|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Shirer H.N. — Nonlinear Hydrodynamic Modeling: A Mathematical Introduction |
|
|
|
| Предметный указатель |
Hysteresis loop 129 130
Identity matrix 169 371 466
Implicit Function Theorem and bifurcation 89 466
Implicit Function Theorem and uniqueness of solutions 86 90 171 466
Implicit Function Theorem, statement of 89
Incommensurate frequencies 387 392
Incommensurate periods 390
Incompressibility condition 449 460
Incompressible fluid 25
Index of, ordinary differential equation 101
Index of, topics in monograph 526 546
Index Theorem, applied 101 105 157 202 203
Index Theorem, statement of 101
Infinite-dimensional systems and finite models 84 85 444 447 457
Infinitesimal stability 72
Inflection point height and development of cloud streets 297 315 318
Inflection point in wind profile, definition of 306
Inflection point in wind profile, development 296 306
Inflection point instability 296 297 308 314 314 321
Inflection point instability, developing from 312 314 319 321
Inflection point instability, energy source for 300 303 310
Inflection point instability, filtering 303
Inflection point instability, streets developing from 309
Information dimension 414 421 422
Inhomogeneous 2
Inhomogeneous, ir-periodic system 336 338
Initial errors and predictability problems 406 407
Initial value function 492 494
Initial/boundary value problem for convection 29 31
Initial/boundary value problem for forced, dissipative systems 106
Inner product 338 339 345 501
Instability, finite-amplitude 96 97 117 122 330 331
Kelvin — Helmholtz type 296 297
Kelvin — Helmholtz type and Frobenius Theorem 493 494
Kelvin — Helmholtz type and Lyapunov exponents 415 417 478 479
Kelvin — Helmholtz type for 296 297
Kelvin — Helmholtz type instability 296 297
Kelvin — Helmholtz type, antisymmetric properties of 27
Kelvin — Helmholtz type, as nonlinear term 39 198
Kelvin — Helmholtz type, as source of energy transfer 198 206
Kelvin — Helmholtz type, as source of secondary branching 210 211
Kelvin — Helmholtz type, as stable manifolds 494
Kelvin — Helmholtz type, definition of 415 473
Kelvin — Helmholtz type, dimensional form of 26
Kelvin — Helmholtz type, dimensionless form of 61
Kelvin — Helmholtz type, Instability process for fixed points 70 79 465 469
Kelvin — Helmholtz type, Integral foliation 490
Kelvin — Helmholtz type, Intermittency 390 395 429 432
Kelvin — Helmholtz type, Invariant set 394
Kelvin — Helmholtz type, Inversion height 281 293
Kelvin — Helmholtz type, Inviscid flows 106
Kelvin — Helmholtz type, Invisible function 179 186
Kelvin — Helmholtz type, Irrationally-related frequencies 387 392
Kelvin — Helmholtz type, Jeffreys' Theorem 190 451 452 464
Kelvin — Helmholtz type, Joseph conjecture 390 399 400
Kelvin — Helmholtz type, manifold 473 474
Kelvin — Helmholtz type, model 460
Kelvin — Helmholtz type, origin of 453 454
Kelvin — Helmholtz type, solution 374 382
Kelvin — Helmholtz type, sufficient condition for 454 457
Kelvin — Helmholtz type, trajectory 474
Kernel, bounded symmetric 499
Kinetic energy, in partial differential system 32 108 281 449
Kinetic energy, in spectral model 40 284
Kloeden and Wells power series method 326 341
Kronecker delta 362 459 489
Landau's hypothesis 389 392 400 424 425
Laplace's equation 458 459
Lapse rates 298
Latent heating rate 122 185
Leray turbulence 385
Leray's conjecture 385
Lie bracket 491
Limit cycle 395 413 418 421 425 427
Limit point 464
Limit set 392 486
Limiting frequency of branching periodic, solution 146 148 269 270 287 305 307 308 312 322 327 333 373 383
Limiting period of branching periodic, solution 373 374
Linear stability analysis 70 79 92 100 359 372 465 469
Linear stability analysis, as first step in nonlinear analysis 34 35 70
Linear translation of waveforms 50 52
Liouville's formula 371 415
Longitudinal kinetic energy, in partial differential system 299
Longitudinal kinetic energy, in spectral model 302
Lorenz attractor 84 404 411 428 432 464
Lorenz attractor and modal truncations 408 411
Lorenz attractor and predictability 404 407
Lorenz attractor, Chang and Shirer model 437 438
Lorenz model 37 46
Lorenz model and intermediate modeling principles 408 411
Lorenz model and Shirer model 208 210 408
Lorenz model, altering versal unfoldings in 183 193
Lorenz model, aperiodic trajectories in 341 351 404 407 428 432
Lorenz model, as basis for Shirer ( 1980
