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

K-integral      13 52 74 219 234
K-integral in diffuse reflection and transmission      213 224 279
K-integral in spherical atmospheres      368
K-integral, role in resolving the ambiguity in principles of invariance      208 212 224 269
Kirchhoff’s law      8 288 321
Lagrange’s formula      58 111
Lambert’s law      147 148 270
Laplace transform      346 347
Laplace transform of Schwarzschild — Milne integral equation      347 349
Law of darkening      15
Law of darkening for conservative isotropic scattering      77 80 124 135
Law of darkening for non-conservative scattering      346 385
Law of darkening for Rayleigh scattering      245 247
Law of darkening for Rayleigh’s phase function      133 135
Law of darkening for “pseudo-problems”      351 et seq.
Law of darkening in a stellar atmosphere      304 et seq.
Law of darkening in sun      303
Law of darkening in terms of H-functions      98 134 159
Law of darkening, definition of      15
Law of darkening, dependence on wave-length      303
Law of darkening, exact      98 135 248
Law of darkening, invariance of      91 92 133
Law of diffuse reflection and transmission for $\varpi_{0}(1+xcos\theta)$       230
Law of diffuse reflection and transmission for conservative isotropic scattering      213 et seq. 218 231
Law of diffuse reflection and transmission for non-conservative isotropic scattering      181 201 209 216 232
Law of diffuse reflection and transmission for Rayleigh scattering      265 et seq
Law of diffuse reflection and transmission for Rayleigh’s phase function      226
Law of diffuse reflection and transmission, effect of ground reflection on      269 273 279
Law of diffuse reflection and transmission, illustrations of      231 et seq.
Law of diffuse reflection and transmission, invariance of      170
Law of diffuse reflection for $1+\varpi_{1}P_{1}(cos\theta)+\varpi_{2}P_{2}(cos\theta)$       158
Law of diffuse reflection for $\varpi_{0}(1+xcos\theta)$       138 140 148 149 160
Law of diffuse reflection for isotropic scattering      85 86 97 124 140 147
Law of diffuse reflection for Rayleigh scattering      259 et seq.
Law of diffuse reflection for Rayleigh’s phase function      132 143
Law of diffuse reflection of natural light on Rayleigh scattering      261
Law of diffuse reflection of primary scattering      145 et seq.
Law of diffuse reflection, illustrations of      147 et seq. 262
Law of diffuse reflection, invariance of      90
Legendre polynomials, addition theorem of      150
Legendre polynomials, differentiation formula based on      365
Legendre polynomials, expansion in terms of      7 149 366
Legendre polynomials, quadrature formula based on      01
Legendre polynomials, relation to characteristic equation      74 242 324
Legendre polynomials, zeros of      62
Light scattered once      145 et seq. 216
Light scattered once as a basis for the approximate solution of X- and Y-equations      202 207
Line scattering coefficient      31S
Local thermodynamic equilibrium      7 288
Local thermodynamic equilibrium as a basis for the analysis for continuous spectrum of stars      288
Local thermodynamic equilibrium, equation of transfer for      289
Local thermodynamic equilibrium, source function for      8
Lommel’s equation      369
Mass absorption coefficient      5
Mass scattering coefficient      5
Maximum-modulus theorem      122
Mean absorption coefficient      291
Mean absorption coefficient in stellar atmospheres      312 et seq.
Mean absorption coefficient, method of defining      298 300
Mean intensity      4 293
Mean intensity in a grey atmosphere      294
Mean intensity in a slightly non-grey atmosphere      299
Mean intensity in a. spherical atmosphere      370
Mean intensity in the problem of imprisoned radiation      359 363
Mean intensity, evaluation by quadrature formula      65 et seq.
Milne — Eddington model      321 343
Milne — Eddington problem      321 313
Milne — Eddington problem, exact solution for      327
Model stellar atmosphere      311
Model stellar atmospheres      311 et seq.
Model stellar atmospheres, early work on      316 317
Molecular scattering      38 53
Molecular scattering, classical theory of      45 et seq.
natural light      30 et seq. 33
Natural light, diffuse reflection of, on Rayleigh scattering      201 et seq.
