Geodesic
Analytical integration of the radiative transfer equation with respect to the mean free path in a problem with barrier geometry and a point source
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 7, pp. 1248-1263 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a problem with a point source located in an infinite homogeneous plane-parallel barrier, the terms of a Neumann series describing the solution to the radiative transfer equation are analytically integrated in part with respect to all the mean free paths. 
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S. N. Shelud'ko. Analytical integration of the radiative transfer equation with respect to the mean free path in a problem with barrier geometry and a point source. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 7, pp. 1248-1263. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_7_a10/

[1] Metod Monte-Karlo v probleme perenosa izlucheniya, Atomizdat, M., 1987

[2] Ermakov S. M., Mikhailov G. A., Statisticheskoe modelirovanie, Nauka, M., 1982 | MR

[3] D. L. Broder (red.), Rukovodstvo po radiatsionnoi zaschite dlya inzhenerov, v. 1, Atomizdat, M., 1972

[4] Berger M. J., Dogget J., “Reflection and transmission of gamma radiation by barriers: semianalytic Monte-Karlo calculation”, J. Res. Nat. Bur. Standard., 56:2 (1956), 89–98 | MR | Zbl

[5] Androsenko P. A., Efimenko B. A., “Modifikatsiya metoda Monte-Karlo dlya rascheta polei izlucheniya za barerami bolshoi tolschiny”, Atomnaya energiya, 45:4 (1978), 290–291

[6] Androsenko P. A., Reshenie uravneniya perenosa PA metodom Monte-Karlo v zadachakh s barernoi geometriei, Preprint No 1169, FEI, Obninsk, 1981

[7] Sheludko S. N., “Analiticheskoe integrirovanie uravneniya perenosa po dline svobodnogo probega v zadache s barernoi geometriei i beskonechnym ploskim istochnikom”, Zh. vychisl. matem. i matem. fiz., 34:10 (1994), 1535–1541 | MR

[8] Sheludko S. N., “Analiticheskoe integrirovanie uravneniya perenosa po dline svobodnogo probega”, Vopr. atomnoi nauki i tekhn. Matem. modelirovanie fiz. protsessov, 1991, no. 2, 30–33

[9] Sheludko S. N., “Analiticheskoe integrirovanie uravneniya perenosa po dline svobodnogo probega dlya nestatsionarnogo sluchaya”, Vopr. at. nauki i tekhn. Matem. modelirovanie fiz. protsessov, 1994, no. 2, 22–26