWitt, B. 120, 121 extended 108 Dicke, R. 174, 176 journals 108 diffusion equation point 108 linear 77, 165 Elsasser, W. 92, 236, 238 nonlinear 65, 244 emergence 4, 8, 9, 43, 80, 87, 93, 95, diffusion, nonlinear 143–144 101, 105, 141, 181, 224, 240, 276, diode 144–148 277, 285, 287, 293, 301 Dirac, P.A.M. 128, 173 chaotic 165, 178, 296–300 directed graph 226 of human culture 289 dislocation dynamics 16, 33, 51, 56, of life 226, 288, 289, 297 84, 133 Emmeche, C. 284 Index 369 energy conservation 30, 49, 55, 61, 67, FitzHugh–Nagumo equation 71–72, 83, 84, 93, 101, 224, 285 81, 96, 246–247 energy localization in biomolecules 2D 73 128–131, 184 3D 76 energy–momentum tensor 167 flame-front propagation 67, 85, 244, engineering 138–147 295 Englander, W. 196 Flaschka, H. 16 Enigma code 73 Flatland 178 entropy 33 flow resistance 164 Enz, U. 107 FLRW model 171 epigenetic drift 299 fluid dynamics 152–165 epilepsy 252, 268 fluxon 48, 53, 55, 133, 145, 146 equifinality 285 fold catastrophe 96 Esaki, L. 143, 145 forcing term 6 Escherischia coli 183, 185, 199, 238 Ford, J. 5, 32, 79 Euler, L. 20 forest fire 15 Everett, H. 120 F¨orster, R. 104 evolution 91, 209, 210, 218, 225, 238, fossil 210, 297 248, 285, 297 Fourier transform 48, 59 punctuated 285, 297 FPU computations 13, 15, 136, 173 expanding universe 171 fractal 25, 27 explosives 132 model of lung 217 extended particle 108 fractional dimension 26, 27 extrasolar planets 39 Fraga, M. 299 extrinsic nonlinearity 129, 133, 136 Frank, L. 87 Frank-Kamenetskii, D. 67 Faddeev, L. 51, 125 Franken, P. 148 fairy ring 73, 231, 233 Franklin, B. 242 Fanselow, E. 274 Franklin, W.S. 35 Faraday, M. 63, 69, 77 Frenkel, Y. 33, 51, 56, 84, 133 Feddersen, H. 137 frequency locking 143, 145, 230 feedback 7, 140–141, 223, 259, 288 frequency–power formulas 142 negative 87, 141, 288 Friedmann, A. 171 positive 10, 79, 86, 87, 141, 152, 194, Friesecke, G. 135 240, 275, 288, 289 Friesecke–Wattis theorem 135 Feigenbaum number 29 Fr¨olich theory 182–183 Feigenbaum, M. 29 Fr¨olich, H. 182, 184 Feir, J. 149 Froude’s law 68 Fermi, E. 13, 46 Froude, W. 68 ferromagnetism 134 functionalism 279 Fessenden, R. 142 fibrillation 76, 86, 232 Gage, P. 260 field theory 15 galaxy 171 filamentation 4, 83, 86, 149 Galileo, G. 3, 14, 36, 82, 166 Filippov, A. 109 Galvani, L. 242 Finkelstein, R. 106 Game of Life 291 firefly 230 Gardner, C. 47 Fisher, R. 70, 83, 85, 233 Gay, J. 40 FitzHugh, R. 71 Gell-Mann, M. 98 370 Index gene Halley’s comet 37, 38, 166, 170 expression 299 Halley, E. 37 propagation 70, 83 hallucination 252, 267, 268 general relativity 104, 105, 166–170 Hamilton, W.R. 312 predictions 167 Hamiltonian 30 tests 174–177 Hamm, P. 131, 151, 188, 190 general systems theory 93–94, 99 Hammack, J. 15 genetic transcription 203 harmonic generation 4 genome 299 