Авторизация
Поиск по указателям
Haken H. — Synergetics: an introduction
Обсудите книгу на научном форуме Нашли опечатку?
Название: Synergetics: an introductionАвтор: Haken H. Аннотация: This book is an often-requested reprint of two classic texts by H. Haken: "Synergetics. An Introduction" and "Advanced Synergetics". Synergetics, an interdisciplinary research program initiated by H. Haken in 1969, deals with the systematic and methodological approach to the rapidly growing field of complexity. Going well beyond qualitative analogies between complex systems in fields as diverse as physics, chemistry, biology, sociology and economics, Synergetics uses tools from theoretical physics and mathematics to construct an unifying framework within which quantitative descriptions of complex, self-organizing systems can be made. This may well explain the timelessness of H. Haken's original texts on this topic, which are now recognized as landmarks in the field of complex systems. They provide both the beginning graduate student and the seasoned researcher with solid knowledge of the basic concepts and mathematical tools. Moreover, they admirably convey the spirit of the pioneering work by the founder of Synergetics through the essential applications contained herein that have lost nothing of their paradigmatic character since they were conceived.
Язык: Рубрика: Физика /Нелинейная динамика, Хаос /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1977Количество страниц: 325Добавлена в каталог: 11.09.2005Операции: Положить на полку |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
Abundance of species 293 Adaptability 200 202 Affinity 60 Approximation, adiabalic 192 195 196 198 Associativity (of sets) 19 Autocatalytic process 300 Autocatalytic reaction 107 128 263 Autonomous system 113 Average over ensemble 100 Balls in boxes 46 Bandwidth 153 Belousov — Zhabotinski reaction 9 276 Benard instability 7 244 Bifurcation 110 126 Bifurcation of limit cycles 112 Binary system 42 Binomial coefficient 33 Binomial distribution 33 34 Binomial distribution, mean value 34 Binomial distribution, variance 34 Biochemical systems 263 Birth and death processes 277 282 Bistable element 290 Bit 42 Boltzmann distribution function 54 Boltzmann distribution of harmonic oscillator 156 Boltzmann's H-theorem 126 Boussinesq approximation 245 box model 33 Browman movement 69 149 Browman movement, distribution function 73 Brusselator 211 270 Brusselator, stochastic treatment 286 Catastrophe 133 Center 117 118 Central limit theorem 39 Chapman — Kolmogorov equation 79 81 Characteristic function 31 85 86 Characteristic function, derivatives 32 33 Chemical network 290 chemical potential 56 Chemical reaction, stochastic model 277 282 chemical systems 263 Chetayev's instability theorem 125 Cloud formation 7 8 Cloud streets 8 Coarse graining 66 Coexistence of species 129 294 Commutativity (of intersection of sets) 19 Commutativity (of union of sets) 19 Competition of species 294 Complement (of a set) 19 Constants of motion 165 Constraint 45 48 Continuity equation 63 Continuity equation of probability 160 Continuity equation of probability distribution 166 Continuous mode laser 233 Convection instability 7 244 Coordinates, Cartesian 111 Coordinates, polar 111 Correlation 31 Correlation function 87 Correlation function of fluctuating forces 149 151 187 188 Correlation function, two point 187 188 Correlation function, two time 150 173 Correlation, length 188 critical exponent 188 Critical fluctuations of laser 230 Critical point 113 Critical slowing down 110 181 Cumulants 86 152 De Morgan's law 19 Density function 24 Detailed balance 89 Detailed balance in chemical reactions 280 Detailed balance, counterexample to 91 Detailed balance, principle 77 95 Dictyostelium disciodeum 9 Diffusion 268 Diffusion coefficient 163 Diffusion constant 71 Diffusion equation 78 83 Diffusion process, correlation functions 87 Diffusion, stochastic model 282 Dirac's 25 Disorder 1 Dissipation-fluctuation theorem, example 150 Dissipative structures 309 distribution 21 23 Distribution function 23 Distributivity (of set relations) 19 Drift-coefficient 163 Dynamic processes 105 Dynamic system theory 308 Ecology 293 Ehrenfest urn model 98 Elastic stability 257 Elimination in Fokker — Planck equation, adiabatic 202 Elimination in master equation, adiabatic 204 Energy, degradation 2 Energy, internal 54 Ensemble 100 entropy 2 54 66 101 Entropy density 63 Entropy density, continuity equation 64 Entropy flux 64 Entropy, additivity 65 Entropy, coarse grained 66 Entropy, production rate 64 Equilibrium points 108 109 114 Equilibrium, thermodynamic 100 Event, simple 17 Evolution 298 Excitation transfer by hopping process 78 Expectation, mathematical 28 Extensive variables 58 60 Ferromagnet 3 179 First passage time problem 169 Flip-flop 291 Fluctuating forces, correlation function of 149 151 187 188 Fluctuations 98 100 Fluctuations in self-organization 200 Fluid, flow of 6 Flux equilibrium 307 Focus 117 118 Focus, stable 112 118 Focus, unstable 111 112 118 Fokker — Planck equation 78 158 163 202 Fokker — Planck of convection instability 249 Fokker — Planck of many variables 164 Fokker — Planck of multimode laser, solution of 233 234 