Blue sky and hot piles: The evolution of radiative transfer theory from atmospheres to nuclear reactors. (English) Zbl 1013.01008
The article gives a brief history of the theories of radiation transfer through matter. Beginning with questions about the extinction of sunlight in the atmosphere, the theory developed during the past 100 years into a rich field of mathematical physics. Instances for the application of mathematical tools to radiation transfer phenomena include the transfer equations for a scattering medium, moment methods, integral equations, the principle of invariance, neutron transport theory, and probabilistic treatments. The paper ends with a chapter on military applications of transfer theory and a survey on important publications.
Reviewer: A.Kleinert (Halle)
MSC:
| 01A60 | History of mathematics in the 20th century |
| 85-03 | History of astronomy and astrophysics |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
| 85A25 | Radiative transfer in astronomy and astrophysics |
| 82D75 | Nuclear reactor theory; neutron transport |
Keywords:
radiation transfer; astrophysics; neutrons; stellar atmospheres; radiation hydrodynamics; brief history; transfer equations; scattering medium; moment methods; integral equations; principle of invariance; neutron transport theory; probabilistic treatments; military applications; survey on important publicationsReferences:
| [1] | Ambartsumian, V., Diffuse reflection of light by a foggy medium, C.R. Acad. Sci. USSR, 38, 257-261 (1943) |
| [2] | Ambartsumian, V., On the problem of the diffuse reflection of light, J. Phys., 8, 65-75 (1944) · Zbl 0060.43604 |
| [3] | Ambartsumian, V., Theoretical astrophysics (1957), Pergamon: Pergamon Oxford |
| [4] | Ambartsumian, R. V., A life in astrophysics: Selected papers of Viktor A. Ambartsumian (1998), Allerton: Allerton New York |
| [5] | Arley, N., Stochastic processes and cosmic radiation (1943), Wiley: Wiley New York · Zbl 0060.29204 |
| [6] | Bauer, W. F., The Monte Carlo method, J. SIAM, 6, 438-451 (1958) · Zbl 0084.34601 |
| [7] | Bellman, R.; Birkhoff, G.; Abu-Shumays, I., Transport theory (1967), Amer. Math. Soc: Amer. Math. Soc Providence · Zbl 0181.22903 |
| [8] | Bellman, R.; Kalaba, R., On the principle of invariant imbedding and propagation in inhomogeneous media, Proc. Natl. Acad. Sci., 42, 629-632 (1956) · Zbl 0071.41605 |
| [9] | Bellman, R.; Kalaba, R.; Prestrud, M., Invariant imbedding and radiative transfer in slabs of finite thickness (1963), Elsevier: Elsevier New York · Zbl 0114.22602 |
| [10] | Bellman, R.; Kalaba, R.; Wing, G. M., On the principle of invariant imbedding and one-dimensional neutron multiplication, Proc. Natl. Acad. Sci., 43, 517-520 (1957) · Zbl 0078.21803 |
| [11] | Bellman, R.; Kalaba, R.; Wing, G., Invariant imbedding and mathematical physics. I. Particle processes, J. Math. Phys., 1, 120-308 (1958) · Zbl 0105.23202 |
| [12] | Bellman, R.; Kalaba, R.; Wing, G. M., Invariant imbedding, conservation relations, and nonlinear equations with two-point boundary values, Proc. Natl. Acad. Sci., 46, 1258-1260 (1960) · Zbl 0105.23204 |
| [13] | Bellman, R.; Wing, G. M., Introduction to invariant imbedding (1975), Wiley: Wiley New York · Zbl 0325.34001 |
| [14] | Berger, M. J., Methods Comput. Phys., 1, 135 (1963) |
| [15] | Birkhoff, G.; Wigner, E., Proc. 11th AMS Symposium on Applied Mathematics: Nuclear reactor theory (1961), Amer. Math. Soc: Amer. Math. Soc Providence |
| [16] | Boissé, P., Radiative transfer in clumpy media—The penetration of UV photons inside molecular clouds, Astron. Astrophys., 228, 483 (1990) |