harmonic oscillator 31 GEO-600 169 Harth, E. 288 geodesic 167 Hasegawa, A. 150 Gerard, R.W. 93 Hasslacher, B. 109 Germer, L. 315 Hawking, S. 173 Ghazanfar, A. 274 Hayashi, C. 34 Giaever, I. 143, 145 heart 232, 238 Gibbs, J.W. 111, 312 Hebb’s cell assembly theory 260–274 Gierer, A. 207, 219, 221 Hebb, D. 260, 298 Ginzburg–Landau equation 85, 133 Heeger, A. 196 Glass, L. 232 Heiles, C. 31 global warming 164 Heisenberg, W. 15, 107, 316 G¨odel, K. 288, 296 heliocentrism 2, 3, 36 Goel, N. 234 as heresy 14 Goklany, I. 190 helium atom 21 Goldbach conjecture 296 Helmholtz, H. 63, 77, 162, 242, 280 Goldenburg, M. 174 H´enon, M. 27 Gollub, J. 27 H´enon–Heiles Hamiltonian 31, 32, 35, Gomez, D. 217 85, 311 Goodsell, D. 290 heteroclinic trajectory 144, 310, 311 Goodwin, B. 285 heterodyne principle 142 googol 236, 281 googolplex 236 heterogeneous set 181, 281 Gordon, W. 319 hierarchical system 5, 181, 197, 203, Gould, S.J. 226, 297 301 graph theory 226 biological 239–240, 282 gravitational attraction 19, 20, 104 cognitive 274–276, 297 gravitational wave 169–170, 177 of universes 296 graviton 110 Hilbert, D. 104, 166, 288 Green function 59 hippocampus 253 Green, D. 129, 182, 183, 190 Hirota, R. 58 Greene, J. 33, 47 histone 203 greenhouse gas 164 Hodgkin, A. 18, 66, 88, 144, 207, 241 Griffith, J. 251 Hodgkin–Huxley nerve model 68, 243–244 hadron 108 Holland, P. 107 Haeckel, E. 226 Holstein, T. 188 Hagen, G. 164 homeostasis 88 Hagen–Poiseuille law 164, 215 Homma, S. 201 Haken, H. 27, 96, 149, 271, 273 homoclinic trajectory 310, 311 Halding, J. 201 homogeneous set 181, 238, 281 Index 371

Hopfield, J. 270 irrational number 31 horseshoe map 25 Italian National Research Council 90 Hozumi, K. 216 Hubble parameter 171 Jacobi elliptic function 33, 46, 48, 59, hunting 87 84, 145, 149 hurricane 162, 163 Jacobi, C. 138 Huxley, A. 18, 66, 88, 144, 207, 241 James, W. 273 Huygens, C. 138, 142, 230 Javan, A. 147 Hydra vulgaris 205–208, 219, 221, 222, Jelly, E. 132 224, 238 Ji, S. 190, 191 hydrogen atom 21, 127, 315 Josephson junction 48, 55, 81, 133, 145 spectrum 40 annular 146 hydrogen bond 185 long 157 deuteration 196 Josephson oscillator 146 stretching 184 Josephson, B. 145 Hyman, M. 184 journals hyperbolic function 48 for mathematical biology 92 hypercycle theory 92, 226 for nonlinear science 12 Hyperion 36, 170 Juarrero, A. 283 Jupiter 289 Icarus 174, 175 Ichthyornis 210 Kac, M. 33 immense number 92, 236–238, 275, Kadomtsev–Petviashvili equation 157 281 Kallenbach, N. 196 Infeld, L. 105 Kaluza, T. 104 initial conditions 17, 50, 67 KAM theorem 30–34, 83–85, 127 ink-jet printing 161 Kasner, E. 236 instability 83, 95–97, 149, 160, 161, Kauffman, S. 285 208, 223 Kaup, D. 16, 51 Benjamin–Feir 149 Keener, J. 229 DH 107 Keller, E.F. 227 dynamic 86 Kemeny, G. 190 modulational 149 Kepler’s law 