Method of investigation of nanoparticles for materials of complex rheologies

Authors

  • Zaretskaya M.V. Kuban State University, Krasnodar, Российская Федерация ORCID 0000-0001-9916-1768
  • Babeshko V.A. Kuban State University, Krasnodar, Российская Федерация ORCID 0000-0002-6663-6357
  • Telyatnikov I.S. Kuban State University, Krasnodar, Российская Федерация ORCID 0000-0001-8500-2133
  • Snetkov D.A. Kuban State University, Krasnodar, Российская Федерация

UDC

539.3

DOI:

https://doi.org/10.31429/vestnik-20-3-50-56

Abstract

In earlier works of the authors, the problem of modeling the self-organization and self-assembly of nanoparticles into fragments of nanomaterials was investigated.

It was assumed that nanoparticles are represented by a material described by the Helmholtz equation, for which the corresponding boundary value problem was solved. In the event that a nanoparticle has a carrier in the form of a strip, the problem of representing the solution of a vector boundary value problem is solved quite simply with the help of a set of solutions to scalar problems in the strip.

However, in the case of regions with a piecewise smooth boundary, this becomes less obvious. In this regard, the paper shows that such a decomposition is feasible for rectangular wedge-type regions. Using solutions in this domain, one can construct asymptotic and approximate solutions for such a nonclassical domain as a rectangle. The approach used in the work is, based on a new universal modeling method.

Keywords:

nanoparticles, boundary value problems, block element method, packed block elements, Lame equations, Helmholtz equations

Acknowledgement

This work was supported by the Russian Science Foundation (project no. 22-21-00128).

Author Infos

Marina V. Zaretskaya

д-р физ.-мат. наук, профессор кафедры математического моделирования Кубанского государственного университета

e-mail: zarmv@mail.ru

Vladimir A. Babeshko

академик РАН, д-р физ.-мат. наук, заведующий кафедрой математического моделирования Кубанского государственного университета

e-mail: babeshko41@mail.ru

Ilya S. Telyatnikov

канд. физ.-мат. наук, канд. физ.-мат. наук, старший научный сотрудник Южного научного центра РАН

e-mail: ilux_t@list.ru

Dmitry A. Snetkov

инженер Научно-исследовательской части Кубанского государственного университета

e-mail: dimons3s@yandex.ru

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Issue

2023. Vol. 20. No. 3

Section

Mechanics

Pages

50-56

Submitted

2023-08-16

Published

2023-09-29

How to Cite

Zaretskaya M.V., Babeshko V.A., Telyatnikov I.S., Snetkov D.A. Method of investigation of nanoparticles for materials of complex rheologies. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2023, vol. 20, no. 3, pp. 50-56. DOI: https://doi.org/10.31429/vestnik-20-3-50-56 (In Russian)

Copyright (c) 2023 Zaretskaya M.V., Babeshko V.A., Telyatnikov I.S., Snetkov D.A.

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