Chandrasekhar S. — Radiative Transfer :: Электронная библиотека попечительского совета мехмата МГУ

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Chandrasekhar S. — Radiative Transfer

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Название: Radiative Transfer

Автор: Chandrasekhar S.

Аннотация:

Foundation for analysis of stellar atmospheres, planetary illumination, sky radiation; physical interest for problems analogous to diffusion of neutrons.

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1960

Количество страниц: 393

Добавлена в каталог: 23.01.2009

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Предметный указатель

$H^{-}$       288
$H^{-}$ as a source of continuous absorption in stellar atmospheres      308 et seq. 316
$H^{-}$ in model stellar atmospheres      311 et seq.
$H^{-}$ , continuous absorption coefficient of      310 310
$H^{-}$ , electron affinity of      288 309
Absorption coefficient      6 355 Mean
Absorption lines      see “Formation of absorption lines”
Albedo      6 81 124 209 325
Albedo for reflecting surface      147 270
Albedo for reflection by surface      147
Albedo for single scattering      6
Angular distribution of emergent radiation      15 83
Angular distribution of emergent radiation for axially symmetric problems in non-conservative cases      346 349 383
Angular distribution of emergent radiation for diffuse reflection      see “Law of diffuse reflection”
Angular distribution of emergent radiation for diffuse reflection and transmission      see “Law of diffuse reflection and transmission”
Angular distribution of emergent radiation for isotropic scattering      76 80 98 124 135
Angular distribution of emergent radiation for line formation problem      320 327
Angular distribution of emergent radiation for planetary problem      see “Planetary problem”
Angular distribution of emergent radiation for problem with a constant net flux      see “Law of darkening”
Angular distribution of emergent radiation for Rayleigh scattering      246 248
Angular distribution of emergent radiation for Rayleigh’s phase function      134 135
Angular distribution of emergent radiation, invariance of      90
Angular distribution of emergent radiation, reciprocity with boundary conditions      76
Anisotropic particle      45
Anisotropic particles, scattering by      45 et seq. 282
Arago point      281 et seq.
Asymptotic solution of equation of transfer      15 18 19 344 383
Asymptotic solution of equation of transfer, invariance arising from      92 345 383
Atmosphere in local thermodynamic equilibrium      7
Atmosphere, electron scattering      43 234 249
Atmosphere, finite      12
Atmosphere, plane-parallel      11
Atmosphere, scattering      7
Atmosphere, semi-infinite      12 14 18
Atmosphere, spherical      23
Atmosphere, stellar      14 288
Average intensity      4
Axially symmetric problem in non-conservative cases      20 383
Axially symmetric problems in non-conservative cases      18 20 344 349 383
Babinet point      281 et seq.
Bessel functions      339 369
boundary conditions      15 20 22 43 45 291
Boundary conditions and interpolation theory      198 379
Boundary conditions for principles of invariance      92 93 167
Boundary conditions in finite approximation      72 82 166
Boundary conditions, reciprocity with emergent radiation      76 83 127 196 241 323
Boundary temperature      293
Boundary-value problem      331 343 357
Brewster point      281 et seq.
Characteristic equation      19 89 105 117 153 285 344 349 363
Characteristic equation as a transcendental equation      19 344 349 383
Characteristic equation for $\varpi_{0}(1+xcos\theta)$       383
Characteristic equation for isotropic scattering      71 81
Characteristic equation for Rayleigh scattering      237
Characteristic equation for scattering by anisotropic particles      285
Characteristic equation, determinantal      361
Characteristic function      105 183
Characteristic function as defining “pseudo-problems” in transfer theory      351 ct seq
Characteristic function for $1+\varpi_{1}P_{1}(cos\theta)+\varpi_{2}P_{2}(cos\theta)$       159
Characteristic function for $\varpi_{0}(1+xcos\theta)$       136 228 230 353
Characteristic function for Rayleigh scattering      246 253 260
Characteristic function for Rayleigh’s phase function      129 130 143 220 222 226 352
Characteristic function, conservative case      107 187 190
Characteristic root      19 105
Characteristic roots      19 79 240 300 344 363
Characteristic roots, complex      360
Characteristic roots, relation to zeros of Legendre polynomials      74 242 324
Christ off el numbers      58
Christoffel numbers      58 63 64 65
Compton effect      328 335
