Evaluating local correlation tracking using CO5BOLD simulations of solar granulation

Flows on the solar surface are linked to solar activity, and LCT is one of the standard techniques for capturing the dynamics of these processes by cross-correlating solar images. However, the link between contrast variations in successive images to the underlying plasma motions has to be quantitatively confirmed. Radiation hydrodynamics simulations of solar granulation (e.g.,CO5BOLD) provide access to both the wavelength-integrated, emergent continuum intensity and the 3D velocity field at various heights in the solar atmosphere. Thus, applying LCT to continuum images yields horizontal proper motions, which are then compared to the velocity field of the simulated (non-magnetic) granulation. In this study, we evaluate the performance of an LCT algorithm previously developed for bulk-processing Hinode G-band images, establish it as a quantitative tool for measuring horizontal proper motions, and clearly work out the limitations of LCT or similar techniques designed to track optical flows. Horizontal flow maps and frequency distributions of the flow speed were computed for a variety of LCT input parameters including the spatial resolution, the width of the sampling window, the time cadence of successive images, and the averaging time used to determine persistent flow properties. Smoothed velocity fields from the hydrodynamics simulation at three atmospheric layers (log tau=-1,0,and +1) served as a point of reference for the LCT results. LCT recovers many of the granulation properties, e.g.,the shape of the flow speed distributions, the relationship between mean flow speed and averaging time, and also--with significant smoothing of the simulated velocity field--morphological features of the flow and divergence maps. However, the horizontal proper motions are grossly underestimated by as much as a factor of three. The LCT flows match best the flows deeper in the atmosphere at log tau=+1.Comment: 11 pages, 16 figures, accepted for publication in Astronomy and Astrophysic

Spectral Properties of the Ruelle Operator for Product Type Potentials on Shift Spaces

We study a class of potentials $f$ on one sided full shift spaces over finite or countable alphabets, called potentials of product type. We obtain explicit formulae for the leading eigenvalue, the eigenfunction (which may be discontinuous) and the eigenmeasure of the Ruelle operator. The uniqueness property of these quantities is also discussed and it is shown that there always exists a Bernoulli equilibrium state even if $f$ does not satisfy Bowen's condition. We apply these results to potentials $f:\{-1,1\}^\mathbb{N} \to \mathbb{R}$ of the form $$f(x_1,x_2,\ldots) = x_1 + 2^{-\gamma} \, x_2 + 3^{-\gamma} \, x_3 + ...+n^{-\gamma} \, x_n + \ldots$$ with $\gamma >1$. For $3/2 < \gamma \leq 2$, we obtain the existence of two different eigenfunctions. Both functions are (locally) unbounded and exist a.s. (but not everywhere) with respect to the eigenmeasure and the measure of maximal entropy, respectively.Comment: To appear in the Journal of London Mathematical Societ

Near-infrared spectropolarimetry of a delta-spot

Sunspots harboring umbrae of both magnetic polarities within a common penumbra (delta-spots) are often but not always related to flares. We present first near-infrared (NIR) observations (Fe I 1078.3 nm and Si I 1078.6 nm spectra) obtained with the Tenerife Infrared Polarimeter (TIP) at the Vacuum Tower Telescope (VTT) in Tenerife on 2012 June 17, which afford accurate and sensitive diagnostics to scrutinize the complex fields along the magnetic neutral line of a delta-spot within active region NOAA 11504. We examine the vector magnetic field, line-of-sight (LOS) velocities, and horizontal proper motions of this rather inactive delta-spot. We find a smooth transition of the magnetic vector field from the main umbra to that of opposite polarity (delta-umbra), but a discontinuity of the horizontal magnetic field at some distance from the delta-umbra on the polarity inversion line. The magnetic field decreases faster with height by a factor of two above the delta-umbra. The latter is surrounded by its own Evershed flow. The Evershed flow coming from the main umbra ends at a line dividing the spot into two parts. This line is marked by the occurrence of central emission in the Ca II 854.2 nm line. Along this line, high chromospheric LOS-velocities of both signs appear. We detect a shear flow within the horizontal flux transport velocities parallel to the dividing line.Comment: 4 pages, will appear as Letter in Astronomy & Astrophysic

Ergodicity of avalanche transformations

PublishedIn this paper, we study dynamical systems of product type and some particular inducing scheme motivated by neural dynamics (called avalanche transformation). We derive the distribution of avalanche sizes and give sufficient conditions such that the avalanche transformation is ergodic. Moreover, we deduce a multivariate central limit theorem as a corollary.We would like to thank Ira Gessel and Wlodek Bryc for some helpful remarks concerning Section 2. The research of M. Denker was supported by the National Science Foundation grant DMS- 1008538. The research of A. Rodrigues is supported by the Swedish Research Council (VR Grant 2010/5905). The authors would like to thank the Goran Gustafsson Foundation UU/KTH for the ¨ financial support

Giant anisotropy of Zeeman splitting of quantum confined acceptors in Si/Ge

Shallow acceptor levels in Si/Ge/Si quantum well heterostructures are characterized by resonant tunneling spectroscopy in the presence of high magnetic fields. In a perpendicular magnetic field we observe a linear Zeeman splitting of the acceptor levels. In an in-plane field, on the other hand, the Zeeman splitting is strongly suppressed. This anisotropic Zeeman splitting is shown to be a consequence of the huge light hole-heavy hole splitting caused by a large biaxial strain and a strong quantum confinement in the Ge quantum well.Comment: 5 figures, 4 page