Modeling of a magnetic field of sources localised within a sphere and beyond
Matematičeskoe modelirovanie, Tome 27 (2015) no. 8, pp. 111-126.

Voir la notice de l'article provenant de la source Math-Net.Ru

We propose three types of formulas for decomposing/reconstructing a magnetic field of magnetic masses and closed electric currents, which are either in a sphere or outside it. A magnetic field can be reconstructed everywhere using the data of continuous observations (or sparse data in approximation theory) about magnetic intensity on sphere surface.
Keywords: magnetic field in sphere, decomposition theorems, data on the sphere surface.
@article{MM_2015_27_8_a7,
     author = {V. V. Aksenov},
     title = {Modeling of a magnetic field of sources localised within a sphere and beyond},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {111--126},
     publisher = {mathdoc},
     volume = {27},
     number = {8},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2015_27_8_a7/}
}
TY  - JOUR
AU  - V. V. Aksenov
TI  - Modeling of a magnetic field of sources localised within a sphere and beyond
JO  - Matematičeskoe modelirovanie
PY  - 2015
SP  - 111
EP  - 126
VL  - 27
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2015_27_8_a7/
LA  - ru
ID  - MM_2015_27_8_a7
ER  - 
%0 Journal Article
%A V. V. Aksenov
%T Modeling of a magnetic field of sources localised within a sphere and beyond
%J Matematičeskoe modelirovanie
%D 2015
%P 111-126
%V 27
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2015_27_8_a7/
%G ru
%F MM_2015_27_8_a7
V. V. Aksenov. Modeling of a magnetic field of sources localised within a sphere and beyond. Matematičeskoe modelirovanie, Tome 27 (2015) no. 8, pp. 111-126. http://geodesic.mathdoc.fr/item/MM_2015_27_8_a7/

[1] K. F. Gauss, Izbrannye trudy po zemnomu magnetizmu, Izd. AN SSSR, M., 1952, 265 pp.

[2] A. N. Tikhonov, A. A. Samarskii, Uravnenia matematicheskoi fiziki, Nauka, M., 1972, 735 pp.

[3] G. Korn, T. Korn, Spravochnik po matematike dlia nauchnykh rabotnikov I inzhenerov. Opredelenia, teoremy, formuly, Nauka, M., 1970, 720 pp.

[4] A. Schmidt, “Besitzt die tagliche erdmagnetische Schwankung in der Erdoberflache ein Potential”, Physik. Zeitschrift, 19 (1918), 349–355

[5] B. M. Ianovskii, Zemnoi magnetism, v. I, II, GITTL, L., 1978, 591 pp.

[6] V. V. Aksenov, “On Some Solenoidal Vector Fields in Sperical Domains”, Differential Equations, 48:7 (2012), 1042–1045 | Zbl

[7] V. V. Aksenov, The Foundations of Geomagnetism, Bulletin of the Novosibirsk Computing Center. Series: Mathematical Modeling in Geophysics, 15, Special Issue, 2012, 100 pp.

[8] V. V. Aksenov, Elektromagnitnoe pole Zemli, Izd. IVMiMG SO RAN, Novosibirsk, 2010, 266 pp.

[9] V. V. Aksenov, “O fizicheskikh svoistvakh elektromagnitnykh polei, nabliudaemykh na Zemle”, Geologia I Razvedka, 2009, no. 4, 51–58

[10] N. P. Benkova, Spokoinye solnechno-sutochnye variatsii zemnogo magnetizma, Gidrometeoizdat, M.–L., 1941, 79 pp.

[11] A. Van Vleuten, “Over de dagelijsche variatie van het Ardmagnetisme”, Koninklijk Ned. Meteor. Instit., 1917, no. 102, 5–30

[12] V. Aharonov, D. Bohm, “Significance of Electromagnetic Potentials in the Quantum Theory”, Phys. Rev., 115:3 (1959), 485–491 | Zbl

[13] G. Moffat, Vozbuzhdenie magnitnogo polia v provodiashchei srede, Mir, M., 1980, 339 pp.

[14] V. V. Aksenov, “Modelirovanie toroidalnykh i poloidalnykh elektromagnitnykh polei”, Matematicheskoe modelirovanie, 26:5 (2014), 3–24