Compton effect, softening of radiation by      329 et seq.
Compton wave-length      329 334
Conservative case      6 7 107
Conservative case, ambiguity in X- and Y-functions      190
Conservative case, characteristic function for      107
Conservative case, H-functions and integral equations of Schwarzschild — Milne type      347
Conservative case, inadequacy of principles of invariance      208 212 222 268
Conservative case, K-integral      13 52 74 208 212 213 219 224 234 279
Conservative case, special integrals in      107 108 109 187 188
Conservative case, X- and Y-functions in      190 et seq.
Conservative scattering      6
Conservative scattering, flux integral for      10 74 213 224 234 246 279 290 297 315 331
Conservative scattering, isotropic      15
Conservative scattering, Rayleigh scattering      35
Conservative scattering, Rayleigh’s phase function      17
Continuous absorption coefficient      288
Continuous absorption coefficient of hydrogen      312
Continuous absorption coefficient of H^{-}      310
Continuous absorption coefficient, dependence on wave-length of solar      307 et seq. 316
Continuous absorption coefficient, mean      291 298 300 312
Continuous absorption coefficient, role of, in line formation      321
Continuous absorption coefficient, stellar      303 et seq.
Continuous spectrum of a stellar atmosphere      288
Continuous spectrum, analysis of      304 et seq.
Continuous spectrum, intensity distribution in sun      303
Darkening      see “Law of darkening”
Degree of polarization      247
Density of radiation      3 4
Depolarization factor      49 50 233 282
Differentiation formula      365
Diffuse radiation      22
Diffuse radiation field      22
Diffuse reflection      20 (see also “Diffuse reflection and transmission”)
Diffuse reflection and transmission      20 208
Diffuse reflection and transmission for $\varpi_{0}(1+xcos\theta)$       227 et seq.
Diffuse reflection and transmission for Rayleigh scattering      249 et seq. 265 286
Diffuse reflection and transmission for Rayleigh’s law      44
Diffuse reflection and transmission for Rayleigh’s phase function      219 et seq.
Diffuse reflection and transmission in Schuster’s problem      319
Diffuse reflection and transmission, effect of ground on      270
Diffuse reflection and transmission, equation of transfer for      22 160
Diffuse reflection and transmission, expressed in terms of X- and Y-functions      181 209 213 226 230 267 268
Diffuse reflection and transmission, flux of      273 274 278 279
Diffuse reflection and transmission, planetary problem      270
Diffuse reflection and transmission, principle of reciprocity in      172
Diffuse reflection and transmission, standard problem in      22 233 269
Diffuse reflection for conservative isotropic scattering      86 125 147 148
Diffuse reflection for isotropic scattering      80 et seq. 88 124 140 147 149
Diffuse reflection for Rayleigh scattering      254 et seq.
Diffuse reflection in accordance with $1+\varpi_{1}P_{1}(cos\theta)+\varpi_{2}P_{2}(cos\theta)$       158
Diffuse reflection in accordance with $\varpi_{0}(1+xcos\theta)$       99 et seq. 138 140
Diffuse reflection in accordance with general phase function      149 et seq.
Diffuse reflection in accordance with Rayleigh’s phase function      101 et seq. 128 132
Diffuse reflection, equation of transfer for      22 150
Diffuse reflection, principle of reciprocity      94
Diffuse transmission      20 (see also “Diffuse reflection and transmission”)
Diffusion of imprisoned radiation      354 371
Dirac’s $\delta$ -function      332 341
Doppler effect      335 343
Effective temperature      290
Effective temperature of sun      301
Einstein coefficients      354
Einstein coefficients, definition of      354
Electron scattering      36 343
Electron scattering atmosphere      43
Electron scattering atmosphere, Hiltner’s observations on      2—19
Electron scattering atmosphere, law of darkening in      245 et seq.
Electron scattering atmosphere, polarization of emergent radiation      247 et seq.
Electron scattering, broadening of lines by      334 et seq.
Electron scattering, Dirac’s formula for      336
Electron scattering, Doppler effect duo to      335
Electron scattering, importance in stellar atmospheres      4 3 249
Electron scattering, softening of radiation by      328 et seq.
Elimination of the constants      77 84 127 158 197 241 286 323
Elliptic equation      331
Elliptically polarized beam      25
Emergent flux as an integral over source function      67 304 305 314
Emergent flux in absorption lines      320 327
Emergent intensity in absorption lines of stars      320 327
Emergent intensity in continuous spectrum of stars      304— et seq.

