13,507 research outputs found
Eigenfunction scarring and improvements in bounds
We study the relationship between growth of eigenfunctions and
their concentration as measured by defect measures. In particular, we
show that scarring in the sense of concentration of defect measure on certain
submanifolds is incompatible with maximal growth. In addition, we
show that a defect measure which is too diffuse, such as the Liouville measure,
is also incompatible with maximal eigenfunction growth.Comment: 10 page
Equilibrium and eigenfunctions estimates in the semi-classical regime
We establish eigenfunctions estimates, in the semi-classical regime, for
critical energy levels associated to an isolated singularity. For Schr\"odinger
operators, the asymptotic repartition of eigenvectors is the same as in the
regular case, excepted in dimension 1 where a concentration at the critical
point occurs. This principle extends to pseudo-differential operators and the
limit measure is the Liouville measure as long as the singularity remains
integrable.Comment: 13 pages, 1 figure, perhaps to be revise
Numerical simulation of prominence oscillations
We present numerical simulations, obtained with the Versatile Advection Code,
of the oscillations of an inverse polarity prominence. The internal prominence
equilibrium, the surrounding corona and the inert photosphere are well
represented. Gravity and thermodynamics are not taken into account, but it is
argued that these are not crucial. The oscillations can be understood in terms
of a solid body moving through a plasma. The mass of this solid body is
determined by the magnetic field topology, not by the prominence mass proper.
The model also allows us to study the effect of the ambient coronal plasma on
the motion of the prominence body. Horizontal oscillations are damped through
the emission of slow waves while vertical oscillations are damped through the
emission of fast waves.Comment: 12 pages, 14 figures, accepted by Astronomy and Astrophysic
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