Approximate Discrete Probability Distribution Representation using a Multi-ResolutionBinary Tree

Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiples random variables. The problem of efficient representation of probability distributions is central in term of computational efficiency in the field of probabilistic reasoning. The main problem arises when dealing with joint probability distributions over a set of random variables: they are always represented using huge probability arrays. In this paper, a new method based on a binary-tree representation is introduced in order to store efficiently very large joint distributions. Our approach approximates any multidimensional joint distributions using an adaptive discretization of the space. We make the assumption that the lower is the probability mass of a particular region of feature space, the larger is the discretization step. This assumption leads to a very optimized representation in term of time and memory. The other advantages of our approach are the ability to refine dynamically the distribution every time it is needed leading to a more accurate representation of the probability distribution and to an anytime representation of the distribution

HINODE Observations of Chromospheric Brightenings in the Ca II H Line during small-scale Flux Emergence Events

\ion{Ca}{2} H emission is a well-known indicator of magnetic activity in the Sun and other stars. It is also viewed as an important signature of chromospheric heating. However, the \ion{Ca}{2} H line has not been used as a diagnostic of magnetic flux emergence from the solar interior. Here we report on Hinode observations of chromospheric \ion{Ca}{2} H brightenings associated with a repeated, small-scale flux emergence event. We describe this process and investigate the evolution of the magnetic flux, G-band brightness, and \ion{Ca}{2} H intensity in the emerging region. Our results suggest that energy is released in the chromosphere as a consequence of interactions between the emerging flux and the pre-existing magnetic field, in agreement with recent 3D numerical simulations.Comment: 12 Pages, 6 Figures, Accepted for publication in ApJ Letter

Scaling and the prediction of energy spectra in decaying hydrodynamic turbulence

Few rigorous results are derived for fully developed turbulence. By applying the scaling properties of the Navier-Stokes equation we have derived a relation for the energy spectrum valid for unforced or decaying isotropic turbulence. We find the existence of a scaling function $\psi$. The energy spectrum can at any time by a suitable rescaling be mapped onto this function. This indicates that the initial (primordial) energy spectrum is in principle retained in the energy spectrum observed at any later time, and the principle of permanence of large eddies is derived. The result can be seen as a restoration of the determinism of the Navier-Stokes equation in the mean. We compare our results with a windtunnel experiment and find good agreement.Comment: 4 pages, 1 figur

Supersonic Downflows at the Umbra-Penumbra Boundary of Sunspots

High resolution spectropolarimetric observations of 3 sunspots taken with Hinode demonstrate the existence of supersonic downflows at or close to the umbra-penumbra boundary which have not been reported before. These downflows are confined to large patches, usually encompassing bright penumbral filaments, and have lifetimes of more than 14 hr. The presence of strong downflows in the center-side penumbra near the umbra rules out an association with the Evershed flow. Chromospheric filtergrams acquired close to the time of the spectropolarimetric measurements show large, strong, and long-lived brightenings in the neighborhood of the downflows. The photospheric intensity also exhibit persistent brightenings comparable to the quiet Sun. Interestingly, the orientation of the penumbral filaments at the site of the downflows is similar to that resulting from the reconnection process described by Ryutova et al. The existence of such downflows in the inner penumbra represents a challenge for numerical models of sunspots because they have to explain them in terms of physical processes likely affecting the chromosphere.Comment: Accepted for publication in Ap

Supersonic Downflows in a Sunspot Light Bridge

We report the discovery of supersonic downflows in a sunspot light bridge using measurements taken with the spectropolarimeter on board the Hinode satellite. The downflows occur in small patches close to regions where the vector magnetic field changes orientation rapidly, and are associated with anomalous circular polarization profiles. An inversion of the observed Stokes spectra reveals velocities of up to 10 km/s, making them the strongest photospheric flows ever measured in light bridges. Some (but not all) of the downflowing patches are cospatial and cotemporal with brightness enhancements in chromospheric Ca II H filtergrams. We suggest that these flows are due to magnetic reconnection in the upper photosphere/lower chromosphere, although other mechanisms cannot be ruled out.Comment: 4 pages, 5 figures, Published in ApJ Letter