Emission coefficient      7
Emission coefficient, Kirchhoff      8 288
Equation of transfer      1 8 9
Equation of transfer for an electron scattering atmosphere      43 234
Equation of transfer for broadening by electron scattering      337
Equation of transfer for diffuse reflection and transmission      22 44
Equation of transfer for diffusion of imprisoned radiation      356
Equation of transfer for general phase function      150
Equation of transfer for integrated intensity      293 296
Equation of transfer for isotropic, scattering      15 70
Equation of transfer for line formation      322
Equation of transfer for local thermodynamic equilibrium      289 292
Equation of transfer for plane-parallel problems      11
Equation of transfer for Rayleigh’s law      37 et seq.
Equation of transfer for softening of radiation by Compton scattering      329
Equation of transfer for spherically symmetric case      23 364
Equation of transfer in (2,1) approximation      299
Equation of transfer in (2,2) approximation      300 et seq.
Equation of transfer in finite approximations      56 70 151 195 235 294 297 322 330 339 360 364
Equation of transfer, boundary conditions for      15 20 22 4 45 291 366 357
Equation of transfer, formal solution of      9 76 83 190 240 289 294
Equation of transfer, Fourier transform of      338
Equation of transfer, fundamental solutions of      357 et seq.
Equation of transfer, orthogonality of the solutions of      357
Equation of transfer, particular integrals of      81 154
Equation of transfer, reduction of, for Rayleigh scattering      249 250 254
Equation of transfer, replacement by systems of linear equations      54 et seq. 68
Equation of transfer, special solutions of      14 19 344 383
Equation of transfer, “pseudo”-      351 et seq.
Exponential integral      16 347 373
Finite atmosphere      12 156 195
Finite atmosphere, principles of invariance for      161 et seq.
Flux in diffuse reflection and transmission      273 279
Flux integral      11
Flux of radiation in a grey atmosphere      295
Flux, derivatives of      296
Flux, distribution in sun      303
Flux, evaluation by quadrature formula      65 et seq. 3
Flux, integral      1 1 13 74 213 224 234 273 279 360
Flux, integrated      290
Flux, monochromatic      295
Flux, not      2
Formation of absorption lines      318 321 342 343
Formation of absorption lines, broadening of      342
Fourier transform      338 et seq.
Function      see “H-functions” “X-
Function $F_{j}(\tau,\lambda)$       203
Function, $F_{j}(\tau,\mu)$       203 207 375 378
Function, $G_{n,m}$ , $G'_{n,m}$       203 207 376 378
Functions $G_{n,m}$ and $G'_{n,m}$       203
Gaussian division      62
Gaussian division, differentiation formula based on      365
Gaussian weight      62
Gaussian weights      50 62
Gauss’s quadrature formula      56 61 62 71
Green’s Theorem      332
Grey atmosphere      291
Grey stellar atmosphere      291
Grey stellar atmosphere, boundary temperature of      293
Grey stellar atmosphere, flux of radiation in      295
Grey stellar atmosphere, law of darkening in      293
Grey stellar atmosphere, radiative equilibrium of      293 et seq.
Ground correction      273 279
Ground corrections      270
Ground corrections on illumination of sky      281 et seq.
Ground corrections on law of diffuse reflection and transmission      273
Ground corrections, matrix representing      279
H-equation      105
H-equation in finite approximation      110 et seq.
H-equation, alternative forms of      107 109
H-equation, approximate form of      110
H-equation, exact form of      105
H-equation, explicit solution of      115 et seq.
H-equation, general solution of      123
H-equation, relation to H-functions in finite approximation      110 et seq.
H-equation, uniqueness of the solution of      122 123
H-function in finite approximation      105
