Schulz M. Control Theory in Physics and Other Fields of Science: Concepts, Tools, and Applications
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Index 299
nondeterministic regime 267, 270
nonisolated tori 125
nonlocal fields 103
nonpolynomial problems 288
nonresonant eigenvalues 66
NP completeness 288
nuclear reactors 89
objective part of control 103
observability 140
observable output 214
observations 244, 269
open-loop control 1, 194
optimal control 19
optimal evolution equation 144
optimal field equations 104
optimal regulator 77
optimal roads 110
optimal strategy 269
optimalization criterion 2
optimum control law 201
optimum curve 18
optimum trajectory 55, 72
orbit periods 142
Ornstein-Uhlenbeck process 209
orthogonal functions 114
oscillations 81
output 214
passive boundary condition 114
path integral 194
p-cycles 134
penalty function 285
pendulum clocks 144
performance 19, 33, 62, 199, 267
periodic doupling 134
perturbation theory 88
phase space 3
Poincar´e66
Poincar´e plot 130
Poincar´eregion66
Poincar´e theorem 66
Pontryagin 42
prediction problem 244
predictor 243
pre-offspring 290
preoptimal control 43
preoptimized field 111
preoptimized Hamiltonian 44
preoptimized Lagrangian 43
price policy 131
probabilistic regime 268, 270
probability density 154
probability vector 273
projection operator 157
protocol 1
provisonal control law 202
pseudorandom numbers 283
quadratic performance 62
quantum mechanics 265
quasi-deterministic 10
quasirandom sequence 284
quasi-stochastic 12
random generator 283
rare events 228
rate equation 175
reachability 137
reaction-diffusion process 101
reaction-limited process 102
recombination procedure 289
recursion law 132
reduced phase space 9
reductionism 153
redundant control 274
relevant probability density 156
relevant quantities 8, 179
refraction index 111
regression 246
relaxation processes 84
renewable ressources 131
renormalization group 217
rescaling step 217
residual force 181
resonances 64
resonant eigenvalues 66
response system 146
Ricatti 75
Ricatti equation 72, 211
saddle point of a game 272
scalar product 37, 179
scalar Ricatti equation 75
Schr¨odinger equation 97
screen condition 131
second-order variation 27
security strategy 272
300 Index
seismic activity 12
selection 244
selection step 291
self-organized dynamics 12
separation of time scales 168
short-range correlation 178
Siegel region 66
simplex algorithm 286
skewness 164
sliding regime 45
smoothing problem 244
soil venting 115
source control 117
space-time continuum 94
spectral function 178
spin glass 252
spin variable 253, 287
spread 162
subjective part of control 103
stability 4
stabilizability 137
stable fixed point 64
standard deviation 162
state variable 19
stationarity 176
statistical independence 157
steepest descent 201, 229, 283
stochastic behavior 185
stochastic differential equation 190
stochastic optimization 283
St. Petersburg paradoxon 227
strategy 269
strategy problem 272
Stratonovich equation 187
stretched exponential decay 84
strong minimum 21
subgradient method 283
successive integration 155
synchronization 144
synchronized state 146
system action 266
system state 256
tails 227
technological system 10
thermodynamic bath 54
thermostat 76
Th¨unen 107
time delay 142
time optimal control 48
tracking problem 74, 135
trade flow 108
training pattern 254
transfer matrix 79
transportation costs 108
transversality condition 38
tree approximation 201
truncated L´evy distribution 227
Turing 9
two-player game 271
uncertainty 213
uncontrolled problem 143
universal computer 9
universal phenomena 144
universal quantity 134
unstable periodic motion 126
variance 162
Verhulst 132
vibrational fields 101
von Neumann 274
wave equation 97
weak minimum 21
Weierstrass criterion 24
Weierstrass variation 25
Wiener 89
Wiener filter 244
Wiener process 183
wild distribution 227
worst case 267
Zwanzig 179, 156
Springer Tracts in Modern Physics
175 Ion-Induced Electron Emission from Crystalline Solids
By Hiroshi Kudo 2002. 85 figs. IX, 161 pages
176 Infrared Spectroscopy of Molecular Clusters
An Introduction to Intermolecular Forces
By Martina Havenith 2002. 33 figs. VIII, 120 pages
177 Applied Asymptotic Expansions in Momenta and Masses
By Vladimir A. Smirnov 2002. 52 figs. IX, 263 pages
178 Capillary Surfaces
Shape – Stability – Dynamics, in Particular Under Weightlessness
By Dieter Langbein 2002. 182 figs. XVIII, 364 pages
179 Anomalous X-ray Scattering