| [17] | Browder, F.; Spanier, E. H.; Gerstenhaber, M., Bull. Amer. Math. Soc., 72, 1 (1966) |
| [18] | Busbridge, I. W., The mathematics of radiative transfer (1960), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0090.21405 |
| [19] | Cannon, C. J., The transfer of spectral line radiation (1985), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0573.76002 |
| [20] | Case, K. W.; Zweifel, F., Linear transport theory (1967), Addison-Wesley: Addison-Wesley Reading · Zbl 0162.58903 |
| [21] | Chandrasekhar, S., Astrophys. J., 100, 76-86 (1944) |
| [22] | Chandrasekhar, S., Astrophys. J., 105, 164-203 (1947) |
| [23] | Chandrasekhar, S., Astrophys. J., 105, 441-460 (1947) |
| [24] | Chandrasekhar, S., Astrophys. J., 107, 48-72 (1947) |
| [25] | Chandrasekhar, S., Bull. Amer. Math. Soc., 53, 641 (1947) · Zbl 0031.23603 |
| [26] | Chandrasekhar, S., Radiative transfer (1950), Oxford Univ. Press: Oxford Univ. Press London · Zbl 0037.43201 |
| [27] | Chandrasekhar, S.\(1989ab\); Chandrasekhar, S.\(1989ab\) |
| [28] | Chandrasekhar, S., Selected papers. Vol. 2. Radiative transfer and negative ion of hydrogen (1989), Univ. of Chicago Press: Univ. of Chicago Press Chicago · Zbl 0749.01014 |
| [29] | Davison, B.; Sykes, J. B., Neutron transport theory (1957), Oxford Univ. Press: Oxford Univ. Press Oxford · Zbl 0077.22505 |
| [30] | Douglas, A. V., The life of Arthur Stanley Eddington (1957), Thomas Nelson: Thomas Nelson New York · Zbl 0070.24406 |
| [31] | Eddington, A. S., The internal constitution of the stars (1926), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · JFM 52.1021.05 |
| [32] | Feautrier, P. 1964, Comptes Rendus; Feautrier, P. 1964, Comptes Rendus |
| [33] | Galison, P., How experiments end (1989), Univ. of Chicago Press: Univ. of Chicago Press Chicago |
| [34] | Galison, P.1996. Computer simulations and the trading zone. In The disunity of science: Boundaries, contexts, and power, P. Galison and D. J. Stump, Eds., pp. 118-157. Berkeley, CA, Univ. of California Press.; Galison, P.1996. Computer simulations and the trading zone. In The disunity of science: Boundaries, contexts, and power, P. Galison and D. J. Stump, Eds., pp. 118-157. Berkeley, CA, Univ. of California Press. |
| [35] | Galison, P., Image and logic: A material culture of microphysics (1997), Univ. of Chicago Press: Univ. of Chicago Press Chicago |
| [36] | Goody, R. M.; Yung, Y. L., Atmospheric radiation: Theoretical basis (1989), Oxford Univ. Press: Oxford Univ. Press Oxford |
| [37] | Greenler, R., Rainbow, halos, and glories (1983), Cambridge Univ. Press: Cambridge Univ. Press Cambridge |
| [38] | Hammersley, J. M.; Handscomb, D. C., Monte Carlo methods (1965), Methuen: Methuen London · Zbl 0121.35503 |
| [39] | Hansen, J. E.; Travis, L. D., Light scattering in planetary atmospheres, Space Sci. Rev., 16, 527-610 (1975) |
| [40] | Hopf, E., Mathematical problems of radiative equilibrium (1934), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · JFM 60.0809.01 |
| [41] | Hunt, G. E.; Grant, I. P., Discrete space theory of radiative transfer and its application to problems of planetary atmospheres, J. Atmos. Sci., 26, 963-972 (1969) |
| [42] | Irvine, W. M., The distribution of photon optical paths in a scattering atmosphere, Astrophys. J., 144, 1140-1147 (1966) |
| [43] | Jeans, J. H., Stars, gaseous, radiative transfer of energy, Mon. Not. R. Astron. Soc., 78, 28-36 (1917) |
| [44] | Jeans, J. H., Astronomy and cosmogony (1928), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · JFM 53.0911.06 |