H-function, exact definition      105
H-functions      77 97 105
H-functions as Laplace transforms      347 et seq.
H-functions as law of darkening for “pseudo-problem”      351
H-functions as limit of X-functions      183 186
H-functions for $\varpi_{0}(1+xcos\theta)$       139 141
H-functions for isotropic scattering      124 et seq.
H-functions for problem of line formation      325
H-functions for Rayleigh scattering      248 261
H-functions for Rayleigh’s phase function      132
H-functions in conservative case      107 108 117 347
H-functions in finite approximation      77 89 110
H-functions in non-conservative case      117 349
H-functions, an identity governing      84 112 116
H-functions, explicit solution for      115 et seq.
H-functions, integral equation for      105
H-functions, integral properties of      106 et seq. 130 133 136 256
H-functions, moments of      106
H-functions, pole of      122 350
H-functions, practical method for evaluating      123
H-functions, representation as a complex integral      114 117
H-functions, tables of      125 132 139 141 248 261
H-functions, tables of moments of      126 133 141 248 328
H-functions, uniqueness of, in conservative cases      123
Helmholtz’s theorem      176 182
Hopf — Bronstein relation      78 88 109
Hopf — Bronstein relation, analogues of      109 134
Hopf — Bronstein relation, derivation of, from principles of invariance      98
Hydrogen-metal ratio      311
Hyperbolic equation      343
identities      73 78 83 87 112 116 245
Independent streams of light      29
Integral equation      see “Reduction of integral equations”
Integral equation for H-functions      97 105
Integral equation for law of darkening      96
Integral equation for problems with spherical symmetry      24
Integral equation for Rayleigh’s phase function      18
Integral equation for scattering and transmission functions      169 et seq. 178
Integral equation for scattering and transmission matrices      170 265
Integral equation for scattering function      94 99
Integral equation for scattering matrix      103 255
Integral equation for source function      10
Integral equation for X- and Y-functions      181 183
Integral equation, generalized Schwarz’s child — Milne type      347 349
Integral equation, Schwarzschfid — Milne      17 93
Integral equation, systems of      100 103 180 220 221 227 255 265 266
Integral equations of the Schwarzsehild — Milne type      347
Integrals $I(\alpha,\beta)$ and $F(\alpha,\beta)$       305
Integrated energy density      4
Integrated intensity      2
Integro-differential equation      9 54
Integro-differential equation, reducible directly in terms of H- or X- and Y-functions      252 353
Intensity, average      4
Intensity, evaluation of      65 305
Intensity, expansion of, in terms of Legendre polynomials      366
Intensity, integrated      2
Intensity, inward      12
Intensity, outward      12
Intensity, specific      1
Interpolation theory, a problem in      198 379
Isotropic scattering      6 15 70
Isotropic scattering, characteristic equation for      19
Isotropic scattering, conservative case of      15 18
Isotropic scattering, constants of integration for      78 79
Isotropic scattering, diffuse reflection and transmission on      180 195
Isotropic scattering, diffuse reflection on      80 et seq.
Isotropic scattering, diffusion of imprisoned radiation      354
Isotropic scattering, equation of transfer for      15 18 22
Isotropic scattering, equation of transfer for, in finite approximation      70 81
Isotropic scattering, integral equations for      96 et seq.
Isotropic scattering, problem with a constant net flux for      70
Isotropic scattering, Schwarzschild — Milne integral equation for      16 346
Isotropic scattering, source function for      75 83

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