zbMATH — the first resource for mathematics

A boundary-value problem for the polarized-radiation transfer equation with Fresnel interface conditions for a layered medium. (English) Zbl 1213.65154
The authors study a boundary value problem for the polarized-radiation transfer equation with Fresnel interface conditions for a layered medium. They provide continuity properties for the solution and prove theorems of solvability for the boundary value problem. Numerical algorithm and examples are given based on Monte Carlo method.

65R20 Numerical methods for integral equations
45K05 Integro-partial differential equations
65C05 Monte Carlo methods
Full Text: DOI
[1] Marchuk, G.I.; Mikhaylov, G.A.; Nazaraliev, M.A.; Drobinyan, R.A.; Kargin, V.A.; Elepov, B.S., Monte Carlo method in atmospherical optics, (1976), Nauka Novosibirsk, (in Russian)
[2] T.A. Germogenova, N.V. Konovalova, M.G. Kuz’mina, Foundation of mathematical theory for polarized radiation transfer, rigorous results, in: Proc. All-Union Symp. on Invariance Principle and its Applications, Byurokan, 1981, Erevan: Academy Sci. of Armyansk. SSR, 1989, pp. 271-284 (in Russian).
[3] Mikhailov, G.A.; Ukhinov, S.A.; Chimaeva, A.S., Variance of standard vector estimate of Monte Carlo method in polarized radiation transfer theory, J. comput. math. math. phys., 46, 11, 2099-2113, (2006)
[4] Sushkevich, T.A., Mathematical models of radiation transfer, (2006), BINOM Laboratoriya Znanii Moscow · Zbl 1101.86305
[5] Latyshev, A.V., Vector boundary-value riemann – hilbert’s problem at the boundary problems of scattering polarized radiation, J. comput. math. math. phys., 35, 7, 1108-1127, (1995)
[6] Kovtanyuk, A.E.; Prokhorov, I.V., Tomography problem for the polarized-radiation transfer equation, J. inv. ill-pos. probl., 14, 6, 1-12, (2006) · Zbl 1109.44001
[7] Vladimirov, V.S., Mathematical problems in the single-velocity theory of particles transport, (), 3-158, (in Russian)
[8] Germogenova, T.A., Local properties of solution of the transfer equation, (1986), Nauka Moscow, (in Russian) · Zbl 0593.35004
[9] Anikonov, D.S.; Kovtanyuk, A.E.; Prokhorov, I.V., Transport equation and tomography, (2002), VSP Utrecht, Boston, pp. viii+208 · Zbl 0929.65143
[10] Rozenberg, G.V., Stoke’s vector-parameter, Uspekhi phys. nauk, 56, 1, 77-109, (1955), (in Russian)
[11] Ishimaru, A., Wave propagation and scattering in random media, vol. 1, (1978), Academic Press New York
[12] Apresyan, L.A.; Kravtsov, Yu.A., Radiation transfer theory, (1983), Nauka Moscow, (in Russian) · Zbl 0954.65096
[13] Potapov, V.S., Method of solution of the radiation transfer equation for an optically thick layer with reflecting boundaries, Theoret. and math. phys., 100, 2, 1012-1022, (1994) · Zbl 0853.45016
[14] Bal, G.; Moscoso, M., Theoretical and numerical analysis of polarization for time dependent radiative transfer equations, J. quant. spectrosc. radiat. transfer, 70, 1, 75-90, (2001)
[15] Bal, G.; Papanicolaou, G.; Ryzhik, L., Probabilistic theory of transport processes with polarization, SIAM J. appl. math., 60, 5, 1639-1666, (2000) · Zbl 0963.60081
[16] Bal, G., Radiative transfer equations with varying refractive index: a mathematical perspective, J. opt. soc. amer. A, 23, 7, 1639-1644, (2006)
[17] Bal, G.; Ryzhik, L., Diffusion approximation of radiative transfer problems with interfaces, SIAM J. appl. math., 60, 6, 1887-1912, (2000) · Zbl 0976.45008
[18] Prokhorov, I.V., On the solubility of the boundary-value problem of radiation transport theory with generalized conjugation conditions on the interfaces, Izvestia math., 67, 6, 1243-1266, (2003) · Zbl 1068.45019
[19] Prokhorov, I.V.; Yarovenko, I.P.; Krasnikova, T.V., An extremum problem for the radiation transfer equation, J. inv. ill-pos. probl., 13, 4, 365-382, (2005) · Zbl 1095.35075
[20] Born, M.; Wolf, E., Principles of optics, (1968), Pergamon Oxford
[21] Smith, O.J.; Siewert, C.E., The half-space green’s function for an atmosphere with a polarized radiation field, J. math. phys., 8, 12, 2467-2474, (1967)
[22] Chandrasekhar, S., Radiative transfer, (1960), Dover New York · Zbl 0037.43201
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.