Natural light, principle of reciprocity for      170
Natural light, Rayleigh scattering of      35
Negative hydrogen ion      see “ $H^{-}$ ”
Net flux      2 (see also “Flux”)
Neutral points      261 281
Neutral points of Arago, Babinet and Brewster      281
Non-conservative scattering      18 344 383
Non-uniqueness of the integral equation derived from the principle of invariance      208 212 222 268
Non-uniqueness of the solution of X- and Y-equations      190
Normal optical thickness      12
nth approximation      62
Opposite polarization      31 34
Optical equivalence      29
Optical thickness      9
Optical thickness in a mean absorption coefficient      291
Optical thickness, definition of      9
Optical thickness, normal      12
Optical thickness, varying as inverse power of r      308 et seq.
Parseval’s formula      340
Pencil of radiation      1
Perfect scattering      see “Conservative scattering”
Phase function      5 (see also “Rayleigh’s phase function”)
Phase function $\varpi_{0}(1+xcos\theta)$       6
Phase function $\varpi_{0}(1+xcos\theta)$ , axially symmetric problem in semi-infinite atmospheres      383 et seq.
Phase function $\varpi_{0}(1+xcos\theta)$ , characteristic equation for      383
Phase function $\varpi_{0}(1+xcos\theta)$ , diffuse reflection and transmission in accordance with      227 et seq.
Phase function $\varpi_{0}(1+xcos\theta)$ , diffuses reflection in accordance with      99 et seq. 135
Phase function, $1+\varpi_{1}P_{1}(cos\theta)+\varpi_{2}P_{2}(cos\theta)$       157
Phase function, $\varpi_{0}(1+xcos\theta)$       see “Phase function $\varpi_{0}(1+xcos\theta)$ ”
Phase function, expansion in Legendre polynomials      7 149 177
Phase function, inadequacy of the concept of      264 286
Phase function, Rayleigh’s      6
Phase matrix      37 40 103 170 250 275 280
Phase matrix for Rayleigh scattering      37 42
Phase matrix for resonance lino scattering      50 et seq.
Phase matrix for scattering by anisotropic particles      49
Phase matrix, reducibility of      42
Phase matrix, symmetry of      173
Photospheric surface      318 321
Planck function      8 28K
Plane of scattering      24
Plane-parallel atmosphere      11
Plane-parallel atmosphere, II      13
Planetary atmospheres, illumination of      44 231 270
Planetary problem      270
Planetary problem for scattering according to phase function      274 et seq.
Planetary problem for scattering according to phase matrix      270 et seq.
Planetary problem, reduction to standard problem      270 et seq. 280
Polarizability tensor      40
Polarization of sky      see “Sky”
Polarization, degree of      25 247
Polarization, elliptcity of      25 27
Polarization, opposite      31
Polarization, plane of      25 27
Polarized light, elliptically      25 175 260
Polarized light, independent streams of      20
Polarized light, left-handed      26
Polarized light, oppositely      31
Polarized light, optically equivalent      20
Polarized light, representation of      24 et seq. 31 33
Polarized light, resolution into oppositely polarized beams      33 31 175
Polarized light, right-handed      26
Polarized light, Stokes parameters of      see “Stokers parameters”
Polarized light, Stokes’s theorem on      32
Principle of reciprocity      21 42 94 171 172
Principle of reciprocity for elliptically polarized light      175
Principle of reciprocity for matter waves      182
Principle of reciprocity for natural light      176
Principle of reciprocity for plane polarized light      174
Principle of reciprocity, allowing for polarization      173 et seq. 182
Principles of in variance      80 et seq. 104 127 133 161 182
Principles of in variance as a guide for solving systems of integral equations      127 208
Principles of in variance as defining “pseudo-problems” in transfer theory      353
Principles of in variance as necessary conditions      208
Principles of in variance for finite atmospheres      161 et seq. 170

Principles of in variance for semi-infinite atmospheres      89 et seq. 165 166
Principles of in variance of Stokes — Rayleigh      104
Principles of in variance, allowing for polarization      103 170
Principles of in variance, arising from asymptotic solution at infinity      92 104 344 383
Principles of in variance, insufficiency in conservative cases      208 212 222 268
Principles of in variance, mathematical formulation of      90 et seq. 162
Principles of in variance, role of K-integral in      208 212 219 224 269
Principles of invariance      90 162—166
Problem with a constant net $\Phi$       351 352
Problem with a constant net flux      14
Problem with a constant net flux for $1+\varpi_{1}P_{1}(cos\theta)+\varpi_{2}P_{2}(cos\theta)$       159
Problem with a constant net flux for an electron scattering atmosphere      234 et seq.
