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Modeling of the subgrid-scale term of the filtered magnetic field transport equation
Accurate subgrid-scale turbulence models are needed to perform realistic
numerical magnetohydrodynamic (MHD) simulations of the subsurface flows of the
Sun. To perform large-eddy simulations (LES) of turbulent MHD flows, three
unknown terms have to be modeled. As a first step, this work proposes to use a
priori tests to measure the accuracy of various models proposed to predict the
SGS term appearing in the transport equation of the filtered magnetic field. It
is proposed to evaluate the SGS model accuracy in term of "structural" and
"functional" performance, i.e. the model capacity to locally approximate the
unknown term and to reproduce its energetic action, respectively. From our
tests, it appears that a mixed model based on the scale-similarity model has
better performance.Comment: 10 pages, 5 figures; Center for Turbulence Research, Proceedings of
the Summer Program 2010, Stanford Universit
The theory of the reentrant effect in susceptibility of cylindrical mesoscopic samples
A theory has been developed to explain the anomalous behavior of the magnetic
susceptibility of a normal metal-superconductor () structure in weak
magnetic fields at millikelvin temperatures. The effect was discovered
experimentally by A.C. Mota et al \cite{10}. In cylindrical superconducting
samples covered with a thin normal pure metal layer, the susceptibility
exhibited a reentrant effect: it started to increase unexpectedly when the
temperature lowered below 100 mK. The effect was observed in mesoscopic
structures when the and metals were in good electric contact. The
theory proposed is essentially based on the properties of the Andreev levels in
the normal metal. When the magnetic field (or temperature) changes, each of the
Andreev levels coincides from time to time with the chemical potential of the
metal. As a result, the state of the structure experiences strong
degeneracy, and the quasiparticle density of states exhibits resonance spikes.
This generates a large paramagnetic contribution to the susceptibility, which
adds up to the diamagnetic contribution thus leading to the reentrant effect.
The explanation proposed was obtained within the model of free electrons. The
theory provides a good description for experimental results [10]
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