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| Myshkis A.D. — Low-Gravity Fluid Mechanics: Mathematical Theory of Capillary Phenomena |
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| Предметный указатель |
Angle, boundary 4 18 116 118 188
Angle, contact 4 18 147 387
Angle, dihedral 189
Angle, flow-back 24 117
Angle, flow-in 24 117
Angle, rotation 237
Angle, wetting 4 18 24 135 235 349 394
Approximation, Boussinesq 466
Bifurcation of axisymmetric shape 246
Bifurcation of axisymmetric shape in circular cylinder 232
Bifurcation of axisymmetric shape of equilibrium shapes 223
Bifurcation of axisymmetric shape of solutions 490
Coefficient(s), expansion 358
Coefficient(s), filling 46 60
Coefficient(s), Lame 393 438
Coefficient(s), Ritz 378
Condition(s), boundary 279f.
Condition(s), Cauchy — Riemann 420
Condition(s), Dupre — Young 18
Condition(s), dynamic 279 423
Condition(s), Euler 17
Condition(s), kinematic 278
Condition(s), Laplace 17f.
Condition(s), no-flow 278
Condition(s), stability 122
Condition(s), strong potential-energy minimum 122
Condition(s), zero-gravity 549f.
Constant, capillary 33
Convection 464ff.
Convection in thin layer 478
Convection, concentration-capillary 507 510f. 516 525
Convection, free 466
Convection, gravitational 464
Convection, longwave 516
Convection, shortwave 516
Convection, thermocapillary 508ff. 517
Criterion, general stability 206
Criterion, Reynolds 268
Critical loads 146
Damping factor 395 432 438 440 442
Diagram, Newton 219 273
Duality patterns 39 148
Ellipsoid, Jacobi 256
Ellipsoid, Maclaurin 256
Energy, kinetic 278
Energy, potential 278 296
Energy, potential, free 3
Energy, surface 3
Equation(s), bifurcation 239 244 251 271 491
Equation(s), boundary-layer 63 97
Equation(s), continuity 278
Equation(s), convection 503
Equation(s), elliptic 446
Equation(s), equilibrium 60
Equation(s), Euler 236 301 309
Equation(s), Euler, linearized 277
Equation(s), Fredholm 228 381 492
Equation(s), Fredholm, abstract 457f.
Equation(s), free-convection 466
Equation(s), Helmholtz 399
Equation(s), integral 481
Equation(s), Laplace 297 335 356
Equation(s), Navier — Stokes 268 392 467
Equation(s), operator 296ff. 313 449 469
Equation(s), Poisson 465
Experiment, Plateau 7
Factor, filling 147
Factor, loading 33
Field, gravitational force 76 83 117 139f. 173 199 207
Field, vector, poloidal 411
Field, vector, toroidal 411
Force(s), Archimedean 11 464 511
Force(s), capillary 3 121 425
Force(s), Coriolis 324 329 344 346 415 419 436
Force(s), gravitational 155
Force(s), self-gravitational 4 433
Force(s), surface 3 5f.
Form, axisymmetric equilibrium 156
Formula(s), Fritz 154
Formula(s), Gauss 19 440
Formula(s), Green 292 297f. 300 303f. 308 321 415 447 449f.
Formula(s), interpolation 101
Formula(s), Ostrogradsky 300
Formula(s), Simpson 357 361 365 373
Function(s), Green’s 356f. 371 385 389 395 471 489
Function(s), Neumann 332
Gyroscopic stabilization 124 160 418
Hausdorff area 29
Hysteresis, wetting 24
Instability, Rayleigh — Taylor 549
Integral, Cauchy 280
Integral, Cauchy — Lagrange 335
Integral, Dirichlet 303
Law, Laplace 295
Line, contact 16 18 21 23 62 116 118 122
Line, contact, perturbed 115
Line, equilibrium 30 32 35f. 55 62 80 83 88 141 146 175f. 179
Line, equilibrium, symmetric 87
Line, wetting 4 209
Liquid(s), capillary 276 459f.
