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Multi-symplectic method to analyze the mixed state of II-superconductors

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Abstract

The mixed state of two-band II-superconductor is analyzed by the multi-symplectic method. As to the Ginzburg-Landau equation depending on time that describes the mixed state of two-band II-superconductor, the multi-symplectic formulations with several conservation laws: a multi-symplectic conservation law, an energy conservation law, as well as a momentum conservation law, are presented firstly; then an eighteen points scheme is constructed to simulate the multi-symplectic partial differential equations (PDEs) that are derived from the Ginzburg-Landau equation; finally, based on the simulation results, the volt-ampere characteristic curves are obtained, as well as the relationships between the temperature and resistivity of a suppositional two-band II-superconductor model under different magnetic intensities. From the results of the numerical experiments, it is concluded that the notable property of the mixed state of the two-band II-superconductor is that: The transformation temperature decreases and the resistivity π increases rapidly with the increase of the magnetic intensity B. In addition, the simulation results show that the multi-symplectic method has two remarkable advantages: high accuracy and excellent long-time numerical behavior.

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Authors and Affiliations

  1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, 710072, China

    WeiPeng Hu & ZiChen Deng

  2. State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian, 116023, China

    ZiChen Deng

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  1. WeiPeng Hu
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  2. ZiChen Deng
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Correspondence to WeiPeng Hu.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 10572119, 10772147 and 10632030), the Doctoral Program Foundation of Education Ministry of China (Grant No. 20070699028), the Natural Science Foundation of Shaanxi Province of China (Grant No. 2006A07), and the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment

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Hu, W., Deng, Z. Multi-symplectic method to analyze the mixed state of II-superconductors. Sci. China Ser. G-Phys. Mech. Astron. 51, 1835–1844 (2008). https://doi.org/10.1007/s11433-008-0192-5

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  • DOI: https://doi.org/10.1007/s11433-008-0192-5

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