Geodesic
Numerical experiments in radiative transfer theory taking Compton scattering into account
Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 2, pp. 135-143.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the applicability of an indicator of nonhomogeneities in the tomography problem of determining the internal structure of an inhomogeneous medium from the results of its x-ray irradiation in the case of strong Compton scattering. As a mathematical model, we use the radiative transfer equation with energy dependence. We give an algorithm for solving the transfer equation for this case by the Monte Carlo method. We present in graphic form some results of the solution of the transfer equation and the problem of the reconstruction of the internal structure of a medium for specific materials. We show that an indicator of nonhomogeneities can be efficiently used to solve the problem considered. 
@article{SJIM_2005_8_2_a12,
     author = {V. G. Nazarov and I. P. Yarovenko and N. V. Solnishko},
     title = {Numerical experiments in radiative transfer theory taking {Compton} scattering into account},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {135--143},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2005_8_2_a12/}
}
TY  - JOUR
AU  - V. G. Nazarov
AU  - I. P. Yarovenko
AU  - N. V. Solnishko
TI  - Numerical experiments in radiative transfer theory taking Compton scattering into account
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2005
SP  - 135
EP  - 143
VL  - 8
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2005_8_2_a12/
LA  - ru
ID  - SJIM_2005_8_2_a12
ER  - 
%0 Journal Article
%A V. G. Nazarov
%A I. P. Yarovenko
%A N. V. Solnishko
%T Numerical experiments in radiative transfer theory taking Compton scattering into account
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2005
%P 135-143
%V 8
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2005_8_2_a12/
%G ru
%F SJIM_2005_8_2_a12
V. G. Nazarov; I. P. Yarovenko; N. V. Solnishko. Numerical experiments in radiative transfer theory taking Compton scattering into account. Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 2, pp. 135-143. http://geodesic.mathdoc.fr/item/SJIM_2005_8_2_a12/

[1] Fano U., Spenser L., Berger M., Perenos gamma izlucheniya, Gosatomizdat, M., 1963

[2] Leipunskii O. I., Novozhilov B. V., Sakharov V. I., Rasprostranenie gamma-kvantov v veschestve, Fizmatgiz, M., 1960

[3] Anikonov D. S., Kovtanyuk A. E., Prokhorov I. V., Ispolzovanie uravneniya perenosa v tomografii, Logos, M., 2000

[4] Anikonov D. S., Konovalova D. S., “Kraevaya zadacha dlya uravneniya perenosa s chisto komptonovskim rasseyaniem”, Sib. mat. zhurn., 46:1 (2005), 3–16 | MR | Zbl

[5] Anikonov D. S., Nazarov V. G., Prokhorov I. V., “Vidimye i nevidimye sredy v tomografii”, Dokl. RAN, 357:5 (1997), 599–603 | MR | Zbl

[6] Mikhailov G. A., Vesovye metody Monte-Karlo, Novosibirsk, 2000 | MR

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

[8] Hubbell J. H., Seltzer S. M., 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

[9] Anikonov D. S., Nazarov V. G., Prokhorov I. V., Poorly Visible Media in $X$-ray Tomography, VSP, Utrecht, Boston, 2002

[10] http://physics.nist.gov/PhysRefData/Xcom