Geodesic
Mathematical modeling of the impact produced by magnetic disks on living cells
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 4, pp. 432-442.

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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. 
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Valery V. Denisenko; Vladimir M. Sadovskii; Sergey S. Zamay. Mathematical modeling of the impact produced by magnetic disks on living cells. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 4, pp. 432-442. http://geodesic.mathdoc.fr/item/JSFU_2016_9_4_a3/

[1] R. M. Bozort, Ferromagnetism, D. Van Nostrand Company Inc., Princeton, New Jersey, 1951

[2] V. V. Denisenko, Energy Methods for Elliptic Equations with Asymmetric Coefficients, Publ. house of the SB RAS, Novosibirsk, 1995 (in Russian) | MR

[3] V. V. Denisenko, “Energy Method for Mathematical Modeling of Heat Transfer in 2-D Flow”, Journal of Siberian Federal University. Mathematics and Physics, 7:4 (2014), 417–428 | DOI

[4] N. C. Gauthier, T. A. Masters, M. P. Sheetz, “Mechanical feedback between membrane tension and dynamics”, Trends in Cell Biology, 22:10 (2012), 527–535 | DOI

[5] D.-H. Kim, E. A. Rozhkova, I. V. Ulasov, S. D. Bader, T. Rajh, M. S. Lesniak, V. Novosad, “Biofunctionalized Magnetic Vortex Microdisks for Targeted Cancer Cell Destruction”, Nature Material, 9:2 (2010), 16–17

[6] P. D. Kim et al., “The anti-tumor effect of magnetic nanodisks and DNA aptamer conjugates”, Doklady Biochemistry and Biophysics, 466 (2016), 66–69 | DOI

[7] L. D. Landau, E. M. Lifshitz, A Course of Theoretical Physics, v. 8, Electrodynamics of Continuous Media, Pergamon Press, 1960 | MR

[8] K. Washizu, Variational Methods in Elasticity and Plasticity, Pergamon Press, Oxford–New York, 1982 | MR | Zbl