3, 19 instanton 110 Kepler, J. 3 integrable system 83 Khodorov, B. 255, 257 intention 282 kidney 217 interatomic potential 57 Kiev Institute of Theoretical Physics intercalation 202 16 internal wave 59, 60 Kim, J. 279, 287, 295 International Society for the Systems kink 51–55, 80, 84, 103, 107, 145, 157, Sciences 93 197 intrinsic local modes 136 Lorentz contraction 52 intrinsic nonlinearity 129, 136 mass 53 inverse scattering transform 15, 16, kink–antikink annihilation 53 46–51, 56, 58, 106, 125–126, 170 Kira, T. 216 inverse-square law 20 Klein, O. 319 ionic current 66–68, 70, 144, 192, 207, Klein–Gordon equation 319 213, 243, 245–247 Knox, R. 188, 190 ionic pump 66 Knuth, D. 237 372 Index

Koch snowflake 25–27, 40 lattice, nonlinear 56–58 Kolmogorov, A. 30, 70, 83, 85, 165, Lax pair 48 233 Lax, P. 15, 16, 48 Kompaneyets, A. 244 Layne, S. 185 Kontorova, T. 33, 51, 56, 84, 133 Lebowitz, J. 29 Korteweg, D. 45, 61 Lecar, H. 247 Korteweg–de Vries equation 15, 47, Leduc, S. 208 50, 58, 67, 82, 83, 138, 145, 157 Lee, T.-D. 49 modified 16 Leg´endy, C. 271 operator formulation 16 Lemaˆıtre, G.H. 171 Krebs cycle 72 Leonardo’s law 214–219, 255 Krinsky, V. 232 lepton 108 Krumhansl, J. 188, 196 Lewontin, R. 91, 219 Kruskal, M. 9, 15, 47, 54, 83 Li, T.Y. 27 Kubie, L. 87 lichen 73 Kuhn, T. 1, 23, 61, 63, 107, 150, 190, Lie, S. 58 225 life 92, 209, 210, 213, 214, 225, 238, Kuhnian revolution 1, 3, 12, 13 242, 276–301 artificial 291–292, 298 La Jolla institute 12 dynamics of 299 Laboratorio di Cibernetica 88, 205 emergence of 226, 289, 297 Lagrange, J. 57, 312 theories of 290–301 LALS 202 LIGO 169, 177 Lamb, H. 165 Lillie, R. 64, 89, 242 Landau, L. 133, 172 limit cycle 310 Langmuir, I. 132 Lindsay, S. 199 Langmuir–Blodgett film 132 linear threshold unit 259 Langton, C. 291 Laplace transform 59 Lineland 25, 52 Laplace, P.S. 172 lipid 212 laser 13, 96, 142, 147–149, 233 bilayer 212, 213 argon 148 membrane 53 carbon dioxide 148 liquid crystal 132 dye 148 Littlewood, J. 35 free-electron 148 Litwin, S. 196 gas 147, 148 local modes in molecules 122–123 helium–neon 148 logistic equation 11 interferometry 169 discrete version 27 liquid 148 logistic map 28, 29, 85 multimode operation 234 Lomdahl, P. 84, 201 nonlinear dynamics 27 Lonngren, K. 157 ruby 148 Lorente de N´o, R. 87 semiconductor-diode 148 Lorentz contraction 52, 102, 103 solid-state 83, 147, 148 Lorentz equations 307 laser-Raman spectra 183, 184 Lorentz invariance 55 Lashley, K. 89, 243 Lorentz transformation 52, 103, 166 Laskar model 39 Lorenz attractor 23–25 Laskar, J. 37 Lorenz equations 85, 311 Lassel, W. 36 Lorenz, E. 13, 16, 36, 84, 163, 282, 311 Index 373

