Homogenization of the Schrodinger equation with a time oscillating potential

We study the homogenization of a Schrodinger equation in a periodic medium with a time dependent potential. This is a model for semiconductors excited by an external electromagnetic wave. We prove that, for a suitable choice of oscillating (both in time and space) potential, one can partially transfer electrons from one Bloch band to another. This justifies the famous "Fermi golden rule" for the transition probability between two such states which is at the basis of various optical properties of semiconductors. Our method is based on a combination of classical homogenization techniques (two-scale convergence and suitable oscillating test functions) and of Bloch waves theory

Can coronal hole spicules reach coronal temperatures?

We aim with the present study to provide observational evidences on whether coronal hole spicules reach coronal temperatures. We combine multi-instrument co-observations obtained with the SUMER/SoHO and with the EIS/SOT/XRT/Hinode. The analysed three large spicules were found to be comprised of numerous thin spicules which rise, rotate and descend simultaneously forming a bush-like feature. Their rotation resembles the untwisting of a large flux rope. They show velocities ranging from 50 to 250 km/s. We clearly associated the red- and blue-shifted emissions in transition region lines with rotating but also with rising and descending plasmas, respectively. Our main result is that these spicules although very large and dynamic, show no presence in spectral lines formed at temperatures above 300 000 K. The present paper brings out the analysis of three Ca II H large spicules which are composed of numerous dynamic thin spicules but appear as macrospicules in EUV lower resolution images. We found no coronal counterpart of these and smaller spicules. We believe that the identification of phenomena which have very different origins as macrospicules is due to the interpretation of the transition region emission, and especially the He II emission, wherein both chromospheric large spicules and coronal X-ray jets are present. We suggest that the recent observation of spicules in the coronal AIA/SDO 171 A and 211 A channels is probably due to the existence of transition region emission there.Comment: 4 pages, 4 figures, accepted for publication in A&

Fourier approach to homogenization problems

This article is divided into two chapters. The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in the first chapter. Following a Fourier approach, we discuss some of the basic issues of the subject: main convergence theorem, Bloch approximation, estimates on second order derivatives, correctors for the medium, and so on. The second chapter is devoted to the discussion of some non-classical behaviour of vibration problems of periodic structures

Exact controllability of vibrations of thin bodies

In this paper, we address the problem of exact controllability of the wave equation in three dimensional domains which are thin in one direction. We prove the existence of exact controls and analyze their asymptotic behaviour as thickness parameter goes to zero. We characterize their limit as the solution of an exact controllability problem in two dimension

Boundary sentinels in cylindrical domains

We study a model describing vibrations of a cylindrical domain with thickness e > 0. A characteristic of this model is that it contains "pollution terms" in the boundary data and "missing terms" in the initial data. The "method of sentinels'' of J.L. Lions [7] is followed to construct a sentinel using the observed vibrations on the boundary. Such a sentinel, by construction, provides information on pollution terms independent of missing terms. This requires resolution of initial-boundary value problems with non-zero boundary data of mixed type and an exact controllability problem. Further, we characterize so called "stealthy pollution terms" present in the model

Boundary sentinels in cylindrical domains

We study a model describing vibrations of a cylindrical domain with thickness e > 0. A characteristic of this model is that it contains “pollution terms” in the boundary data and “missing terms” in the initial data. The “method of sentinels” of J.L. Lions [7] is followed to construct a sentinel using the observed vibrations on the boundary. Such a sentinel, by construction, provides information on pollution terms independent of missing terms. This requires resolution of initial-boundary value problems with nonzero boundary data of mixed type and an exact controllability problem. Further, we characterize so called “stealthy pollution terms” present in the model

Coronal response to an EUV wave from DEM analysis

EUV (Extreme-Ultraviolet) waves are globally propagating disturbances that have been observed since the era of the SoHO/EIT instrument. Although the kinematics of the wave front and secondary wave components have been widely studied, there is not much known about the generation and plasma properties of the wave. In this paper we discuss the effect of an EUV wave on the local plasma as it passes through the corona. We studied the EUV wave, generated during the 2011 February 15 X-class flare/CME event, using Differential Emission Measure diagnostics. We analyzed regions on the path of the EUV wave and investigated the local density and temperature changes. From our study we have quantitatively confirmed previous results that during wave passage the plasma visible in the Atmospheric Imaging Assembly (AIA) 171A channel is getting heated to higher temperatures corresponding to AIA 193A and 211A channels. We have calculated an increase of 6 - 9% in density and 5 - 6% in temperature during the passage of the EUV wave. We have compared the variation in temperature with the adiabatic relationship and have quantitatively demonstrated the phenomenon of heating due to adiabatic compression at the wave front. However, the cooling phase does not follow adiabatic relaxation but shows slow decay indicating slow energy release being triggered by the wave passage. We have also identified that heating is taking place at the front of the wave pulse rather than at the rear. Our results provide support for the case that the event under study here is a compressive fast-mode wave or a shock.Comment: Accepted for publication in Ap

Magnetic Reconnection resulting from Flux Emergence: Implications for Jet Formation in the lower solar atmosphere?

We aim at investigating the formation of jet-like features in the lower solar atmosphere, e.g. chromosphere and transition region, as a result of magnetic reconnection. Magnetic reconnection as occurring at chromospheric and transition regions densities and triggered by magnetic flux emergence is studied using a 2.5D MHD code. The initial atmosphere is static and isothermal, with a temperature of 20,000 K. The initial magnetic field is uniform and vertical. Two physical environments with different magnetic field strength (25 G and 50 G) are presented. In each case, two sub-cases are discussed, where the environments have different initial mass density. In the case where we have a weaker magnetic field (25 G) and higher plasma density ($N_e=2\times 10^{11}$ cm$^{-3}$), valid for the typical quiet Sun chromosphere, a plasma jet would be observed with a temperature of 2--3 $\times 10^4$ K and a velocity as high as 40 km/s. The opposite case of a medium with a lower electron density ($N_e=2\times 10^{10}$ cm$^{-3}$), i.e. more typical for the transition region, and a stronger magnetic field of 50 G, up-flows with line-of-sight velocities as high as 90 km/s and temperatures of 6 $\times$ 10$^5$ K, i.e. upper transition region -- low coronal temperatures, are produced. Only in the latter case, the low corona Fe IX 171 \AA\ shows a response in the jet which is comparable to the O V increase. The results show that magnetic reconnection can be an efficient mechanism to drive plasma outflows in the chromosphere and transition region. The model can reproduce characteristics, such as temperature and velocity for a range of jet features like a fibril, a spicule, an hot X-ray jet or a transition region jet by changing either the magnetic field strength or the electron density, i.e. where in the atmosphere the reconnection occurs.Comment: 11 pages, 13 figures, 2 table