Kulish V.V. — Hierarchical Methods: Hierarchy and Hierarchical Asymptotic Methods In Electrodynamics, Volume 1 :: Электронная библиотека попечительского совета мехмата МГУ

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Kulish V.V. — Hierarchical Methods: Hierarchy and Hierarchical Asymptotic Methods In Electrodynamics, Volume 1

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Название: Hierarchical Methods: Hierarchy and Hierarchical Asymptotic Methods In Electrodynamics, Volume 1

Автор: Kulish V.V.

Аннотация:

Written for students and postgraduates who specialize in computer calculations, this book, volume I of a two-volume set, describes a new hierarchical model for dynamic nonlinear systems and discusses a set of new hierarchical principles. Modern hierarchical asymptotic methods are set forth, taking into account specific features of electrodynamic problems, and the phenomenon of hierarchy in electrodynamics is discussed. A set of hierarchical asymptotic calculative methods of two types is discussed in detail. Kulish is affiliated with the National Aviation University, Ukraine

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Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2004

Количество страниц: 355

Добавлена в каталог: 17.12.2009

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Предметный указатель

Ability to model principle      38
Action postulate      41
algorithmic complexity      45 46
Amplitude      11 14 20—22 24 28 91 92 113 129 160 164 172 187 194 199 201 202 249 258 279 284 287—289 291 297 306 308—310 344—346
Analysis problem      64
Analytical-numerical methods      xvii 1 52 89
Angular acceleration      9 30
Angular displacement      30
Angular velocity      30 34 35
Approximation of strong pumping      288
Artificial system      60
Autonomy postulate      39
Averaged current-density equation      242 314
Averaged equilibrium state      315
Averaged kinetic equation      246 348
Averaged Maxwell’s equation      275
Averaged quasi-hydrodynamic equation      237 239 240 339 340
Averaged quasilinear equation      259 261 268 270 271 275
Averaging operator      63 76 77 92 96
Averaging operator on spatial coordinates      76
Averaging operator on time      76
Bhatnahar — Gross — Krook collision model      210
Big Bang point      116
Bucket      179 181 182 198 201 202
Bunch      196 203 204
Canonical form      208 228 323
Canonical variable      33 168
Case of small oscillations      181 188 201
Cauchy problem      223 225 226
Chaotic system      37 60
Characteristic root      228
Cherenkov instability      194 195
Closed hierarchical system      59 61 115
Closed system      32 36 44
Collision integral      80 208 246
Collision scale parameter      80
Combination oscillations      22
Comparison equation      10 287
Comparison system      10
Complementarity postulate      40
Complex system      37 39—42 44 49 50 68 208
Condition of parametric resonance      291
Conditions of compatibility      213
Conservation laws      32
Continuity equation      211 238 262 263 271 342
Convergence problem      310
Coupled resonance      17
Cyclic frequency      11 15 20 23 91 193 254 287 295
Definition of resonance      14
Determined system      36 60
Dielectric permittivity      34
Dirichlet — Jordan theorem      77
Dispersion equation      27 207 250 278 295
Dispersion function      27 295 300
Dispersion law      27 289
dispersion relation      27 109 278
distributed system      72 78 82 293
Distribution function      79 208 209 211
Drift motion      182
Drifting standing electromagnetic wave      160
Duffing’s equation      11 146 189 194
Duffing’s parameter      189
Dynamical hierarchy      101 115
Dynamical operator      176 241 296
Dynamical parameter      54