Lorenz model, as family of models 199
Lorenz model, as submodel in larger models 435 440 484 485
Lorenz model, band-splitting in 431
Lorenz model, bifurcation diagram for 45 113 341 354
Lorenz model, bifurcation points in 42 77 79 92 342
Lorenz model, branching in 93 119 121 351 354 428 432
Lorenz model, chaotic attractors in 431 432
Lorenz model, chaotic solutions in 404 407
Lorenz model, characteristic equation for 41 76 77 210
Lorenz model, conductive solution in 41 42 77 92 112
Lorenz model, convective solutions in 42 45 77 79 92 342
Lorenz model, corank of singularities in 173 174
Lorenz model, deficiencies of 191
Lorenz model, dimensions of attractors in 427 434
Lorenz model, energetics of 40 41
Lorenz model, equations for 39 66 112 166 342
Lorenz model, expansions for 38
Lorenz model, extension of 197 198 206 210 435 443
Lorenz model, generalized form of 39 132
Lorenz model, harmonic bifurcation in 430
Lorenz model, Hopf bifurcation point in 78 79 341
Lorenz model, intermittency in 429 432
Lorenz model, model 282
Lorenz model, periodic solution in 351 354
Lorenz model, principles 45 165
Lorenz model, temporally periodic solution 342
Lorenz-type primary branches 208 210 408 435
Lorenz-type submodels 435 443
Loss of clarity, owing to pull-back operation 176 177
Loss of information, owing to pull-back operation 176 177
Low-order models, advantages of using 48
Low-order models, constructing optimum 484 504
Low-order models, constructing realistic 84 85 184 326 408 411 412
Low-order models, family of 198 199 218 224
Low-order models, representing turbulence in 385 386 389 408 411
Lyapunov dimension 414 443
Lyapunov dimension and bifurcations 420 425 432 435 436
Lyapunov dimension and routes to chaos 424 428
Lyapunov dimension, definition of 418
Lyapunov dimension, dimension 421 422 436 438 441 442
Lyapunov dimension, global 420 421
Lyapunov dimension, motivation of definition of 418 419
Lyapunov exponent spectrum in 428 429
Lyapunov exponents 414 443
Lyapunov exponents and characteristic exponents 433
Lyapunov exponents and classifying attractors 418 421 424 428
Lyapunov exponents and eigenvalues of Ruelle matrices 478 479
Lyapunov exponents and identifying bifurcation points 425 426 428 432 435 436
Lyapunov exponents and predictability 417 431 434
Lyapunov exponents and refined unstable manifolds 495
Lyapunov exponents and routes to chaos 424 428
Lyapunov exponents and stability properties of orbits 416 417
Lyapunov exponents for stationary, points in 433 434
Lyapunov exponents of phase space 433 434
Lyapunov exponents, at stationary points 433 434
Lyapunov exponents, checking accuracy of 417
| Lyapunov exponents, definition of 416
Lyapunov exponents, global 420 421
Lyapunov exponents, spectrum of 417 418 424 429 438
Lyapunov exponents, the trivial solution 433
Lyapunov exponents, trajectories 472
Lyapunov — Schmidt Reducing Lemma 181 182
Lyapunov — Schmidt Splitting Lemma 168 172
Lyapunov — Schmidt Splitting Lemma, sketch of proof of 169 171
Lyapunov — Schmidt Splitting Procedure 166 174 225
Lyapunov — Schmidt Splitting Procedure, in 172 174
Lyapunov — Schmidt Splitting Procedure, motivating formation of 37 38 137
Lyapunov — Schmidt Splitting Procedure, noisy periodicity in 429 432
Lyapunov — Schmidt Splitting Procedure, period doubling in 395 429 432
Lyapunov — Schmidt Splitting Procedure, periodic solution in 341 354
Lyapunov — Schmidt Splitting Procedure, semi-periodicity in 431
Lyapunov — Schmidt Splitting Procedure, singular point in 172
Lyapunov — Schmidt Splitting Procedure, solutions in 112 172 174 180
Lyapunov — Schmidt Splitting Procedure, subharmonic bifurcation in 395 429 432
Lyapunov — Schmidt Splitting Procedure, sudden transition to chaos in 400 408 429
Lyapunov — Schmidt Splitting Procedure, summary of 171 172
Lyapunov — Schmidt Splitting Procedure, summary of solution regimes in 429
Lyapunov — Schmidt Splitting Procedure, variational equations for 76
Lyapunov — Schmidt Splitting Procedure, window of periodicity in 430 432
Maintanence of balances 7 9
Manifolds, abstract description of 473
Manifolds, as submodels 435 438
Maps, one-dimensional 392 395
Marcus models 408 411
Mather's Theorem, applications of 174 178 181 188
Mather's Theorem, statement of 179
Matrix, corank of 170
Matrix, differential 72 89 168 178 269 466 470 473
Matrix, exponential of 467
Matrix, identity 169 371 466
Matrix, positive definite 503 504