Liquid(s), heavy 276 432
Liquid(s), ideal 276ff. 334ff. 409 421 431 459
Liquid(s), immiscible 312 320 331
Liquid(s), immobile 466
Liquid(s), incompressible 541
Liquid(s), low-viscosity 425 427 442
Liquid(s), Newtonian 524
Liquid(s), non-rotating capillary 441
Liquid(s), non-rotating capillary, heavy 439
Liquid(s), rotating 322 375
Liquid(s), rotating, viscous capillary 445
Liquid(s), self-gravitating 121 427 464 506f.
Liquid(s), viscous 392 435 460
Liquid(s), zero-gravity 373 442 445
Loading, critical 146
Loading, negative 40
Loading, positive 39
Low-gravity 1f. 6 12
Method(s) of collocation 355
Method(s) of indeterminate coefficients 494
Method(s) of integral equations 359
Method(s) of local variations 99
Method(s) of stability calculation 213
Method(s), boundary-layer 62 422 428f 435ff.
Method(s), finite-difference 81
Method(s), floating zone 198
Method(s), Galerkin 257 397f. 476 485 522ff.
Method(s), graphic 37
Method(s), Lyapunov — Schmidt 269 271 273f. 469
Method(s), narrow-band 485
Method(s), Newton — Kantorovich 80f 533f.
Method(s), Newton’s 37 60 101 146 377
Method(s), numerical 98
Method(s), optical discretization 101
Method(s), Plateau 7
Method(s), Ritz 310f 315 330 332 349f. 366 389f. 459
Method(s), small-parameter 388
Method(s), trial-and-error 74
Method(s), variational 304
Mode(s), geostrophic 340
| Mode(s), hard 221
Mode(s), soft 221
Modelling 34
Number, Biot’s 480 545 548
Number, Bond 34 61 109 116 147
Number, Froude 479
Number, Galileo 543 549
Number, Marangoni 511 526f. 550
Number, Prandtl 500 535 540 551
Number, Prandtl, diffusion 525
Number, Rayleigh 479 490 504 550f.
Number, Reynolds 500 552
Number, Schmidt 525 551
Number, Weber 480
Operator(s), Fredholm 269 271
Operator(s), gyroscopic 338 446
Operator(s), kinetic energy 297
Operator(s), Legendre 364
Operator(s), potential energy 297
Oscillation(s), free 398
Oscillation(s), inertial 329
Oscillation(s), linear 349 392
Oscillation(s), natural (normal) 281 293 304 394 421 433f.
Oscillation(s), nonlinear 294
Oscillation(s), plane 349 355 358 366f.
Oscillation(s), small 276ff.
Parameter(s), bifurcation 506
Parameter(s), boundary 136f.
Parameter(s), correctness 368
Parameter(s), spectral 468
Perturbation(s), allowed 163 184
Perturbation(s), antisymmetric 141f. 149 151 176f. 242
Perturbation(s), axisymmetric 137 149 152 154 159 161ff. 188 196f. 200 202 242 252
Perturbation(s), dangerous 129f. 136 138 141 149 151 159 162f. 171f. 174 176f 181 209 211
Perturbation(s), first-harmonic 162
Perturbation(s), non-axisymmetric 155 159 161 164 188 195 200 205 211 214
Perturbation(s), plane 171
Perturbation(s), second-harmonic 162
Perturbation(s), small 104
Perturbation(s), symmetric 142
Perturbation(s), zero-volume 210
Phenomena, capillary 13
Potential, gravitational 428
Potential, Newtonian 465
Potential, well 220
Principle of exchange of stabilities 468
Principle of minimum potential energy 120
Problem(s), axisymmetric 30 38 57f. 61 129 134 211 260
Problem(s), bifurcation 249 254
Problem(s), boundary-value 97f. 106f. 110 118 129 132 224 226f. 231f. 234 237f. 243f. 249ff. 282f. 289 297f. 317 325 379 386 395 420 428 448f. 471 475 480f. 494 496 498 509 512 534 538
Problem(s), Cauchy 60 77 337 350 456 547
Problem(s), eigenvalue 304 471 474
Problem(s), equilibrium surface 25 32 128
Problem(s), linearized 82 92
Problem(s), Maxwell 209
Problem(s), Neumann 103 335 382 385 447
Problem(s), plane 83 257
Problem(s), Plateau 12
Problem(s), Sobolev 340
Problem(s), stationary-value 309
Problem(s), two-dimensional 94
Problem(s), unperturbed 224
Problem(s), variational 98f.
