Far Eastern Mathematical Journal

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About diffusion approximation for the radiation transfer equation with account of Ñompton scattering


I. P. Yarovenko

2009, issue 1-2, Ñ. 209–218


Abstract
This paper deals with diffusion approximation for the radiation transfer equation which takes into account Ñompton scattering on electrons. Considered approximation is degenerate parabolic equation. The choice of initial conditions is discussed.

Keywords:
radiation transfer theory, diffusion approximation, Ñompton scattering

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References

[1] O. I. Lejpunskij, B. V. Novozhilov, V. I. Saxarov, Rasprostranenie gamma-kvantov v veshhestve, GIFML, M., 1960.
[2] V. V. Smelov, Lekcii po teorii perenosa nejtronov, Atomizdat, M., 1976.
[3] A. Ishimaru, Wave Propagation and Scattering in Random Media, 1, Academic Press, New York, 1978.
[4] V. M. Podgaeckij, S. V. Selishhev, S. A. Tereshhenko, “Modeli rasprostraneniya izlucheniya dlya sistem medicinskoj lazernoj tomografii”, Medicinskaya texnika, 1999, ¹ 6, 3–11.
[5] V. V. Tuchin, “Issledovanie biotkanej metodami svetorasseyaniya”, Uspexi Fizicheskix nauk, 167:5 (1997), 517–539.
[6] S. R. Arridge, “Optical tomography in medical imaging”, Inverse Problems, 15:2 (1999), R41–R93.
[7] K. Ren, G. S. Abdoulaev, G. Bal, A. H. Hielscher, “Algorithm for solving the equation of radiative transfer in the frequency domain”, Optics Letters, 29:6 (2004), 578–580.
[8] K. Ren, G. Bal, A. Hielscher, “Frequency Domain Optical Tomography Based on the Equation of Radiative Transfer”, SIAM Journal on Scientific Computing, 28:4 (2006), 1463–1489.
[9] U. Fano, L. Spenser, M. Berger, Perenos gamma izlucheniya, Gosatomizdat, M., 1963.
[10] D. S. Anikonov, D. S. Konovalova, “Komptonovskij e'ffekt v teorii perenosa izlucheniya”, Doklady AN, 398:4 (2004), 462–465.
[11] D. S. Anikonov, D. S. Konovalova, “Kraevaya zadacha dlya uravneniya perenosa s chisto komptonovskim rasseyaniem”, Sibirskij matematicheskij zhurnal, 46:1 (2005), 3–16.
[12] V. G. Nazarov, N. V. Solnyshko, I. P. Yarovenko, “Chislennye e'ksperimenty v teorii perenosa izlucheniya s uchetom komptonovskogo rasseyaniya”, SibZhIM, 8:2 (2005), 135–143.
[13] S. M. Ermakov, G. A. Mixajlov, Statisticheskoe modelirovanie, Nauka, M., 1982.
[14] G. I. Marchuk, V. I. Lebedev, Chislennye metody po teorii perenosa nejtronov, Atomizdat, M., 1981.
[15] G. A. Mixajlov, Vesovye metody Monte-Karlo, Izd. SORAN, Novosibirsk, 2000.
[16] J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer and R. J. Howerton, “Atomic Form Factors, Incoherent Scattering Functions, and Photon Scattering Cross Sections”, J. Phys. Chem. Ref., 4 (1975), 471–538; 6 (1977), 615–616.
[17] D. S. Anikonov, V. G. Nazarov, and I. V. Prokhorov, Poorly Visible Media in X-Ray Tomography, VSP, Utrecht – Boston, 2002, viii+294 pp.
[18] J. H. Hubbell and S. M. Seltzer, Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients 1 Kev to 20 Mev for Elements Z = 1 to 92 and 48 Additional Substances of Dosimetric Interest, NISTIR 5632, 1995.
[19] R. E. Marshak, “Note on the spherical harmonic method as applied to the Milne problem for a sphere”, Phys. Rev., 71 (1947), 443–446.
[20] T. A. Germogenova, O. V. Nikolaeva, “Boundary condition for asymptotic approximations in two-region transport problem”, Proc. Mathematics and Computations, Reactor Physics and Environmental Analysis in Nuclear Applications, Madrid, 1999, 1977–1986.
[21] A. E. Kovtanyuk, E. V. Mal'ceva, “Vliyanie razlichnyx faktorov na tochnost' diffuzionnogo priblizheniya uravneniya perenosa v ploskoparallel'nom sluchae”, SibZhIM, 6:1 (2003), 40–50.

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