Los Alamos National Laboratory 12, McClare, C. 129, 131, 182, 190 13, 90, 184, 291 McCowan, J. 45 Lotka, A. 72, 132, 233 McCulloch, W. 87, 91, 257, 288 lung 217 McCulloch–Pitts model 257–260 fractal model 217 McCulloh, K. 216 Luther, R. 64, 72, 242 McKean, H. 18, 33, 70 Lyapunov exponent 24, 79 McLaughlin, D. 184 Lyapunov time 8, 24, 37, 170 McLaughlin, J. 27 for Solar System 37, 40 Mead, M. 87 lynch mob 7, 96, 224 mechanical vibration, nonlinear 138 Mecke, R. 122, 136 MacKay, R. 136 meditation 273 Macy conferences 87 Meinhardt, H. 207, 208, 219, 221, 228 magnetic flux vortex 133 Mel’nikov, A. 32 magnetohydrodynamics 156 Menger, K. 91 magnetosphere 156 mental phenomena 252, 280 Maiman, T. 147 Mercury 166, 168, 174–176 Maitra, S. 234 metatheory 86–100, 182 Makhankov, V. 109 meteor impact 162 Mandelbrot map 296 metric tensor 166 Mandelbrot, B. 25, 27, 85, 217 Meyers, R. 91 MANIAC 13, 46 Mie theory 102, 108 Manley, J. 142 Mie, G. 102 Manley–Rowe equation 142, 183 milk-drop coronet 160, 161, 205, 208, Marangoni, C. 155 222 Margulis, L. 301 Miller, J.G. 93 Mar´ın, J. 137 millimeter-wave oscillator 55 Markin, V. 244, 254 Markin–Chizmadzhev equation Milner cell assembly theory 270, 271 244–246 Milner, P. 270 Mars 175 Minding, F. 57 Martin, P. 27 Minkowski, H. 166 Marx, G. 288 Mitchell, J. 172 maser 147 Mitchell, P. 129 Maslow, A. 276 Mittag-Leffler, G. 21 mass–spring lattice 56 Miura, R. 16, 47 master 97 mode locking 157 mathematical biology 88–93, 99, 225, molecular dynamics 127–128 227–230, 242, 243 Molenauer, L. 150 matter wavelength 23 Monod, J. 94, 194, 278, 283 matter, theories of 101–110 Montroll, E. 234 Maturana, H. 292 Moore’s law 13, 14 Max Planck Institute 15, 184, 207 Mornev, O. 76, 247, 254 MAXWAVE project 158 morphogen 220, 222 Maxwell equations 103 morphogenesis 18, 91, 204–229 nonlinear 103 Morris, C. 247 Maxwell, J.C. 312 Morris–Lecar system 247, 255 May, R. 27, 28, 232 Moser, J. 30 Mayr, E. 279 Moss, L. 223 374 Index

Mueller, P. 212 Nicolelis, M. 274 Murray’s law 215–217 Nicolis, G. 95 Murray, C. 215, 216 Nishizawa, J. 144 Murray, J. 229 nonequilibrium statistical mechanics muscovite mica 137 15, 94–95, 99 muscular contraction 191 normal mode 59 Muto, V. 201 Nottale model 40 myoglobin 189 Nottale, L. 39, 40 myosin 191 nucleosome 203

N-body problem 20, 85 oily molecule 212 Nagumo, J. 71, 241, 242 open system 93, 285–286 Navier–Stokes equation 164, 296 steady state 285 Necker cube 1, 264, 265 Oppenheimer, J.R. 127, 173 perception reversal 272, 273 optical fiber 50, 149–150 neocortex 250–253, 266 optics, nonlinear 15, 16, 50, 247 electrical stimulation 268 order parameter 97, 135, 273 structure 267 non-conventional 146 Neptune 38, 166 Osborne, A. 158 nerve 8, 144 oscillating chemical reaction 72 branching 217 Ostrovsky, L. 149 FN pulse 96 oxygen transport 215 membrane 191–193 models 242–252 Painter, P. 216 myelinated 69, 243, 248–250 paradigm 1, 14, 22 pulse 82, 83, 95, 289, 293 Kuhnian 35, 61, 133, 141 