Mathematical modelling of composite objects. Part II (Q2709276)

Part 1/ 1994 has been reviewed (see Zbl 0919.00031). NEWLINENEWLINENEWLINEContents: V. R. Khachaturov, K. K. Abgaryan, A. V. Bakaev, R. V. Galiulin and V. I. Kabanovich, Enumeration of all possible crystalline structures for a given chemical formula and symmetry illustrated by perovskite case (6-22); A. V. Bakaev and V. I. Kabanovich, Calculation of optical properties of solid matter in the tight-binding approximation (23-32); A. V. Vlasov, A module for calculation of all crystallographical structures having the given chemical formula (33-41); R. V. Galiulin, Delone systems in Riemann space as discrete mathematical models of solid matter (42-102); S. N. Bobrov and V. R. Khachaturov, Determination of chemical composition and conditions of thermic processing to obtain steel with preassigned properties (103-122). The present collection of papers is devoted to the development of the original approximation-combinatorial method of composition and decomposition of solid systems. The concrete algorithms and programs to solve this problem are considered and the possibility to realize this approach is illustrated by considering some concrete substances. The collection is divided into five papers. In the first paper (V. R. Khachaturov et al.) the authors carry out an estimation of stability for all crystalline structures compatible with a given chemical formula and symmetry, based on the case of perovskite. In the result, the metrical parameters of stable structures are calculated. The second paper (A. V. Bakaev and V. I. Kabanovich) presents a numerical algorithm for definition of optical properties of the rock-salt structure in the tight-binding approximation. In the third paper (A. V. Vlasov) the programmed module to calculate all crystalline structures having the given chemical formula is described. The output of results is fulfilled in hierarchical form, allowing one to obtain the most interesting intermediate results as well as some statistics. The central article of this collection, the paper of R. V. Galiulin, is devoted to a discussion of mathematical models for discrete states of the matter on the base of point systems, which were introduced into consideration by Delone. The presented system of definitions, axioms and proofs allows one to discuss a broad set of crystallographical properties in the Euclidean, Lobachevskian and spherical spaces, by using the geometrical approaches and the Fedorov and Bravais groups. This consideration makes it possible to describe the recently discovered states of matter as quasi-crystals and fullerene being ideal crystals in corresponding non-Euclidean spaces. Regrettably, the tables in the paper have no numbering or titles, which impedes reading this article. The final paper (S. N. Bobrov and V. R. Khachaturov) presents the review of principles to optimize and select the compositions and technological parameters for steels. The process of search for steel with pre-determined properties is modelled. The method developed allows one to reduce the region of search and to narrow the range of parameters, which can contain the required steels.