Eigenfunction scarring and improvements in L∞L^{\infty} bounds

We study the relationship between $L^\infty$ growth of eigenfunctions and their $L^2$ 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 $L^\infty$ 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