Problem with a constant net flux for general phase function      156
Problem with a constant net flux for isotropic scattering      15 70 97 127
Problem with a constant net flux for Rayleigh scattering      234 et seq.
Problem with a constant net flux for Rayleigh’s phase function      17
Problem with a constant net flux for Thomson scattering      43 234
Problems with spherical symmetry      23 364 371
Quadrature formula      54 et seq. 56 68
Quadrature formula for mean intensities and fluxes      57 65
Quadrature formula, based on Laguerre polynomials      57 64
Quadrature formula, construction of      57 et seq.
Quadrature formula, Gauss’s      56 61
Quadrature formula, Radau’s      63
Quadrature formula, Reiz’s      66 et seq. 315
Radial optical thickness      307
Radiation field in finite atmosphere      161 et seq.
Radiation field in semi-infinite atmosphere      165 166
Radiation field in spherical atmosphere      370
Radiation field in stellar atmosphere      295
Radiation field, axially symmetric      2
Radiation field, diffuse      22
Radiation field, division into streams      55
Radiation field, homogeneous      1
Radiation field, isotropic      1
Radiation field, reduced      22 162
Radiation field, spherical symmetric      2
Radiation, density of      3
Radiation, integrated energy density      4
Radiative equilibrium      290
Radiative equilibrium of a grey atmosphere      293 et seq.
Radiative equilibrium of a slightly non-grey atmosphere      296 et seq.
Radiative equilibrium of a stellar atmosphere      288 et seq. 315
Radiative equilibrium, condition of      290
Rayleigh scattering      35 et seq. 233
Rayleigh scattering as a basis for illumination of sky radiation      44 233 280
Rayleigh scattering, phase matrix for      37 42 250
Rayleigh’s phase function      6
Rayleigh’s phase function, diffuse reflection and transmission in accordance with      219 et seq.
Rayleigh’s phase function, diffuse reflection in accordance with      101 et seq. 128
Rayleigh’s phase function, error in the concept of      264 286
Rayleigh’s phase function, problem with a constant net flux      17 133
Rayleigh’s phase matrix      37 42
Rayleigh’s phase matrix, an integral property of      251
Rayleigh’s phase matrix, explicit form of      42 250
Rayleigh’s phase matrix, reducibility of      249
Reciprocity, principle of      see “Principle of reciprocity”
Recursion formulae for $D^{m}_{l,\lambda}$       152
Recursion formulae for $D_{m}$       73 236
Recursion formulae for $\gamma^{m}_{l}$       155
Recursion formulae for $\xi^{m}_{l}$       153 156
Reduced incident radiation      22 162
Reduction of integral equations      99 101 130 137 177 221 227 256 265
Reflection effect      88
Residual intensity      320 327 328
Reversing layers      318 321
Scattering      5
Scattering and transmission functions for $\varpi_{0}(1+xcos\theta)$       227 et seq.
Scattering and transmission functions for isotropic scattering      181 201 209 213
Scattering and transmission functions for planetary problem      273 et seq.
Scattering and transmission functions for Rayleigh’s phase function      220 et seq.