pulse generation 241 nonlinear 16, 72 pulse propagation 13, 63–77, 85, solitary wave 61 144, 207, 218, 241, 295 Parkinson’s disease 288 simple model 69–72 Parry, W.E. 57, 135, 152 nested cycle 310 particle accelerator 13 neural network 243 passive-iron-wire model 64, 242 neuristor 70, 241, 246 Pasta, J. 13, 15, 46 neuron 7, 230, 252–258, 262, 274 Patushenko, V. 254 coupling of 143 Pauli, W. 104, 108 excitatory 251 Pego, R. 136 inhibitory 251 Peierls, R. 133 McCulloch–Pitts 259, 270 pendulum 138, 142, 230 multiplex 254, 258 nonlinear 84 neocortical 251 Penfield, W. 268 neuroscience 240–276 Penrose, R. 113, 173 neutron 108 peptide 129, 184, 185 neutron star 168, 170, 172 perceptron 259 Neveu, A. 109 Peregrine, H. 161 Newell, A. 15, 16, 51, 84 Perelman, G. 210 Newton, I. 3, 8, 19, 36, 57, 63, 166, 211, perihelion advance 174–176 277 Perring, J. 53 Newtonian dynamics 82 perturbation theory 30–32, 55–56, 82, Newtonian limit 82 127, 166 Index 375

Peyrard, M. 201 population inversion 147, 233 phase change 4, 7, 133–135 positron 105, 117 phase sequence 262 positronium 54 phase space 22, 24, 30, 97, 144, 234, predator–prey dynamics 148, 233–235 235, 244, 285, 307–313 premelton 202, 203 low-dimensional 84 Pribram, K. 264 phase-plane analysis 140, 307, 309, Prigogine, I. 15, 33, 94–95 310 probability 40, 110 phase-space analysis 59, 311 in quantum theory 111–112, 317 phi-four equation 55 Prohofsky, E. 201 Phobos 37, 170 Prokhorov, A. 147 phonon 133, 136, 188 property dualism 279, 280 photoelectric effect 315 protein 7, 50 physicalism 209, 279–280, 295, 299 ACN 130, 151, 186–189, 195 Pitts, W. 87, 257–260 alpha-helical 129, 183, 185, 188, 191 Planck constant 315 folding 131, 298 Planck scale 110 model 136 Planck’s law 122 soliton 128, 182–196 Planck, M. 315 protoenzyme 196, 208 planetary moon 36 proton 108 planetary motion 2, 14, 19, 37–41, 84, psychological phenomena 5, 263–274, 85, 165, 310, 311 279, 289 psychon 257 KAM theory 31 Ptolemaic system 36 retrograde 3 Ptolemy 2 three-body problem 20–21, 55 Pulverm¨uller, F. 264 two-body problem 8, 19 pump–probe spectroscopy 131, planetesimal 39, 171 149–151, 188, 189 plasma 15 punctuated evolution 1 confinement 13, 23, 35, 48, 53, 157 Purkinje cell 253 frequency 157 turbulence 129 quantum field operator 126 wave 16, 50, 156–157 quantum field theory 125, 182 Pluto 37, 38 quantum theory 14, 40, 55, 104, Podolski, B. 113 110–127, 315–319 Poincar´e conjecture 210 Bohr interpretation 114 Poincar´e section 25, 32, 312 Bohr–Sommerfeld 23 Poincar´e, H. 19, 21, 43, 126, 163, 165, causal interpretation 106 282, 312 chaos 126–127 point particle 108 Copenhagen interpretation 107, 111 Poiseuille, J. 164 de Broglie–Bohm interpretation Poisson statistics 127 107, 121 Pojman, J. 131 decoherence 113 polaron 125, 133, 188, 193 double wave theory 106 polymer 131 energy localization 122–127 conductive 196 entanglement 116–119 Popper, K. 111 EPR paradox 113–116 population growth 11, 27–30, 85, hidden variables 118 232–235 joint measurability 119–120 376 Index

