Damped transverse oscillations of interacting coronal loops

Damped transverse oscillations of magnetic loops are routinely observed in the solar corona. This phenomenon is interpreted as standing kink magnetohydrodynamic waves, which are damped by resonant absorption owing to plasma inhomogeneity across the magnetic field. The periods and damping times of these oscillations can be used to probe the physical conditions of the coronal medium. Some observations suggest that interaction between neighboring oscillating loops in an active region may be important and can modify the properties of the oscillations compared to those of an isolated loop. Here we theoretically investigate resonantly damped transverse oscillations of interacting non-uniform coronal loops. We provide a semi-analytic method, based on the T-matrix theory of scattering, to compute the frequencies and damping rates of collective oscillations of an arbitrary configuration of parallel cylindrical loops. The effect of resonant damping is included in the T-matrix scheme in the thin boundary approximation. Analytic and numerical results in the specific case of two interacting loops are given as an application.Comment: Accepted for publication in A&

Two-dimensional wave propagation in layered periodic media

We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with constant impedance exhibit no effective dispersion. We show that a new kind of effective dispersion may arise in two dimensions, even in materials with constant impedance. This dispersion is a macroscopic effect of microscopic diffraction caused by spatial variation in the sound speed. We analyze this dispersive effect by using high-order homogenization to derive an anisotropic, dispersive effective medium. We generalize to two dimensions a homogenization approach that has been used previously for one-dimensional problems. Pseudospectral solutions of the effective medium equations agree to high accuracy with finite volume direct numerical simulations of the variable-coefficient equations

Are tornado-like magnetic structures able to support solar prominence plasma?

Recent high-resolution and high-cadence observations have surprisingly suggested that prominence barbs exhibit apparent rotating motions suggestive of a tornado-like structure. Additional evidence has been provided by Doppler measurements. The observations reveal opposite velocities for both hot and cool plasma on the two sides of a prominence barb. This motion is persistent for several hours and has been interpreted in terms of rotational motion of prominence feet. Several authors suggest that such barb motions are rotating helical structures around a vertical axis similar to tornadoes on Earth. One of the difficulties of such a proposal is how to support cool prominence plasma in almost-vertical structures against gravity. In this work we model analytically a tornado-like structure and try to determine possible mechanisms to support the prominence plasma. We have found that the Lorentz force can indeed support the barb plasma provided the magnetic structure is sufficiently twisted and/or significant poloidal flows are present.Comment: Accepted for publication in ApJ

Asymptotic behavior of an elastic beam fixed on a small part of one of its extremities

We study the asymptotic behavior of the solution of an anisotropic, heterogeneous, linearized elasticity problem in a cylinder whose diameter $\epsilon$ tends to zero. The cylinder is assumed to be fixed (homogeneous Dirichlet boundary condition) on the whole of one of its extremities, but only on a small part (of size $\epsilon r^\epsilon$) of the second one; the Neumann boundary condition is assumed on the remainder of the boundary. We show that the result depends on $r^\epsilon$, and that there are 3 critical sizes, namely $r^\epsilon=\epsilon^3$, $r^\epsilon=\epsilon$, and $r^\epsilon=\epsilon^{1/3}$, and in total 7 different regimes. We also prove a corrector result for each behavior of $r^\epsilon$.Comment: Preliminary version of a Note to be published in a slightly abbreviated form in C. R. Acad. Sci. Paris, Ser. I, 338 (2004), pp. 975-98

Continuidad y reflexión en G. W. Leibniz

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