Region, maximal stability 39ff. 135f. 141 146 169ff. 187
Scheme(s), difference 529
Scheme(s), Kelvin 123f. 126 130 156 165f. 256f.
Scheme(s), Poincare 123f. 126 130 132 156 165 256
Self-gravitation 419
Sessile drop 49
Shape(s), axisymmetric 50
Shape(s), equilibrium 55 59 74 78 100 109 118 124
Shape(s), equilibrium, annular 83 167
Shape(s), equilibrium, stable 122
Shape(s), non-axisymmetric 115
Space, Banach 269f. 467
Space, Hilbert 281 336 347 395 446ff. 450 460 469 523
Space, Holder 274
Space, Pontryagin 307
Stability boundary 487ff. 511
Stability boundary, Marangoni 524
Stability of convective motion 494
Stability of cylindrical equilibrium surface 133
Stability, criteria 167
Stability, criteria, spectral 167
Stability, equilibrium 149 194
Stability, loss in cylindrical vessel 237
Stability, loss in cylindrical vessel, dangerous 222
Stability, loss in cylindrical vessel, safe 222
Stability, margin 220 240 246 260ff. 265ff.
State(s), axisymmetric 150 154 170
State(s), equilibrium 16 120 139f.
State(s), non-axisymmetric 193
State(s), stability of 120
Surface(s), critical 159
Surface(s), cylindrical free 160f.
Surface(s), equilibrium 32f. 53 55 57f. 73 80 87 101 104 119 127 190
Surface(s), equilibrium, axisymmetric 67 137
Surface(s), equilibrium, cylindrical 167 170
Surface(s), equilibrium, doubly connected 194
Surface(s), equilibrium, horizontal 139 173
Surface(s), equilibrium, stability of 146
Surface(s), flat (gently sloping) 110
Surface(s), free 65 190 192
Surface(s), nonsymmetric 197
Surface(s), tension 37f. 97
System, parameter-dependent 130
Technique, floating zone 194
Theorem on explicit functions 271
Theorem, Gagliardo’s 524
Theorem, instability 124
Theorem, Keldysh’ 455
Theorem, Krasnosel’skii 490
Theorem, Krein’s 473
Theorem, Lagrange’s 323
Theorem, Meusnier’s 31
Theorem, Mikhlin 304
Theorem, Riesz’s 447 460
Theorem, Rouche’s 416
Theorem, Sobolev’s embedding 396 447 449
Theorem, stability 124 397
Theorem, Weyl’s 347
Theorem, Yudovich’s 492f.
Theory of bifurcation of solutions 507
Theory of bifurcation of solutions of oscillating kernels 507
Theory of bifurcation of solutions, boundary-layer 62
Theory of bifurcation of solutions, Fredholm’s abstract 454
Theory of bifurcation of solutions, Frobenius 474
Theory of bifurcation of solutions, Kato’s general 457
Theory of bifurcation of solutions, Krasnosel’skii’s 474
Theory of bifurcation of solutions, Landau phenomenological 491
Viscosity, high 410
Viscosity, low 409 422 425
Wave(s), backward 325
Wave(s), capillary 81
Wave(s), forward 325
Wave(s), inertial 340
Wave(s), internal 326 330
Wave(s), standing 325
Wave(s), surface 326 328 441
Weyl’s sequence 346
Zero-gravity 1f. 6 43 50 72 82 100 137 143 145 154 156 159 164 166 172f. 188 194 203f. 206 253 433 464
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