macroscopic 41 ring wave 73, 160, 161 many-worlds interpretation 120– self-oscillatory 73, 74 121 Robertson, H. 171 nonlinear 121 Roger, G. 118 nonlocality 116–119 rogue wave 83, 157–160, 162, 289 probability 111–112 Rosalind, F. 90 standard interpretation 106 Rosen, N. 113 superposition 113 Rosen, R. 89, 92, 292–296, 299–301 wave function 317 Rosenblueth, A. 87 wave function collapse 112 R¨ossler, O. 27 quark 108 row-boat theory 191, 195 quasar 156, 175 Rowe, H. 142 Rudin, D. 212 radio 142 Ruelle, D. 27 radio astronomy 145, 174 Russell, B. 288 Rall’s law 217–219, 252, 253, 255 Russell, J.S. 43–46, 57, 61, 68, 106, 152 Rall, W. 217 Russell, M. 137 Rapoport, A. 93 Rashevsky, N. 64, 70, 72, 88–93, 201, Saffer, J. 197 215, 219, 225–226, 229, 241, 243, Saffman, P. 15 257, 258, 277, 286, 292, 301 Sagan, D. 301 rational number 31 Sagdeev, R. 15 Rayleigh number 155 Saint-Venant, A. 45, 61 Rayleigh, Lord 45, 61, 77, 155 Sakharov, A. 173 Rayleigh–B´enard cell 95, 155–156 Salerno, M. 201 Rayleigh–B´enard convection 156 saltatory conduction 243 Rayleigh–Taylor instability 77 Santa Fe Institute 12, 97 reaction diffusion 8, 9, 18, 63–77, 79, Schawlow, A. 147 82, 83, 85–86, 132, 219, 231, 233, Scheibe aggregate 132 241, 243, 246 Scheibe, G. 132 in neocortex 250 Schiff, L. 318 recovery variable 70 Schr¨odinger equation 47, 48, 110, 316 reductionism 6, 93, 94, 224, 277–301 discrete nonlinear 124, 201 constitutive 279 general construction 318 explanatory 278, 280, 284, 295 nonlinear 16, 50, 58, 82, 106, 126, objections 280–290 129, 132, 133, 149, 150, 158, 184 refractory period 64, 66 solutions 316–317 refractory zone 74 Schr¨odinger, E. 40, 105, 112, 300, 301, Reid, E. 191, 280 315 Reinitzer, F. 132 Schumacher, G. 40 relational biology 89, 225–226, Schuster, P. 92, 226, 288 292–293, 301 Schwarzschild radius renormalization 108 of Universe 177 group 135 Schwarzschild spacetime 172 Reynolds number 164 Schwarzschild, K. 172 Reynolds, O. 164 Sciama, D. 173, 176 Ricci tensor 167, 170 scientific model 293, 296 Richardson, L. 165 analytic 294 Rikitake, T. 35 synthetic 294 Index 377 scroll ring 75, 76 evolution 171 scroll wave 75 solder-drop dispensing 161 SDIC 24, 25 solid-state electronics 143, 145 Seeger, A. 51 solitary wave 43–46, 106 Segur, H. 15, 16, 51 energy-conserving 79, 82 self-excitation 75 hydrodynamic 152 self-organizing phenomena 93 lossless 82 self-trapping 188–190 RD 86 sensory cortex 267 supersonic 135–136 servomechanism 7 soliton 8, 9, 13, 43–61, 79, 82, 83, 101, Shabat, A. 16, 50 108, 109, 130, 145–146, 170, 173, shallow water wave 48, 57 293 