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Thin films of YBCO with or without Nb added were prepared on (100) ZrO 2 single crystalline substrate by dc magnetron sputtering method. A phase of YBa 2 NbO 6 was found to form not only in the target materials of YBCO but also in the sputtered thin films. The second phase of YBa 2 NbO 6 in the superconducting films destroyed a match relation between the lattice of YBCO and the lattice of ZrO 2 substrate. The measurements of critical current density J c under magnetic field (H // c axis, up to 5T) showed that the J c in Nb-added YBCO films reduced more apparently than that in YBCO films. It is concluded that the existence of second phase of YBa 2 NbO 6 in superconducting phase does not play a rule of flux pinning.

In this paper, we present a model order reduction (MOR) method based on Laguerre polynomials and singular value decomposition (SVD) for coupled systems in the frequency domain. By constructing projection matrices from the global perspective and then blockdiagonalizing them, the reduced system is produced, which not only retains the structure of the original system, but also matches the first several Laguerre coefficients. In addition, the connection between our algorithm and the moment matching approximation is also discussed. The error estimation of our method is given as well. Besides, the stability of the reduced system is also studied. Finally, two numerical examples are provided to verify the effectiveness of our algorithm.

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