×

The driving torque of a rotating levitated cylindrical permanent magnet above a superconductor. (English) Zbl 1148.82041

This paper develops a model for the study of continuous rotations of a permanent magnet. In the first part of the paper the author develops a set of partial differential equations for the description of rotations of the permanent magnet. This mathematical model describes magnetic forces, the equation of motion and the coupled equations. Next, the author is interested in the study of constant angular velocities with which the permanent magnet can rotate. Important contributions are played by the mean temperature, the moments of temperature, as well as by the driving torque and equilibrium states. An interpretation of the main abstract results from a physical point of view concludes the present paper.

MSC:

82D55 Statistical mechanics of superconductors
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Arkadiev, V., A floating magnet, Nature, 160, 330 (1947)
[2] Hellmann, F., Levitation of a magnet over a flat type II superconductor, J. Appl. Phys., 63, 447-450 (1988)
[3] Moon, F., Superconducting Levitation: Applications to Bearings and Magnetic Transportation (with Selected Sections by Pei-Zen Chang) (1994), John Wiley & Sons: John Wiley & Sons New York
[4] Palmy, C.; Fullemann, F., Thermal induced rotation of a levitated permanent magnet above a superconducting disk, Helv. Phys. Acta, 63, 6, 805-806 (1990)
[5] Ma, K., Spontaneous and persistent rotation of cylindrical magnets levitated by Y-Ba-Cu-O superconductors, J. Appl. Phys., 70, 7, 3961-3963 (1991)
[6] Martini, G.; Rivetti, A.; Pavese, F., A self rotating magnet levitation above a YBCO specimen, Adv. Cryog. Eng., 35, 639-646 (1990)
[7] Schreiner, M.; Palmy, C., Why does a cylindrical magnet rotate when levitated above a superconducting plate?, Am. J. Appl. Phys., 72, 243-248 (2004)
[8] Kittel, C., Introduction to Solid State Physics (1996), John Wiley & Sons: John Wiley & Sons New York
[9] Incropera, F. P.; DeWitt, D. P., Fundamentals of Heat and Mass Transfer (1996), John Wiley & Sons: John Wiley & Sons New York
[10] Moon, F., Magneto-Solid Mechanics (1984), John Wiley & Sons: John Wiley & Sons New York
[11] Kellog, O. D., Foundation of Potential Theory (1967), Springer: Springer Berlin
[12] Tveito, A.; Winther, R., Introduction to Partial Differential Equations (1998), Springer: Springer New York · Zbl 0906.35001
[13] Magnus, W.; Oberhettinger, F.; Soni, R. P., Formulas and Theorems for the Special Functions of Mathematical Physics (1966), Springer: Springer Berlin · Zbl 0143.08502
[14] Verhulst, F., Differential Equations and Dynamical Systems (2000), Springer: Springer Berlin · Zbl 1004.70015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.