Shapiro, I. 174 aristocratic 49 Sherman, T. 216 band 124 Shinozaki, K. 216 DNA 196–203 Shnol’, S. 73 hydrodynamic 15, 43, 45 shock wave 5, 145–146, 153–155 in biopolymer 125 Shockley, W. 143 in protein 128, 182–196 Shohet, L. 157 KdV 48, 50, 56, 82 Sievers, A. 136 NLS 50, 55, 83, 106, 125, 126, 149, simulation 295, 299 183 sine-Gordon equation 15, 51–56, 58, oceanic 59 80, 84, 103, 107, 133, 145, 146, 157, on optical fiber 150 196, 319 optical 289 discrete 84 plebian 50 perturbed 81 quantum 122, 124–125 quantum analysis 109 research 109 singing 87, 141 SG 84 singular point 307, 309 TL 56, 57, 83, 135 Skou, J. 193 Yang–Mills 110 Skyrme, T. 53, 107 sonic boom 153 skyrmion 107 special relativity 52, 105, 166 slave 97 violation 118, 171 slaving principle 97 Sperry, J. 216 slime mold 73, 95, 226 spin 106, 117–119 slinky mode 48, 53, 157 spin glass 270 Smale, S. 25 spiral wave 73 Smith, D. 218 self-exciting 73, 242 Smolin, L. 110 splashing 161, 162, 206, 208 Snell’s law 76 splay wave 53, 133 Sneyd, J. 229 Sponer, H. 122 Snyder, H. 173 spontaneous pattern formation 4, 73, Sobell, H. 201 95 social phenomena 5, 7, 289 spray cooling 161 social system 95 spring–mass lattice 135 sodium pump 193 squid 64–66, 69, 88, 144, 192, 218, 241, solar physics 156 243, 248, 249, 256 Solar System 36–41, 170 standard map 33, 56, 84, 85 378 Index

Standard Model 108, 126, 278 Thacker, H. 125 Stapp, H. 112 theory of everything 280 steam-engine governor 141 theory of types 288 Steklov Institute 51 thermodynamics 33 stellar collapse 172 nonequilibrium 94–95 Stepanyants, A. 218 theta function 48 stimulated emission 147 Thom, R. 95, 208 stimulation–response 6, 282 Thompson, D.W. 73, 91, 162, 204, 206, stochastic motion 23, 35 208–210, 215, 225 Stokes, G. 45, 59, 61 three-body problem 20–22 strange attractor 24, 27, 86, 293, 311 threshold logic unit 259 stretching oscillation 122, 123, 129, threshold phenomena 4, 10, 64, 67, 72, 130, 136, 143, 151, 184, 185, 188, 139, 218, 251, 253, 258, 274, 282 189, 195, 196 tidal bore 154, 155, 164 string theory 110 Tien, T. 212 Strogatz, S. 143 tipping point 282 substance dualism 279, 299 Titius, J. 38 Sun 174 Titius–Bode rule 38, 39 superconducting metals 125 Titor, J. 121 Superconducting Super Collider 278 Toda lattice 56–58, 83, 135, 199, 201 superconductivity 133, 145–146, 182 Toda, M. 56 supercooled fluid 15 topological charge 107, 108 supersonic compression wave 56, topological transformation 209, 210 135–136, 152–153 tornado 49, 95, 141, 162, 163, 289 supervenience 279–280 torus 30, 127 Swicord, M. 197 non-resonant 30, 31 Swift–Hohenberg equation 82, 83, 85 Townes, C. 147 Swinney, H. 27 transistor 143 symmetry breaking 224 transmission line 145 synapse 250, 258 traveling wave 59, 61, 66, 68, 70, 84, Hebbian 262 86, 144, 244, 246, 248 synchronization 