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

作　　者：HU WeiPeng1↑ & DENG ZiChen1,2 1 School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710072, China 2 State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, China 

出　　处：《Science China(Physics,Mechanics & Astronomy)》2008年第12期1835-1844,共10页中国科学：物理学、力学、天文学（英文版）

基　　金：the National Natural Science Foundation of China (Grant Nos. 10572119, 10772147 and 10632030);the Doctoral Program Founda-tion of Education Ministry of China (Grant No. 20070699028);the Natural Science Foundation of Shaanxi Province of China (Grant No. 2006A07);the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment

摘　　要：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 con- servation 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 intensi- ties. 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 trans- formation temperature decreases and the resistivity ρ 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.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 con- servation 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 intensi- ties. 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 trans- formation temperature decreases and the resistivity ρ 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.

关 键 词：two-band GINZBURG-LANDAU equation mixed state MULTI-SYMPLECTIC CONSERVATION LAW 

分 类 号：O511[理学—低温物理]