Issues »  Volume 44, Issue 10

Formation of Ordered Structure from Vacancies at Two-Dimensional Rectangular Plate

E. E. Zasimchuk, V. I. Zasimchuk, O. S. Gatsenko

G. V. Kurdyumov Institute for Metal Physics, NAS of Ukraine, 36 Academician Vernadsky Blvd., UA-03142 Kyiv, Ukraine

Received: 08.05.2022; final version - 19.07.2022. Download: PDF

The conditions of vacancies’-concentration ordered-distribution formation inside the two-dimensional rectangular plate are considered. Corresponding equation for the stationary case is analysed. The interaction between vacancies is described by the function $S(x, y)$; in the work, evident expression for $S(x, y)$ is found. As shown, for the constant temperature on a surface plate, self-organization (ordered-distribution formation) can take place only inside the very little plate. It is possible the onset of complicated dependence of vacancies’ density on the co-ordinates within the big plate, if there is a functional dependence of temperature on the plate co-ordinates.

Key words: self-organization, vacancies, ordered solutions, boundary conditions, eigenvalues, eigenfunctions.

URL: https://mfint.imp.kiev.ua/en/abstract/v44/i10/1335.html

DOI: https://doi.org/10.15407/mfint.44.10.1335

PACS: 02.30.Jr, 05.65.+b, 61.72.Bb, 61.72.Cc, 61.72.jd

Citation: E. E. Zasimchuk, V. I. Zasimchuk, and O. S. Gatsenko, Formation of Ordered Structure from Vacancies at Two-Dimensional Rectangular Plate, Metallofiz. Noveishie Tekhnol., 44, No. 10: 1335—1346 (2022) (in Ukrainian)

REFERENCES
  1. G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems. From Dissipative Structures to Order Through Fluctuations (New York: Wiley: 1977).
  2. P. Glansdorff and I. Prigogine, Termodinamicheskaya Teoriya Struktury, Ustoychivosti i Fluktuatsiy [Thermodynamic Theory of Structure, Stability and Fluctuations] (Moscow: Mir: 1973) (in Russian).
  3. W. Ebeling, Strukturbildung Bei Irreversiblen Prozessen: Eine Einfu Ehrung in die Theorie Dissipativer Strukturen (Teubner: 1966), p. 194 (in German).
  4. Dzh. Matyuz and R. Uoker, Matematicheskie Metody Fiziki (Moscow: Atomizdat: 1972) (in Russian).
  5. O. V. Oliinyk and V. A. Tatarenko, Dopovidi Natsionalnoyi Akademii Nauk Ukrayiny, No. 3: 55 (2019) (in Ukrainian).
  6. E. Kamke, Spravochnik po Obyknovennym Differentsialnym Uravneniyam (Moscow: Nauka: 1976) (in Russian).
  7. G. Korn and T. Korn, Spravochnik po Matematike dlya Nauchnykh Rabotnikov i Inzhenerov (Moscow: Nauka: 1978) (in Russian).
  8. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integraly i Ryady (Moscow: Nauka: 1981) (in Russian).
  9. E. E. Zasimchuk, V. I. Zasimchuk, T. V. Turchak, O. S. Gatsenko, and O. I. Baskova, Metallofiz. Noveishie Tekhnol., 42, No. 2: 281 (2020) (in Russian). Crossref
  10. V. E. Panin, V. E. Yegorushkin, Yu. A. Hon, and T. F. Yelsukova, Izvestiya Vuzov. Fizika, 25, No. 12: 5 (1982) (in Russian).

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