| [45] | Kattawar, G. W., Selected papers on multiple scattering in plane parallel atmospheres and oceans: Methods (1991), SPIE Milestone Series MS42: SPIE Milestone Series MS42 Bellingham |
| [46] | Knowles, Middleton W. E., Random reflections on the history of atmospheric optics, J. Opt. Soc. Amer., 50, 97-100 (1960) |
| [47] | Knowles, Middleton W. E., Pierre Bourguer’s optical treatise on the gradation of light (1961), Univ. of Toronto Press: Univ. of Toronto Press Toronto |
| [48] | Kourganoff, V.; Busbridge, I. W., Basic methods in transfer problems (1952), Dover: Dover New York · Zbl 0048.20105 |
| [49] | Lathrop, K. D., Discrete-ordinates methods for the numerical solution of the transport equation, Reactor Technol., 15, 107-135 (1972) |
| [50] | Mark, C., Neutron density near a plane surface, Phys. Rev., 72, 558-564 (1947) · Zbl 0029.33502 |
| [51] | Marshak, R., Note on the spherical harmonic method as applied to the Milne problem for a sphere, Phys. Rev., 71, 443-446 (1947) · Zbl 0032.37504 |
| [52] | Masani, P., Wiener’s contributions to generalized harmonic analysis, prediction theory, and filter theory, Bull. Amer. Math. Soc., 72, 73-125 (1966) · Zbl 0144.19402 |
| [53] | Meadows, A. J., Early solar physics. (1970) |
| [54] | Menzel, D. H., Selected papers on radiative transfer (1966), Dover: Dover New York |
| [55] | Meyer, H. A., Symposium on Monte Carlo methods (1956), Wiley: Wiley New York · Zbl 0070.13402 |
| [56] | Mihalas, D.1970. Stellar atmospheres; Mihalas, D.1970. Stellar atmospheres |
| [57] | Mihalas, D.; Mihalas, B., Foundations of radiation hydrodyamics (1984), Oxford Univ. Press: Oxford Univ. Press Oxford · Zbl 0651.76005 |
| [58] | Milne, E., Thermodynamics of the stars, Handbuch Astrophys., 3, 63-255 (1930) · JFM 56.0790.02 |
| [59] | Minnaert, M., The reciprocity principle in lunar photometry, Astrophys. J., 93, 403-410 (1941) |
| [60] | Mnatsakanian, M. A.; Pickichian, H. V., Principle of invariance and its applications (1989), Byutakan Astophysical Observatory: Academy of Sciences: Byutakan Astophysical Observatory: Academy of Sciences Armenia |
| [61] | Noble, B., Methods based on the Wiener-Hopf technique for the solution of partial differential equations (1958), Pergamon: Pergamon New York · Zbl 0082.32101 |
| [62] | Oxenius, J., Kinetic theory of particles and photons (1986), Springer-Verlag: Springer-Verlag Berlin |
| [63] | Peraiah, A., Principles of invariance in radiative transfer, Space Sci. Rev., 87, 465-538 (1999) |
| [64] | Placzek, G.; Seidel, W., Miline’s problem in transport theory, Phys. Rev., 72, 550-555 (1947) · Zbl 0029.33404 |
| [65] | RAND Corp, 1956, A million random digits with 100,000 normal deviates; RAND Corp, 1956, A million random digits with 100,000 normal deviates |
| [66] | Rayleigh, On the light from the sky, its polarization and colour, Scientific papers., 1:87-103 (1871) |
| [67] | Rayleigh, On the reflection of light from a regularly stratified medium, Proc. R. Soc., 93, 565-577 (1917) |
| [68] | Redheffer, R. W., On the relation of transmission-line theory to scattering and transfer, J. Math. and Phys., 41, 1-41 (1962) · Zbl 0104.43605 |
| [69] | Richtmeyer, R. D., Monte Carlo methods, Reactor Theory, Proc. AMS Symp. Appl. Math., 11, 190-205 (1961) |
| [70] | Ralston, A.; Wilf, H. S., Mathematical methods for digital computers (1960), Wiley: Wiley New York · Zbl 0183.18601 |
| [71] | Reid, C., Courant in Göttingen and New York (1976), Springer-Verlag: Springer-Verlag New York · Zbl 0353.01010 |
