We present the results of numerical analysis of a model of normal zone propagation in coated conductors. The main emphasis is on the effects of increased contact resistance between the superconducting film and the stabilizer on the speed of normal zone propagation, the maximum temperature rise inside the normal zone, and the stability margins. We show that with increasing contact resistance the speed of normal zone propagation increases, the maximum temperature inside the normal zone decreases, and stability margins shrink. This may have an overall beneficial effect on quench protection quality of coated conductors. We also briefly discuss the propagation of solitons and development of the temperature modulation along the wire.PACS numbers: 74.72.-h, 85.25.-j, 05.65.+b, 05.45.-a, 74.90.+n arXiv:0909.5209v1 [cond-mat.supr-con]

'ublic reporting burden tor this collection ot intormation is estimated to average 1 hour per response, including the time tar reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Abstract. We present a one-dimensional time-dependent semiclassical transport model for mixed state scattering with thin quantum barriers. The idea is to solve a stationary Schr6dinger equation in the thin quantum barrier to obtain the scattering coefficients, and then use them to supply the interface condition that connects the two classical domains. We then build in the interface condition to the numerical flux, in the spirit of the Hamiltonian-preserving scheme introduced by Jin and Wen for a classical barrier. The overall cost is roughly the same as solving a classical barrier. We construct a numerical method based on this semiclassical approach and validate the model using various numerical examples.

We present the results of numerical analysis of normal zone propagation in a stack of Y Ba2Cu3O7−x coated conductors which imitates a pancake coil. Our main purpose is to determine whether the quench protection quality of such coils can be substantially improved by increased contact resistance between the superconducting film and the stabilizer. We show that with increased contact resistance the speed of normal zone propagation increases, the detection of a normal zone inside the coil becomes possible earlier, when the peak temperature inside the normal zone is lower, and stability margins shrink. Thus, increasing contact resistance may become a viable option for improving the prospects of coated conductors for high Tc magnets applications.

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Abstract. We present a time-dependent semiclassical transport model for coherent pure-state scattering with quantum barriers. The model is based on a complex-valued Liouville equation, with interface conditions at quantum barriers computed from the steady-state Schrödinger equation. By retaining the phase information at the barrier, this coherent model adequately describes quantum scattering and interference at quantum barriers, with a computational cost comparable to that of classical mechanics. We construct both Eulerian and Lagrangian numerical methods for this model, and validate it using several numerical examples, including multiple quantum barriers.Key words. multiscale method, semiclassical limit, Liouville, coherent, quantum barrier.AMS subject classifications. 65M06, 65Z05, 81Q20, 81S30, 81T80. IntroductionThe motion of electrons in a plasma or a semiconductor can be modeled with classical mechanics when the change in the applied potential is moderate. But in a region where the potential changes rapidly over a length on the order of a de Broglie wavelength, quantum mechanics is required to accurately capture wave phenomena such as tunneling, resonance, and partial transmission and reflections. Because quantumscale parameters often control the accuracy and consistency of the solution, one often must resolve the dynamics entirely at the quantum scale. But for large-scale problems, such an approach is numerically infeasible. If the quantum region is sufficiently localized, a viable approach is to solve the problem using a multiscale method that combines the large-scale classical model with the small-scale quantum model.In [7,8] the authors presented a multiscale approach which accurately models the interaction of a quantum wave packet with a thin barrier in the semiclassical regime as the scaled Planck constant ε vanishes. This thin-barrier model accurately describes the weak limit of the moments of solutions to the pure-state Schrödinger and mixedstate von Neumann equation for an isolated thin quantum barrier (a barrier of width on the order of a de Broglie wavelength). This model assumes that the dwell time of the particle in the barrier is sufficiently short so that the behavior of the wave packet may be adequately described by the steady-state Schrödinger equation. Such an assumption is realistic for O(ε) thin barriers in the semiclassical limit as ε → 0, but it is inadequate when either ε is finite or the width of the barrier is significant in comparison to the width of the wave packet.Another shortcoming of the thin-barrier model is that it can only generate a decoherent solution. Quantum mechanics is in essence wave mechanics and the Schrö-

'ublic reporting burden tor this collection ot intormation is estimated to average 1 hour per response, including the time tar reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Abstract. We present a one-dimensional time-dependent semiclassical transport model for mixed state scattering with thin quantum barriers. The idea is to solve a stationary Schr6dinger equation in the thin quantum barrier to obtain the scattering coefficients, and then use them to supply the interface condition that connects the two classical domains. We then build in the interface condition to the numerical flux, in the spirit of the Hamiltonian-preserving scheme introduced by Jin and Wen for a classical barrier. The overall cost is roughly the same as solving a classical barrier. We construct a numerical method based on this semiclassical approach and validate the model using various numerical examples.