Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-01-10T19:19:27.639Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Bean critical-state model in superconductivity

Published online by Cambridge University Press:  26 September 2008

L. Prigozhin
L. Prigozhin
Affiliation:
Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel and University of Oxford, Mathematical Institute, OCIAM, Oxford, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider two-dimensional and axially symmetric critical-state problems in type-II superconductivity, and show that these problems are equivalent to evolutionary quasi-variational inequalities. In a special case, where the inequalities become variational, the existence and uniqueness of the solution are proved.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 7 , Issue 3 , June 1996 , pp. 237 - 247
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Bean, C. P. 1964 Magnetization of high-field superconductors. Rev. Mod. Phys. 36, 31–39.CrossRefGoogle Scholar
[2] De Gennes, P. G. 1966 Superconductivity of Metals and Alloys. Benjamin.Google Scholar
[3] Bossavit, A. 1994 Numerical modelling of superconductors in three dimensions: a model and a finite element method. IEEE Trans. Magn. 30, 3363–3366.CrossRefGoogle Scholar
[4] Kim, Y. B., Hempstead, C. F. & Strnad, A. R. 1963 Magnetization and critical supercurrents. Phys. Rev. 129, 528–535.Google Scholar
[5] Kim, Y. B., Hempstead, C. F. & Strnad, A. R. 1962 Critical persistent currents in hard superconductors. Phys. Rev. Lett. 9, 306–309.Google Scholar
[6] Wang, J. & Sayer, M. 1993 Critical current models and shielding of high temperature superconductors. Physica C 212, 395–406.Google Scholar
[7] Dautray, R. & Lions, J. L. 1990 Mathematical Analysis and Numerical Methods for Science and Technology v. 3. Springer-Verlag.Google Scholar
[8] Dunford, N. & Schwartz, J. T. 1963 Linear Operators. Part II. Wiley.Google Scholar
[9] Ekeland, I. & Temam, R. 1976 Convex Analysis and Variational Problems. Elsevier.Google Scholar
[10] Kantorovich, L. V. & Akilov, G. P. 1982 Functional Analysis. Pergamon.Google Scholar
[11] Barbu, V. 1976 Nonlinear Semigroups and Differential Equations in Banach Spaces. Ed. Academiei, Bucuresti.Google Scholar
[12] Glowinski, R., Lions, J. L. & Trémoliérs, R. 1976 Analyse Numérique des Inéquations Variationnelles. Dunod, Paris.Google Scholar
[13] Prigozhin, L. 1996 The Bean model: variational formulation and numerical solution. J. Comp. Phys. (submitted).Google Scholar
[14] Bak, P. & Chen, K. 1991 Self-organized criticality. Sci. Am. 264, 01, 26–33.CrossRefGoogle Scholar
[15] Bak, P., Tang, C. & Wiesenfeld, K. 1988 Self-organized criticality. Phys. Rev. A 38, 364–374.Google Scholar
[16] Prigozhin, L. 1994 Sandpiles and river networks: extended systems with nonlocal interactions. Phys. Rev. E 49, 1161–1167.CrossRefGoogle ScholarPubMed