Fokker — Planck of single mode laser 230 Fokker — Planck, derivation 160 Fokker — Planck, functional 187 188 Fokker — Planck, stationary solution 165—167 171 187 188 Fokker — Planck, time-dependent solutions 172 174 Force, friction 147 153 Forces, fluctuating(random), Gaussian distribution 151 Forces, fluctuating, correlation functions 156 157 Forces, random 152 Free energy 54 57 179 186 Friction force 105 Gambling machine with binomial distribution 74 Gas atoms in box 44 Gaussian distribution 37 Gaussian probability density of several variables 38 Gaussian probability density, characteristic functions 39 Gaussian probability density, first moment 39 Gaussian probability density, mean 38 Gaussian probability density, moments 39 Gaussian probability density, second moment 39 Gaussian probability density, variance 38 Gaussian process 85 86 General systems theory 307 Generating function 31 Ginzburg functional 186 Ginzburg theory of superconductivity 235 Ginzburg — Landau equation, generalized 206-215 Ginzburg — Landau, time dependent 187 216 graphs 95 Graphs, examples 96 Green's function 218 Green's function of Fokker — Planck equation 173 174 Growth, density-dependent 294 Growth, density-independent 294 Gunn instability 253 H-Theorem 126 Half-trajectory 119 Hamiltonian equations 165 Hard excitation 112 Hard mode 112 Hard mode instability 218 222 Harmonic oscillator at different temperatures 157 Harmonic oscillator coupled to reservoirs 153 Harmonic oscillator, coupled, Hamiltonian 158 Heat 56 Heat flow 64 Heat, generalized 52 56 Hexagon formation in fluids 251 Hurwitz criterion 123 Hydra 299 Hypothesis 30 Hysteresis 182 information 41 Information entropy 48 Information entropy as solution of Liouville equation 165 Information entropy of population 46 Information entropy, variational principle for 49 Information gain 46 48 126 Information per symbol 43 Information, extremal condition for 44 Inhibition 299 Instabilities in fluid dynamics 244 Instabilities in lasers 239 Instabilities, classification 133 Instabilities, symmetry breaking 110 Invariance 109 inversion 109 Irreversible expansion of a gas 1 Irreversible heat exchange 1 Irreversible process 101 102 Irreversible thermodynamics 57 Irreversible thermodynamics, limitations 102 Joint probability of time-dependent processes 75 76 Lagrange parameters 49 Lagrangian multipliers 45 Landau theory of phase transitions 180 Langevin equation 147 162 163 168 169 187 188 Langevin equation of fluids 249 Laser 4—6 127 225 Laser equations 226 Laser phase transition 225 230 Laser phase transition analogy 307 Laser pulses, ultrashort 239 Laser threshold 128 Laser, two-mode 128 129 Likelihood, equal 21 Limit cycle 110 113 119 Limit cycle, stable 111 112 Limit cycle, unstable 111 112 Liouville equation 165 Ljapunov function 124 Ljapunov function, examples for 131 132 Ljapunov instability theorem 125 Ljapunov stability theorem 125 Lotka model 130 131 Lotka — Volterra equations 296 Lotka — Volterra, stochastic treatment 297 magnetization 3 179 Malfunctioning, suppression 202 Markov process 79 80 Mass action, law of 279 Master equation 75 83 88 204 Master equation for chemical reaction 277 286 Master equation for chemical reaction, stationary solution 279 Master equation with detailed balance 92 Master equation with detailed balance, stationary solution 89 Master equation, Kirchhoff's method of solution of 95 Master equation, Ljapunov function of 126 Master equation, theorems about solutions of 97 Maxwell's construction 270 Mean 28 Mean value 28 Memory 201 memory device 201 Microreversibility 126 MODE 14 15 Moments 29 33 85 152 Moments, time-dependent 173 Morphogenesis 299 Multimode laser 231 Network, chemical 290 Network, electrical 290 Newton's law 105 Niche, ecological 295 Node 115 116 Nonautonomous system 126 Nonequilibrium phase transition 206 Nonequilibrium phase transition of chemical reactions 289 Normal distribution 37 Normal distribution of several variables 38 Onsager coefficients 64 Order 1 Order parameter 14 15 180 195 198 199 227 303 307 Order parameter, space dependent 186 Oregonator 270 276 ORGANIZATION 191 Oscillations in biology 9 11 Oscillator 106 Oscillator, anharmonic 108 Oscillator, harmonic 152 Oscillator, overdamped 107 Overdamped motion 106 Parameters, external 15 Partition function 50 54 56 Partition function, variational principle for 52 53 path integral 79 83 84 176 Path integral, solution of Fokker — Planck equation 176 Paths 79 Phase plane 113 Phase transition 3 179 Phase transition analogy 179 184 Phase transition analogy for convection instability 252 Phase transition analogy for lasers 230 235 Phase transition analogy in continuous media 186 Phase transition of chemical reactions 265 266 284 Phase transition, continuous 186 Phase transition, first order 182 Phase transition, first order, of single-mode laser 236 Phase transition, Landau theory 181 185 Phase transition, second order 181 Phases 2 3 Poincare — Bendixson theorem 119 Poisson distribution 35 36 92 Poisson distribution of molecules 281 Poisson distribution, generating function 36 Poisson distribution, mathematical expectation 36 Poisson distribution, variance of 36 Polarization of public opinion 305
Реклама
-function 
|
|
О проекте