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Resonances for a Solvable Model of Ultrasound Scattering by a Cell Membrane
- Authors: Popov I.Y.1, Yurova T.S.1
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Affiliations:
- ITMO University
- Issue: Vol 118, No 1-2 (7) (2023)
- Pages: 135-140
- Section: Articles
- URL: https://rjeid.com/0370-274X/article/view/663130
- DOI: https://doi.org/10.31857/S1234567823140124
- EDN: https://elibrary.ru/HACAWB
- ID: 663130
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Abstract
We study the resonances for scattering of acoustic waves by cell membrane. Due to the fact that we deal with this phenomenon only, we use the simplest model of the membrane as a potential supported by a surface. The asymptotics of the Green’s function with the singularity at the surface is obtained. The influence of the surface curvature on the resonances is investigated. An application of the result to explanation of selective cancer cell membrane destruction in ultrasonic field is discussed.
About the authors
I. Yu. Popov
ITMO University
Email: popov1955@gmail.com
St. Petersburg, 197101 Russia
T. S. Yurova
ITMO University
Author for correspondence.
Email: tatiana.yurova@metalab.ifmo.ru
St. Petersburg, 197101 Russia
References
- B. Alberts, A. Johnson, J. Lewis, M. Ra, K. Roberts, and P. Walter, Molecular Biology of the Cell, fourth edition, Garland Science, N.Y. (2002).
- T. Baumgart, S. T. Hess, and W. W. Webb, Nature 425, 821 (2003).
- K. Bacia, P. Schwille, and T. Kurzchalia, Proceedings of the National Academy of Sciences of the United States of America 102, 3272 (2005).
- I. F. Melikhov and I. Y. Popov, Chin. J. Phys. 65, 334 (2020).
- I. F. Melikhov and I. Y. Popov, Nanosystems: Physics, Chemistry, Mathematics 9(4), 447 (2018).
- S. J. Marrink, V. Corradi, P. C. T. Souza, H. I. Ingolfsson, D. P. Tieleman, and M. S. P. Sansom, Chem. Rev. 119(9), 6184 (2019).
- P. L.Yeagle, The Membranes of Cells, third edition, Academic Press, N.Y. (2016).
- O. K. Kosheleva, T.-C. Lai, N. G. Chen, M. Hsiao, and C. H. Chen, Journal of Nanobiotechnology 14, 46 (2016).
- T. A. Tran, J. Y. L. Guennec, P. Bougnoux, F. Tranquart, and A. Bouakaz, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 55, 43 (2008).
- I. Yu. Popov, Math. Proc. Cambridge Phil. Soc. 118, 555 (1995).
- I. Yu. Popov, J. Math. Phys. 33(5), 1685 (1992).
- T. Ikebe and S. Shimada, J. Math. Kyoto Univ. 31(1), 219 (1991).
- I. Yu. Popov, Proc. Royal Soc. London A 452, 1505 (1996).
- P. Exner and D. Kreicirik, Rev. Math. Phys. 13, 307 (2001).
- J. Behrndt, M. Langer, and V. Lotoreichik, Nanosystems: Phys. Chem. Math. 7(2), 290 (2016).
- A. Mantile and A. Posilicano, Nanosystems: Phys. Chem. Math. 7(2), 315 (2016).
- P. Exner, S. Kondej, and V. Lotoreichik, J. Math. Phys. 59, 013051 (2018).
- A. M. Vorobiev, A. S. Bagmutov, and A. I. Popov, Nanosystems: Phys. Chem. Math. 10(4), 415 (2019).
- J. Behrndt, P. Exner, M. Holzmann, and V. Lotoreichik, Math. Nachr. 290, 12151248 (2017).
- B. S. Pavlov, Russ. Math. Surv. 42 (6), 127 (1987).
- I. Yu. Popov, Matematicheskii sbornik, 181(10), 1366 (1990)
- English: Mathematics of the USSR-Sbornik 71(1), 209 (1992).
- A. S. Melikhova, M. P. Faleeva, and I. Y. Popov, Nanosystems: Phys. Chem. Math. 12(2), 115 (2021).
- Yu. N. Demkov and V. N. Ostrovskii, Zero-Range Potentials and Their Applications in Atomic Physics, Springer, Berlin (1988).
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