Matrix, rank of 168
Matrix, unfolding 180
Matrix, unit 371
Metamodel 507
Metamodeling 505 507
Minimal attractor 464
Minimum model 37 46 85 206 224 282 291 408 411
Minors 78 508
Modal truncations and chaos 408 411 441 442
Model of the atmosphere 444 445
Model size and occurrence of chaos in 386 408 411 442
Modeling and metamodeling 505 507
Modeling principles, four fundamental 22 40 46
Modeling principles, summarized 18 21
Modeling principles, three intermediate 22 46 164 165 197 198 292 386 408 411 412 485
Modeling, as a mathematical endeavor 444
Modeling, fundamental conflict in 6
Modeling, key to 13
Modeling, process of 14 505 507
Modeling, projection onto N-space during 446 447
Modeling, strategy of 10 11 15
Modeling, two critical issues in 485 486
Models of the modeling process 505 507
Models, abstract dynamical 17 18
Models, appropriate approximate forms of 445 447
Models, axiomatic mathematical 444
Models, bottom-up design of 19
Models, definition of 13
Models, descriptive 2 6
Models, development and use of 444
Models, dynami cal 16 18
Models, evaluating adequacy of 40 46 165 166 412 443
Models, experimental 18 384 411
Models, implications of 444
Models, in Geophysical Fluid Dynamics 6 12
Models, inferential 2
Models, kinematical 15 16
Models, organizational 15 16
Models, predictive dynamical 17
Models, preliminary description of 1
Models, purposes of 13 15
Models, reduction of dimension in 457 504
Models, representational dynamical 17
Models, representing turbulence in finite 385 386 389 408 411 442
Models, structural 14
Models, top-down design of 18 19
Models, types of 15 18
Modes, active 391
modes, fundamental 411
Modes, gravest 137
Modes, pure 73 74
Motionless flow, as a regime 8 384
Multiplicity of a bifurcation point 202 401
n-cycle 393 396 398
n-torus 391 424 426
Navier — Stokes equations 226 385 391 425 447 450
Neutral stability 71
Neutral subspace 468
Newton — Raphson scheme 240 246
Newton's method 240 246
Newtonian heating coefficients 194 195
Noise, random in system 423
Noisy periodicity 390 393 429 432
Nondimensionalization, process of 27 29
Nondivergent fluid 26
Nonlinear analysis, linear analysis as first step in 34 35 70
Nonlinear equations, having nonunique solutions 91 92
Nonlinear solutions and linear, stability 72
Nonlinear terms, including in a model 64 66 198
Nonlinearity, consequences of 11 48 86 198 206 207 210 211 226 454 464
Nonlinearity, introduction of 445
Nontrivial solution 36 115 118 122 128 130
Nontrivial solution, existence of 91 92
Nontrivial solution, stability properties of 102 105
Norm 252 339 345 422 455
Observable solution and decaying perturbations 33 45 70 71
Observable solution, even when unstable 82 84
Observable wave and maximum growth rates 136 138
Observations, from 422
Onset of convection 111
Optimum spectral models and empirical orthogonal functions 496 504
Optimum spectral models for certain flow regimes 500 504
Optimum spectral models, existence of 485 486
Optimum spectral models, manifolds 472 485 496
Orbit, along 359
Orbital instability, conditions for 362 365 367
Orbital instability, definition of 358
Orbital stability 357 359
Orbits, closed 266 273 356 357 373 382 425 427 464
Orbits, Lyapunov exponents 416 417
Orbits, period-three and intermittency 390
Ordinary differential system, general form for 72 86 87 166 167 331 332 359
Ordinary differential system, system 47 60 69
Orientation angle for cloud streets 279 293 294 297 304 311
Orientation angle, preferred 292 297 305 307 312 324
Orthogonal functions, boundary conditions for 56 57
Orthogonal functions, definition of 56
Orthogonal functions, trigonometric 63 64
Orthonormal functions, as analogues of unit vectors 458 497
Orthonormal functions, complete set of 497 498
Orthonormal functions, definition of 56
Orthonormal functions, optimum set of 497 498
Orthonormality relations 459
Osledec Theorem 417 418
Ostlund et al. conjecture 390 395 399 402 403 426 427
Parallel instability 296 297 300 308 314 321
Parallel instability, developing from 301 302
Parallel instability, energy source for 300 304
Parallel instability, filtering 309
Parameter space, paths in and routes to chaos 400 404
Parameter space, regions in 106 110 111 124 130
Parameter values, effects of errors in 129 130
Parameters and transition types 119 130 400 403
Parameters, location of unfolding 182 196
Parameters, passive 166
|
|
|
| Реклама |
|
|
|
|
|
|
|
|
О проекте