Evidence of convective rolls in a sunspot penumbra

aims: We study the recently discovered twisting motion of bright penumbral filaments with the aim of constraining their geometry and the associated magnetic field. methods: A large sunspot located 40\degr from disk center was observed at high resolution with the 1-m Swedish Solar Telescope. Inversions of multi-wavelength polarimetric data and speckle reconstructed time series of continuum images were used to determine proper motions, as well as the velocity and magnetic structure in penumbral filaments. results: The continuum movie reveals apparent lateral motions of bright and dark structures inside bright filaments oriented parallel to the limb, confirming recent Hinode results. In these filaments we measure upflows of $\approx 1.1 \mathrm{km/s}$ on their limbward side and weak downflows on their centerward side. The magnetic field in them is significantly weaker and more horizontal than in the adjacent dark filaments. conclusions: The data indicate the presence of vigorous convective rolls in filaments with a nearly horizontal magnetic field. These are separated by filaments harbouring stronger, more vertical fields. Because of reduced gas pressure, we see deeper into the latter. When observed near the limb, the disk-centerward side of the horizontal-field filaments appear bright due to the \textit{hot wall} effect known from faculae. We estimate that the convective rolls transport most of the energy needed to explain the penumbral radiative flux.Comment: 4 pages, 4 figures, letter to Astronomy & Astrophysic

Simulation of free surface and molten metal behavior during induction melting of an aluminium alloy

International audienceElectromagnetic forces are widely used for processing metal alloys in particular in the aluminium casting industry. Induction is used in melting technologies (both crucible and channel induction furnaces). Magnetic stirrers are also used in melting or casting furnaces. However these technologies applied to opaque melts require modelling to be done to understand the resultant impact on the fluid and improve the process control. This is especially the case of crucible induction furnaces. A 2D axially symmetric numerical model describing the coupled magnetohydrodynamic and free surface phenomena taking place in an induction metal bath has been developed. The model uses the Ansys Fluent software, supplemented with additional User Defined Functions for the calculation of the Lorentz forces acting on the metal. The calculation of the shape of the free surface is based on the Volume Of Fluid method and a RANS k-ω Shear Stress Transport (SST) approach is used to describe the turbulent stirring of the metal. An original feature of our model is the consideration of an oxide skin covering the metal free surface. It was considered that the oxide film behaves similarly to a deforming wall and that friction effects between the oxide film and the metal result in the development of a shear stress at the top surface of the melt. Two examples of application of model are reported, for lab scale and industrial scale induction furnaces. The lab scale results are compared with measurements of the free surface shape obtained using a fringe projection technique

On the estimate of magnetic non-potentiality of sunspots derived using Hinode SOT/SP observations: Effect of polarimetric noise

The accuracy of Milne-Eddington (ME) inversions, used to retrieve the magnetic field vector, depends upon the signal-to-noise ratio (SNR) of the spectro-polarimetric observations. The SNR in real observations varies from pixel to pixel, therefore the accuracy of the field vector also varies over the map. The aim of this work is to study the effect of polarimetric noise on the inference of magnetic field vector and the magnetic non-potentiality of a real sunspot. To this end, we use Hinode SOT/SP vector magnetogram of a real sunspot NOAA 10933 as an input to generate synthetic Stokes profiles under ME model assumptions. We then add normally-distributed polarimetric noise of the level 0.5\% of continuum intensity to these synthetic profiles and invert them again using ME code. This process is repeated 100 times with different realizations of noise. It is found that within most of the sunspot area (> 90% area) the spread in the (i) field strength is less than 8 Gauss, (ii) field inclination is less than 1 degree, and (iii) field azimuth is less than 5 degrees. Further, we determine the uncertainty in the magnetic non-potentiality of a sunspot as determined by the force-free parameter alpha_g and Spatially Averaged Signed Shear Angle (SASSA). It is found that for the sunspot studied here these parameters are alpha_g = -3.5 +/- 0.37 (x 10^{-9} m^{-1}) and SASSA = -1.68 +/- 0.014 degrees. This suggests that the SASSA is a less dispersion non-potentiality parameter as compared to alpha_g. Further, we examine the effect of increasing noise levels viz. 0.01, 0.1, 0.5 and 1% of continuum intensity and find that SASSA is less vulnerable to noise as compared to alpha_g parameter.Comment: Astrophysical Journal (In Press) 29 pages, 5 figures (scatterplots do not appear in soft-copy but appear on laser-printer