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J. Sib. Fed. Univ. Math. Phys., 2016, Volume 9, Issue 4, Pages 432–442 (Mi jsfu502)  

Mathematical modeling of the impact produced by magnetic disks on living cells

Valery V. Denisenkoab, Vladimir M. Sadovskiiab, Sergey S. Zamayc

a Institute of Computational Modeling SB RAS, Akademgorodok, 50/44, Krasnoyarsk, 660036
b Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia
c Krasnoyarsk Scientific Center SB RAS, Akademgorodok, 50, Krasnoyarsk, 660036, Russia

Abstract: An analytical solution of the problem on elastic deformation of a membrane allows analyzing deformation of typical living cells under the influence of magnetic disks attached to the cells. Based on the numerical solution of two-dimensional elliptic boundary value problems, the magnetic polarizabilities of the disks are obtained as the functions of magnetic permeability of the disk substance. It is shown that typical thin disks made of iron, nickel and cobalt in the mode far from saturation are magnetized substantially the same as a disk with infinite magnetic permeability. Though the solved problems are stationary, the results are also usable in the analysis of quasi-stationary processes such as low-frequency variation of external magnetic field.

Keywords: elliptic boundary value problem, magnetic polarizability, elastic membrane, living cell.

Funding Agency Grant Number
Russian Science Foundation 14-15-00805
This study has been supported by the Russian Science Foundation (project 14-15-00805).


DOI: https://doi.org/10.17516/1997-1397-2016-9-4-432-442

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UDC: 517.95+537.63+57.04
Received: 23.05.2016
Received in revised form: 25.06.2016
Accepted: 17.07.2016
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Citation: Valery V. Denisenko, Vladimir M. Sadovskii, Sergey S. Zamay, “Mathematical modeling of the impact produced by magnetic disks on living cells”, J. Sib. Fed. Univ. Math. Phys., 9:4 (2016), 432–442

Citation in format AMSBIB
\Bibitem{DenSadZam16}
\by Valery~V.~Denisenko, Vladimir~M.~Sadovskii, Sergey~S.~Zamay
\paper Mathematical modeling of the impact produced by magnetic disks on living cells
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2016
\vol 9
\issue 4
\pages 432--442
\mathnet{http://mi.mathnet.ru/jsfu502}
\crossref{https://doi.org/10.17516/1997-1397-2016-9-4-432-442}
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