4, 138, 142–143, 230 synergetics 96–97, 99, 149, 271 traveling-wave tube 13 Szent-Gy¨orgyi, A. 91 tree 214, 216 unit-pipe model 216 Tacoma Narrows Bridge 138–140 Trinity explosion 152 Takeno, S. 131, 136, 190, 200 triode vacuum tube 139 Takens, F. 27 Triton 37 Takhta jan, L. 51 Truesdale, C. 15 TAMA-300 169 tsunami 15, 59, 60, 153, 157, 289 Tappert, F. 16, 150 tunnel diode 13 Taylor, G. 77 turbulence 4, 15, 34, 85, 164–165 Taylor, J.B. 33 as complex system 296 Taylor–Chirikov map 33, 84, 85 in plasma 129 Technical University of Denmark 90 Turing mechanism 132 teleology 6 Turing pattern 95, 219–222 telephone, intercontinental 140, 141 Turing, A. 18, 73, 88, 207, 241, 285, Teller, E. 173 291 ter Haar, D. 157 turning wheel 194–196 Index 379

Tuzy´nski, J. 184 line 75 twistor 110 ring 76 two-body problem 8, 19 two-factor theory 243 Walker, A. 171 Walker, G. 32 Ueda, Y. 34, 147 Wallace, A. 209 Ulam, S. 13, 15, 46, 90, 173 war 7, 96 uncertainty principle 319 Watson, J. 90, 300 unified theories 104, 108, 110 Watt, J. 288 Union Canal 44 Wattis, J. 135 universality 29, 135 wave motion 15 university courses 14, 36 wave of information 250 University of Arizona 90, 228 wave–particle duality 106 University of California at San Diego Waxman, S. 254 12 weather forecasting 13, 16, 17, 23, 35, University of Chicago 89–93, 172, 225, 163 243 Webb, S. 183–185 University of Wisconsin 90, 182, 190, Weber, J. 169 228 Weibel, E. 217 Uranus 38 Weinberg, S. 278 Wescott, W. 212 vacuum tube electronics 64, 139–140 West, B. 217 van der Mark, J. 146 Weyl, H. 104 van der Pol equation 139, 143, 147, Wheeler, J. 15, 120, 173 230, 234, 272 white dwarf 172 higher dimensional 149 Whitham, G. 149 van der Pol, B. 139, 140, 142, 146, 241 Whittaker, E.T. 21 varactor 145 Wiener, N. 7, 35, 86–88, 94, 99, 143, Varela, F. 292 163, 230, 259, 260, 288 Vecheslavov, V. 37 Wigner statistics 127 Venus 175 Wigner, E. 112 Verdaguer, E. 170 Will, C. 174 Verhulst equation 11, 85, 131, 271 Williams, R. 238 discrete version 27 Verhulst, P.-F. 11, 232 Wilson, H. 251 VIRGO 169 Wilson, T. 217 vitalism 192, 209, 279, 280, 284, 285 Winfree, A. 73, 76, 86, 232, 242 Vol’kenstein, M. 190 Woit, P. 110 Volkoff, G. 173 Worthington, A. 160, 206, 208 Volta, A. 242 Wyman, J. 194, 195, 208 Volterra, V. 233 von Bertalanffy, L. 70, 93–94, 97, 98, X-ray astronomy 174 100, 285 von Bonin, G. 91 Yakushevich, L. 197 von Foerster, H. 87 Yang–Mills theory 110 von Koch, N. 25 Yoda, K. 216 von Neumann, J. 87, 112, 259 Yomosa, S. 200 von Senden, M. 261, 264 Yorke, J. 27 vortex 162, 163 Young, J.Z. 64 380 Index

Zabusky, N. 9, 15, 47, 49, 54, 83 Zeldovich–Frank-Kamenetskii equation Zaikin, A. 73 67, 80, 85, 244, 254, 295 Zakharov, V. 16, 50, 129, 158 Zhabotinsky, A. 73 Zeeman, C. 95 Zhang, C.-T. 201 Zeldovich, Y. 67, 173 Zwicky, F. 172