Nucleation of vortices with a temperature and time-dependent Ginzburg–Landau model of superconductivity

• Published in: European journal of applied mathematics Vol. 14; no. 1; pp. 111 - 127
• Main Authors: COSKUN, E., CAKIR, Z., TAKAC, P.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.02.2003
• Subjects: Applied mathematics
• ISSN: 0956-7925; 1469-4425
• DOI: 10.1017/S0956792502004990

The standard scales that are used to non-dimensionalize the temperature- and time-dependent Ginzburg–Landau (TTDGL) model developed by Schmid [27], eliminate temperature- dependent parameters, and thus do not allow for superconducting phenomena due to variations in temperature. In this study, a set of new scales is presented to non-dimensionalize the TTDGL model so that the resulting dimensionless system depends upon a temperature parameter as well. Moreover, some properties of solutions to TTDGL system as a function of temperature are explored. Numerical experiments illustrating the temperature-dependency of vortex nucleation in type-II superconductors as well as the transition to the Meissner state in type-I superconductors are presented.