Development of a method for the exact solution of systems of Wiener-Hopf integral equations for modeling of self-organization and self-assembly of nanoparticles of complex rheology

Authors

UDC

539.3

DOI:

https://doi.org/10.31429/vestnik-20-3-24-29

Abstract

The paper describes a method for the exact solution of a system of Wiener–Hopf integral equations arising during the construction of nano-particles from materials of complex rheologies. It is assumed that the contact problem for a nanoparticle is formulated at the boundary of a multilayer multicomponent material. It is assumed that nano particles have carriers in areas of non-classical shape, for example, in the simplest case, band-shaped. By the Fourier transform along the coordinate directed along the axis of the strip, the problem becomes one-dimensional and its exact solution can be constructed using the solution of the Wiener-Hopf equation. In the case of materials of complex rheologies, the solution becomes multicomponent and a system of Wiener–Hopf integral equations is obtained. In the same way, solutions can be built in other non-classical areas. In the contact area, there can be any conditions of a mechanical, physical or chemical nature that lead the boundary problem to a system of arbitrary finite number of Wiener–Hopf integral equations with a meromorphic matrix in the core. A new universal modeling method developed earlier by the authors has been applied. It allows you to represent the solutions of vector boundary value problems in the form of decomposition by solutions of scalar boundary value problems. Together with the factorization approach, this made it possible for the first time to construct an exact solution of such a system of integral equations. The article provides a summary of the method.

Keywords:

nanoparticles, self-organization, self-assembly, system of Wiener-Hopf integral equations, boundary value problems

Acknowledgement

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

Author Infos

Vladimir A. Babeshko

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

e-mail: babeshko41@mail.ru

Olga V. Evdokimova

д-р физ.-мат. наук, главный научный сотрудник научно-исследовательской части Кубанского государственного университета

e-mail: evdokimova.olga@mail.ru

Olga M. Babeshko

д-р физ.-мат. наук, главный научный сотрудник научно-исследовательского центра прогнозирования и предупреждения геоэкологических и техногенных катастроф Кубанского государственного университета

e-mail: babeshko49@mail.ru

Dmitry A. Khripkov

научный сотрудник Кубанского государственного университета

e-mail: vestnik@fpm.kubsu.ru

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Issue

2023. Vol. 20. No. 3

Section

Mechanics

Pages

24-29

Submitted

2023-08-16

Published

2023-09-29

How to Cite

Babeshko V.A., Evdokimova O.V., Babeshko O.M., Khripkov D.A. Development of a method for the exact solution of systems of Wiener-Hopf integral equations for modeling of self-organization and self-assembly of nanoparticles of complex rheology. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2023, vol. 20, no. 3, pp. 24-29. DOI: https://doi.org/10.31429/vestnik-20-3-24-29 (In Russian)

Copyright (c) 2023 Babeshko V.A., Evdokimova O.V., Babeshko O.M., Khripkov D.A.

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