Dynamical system      xix 18 32 35 36 50 52 57 59—63 65 67 68 71 73 75 83 111 175 314
Dynamical variables      50 56 61 83 296
Effect of electron beam modulation      159
Effective potential      176
Electron clusters      197
Electron oscillation phase      13 168
Electrostatic support      329
Elliptic function      179
Energy conservation law      32 44 178
Energy parameter      179
Equation of nonlinear pendulum      10 178 179 186 188
Equation of stimulated nonlinear pendulum      194
Equations of comparison      99
Equations of higher hierarchical level      4
Equations of the first hierarchical level      81 93 94 127 139 184 239 256 332
Equivalent linear system      81 286 295
Essentially nonlinear system      11
Euler variable      35
Euler’s variable      34 112
Explicit oscillation phase      13
Extended combinative phase      186
Extended coordinate vector      86
Extended nonlinear dynamical vector-function      86
Fast oscillation phase      13
Fast rotating phase      12 102 107 108 111 119 130 138 145—147 167 168 171 215 331
Fast variable      90—92 101 102 119 134 233 245 295
Fast varying combination phase      16
Field of forces      31
Field oscillation phase      13
First integral of motion      178
First law of thermodynamics      44
force      9 12—14 29 30 32—34 51 110 113 167 176 177 194 199—202 249 295
Four-wave parametric resonance      16
Fourier — Bessel series      188
Free electron laser (FEL)      1 4 5 13 18 22 77 94 161
Functional operator      64 73 75 84 88 96 245
General hierarchical principle      58 60 64 83
General standard form      83 285
Generalized hierarchical equation of the first order      73 96 120
Generated form of solution      286
Generating equation      10 91 99
Gravitational field      174 175
Gray zone      143
Grebennikov’s method      113
Group velocity      25 301 307
Grouping mechanism      196 197
Hamiltonian equations      33 244
Hamiltonian formalism      33
Hamilton’s function      33
Harmonic oscillations      21 22
Heisenberg’s uncertainty principle      41
Hidden oscillation phase      12
Hierarchical analogue of the second thermodynamic principle      59 67
Hierarchical analogue of the third thermodynamic principle      187
Hierarchical asymptotic analytical-numerical methods      xvii xix xx 4
Hierarchical military unit      114
Hierarchical oscillation system      13 111
Hierarchical principles      xx 50 58 60 63 73 74 83 84 113 114 176 218 239 302
Hierarchical series      53 54 57 58 61 90 114 117 119 215 240 242 246 255 313
Hierarchical series in the normalized dimensionless form      58
Hierarchical system      xviii xix 36 39 44 49—58 60 62 64 67 69 71 72 78 95 107 108 111 114 116 130 182 192 195 218 239
Hierarchical theory of oscillations and waves      17
Hierarchical transformations      xviii 89 218 256 318
Hierarchical tree      51 52 66—69 78 114—116 185 196
Hierarchy      xviii xix xxi 4 5 13 17 49 52—54 56—58 61 64 73 84 90 101 111 114 117 118 213 218 241 242 246 265 316 317
Highest hierarchical scale parameter      4
Holographic principle      52 59
Homogeneous equation      213
Improper wave      27
Information entropy      44 59 61 115
Initial phase of oscillations      11
Instability      14 49 249—252 258 282 315 329 342
Instantaneous acceleration      29
Instantaneous velocity      29 208
Intensity vector      34
Inverse problem      64 65 71 72
kinetic energy      19 31 32 115 198—200 203
Kinetic equation      59 79—81 83 208 236 244 245 310 311 313 326
Klystron      251 252
Kramer’s formula      296 300
Krylov — Bogolyubov’s substitution      88 96 117 120 127 150 153 155 173 189 215 220 221 233 234 239 242 244 245 256 265 268 275 321 332 338 340
Lag-effect      24 26
Lagrange oscillation phase      34
Langmuir’s electron wave      159
Lantzos’ method      112

