The Fokker-Planck Equation: Methods of Solution and ApplicationsSpringer Science & Business Media, 17.09.1996 - 472 Seiten One of the central problems synergetics is concerned with consists in the study of macroscopic qualitative changes of systems belonging to various disciplines such as physics, chemistry, or electrical engineering. When such transitions from one state to another take place, fluctuations, i.e., random processes, may play an im portant role. Over the past decades it has turned out that the Fokker-Planck equation pro vides a powerful tool with which the effects of fluctuations close to transition points can be adequately treated and that the approaches based on the Fokker Planck equation are superior to other approaches, e.g., based on Langevin equa tions. Quite generally, the Fokker-Planck equation plays an important role in problems which involve noise, e.g., in electrical circuits. For these reasons I am sure that this book will find a broad audience. It pro vides the reader with a sound basis for the study of the Fokker-Planck equation and gives an excellent survey of the methods of its solution. The author of this book, Hannes Risken, has made substantial contributions to the development and application of such methods, e.g., to laser physics, diffusion in periodic potentials, and other problems. Therefore this book is written by an experienced practitioner, who has had in mind explicit applications to important problems in the natural sciences and electrical engineering. |
Inhalt
I | 1 |
III | 2 |
IV | 3 |
V | 4 |
VII | 5 |
IX | 6 |
X | 7 |
XII | 8 |
CXIV | 196 |
CXV | 197 |
CXVI | 199 |
CXVII | 203 |
CXVIII | 209 |
CXIX | 214 |
CXX | 216 |
CXXI | 217 |
XIII | 9 |
XIV | 11 |
XV | 13 |
XVII | 16 |
XVIII | 19 |
XIX | 21 |
XXI | 23 |
XXII | 25 |
XXIII | 26 |
XXIV | 28 |
XXV | 29 |
XXVI | 30 |
XXVII | 32 |
XXIX | 34 |
XXX | 36 |
XXXII | 38 |
XXXIII | 39 |
XXXIV | 41 |
XXXV | 42 |
XXXVI | 44 |
XXXVII | 45 |
XXXVIII | 48 |
XXXIX | 50 |
XL | 54 |
XLI | 56 |
XLII | 57 |
XLIII | 58 |
XLIV | 59 |
XLV | 60 |
XLVI | 63 |
XLVIII | 66 |
XLIX | 67 |
L | 69 |
LII | 70 |
LIII | 72 |
LIV | 73 |
LV | 74 |
LVI | 76 |
LVII | 77 |
LVIII | 81 |
LIX | 84 |
LX | 85 |
LXII | 86 |
LXIV | 87 |
LXVI | 88 |
LXVIII | 91 |
LXIX | 96 |
LXXI | 98 |
LXXII | 99 |
LXXIII | 101 |
LXXIV | 108 |
LXXVI | 109 |
LXXVII | 110 |
LXXVIII | 111 |
LXXIX | 112 |
LXXX | 114 |
LXXXI | 117 |
LXXXII | 119 |
LXXXIII | 120 |
LXXXV | 121 |
LXXXVI | 122 |
LXXXVII | 123 |
LXXXVIII | 125 |
LXXXIX | 133 |
XC | 134 |
XCI | 137 |
XCII | 139 |
XCIII | 145 |
XCIV | 153 |
XCV | 158 |
XCVIII | 159 |
CI | 160 |
CII | 162 |
CIII | 163 |
CIV | 164 |
CV | 166 |
CVI | 172 |
CVII | 179 |
CIX | 183 |
CX | 184 |
CXI | 188 |
CXII | 192 |
CXIII | 194 |
CXXII | 220 |
CXXIII | 222 |
CXXV | 225 |
CXXVI | 226 |
CXXVII | 227 |
CXXVIII | 229 |
CXXX | 230 |
CXXXI | 231 |
CXXXII | 233 |
CXXXIII | 234 |
CXXXIV | 237 |
CXXXV | 238 |
CXXXVI | 241 |
CXXXVII | 249 |
CXXXVIII | 251 |
CXXXIX | 255 |
CXL | 257 |
CXLI | 259 |
CXLII | 264 |
CXLIII | 266 |
CXLIV | 273 |
CXLV | 274 |
CXLVI | 278 |
CXLVIII | 279 |
CXLIX | 280 |
CL | 281 |
CLI | 283 |
CLII | 284 |
CLIII | 285 |
CLIV | 292 |
CLV | 298 |
CLVI | 299 |
CLVII | 302 |
CLVIII | 304 |
CLIX | 305 |
CLX | 308 |
CLXI | 312 |
CLXII | 313 |
CLXIII | 315 |
CLXIV | 318 |
CLXV | 323 |
CLXVI | 326 |
CLXVII | 327 |
CLXVIII | 332 |
CLXIX | 333 |
CLXX | 335 |
CLXXI | 340 |
CLXXII | 341 |
CLXXIII | 345 |
CLXXIV | 353 |
CLXXV | 357 |
CLXXVI | 363 |
CLXXVII | 372 |
CLXXVIII | 375 |
CLXXX | 377 |
CLXXXI | 380 |
CLXXXII | 382 |
CLXXXIII | 385 |
CLXXXIV | 392 |
CLXXXV | 394 |
CLXXXVI | 396 |
CLXXXVIII | 399 |
CLXXXIX | 402 |
CXC | 406 |
CXCI | 407 |
CXCII | 410 |
CXCIII | 412 |
CXCV | 418 |
CXCVI | 420 |
CXCVII | 423 |
CXCVIII | 427 |
CXCIX | 429 |
CC | 434 |
CCI | 435 |
CCII | 436 |
CCIII | 437 |
CCV | 438 |
CCVI | 439 |
CCVII | 441 |
CCVIII | 443 |
CCIX | 446 |
CCX | 461 |
Andere Ausgaben - Alle anzeigen
The Fokker-Planck Equation: Methods of Solution and Applications Hannes Risken,Till Frank Eingeschränkte Leseprobe - 2012 |
The Fokker-Planck Equation: Methods of Solution and Applications Hannes Risken Eingeschränkte Leseprobe - 2012 |
The Fokker-Planck Equation: Methods of Solution and Applications Hannes Risken Keine Leseprobe verfügbar - 2012 |
Häufige Begriffe und Wortgruppen
approximation bistability boundary conditions Brownian motion c₁ calculate correlation function cosine potential damping constants derivative detailed balance differential equations diffusion coefficients distribution function drift and diffusion drift coefficient eigenfunctions eigenvalues equation of motion expansion coefficients expression finite Fokker-Planck equation Fokker-Planck operator follows Fourier transform friction constants Gaussian given Green's function Hermite functions initial condition inserting integral inverse Kramers equation Kramers-Moyal Langevin equation Langevin force Laplace transform laser matrix continued fractions matrix continued-fraction method noise normalized obtain Ornstein-Uhlenbeck process oscillator particles periodic potential potential f(x probability current probability density pump parameter random variable recurrence relation Schrödinger equation shown Smoluchowski equation solved stationary distribution stationary solution stochastic variable t₁ tion transition probability truncated vanish vector recurrence relation velocity W₁ x₁ Xmax Xmin zero дх
Verweise auf dieses Buch
Spiking Neuron Models: Single Neurons, Populations, Plasticity Wulfram Gerstner,Werner M. Kistler Eingeschränkte Leseprobe - 2002 |
Continuous-time Markov Chains and Applications: A Singular Perturbation Approach George Yin,Qing Zhang Keine Leseprobe verfügbar - 1998 |