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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2005, Volume 45, Number 8, Pages 1359–1373 (Mi zvmmf608)  
Construction of a unified model for crystal and nearly crystal structures

D. V. Kovalenko

Novgorod State University after Yaroslav the Wise
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Abstract: Mathematical models (point systems) of the atom arrangement in solids are considered. A new approach to the design of such models is proposed. It is based on the operation of differentiation introduced for point systems. The differentiation operation is used to obtain a general mathematical criterion for distinguishing between various types of crystal and nearly crystal structures. Several theorems are proved that specify the constraints on point systems that lead to such structures.
Key words: models of crystal structures, numerical grid generation, unstructured meshes.
Received: 11.11.2004
Bibliographic databases:
Document Type: Article
UDC: 519.677
Language: Russian
Citation: D. V. Kovalenko, “Construction of a unified model for crystal and nearly crystal structures”, Zh. Vychisl. Mat. Mat. Fiz., 45:8 (2005), 1359–1373; Comput. Math. Math. Phys., 45:8 (2005), 1311–1324
Citation in format AMSBIB
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\by D.~V.~Kovalenko
\paper Construction of a unified model for crystal and nearly crystal structures
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 8
\pages 1359--1373
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2191850}
\zmath{https://zbmath.org/?q=an:1117.82326}
\elib{https://elibrary.ru/item.asp?id=9142411}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 8
\pages 1311--1324
\elib{https://elibrary.ru/item.asp?id=13494609}
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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