Inverse Problem of Magnetostatics in Saturation Fields
Source abstract
Abstract
Abstract We have derived integro-differential equations whose solutions determine the shape of an arbitrary ferromagnetic saturation-magnetized body, or a cavity in it, without an a priori assumption that domains they occupy belong to any particular geometric class. The uniqueness of such determination is proved for a wide class of cases encountered in practice. As an important illustrative example, analytical formulas are derived for determining the resulting field of a spherical ferromagnetic body. These formulas uniquely determine the position and dimensions of the body.
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Research context
OpenAlex topics: Magnetic Properties and Applications · Non-Destructive Testing Techniques · Numerical methods in inverse problems
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References (23)
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1. Pechenkov, A.N. and Shcherbinin, V.E., Nekotorye pryamye i obratnye zadachi tekhnicheskoi magnitostatiki (Some Direct and Inverse Problems of Technical Magnetostatics), Yekaterinburg: Ural Branch, Russ. Acad. Sci., 2004.
2. Pechenkov, A.N. and Shcherbinin, V.E., On the solution of the inverse problem of magnetostatic tomography, Russ. J. Nondestr. Test., 2009, vol. 45, no. 3, pp. 176–190.10.1134/S106183090903005X ↗
3. Pechenkov, A.N. and Shcherbinin, V.E., On the question of the nonuniqueness of solution to the inverse problem of magnetostatic flaw detection, Kontrol’ Diagn., 2006, no. 9, pp. 59–60.
4. Pechenkov, A.N., Effect of the shape of a body on the uniqueness of the solution to the inverse problem of magnetostatic flaw detection, Russ. J. Nondestr. Test., 2006, vol. 42, no. 10, pp. 653–655.10.1134/S1061830906100032 ↗
5. Dyakin, V.V., Direct and inverse problem of magnetostatics, Defektoskopiya, 1996, no. 3, pp. 3–6.
6. Dyakin, V.V., Kudryashova, O.V., and Rayevskii, V.Ya., On the well-posedness of the direct and inverse problem of magnetostatics. Part 2, Russ. J. Nondestr. Test., 2018, vol. 54, no. 10., pp. 687–697.10.1134/S1061830918100030 ↗
7. Reutov, Yu.Ya., Gobov, Yu.L., and Loskutov, V.E., Feasibilities of using the ELCUT software for calculations in nondestructive testing, Russ. J. Nondestr. Test., 2002, vol. 38, no. 6, pp. 425–430.10.1023/A:1022174825844 ↗
8. Zagidulin, R.V., Dyakin, V.V., Dudarev, M.S., and Shcherbinin, V.E., To the determination of the geometrical dimensions of a surface defect. Physical methods and instruments of NDT, Tezisy dokl. X Ural. nauchno-tekh. konf. (Abstr. Rep. X Urals Sci.-Tech. Conf.), Izhevsk, 1989, p. 83.
9. Novoslugina, A.P. and Smorodinskii, Ya.G., A calculation method for evaluating defect parameters in steel, Russ. J. Nondestr. Test., 2017, vol. 53, no. 11, pp. 765–771.10.1134/S1061830917110067 ↗
10. Dyakin, V.V., Rayevskiy, V.Y., and Kudrjashova, O.V., The field of a finite defect in a plate, Russ. J. Nondestr. Test., 2009, vol. 45, no. 3, pp. 199–209.10.1134/S1061830909030073 ↗
11. Krotov, L.N., Reconstruction of a media Interface from the spatial distribution of a magnetic stray field: I. Analysis of the properties of the solution of the auxiliary direct problem (linear approximation), Russ. J. Nondestr. Test., 2004, vol. 40, no. 2, pp. 130–134.10.1023/B:RUNT.0000036557.88751.ea ↗
12. Krotov, L.N., Reconstruction of a media boundary based on the spatial distribution of stray magnetic fields. II. Definition and method of solving the inverse geometric problem of magnetostatics, Russ. J. Nondestr. Test., 2004, vol. 40, no. 6, pp. 385–390.10.1023/B:RUNT.0000049846.21618.ec ↗
13. Slesarev, D.A., Barat, V.A., and Chobanu, O.M., A decrease in the error of the statistical method for estimating the parameters of flaws in magnetic flaw detection, Russ. J. Nondestr. Test., 2012, vol. 48, no. 1, pp. 55–58.10.1134/S1061830912010111 ↗
14. Khizhnyak, N.A., Integral’nye uravneniya makroskopicheskoi elektrodinamiki (Integral Equations of Macroscopic Electrodynamics), Kiev: Naukova Dumka, 1986.
15. Dyakin, V.V., Matematicheskie osnovy klassicheskoi magnitostatiki (Mathematical Foundations of Classical Magnetostatics), Yekaterinburg: Ural Branch, Russ. Acad. Sci., 2016.
16. Timan, A.F. and Trofimov, V.N., Vvedenie v teoriyu garmonicheskikh funktsii (Introduction to the Theory of Harmonic Functions) Moscow: Nauka, 1968.
17. Mikhlin, S.G., Kurs matematicheskoi fiziki (Course of Mathematical Physics), Moscow: Nauka, 1968.
18. Prilepko, A.I., Inverse problems of potential theory (elliptic, parabolic, hyperbolic, and transport equations), Math. Notes Acad. Sci. USSR, 1973, vol. 14, no. 5, pp. 990–996.
19. Antonov, V.A., Timoshkova, E.I., and Kholshevnikov, K.V., Vvedenie v teoriyu n’yutonovskogo potentsiala (Introduction to Newtonian Potential Theory), Moscow: Nauka, 1988.
20. Prilepko, A.I., On inverse problems of potential theory, Differ. Uravn., 1967, vol. 3, no. 1, pp. 30–44.
21. Aleksidze, M.A., Priblizhennye metody resheniya pryamykh i obratnykh zadach gravimetrii (Approximate Methods for Solving Direct and Inverse Problems of Gravimetry), Moscow: Nauka, 1987.
22. Prudnikov, A.P., Brychkov, Yu.A., and Marichev, O.I., Integraly i ryady (Integrals and Series), Moscow: Nauka, 1981.
23. Fikhtengol’ts, G.M., Kurs differentsial’nogo i integral’nogo ischisleniya (Course of Differential and Integral Calculus), Moscow: Nauka, 1966, vol. 3.