Large particle      34 197 204
Large scale parameter of the problem      103
Linear differential equation      xviii 10 91
Linear frequency      202 203
Longitudinal wave      26
Lumped system      71 82
Magnetic permeability      34
Many-particle description      35
Mathematical pendulum      9 12 13
Maxwell’s equations      33 83 210 211 236 238 262 271 309 311 315 317 326 327 342
Method of averaged characteristics      xx 7 72 89 207 213 222 225 231 232 235—237 244 250 254 271 273 280 283 285 320 329 339
Method of averaged current-density equation      240
Method of averaged kinetic equation      79 236 244
Method of averaged quasi-hydrodynamic equation      236
Method of characteristics      85 207 213 219 222 227 228 261 276 283 288 340
Method of exact solutions      186
Microstate      42
Miller — Gaponov potential      176 177 198 199
Moderately nonlinear system      11
Modernized standard system      309 317 320
Modernized version of the method of slowly varying amplitudes      293
Moment of inertia      9 30
Moment of momentum      30 32
Moment of momentum conservation law      32
Momentum      5 29 30 32 33 79 80 111 164 166 167 208 212 214 219 232 236 237 239 245
Momentum conservation law      32
Motion integral      32 174 178
Motion integral of the first hierarchical level      174
Multi-frequency nonlinear resonant oscillation-wave problem      3
Multi-frequency nonlinear resonant oscillation-wave systems      3
Multi-harmonic periodic oscillations      22
Multi-resonance system      17
Multiple resonance      16
Natural hierarchical system      51 54 55 60 69
Negentropyness      37
New fast oscillatative phase      184
Newtonian formalism      33
Non-bound resonances      17
Non-harmonic oscillations      21 22
Non-isochronous oscillator      181
Non-resonant case      146 151
Non-resonant zone      143
Nonlinear dynamical system      10 143
Nonlinear equation      xviii 10 91
Nonlinear oscillatative system      9
Nonlinear oscillation dynamical system      10
Normalized combinative phase      188
Normalized energy      181
Normalized potential function      179 180
Normalized time      188
One-particle description      35
Open system      36 38 60
Oscillation      21
Oscillation amplitude      12
Oscillation phase      12
Overdetermined system      212
Parabolic type      228
Parametric amplification      288 293
Parametric electron-wave lamp      113
Parametric resonance      16 113 193
Parametric resonant damping      293
Partial solution      212
Particle ensemble      196 197 209
Passage motion of particle      198
Percussive excitation of highest harmonics      258
Period of oscillations      14
Period of the oscillations      3
Perturbed model      201 203 204
Phase grouping      204 205
Phase mismatch      291
phase velocity      25 26 160 161 164 194 288
Physical definition of the concept of God      68
potential energy      31 32 177 179 198 199
Potential field      32 174
Potential function      32 176 177 179
Potential well      174 177 179 199 202
Principle of hierarchical resemblance      59 61 83
Principle of information compression      58 64 83 93
Principle of physicality      38
Principle of quasi-stationary interaction      200
Problem small parameter      61 189 309 314
Proper field of the zeroth hierarchical level      174
Proper oscillations      13 249
Proper wave      27 109 250 290 295 297 299
Pumping wave      14 26 161 288
Purposefulness      37 42 49 50
Purposefulness principle      38 42
Quasi-harmonic oscillations      21
Quasi-potential field      175—177 180
Quasilinear resonance      16 193
Rabinovich’s standard form      85 307 310
Relationship of characteristics      228
Relativistic factor      15 111 172 210 241 253 258 261 278 344
Resonance      13 14 18—20 38 108 113 114 130 134—139 150 161 170 192 197 200 238 249 250 284 291 296 305
Resonances of the same hierarchy      17
Resonant case      143 146 195
Resonant condition      15 16 18 20 143 144 150. 197 200 249 250 287 290 297
Resonant curve      18 19
Resonant point      18—20 135 249
Resonant zone      144
Rigorous version of the method of slowly varying amplitudes      285 294
Rotating motion of the nonlinear pendulum      198
Rotating vector phase      102
Russian matryoshka      53
Saturation of amplification      20 345
SCW      28 254
Second law of dynamics      9 29 31 33 177
Second law of thermodynamics      44
Secular term      99 100 120 129 133 190
Sefirot      51
Self-consistent system      344
Self-modeling principle      50 52 56 59 116
Self-organization      50 204
Self-resemblance      50 51
Separatrix      179 181 182
Shortened form      xvii
Simplified version of slowly varying amplitude method      284
Single particle problem      163
Slow electron wave      330
Slow resonance      17
Slow variable      102 112 114 118 136 147 167 169 170 233 238 313 331
Slowest dynamical variables      4
Slowly varying amplitude      xix xx 7 20 21 72 82 89 207 208 250 279 283—285 287—289 291 293 295 297 302 305 309 310 312 314 320 324 326 329 330 342 343 345
Slowly varying amplitude method      320
Slowly varying combination phase      16 137
Slowly varying cyclic frequency      21
Slowly varying initial oscillation phase      20
Small oscillations      10 203
Small parameter of the problem      16 91 186 189 322
Space charge wave      254 277 305
Spatially one-dimensional model      288 294
Standard equation of zeroth hierarchical level      6
Standard system with partial derivatives      213
Standing electromagnetic wave      158 164 176 185
Static hierarchical system      54
Static system      36
Stimulated Duffing’s equation      146
Stimulated oscillations      13—15 146 249 250
Stochastic system      36 60 79 80 208
Straight problem      64
Strong hierarchical series      111
Strong synchronism      160
Structural complexity      45 46
Structural hierarchical scale parameter      53
Structural hierarchy      53 54 57 62
Structural operator      62 63 73 75 84 85 99 109 111
Successive approximation method      244
Successive approximations      128
Surface wave      27
Synchronous condition      162 164 170

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