Classification of heterogeneous structures and condtions of their doubly periodicity

Authors

  • Станислав Трофимович Толмачев KrivoyRog National University XXII Partz’yizdu str., 11, KrivoyRog, Ukraine, 50027, Ukraine
  • Станислав Львович Бондаревский KrivoyRog National University XXII Partz’yizdu str., 11, KrivoyRog, Ukraine, 50027, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2013.18108

Keywords:

doubly periodic structure, classification, period parallelogram, condition of double periodicity

Abstract

Despite a rather active interest in the theoretical and practical aspects of heterogeneous environment and structures (HES) – semiconductors, mixtures, solutions, reinforced and composite materials, magnetic filters, etc. – the scientific literature has not yet paid sufficient attention to the issue of their classification. The paper partially makes up the deficiency suggesting, in particular, a possible classification of HES based on the difference between the geometric and physical parameters of the components, the scale of inclusions, etc. Special attention is paid to ordered (correct) HES with a doubly periodic structure, since they are components of many technological devices and materials. The paper emphasizes the difference between the concepts “doubly lattice periods” and “doubly HES”. Also, it illustrates the importance of identifying equivalent periods and gives their equality relation; presents necessary and sufficient conditions of forming the global doubly periodic lattice by compiling a limited set of primitive doubly periodic lattices, and demonstrates when these conditions may be used for the synthesis of complex doubly periodic HES by combining correct HES of a lower level.

Author Biographies

Станислав Трофимович Толмачев, KrivoyRog National University XXII Partz’yizdu str., 11, KrivoyRog, Ukraine, 50027

Doctor of technical sciences, prof., Head of Department of Electromechanics

Department of Electromechanics

Станислав Львович Бондаревский, KrivoyRog National University XXII Partz’yizdu str., 11, KrivoyRog, Ukraine, 50027

Senior lecturer

Department of Electromechanics

References

  1. Касаткин, А.Г. Основные процессы и аппараты химической технологии [Текст] / А.Г. Касаткин. – М.: Госхимиздат, 1961. – 831 с.
  2. Островский, Г.М. Прикладная механика неоднородных сред [Текст] / Г.М. Островский. – СПб.: Наука, 2000. – 359 с.
  3. Бекман, И.Н. Феноменологическая теория диффузии в гетерогенных средах и ее применение для описания процессов мембранного разделения [Текст] / И.Н. Бекман, И.П. Романовский // Успехи химии. – 1988. – Вып. 6. – С. 944–958.
  4. Высокочастотный нагрев диэлектриков и полупроводников [Текст] / А.В. Нетушил, Б.Я. Жуховицкий, В.Н. Кудин, Е.П. Парини. – М.: Госэнергоиз-дат, 1959. – 480 с.
  5. Емец, Ю. П. Электрические характеристики композиционных материалов с регулярной структурой [Текст] / Ю. П. Емец. – К.: Наукова думка, 1986. – 192 с.
  6. Толмачев, С.Т. Однородное поле, возмущенное периодической системой круговых цилиндров [Текст] / С.Т. Толмачев // Теоретическая электротехника: Респ. межвед. научн.-техн. сб. – 1977. – Вып. 23. – C. 97–106.
  7. Толмачев, С.Т. Однородное поле, возмущенное периодической системой эллиптических цилиндров [Текст] / С.Т. Толмачев // Теоретическая электротехника: Респ. межвед. научн.-техн. сб. – 1978. – Вып. 24. – С. 96–105.
  8. Толмачев, С. Т. Расчет потенциала в прямоугольной пространственной системе сферических элементов, помещенных во внешнее однородное поле [Текст] / С.Т. Толмачев // Электричество. – 1974. – № 10. – С. 30–33.
  9. Толмачев, С. Т. Потенциальное поле в периодической системе взаимодействующих сфероидов [Текст] / С. Т. Толмачев // Изв. АН СССР. Энергетика и транспорт. – 1975. – № 1. – С. 52–61.
  10. Емец, Ю.П. Эффективные параметры многокомпонентных диэлектриков с гексагональной структурой [Текст] / Ю.П. Емец // Журнал технической физики. – 2002. – Т. 72, вып. 1. – С. 51–59.
  11. Вайнштейн, Б.К. Современная кристаллография [Текст]. Т. 1. Симметрия кристаллов. Методы структурной кристаллографии / Б.К. Вайнштейн. – М.: Наука, 1979. – 384 с.
  12. Гурвиц А. Теория функций / А. Гурвиц, Р. Курант. – М.: Наука, 1968. – 648 с.
  13. Безымянный, Ю.Г. Методология акустического контроля многофазных гетерогенных материалов [Текст] / Ю.Г. Безымянный // Сборник трудов акустического симпозиума «КОНСОНАНС-2005». Киев, 27-29 сентября 2005 г. – Киев, 2005. – С. 50-55.
  14. Kasatkin, A.G. (1961). Basic processes and devices of chemical technologies. Moscow, USSR: Goskhimizdat, 831.
  15. Ostrovskii, G.M. (2000). Applied mechanics of heterogeneous media. St. Pe-tersburg, Russia: Science, 359.
  16. Beckman, I.N., Romanovskii, I.P. (1988). The phenomenological theory of diffusion of heterogeneous environments and its application to the description of membrane separation processes. RUSS CHEM Rev, 6, 944–958.
  17. Netushil, A.V., Zhukhovitskii, B.Ya., Kudin, V.N., Parini, Ye.P. (1959). Frequency heating of dielectrics and semiconductors, Moscow, USSR: Gosenergoizdat, 480
  18. Emets, Yu.P. (1986). Electrical characteristics of composite materials with a regular structure. Kiev, USSR: Naukova Dumka, 192.
  19. Tolmachev, S.T. (1977). Homogeneous field, the perturbed periodic system of circular cylinders. Theoretical Electrical Engineering, 23, 97–106.
  20. Tolmachev, S.T. (1978). Homogeneous field, the perturbed periodic system of elliptic cylinders. Theoretical Electrical Engineering, 24, 96–105.
  21. Tolmachev, S.T. (1974). The calculation of the potential in a rectangular system of spherical spatial elements in an external homogeneous field. Electrical Engineering, 10, 30–33.
  22. Tolmachev, S.T. (1975). The potential field in the periodic system of interacting spheroids. Izv. Academy of Sciences of the USSR. Energy and transport, 1, 52–61.
  23. Emets, Yu.P. (2002). The effective parameters of multicomponent dielectrics with a hexagonal structure. Journal of Technical Physics, 1, 51–59.
  24. Wainstein, B.K. (1979). Modern crystallography. V. 1. The symmetry of the crystals. Methods of structural crystallography. Moscow, USSR: Science, 384.
  25. Hurwitz, A., Courant, R. (1968). Function Theory. Moscow, USSR: Science, 648
  26. Bezymiannyi, Yu.G. (2005). Methodology of acoustic control of multiphase heterogeneous materials. Collection of works of Symposium acoustic "CON-SONANCE-2005", 50-55.

Downloads

Published

2013-10-24

How to Cite

Толмачев, С. Т., & Бондаревский, С. Л. (2013). Classification of heterogeneous structures and condtions of their doubly periodicity. Eastern-European Journal of Enterprise Technologies, 5(5(65), 24–29. https://doi.org/10.15587/1729-4061.2013.18108

Issue

Vol. 5 No. 5(65) (2013): Applied physics

Section

Applied physics

License

Copyright (c) 2014 Станислав Трофимович Толмачев, Станислав Львович Бондаревский

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.