| [72] | Rosseland, S., Theoretical astrophysics (1936), Oxford Univ. Press: Oxford Univ. Press Oxford · Zbl 0014.23403 |
| [73] | Schuster, A., Radiation through a foggy atmosphere, Astrophys. J., 21, 1-22 (1905) |
| [74] | Schwarzschild, K.1906. Nachr. K. Gesell. Wiss. Math.-Phys. Klasse195, 41; reprinted and translated in Menzel 1966, pp. 25-34.; Schwarzschild, K.1906. Nachr. K. Gesell. Wiss. Math.-Phys. Klasse195, 41; reprinted and translated in Menzel 1966, pp. 25-34. |
| [75] | Schwarzschild, K.1914. Sitz. Preuss. K. Akad. Wiss., 1183; reprinted and translated in Menzel 1966, pp.35-51.; Schwarzschild, K.1914. Sitz. Preuss. K. Akad. Wiss., 1183; reprinted and translated in Menzel 1966, pp.35-51. |
| [76] | Sobolev, V. V., Treatise on radiative transfer (1963), Van Nostrand: Van Nostrand Princeton |
| [77] | Sobolev, V. V., Light scattering in planetary atmospheres (1975), Pergamon: Pergamon Oxford |
| [78] | Spanier, J.; Gelbard, E. M., Monte Carlo principles and neutron transport problems (1969), Addison-Wesley: Addison-Wesley Reading · Zbl 0244.62004 |
| [79] | Stokes, G. G., On the intensity of light reflected from or transmitted through a pole of plates, Philos. Trans. R. Soc. London, 11, 545-556 (1860-1862) |
| [80] | Tessendorf, J., Radiative transfer as a sum over paths, Phys. Rev. A, 35, 872-878 (1987) |
| [81] | Titchmarsh, E. C., Theory of Fourier integrals (1937), Oxford Univ. Press: Oxford Univ. Press Oxford · Zbl 0017.40404 |
| [82] | Titov, G. A., Statistical description of radiation transfer in clouds, J. Atmos. Sci., 47, 24-38 (1990) |
| [83] | Ueno, S., The probabilistic methods for problems of radiative transfer. X. Diffuse reflection and transmission in finite inhomogeneous atmosphere, Astrophys. J., 132, 729-745 (1960) · Zbl 0103.23102 |
| [84] | Ueno, S.; Kalaba, R.; Kagiwaja, H. H.; Bellman, R., Some mathematical aspects of multiple scattering in a finite inhomogeneous slab with anisotropic scattering, Pub. Astron. Soc. Japan, 22, 75-83 (1970) |
| [85] | Unsöld, A., Phystk der Sternatmosphären (1955), Springer-Verlag: Springer-Verlag Berlin · Zbl 0067.45804 |
| [86] | van de Hulst, H. C., Scattering in a planetary atmosphere, Astrophys. J., 107, 220-246 (1948) |
| [87] | van de Hulst, H. C., A new look at multiple scattering (1963), NASA Institute for Space Studies: NASA Institute for Space Studies New York |
| [88] | van de Hulst, H. C., Multiple light scattering (1980), Academic Press: Academic Press New York |
| [89] | van de Hulst, H. C., Scaling laws in multiple light scattering under very small angles, Rev. Mex. Astron. Astrofis., 9, 1-16 (1996) |
| [90] | Wali, K. C., Chandra: A biography of S. Chandrasekhar (1991), Univ. of Chicago Press: Univ. of Chicago Press Chicago · Zbl 0755.01045 |
| [91] | Wiener, N., I am a mathematician (1956), MIT Press: MIT Press Cambridge · Zbl 0071.00415 |
| [92] | Wiener, N., and Hopf, E.1931. Übereine Klasse singulärer Integralgleichungen.Sitzber. Preuss. Akad. Wiss. Berlin, Kl. Math. Phys. Tech., 696-706, reprinted in The Selected Papers of Norbert Wiener; Wiener, N., and Hopf, E.1931. Übereine Klasse singulärer Integralgleichungen.Sitzber. Preuss. Akad. Wiss. Berlin, Kl. Math. Phys. Tech., 696-706, reprinted in The Selected Papers of Norbert Wiener · JFM 57.0463.01 |
| [93] | Woolley, R.v.d. R.; Stibbs, D. W.N., The outer layers of stars (1953), Oxford Univ. Press: Oxford Univ. Press Oxford · Zbl 0053.19002 |
| [94] | Young, A. T.1982. Rayleigh scattering. Phys. TodayJan., 2-8.; Young, A. T.1982. Rayleigh scattering. Phys. TodayJan., 2-8. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
