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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 6, Pages 977–987
DOI: https://doi.org/10.7868/S0044466914060106 (Mi zvmmf10050) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Direct and inverse problems of studying the properties of multilayer nanostructures based on a two-dimensional model of $X$-ray reflection and scattering

R. V. Khachaturov

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
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DOI: https://doi.org/10.7868/S0044466914060106
Abstract: A mathematical model of $X$-ray reflection and scattering by multilayered nanostructures in the quasi-optical approximation is proposed. $X$-ray propagation and the electric field distribution inside the multilayered structure are considered with allowance for refraction, which is taken into account via the second derivative with respect to the depth of the structure. This model is used to demonstrate the possibility of solving inverse problems in order to determine the characteristics of irregularities not only over the depth (as in the one-dimensional problem) but also over the length of the structure. An approximate combinatorial method for system decomposition and composition is proposed for solving the inverse problems.
Key words: mathematical modeling, multilayered nanostructures, inverse problems, numerical methods, approximate combinatorial method.
Received: 15.05.2013
Revised: 09.12.2013
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 6, Pages 984–993
DOI: https://doi.org/10.1134/S0965542514060104
Bibliographic databases:
Document Type: Article
UDC: 519.634
MSC: 78A45
Language: Russian
Citation: R. V. Khachaturov, “Direct and inverse problems of studying the properties of multilayer nanostructures based on a two-dimensional model of $X$-ray reflection and scattering”, Zh. Vychisl. Mat. Mat. Fiz., 54:6 (2014), 977–987; Comput. Math. Math. Phys., 54:6 (2014), 984–993
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
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