Scattering and transmission functions, ambiguity in      208 212 224 268
Scattering and transmission functions, expansion of, in Fourier series      177
Scattering and transmission functions, expression in terms of X- and Y-functions      209 226 230
Scattering and transmission functions, expression of, in functions of one variable      180
Scattering and transmission functions, integral equations for      169 et seq. 178
Scattering and transmission functions, resolution of ambiguity in      214 224 268
Scattering and transmission functions, symmetry of      172
Scattering and transmission matrices for planetary problem      279 280
Scattering and transmission matrices, expression in terms of X- and F-functions      267 268
Scattering and transmission matrices, form of, for Rayleigh scattering      252 et seq. 265
Scattering and transmission matrices, integral equations for      170 265
Scattering and transmission matrices, reducibility with respect to ellipticity of      249
Scattering and transmission matrices, symmetry of      173
Scattering atmosphere      7 (see also “K-integral”)
Scattering atmosphere, definition of      7
Scattering atmosphere, source function for      8
Scattering atmosphere, the K-integral for      13
Scattering by anisotropic particles      45 282
Scattering by free electrons      36 43 249 328 334
Scattering function      20 161
Scattering function for $\varpi_{0}(1+xcos\theta)$       99 135 138 140
Scattering function for diffuse reflection of natural light and Rayleigh scattering      261
Scattering function for isotropic scattering      85 140
Scattering function for Rayleigh’s phase function      101 128 132 143
Scattering function, expression of, in terms of H-functions      85 86 124 132 138 140 143 158
Scattering function, integral equation for      92 et seq.
Scattering function, symmetry of      95 176
Scattering matrix      44 103
Scattering matrix for Rayleigh scattering      260 261
Scattering matrix, form of, for Rayleigh scattering      252 et seq.
Scattering matrix, integral equation for      103 255
Scattering matrix, symmetry of      173 176
Scattering, coefficient      5
Scattering, conservative      6
Scattering, plane of      24
Scattering, primary      145 202 216 263
Scattering, Rayleigh      35 et seq.
Scattering, resonance line      50 et seq. 282
Scattering, theory of light      53
Scattering, Thomson      35 36
Schuster — Schwarzschild method of approximation      55 330 339 363 366
Schuster’s problem      318 342 354
Schuster’s problem, solution of, in terms of X- and Y-functions      320
Schwarzschild — Milne integral equation      17 52 93 344
Schwarzschild — Milne integral equation, generalized      347
Schwarzschild — Milne integral equation, relation to H-functions      346 et seq.
Schwarzschild — Milne integral equation, special solution of      19 350
Schwarzsehild — Milne integral equation      17
Semi-infinite atmosphere      12 14 159
Semi-infinite atmosphere, axially symmetric problems in non-conservative cases      18 20 344 383
Semi-infinite atmosphere, principles of invariance for      89 et seq.
Semi-infinite atmosphere, role of H-functions in      105
Semi-infinite atmosphere, under conditions of radiative equilibrium      291
Sky, illumination and polarization of      280 et seq. 286
Sky, illumination and polarization of, basic problem in      44 270
Sky, illumination and polarization of, neutral points in      281 et seq.
Source function      8
Source function for a scattering atmosphere      8 10
Source function for an electron scattering atmosphere      240
Source function for broadening of lines by electron scattering      337
Source function for diffuse reflection and transmission      93 167
Source function for isotropic scattering      75
Source function for local thermodynamic equilibrium      8 288
Source function for Rayleigh scattering      38 40
Source function for softening of radiation by Compton scattering      329
Source function for “pseudo-problem”      351
Source function, definition of      8
Source function, integral equation for      10
Specific intensity      1
Spherical atmosphere      23 371
Spherical atmosphere, a problem of radiative transfer in      364 et seq.
Spherical atmosphere, solution in first approximation      366
Spherical atmosphere, solution in second approximation      367 et seq.
Spherical harmonies      see “Legendre polynomials”
Spherically symmetric problems      23 304 371
Standard problem      22 45
Standard problem in diffuse reflection and transmission      22 233 269 273
Standard problem in diffuse reflection and transmission, reduction of planetary problem to      269 et seq.
Standard solution      191

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