for Materials Characterization
Atomic-Scale Structure Determination
By Yoshio Waseda 2002. 132 figs. XIV, 214 pages
180 Coverings of Discrete Quasiperiodic Sets
Theory and Applications to Quasicrystals
Edited by P. Kramer and Z. Papadopolos 2002. 128 figs., XIV, 274 pages
181 Emulsion Science
Basic Principles. An Overview
By J. Bibette, F. Leal-Calderon, V. Schmitt, and P. Poulin 2002. 50 figs., IX, 140 pages
182 Transmission Electron Microscopy of Semiconductor Nanostructures
An Analysis of Composition and Strain State
By A. Rosenauer 2003. 136 figs., XII, 238 pages
183 Transverse Patterns in Nonlinear Optical Resonators
By K. Stali
¯
unas, V. J. Sánchez-Morcillo 2003. 132 figs., XII, 226 pages
184 Statistical Physics and Economics
Concepts, Tools and Applications
By M. Schulz 2003. 54 figs., XII, 244 pages
185 Electronic Defect States in Alkali Halides
Effects of Interaction with Molecular Ions
By V. Dierolf 2003. 80 figs., XII, 196 pages
186 Electron-Beam Interactions with Solids
Application of the Monte Carlo Method to Electron Scattering Problems
By M. Dapor 2003. 27 figs., X, 110 pages
187 High-Field Transport in Semiconductor Superlattices
By K. Leo 2003. 164 figs.,XIV, 240 pages
188 Transverse Pattern Formation in Photorefractive Optics
By C. Denz, M. Schwab, and C. Weilnau 2003. 143 figs., XVIII, 331 pages
189 Spatio-Temporal Dynamics and Quantum Fluctuations in Semiconductor Lasers
By O. Hess, E. Gehrig 2003. 91 figs., XIV, 232 pages
190 Neutrino Mass
Edited by G. Altarelli, K. Winter 2003. 118 figs., XII, 248 pages
191 Spin-orbit Coupling Effects in Two-dimensional Electron and Hole Systems
By R. Winkler 2003. 66 figs., XII, 224 pages
192 Electronic Quantum Transport in Mesoscopic Semiconductor Structures
By T. Ihn 2003. 90 figs., XII, 280 pages
193 Spinning Particles – Semiclassics and Spectral Statistics
By S. Keppeler 2003. 15 figs., X, 190 pages
194 Light Emitting Silicon for Microphotonics
By S. Ossicini, L. Pavesi, and F. Priolo 2003. 206 figs., XII, 284 pages
Springer Tracts in Modern Physics
195 Uncovering CP Violation
Experimental Clarification in the Neutral K Meson and B Meson Systems
By K. Kleinknecht 2003. 67 figs., XII, 144 pages
196 Ising-type Antiferromagnets
Model Systems in Statistical Physics and in the Magnetism of Exchange Bias
By C. Binek 2003. 52 figs., X, 120 pages
197 Electroweak Processes in External Electromagnetic Fields
By A. Kuznetsov and N. Mikheev 2003. 24 figs., XII, 136 pages
198 Electroweak Symmetry Breaking
The Bottom-Up Approach
By W. Kilian 2003. 25 figs., X, 128 pages
199 X-Ray Diffuse Scattering from Self-Organized Mesoscopic Semiconductor Structures
By M. Schmidbauer 2003. 102 figs., X, 204 pages
200 Compton Scattering
Investigating the Structure of the Nucleon with Real Photons
By F. Wissmann 2003. 68 figs., VIII, 142 pages
201 Heavy Quark Effective Theory
By A. Grozin 2004. 72 figs., X, 213 pages
202 Theory of Unconventional Superconductors
By D. Manske 2004. 84 figs., XII, 228 pages
203 Effective Field Theories in Flavour Physics
By T. Mannel 2004. 29 figs., VIII, 175 pages
204 Stopping of Heavy Ions
By P. Sigmund 2004. 43 figs., XIV, 157 pages
205 Three-Dimensional X-Ray Diffraction Microscopy
Mapping Polycrystals and Their Dynamics
By H. Poulsen 2004. 49 figs., XI, 154 pages
206 Ultrathin Metal Films
Magnetic and Structural Properties
By M. Wuttig and X. Liu 2004. 234 figs., XII, 375 pages
207 Dynamics of Spatio-Temporal Cellular Structures
Henri Benard Centenary Review
Edited by I. Mutabazi, J.E. Wesfreid, and E. Guyon 2005. approx. 50 figs., 150 pages
208 Nuclear Condensed Matter Physics with Synchrotron Radiation
Basic Principles, Methodology and Applications
By R. Röhlsberger 2004. 152 figs., XVI, 318 pages
209 Infrared Ellipsometry on Semiconductor Layer Structures
Phonons, Plasmons, and Polaritons
By M. Schubert 2004. 77 figs., XI, 193 pages
210 Cosmology
By D.-E. Liebscher 2005. Approx. 100 figs., 300 pages
211 Evaluating Feynman Integrals
By V.A. Smirnov 2004. 48 figs., IX, 247 pages
213 Parametric X-ray Radiation in Crystals
By V.G. Baryshevsky, I.D. Feranchuk, and A.P. Ulyanenkov 2006. 63 figs., IX, 172 pages
214 Unconventional Superconductors
Experimental Investigation of the Order-Parameter Symmetry
By G. Goll 2006. 67 figs., XII, 172 pages
215 Control Theory in Physics and other Fields of Science
Concepts, Tools, and Applications
By M. Schulz 2006. 46 figs., X, 294 pages