Sparse inversion of Stokes profiles. I. Two-dimensional Milne-Eddington inversions

Inversion codes are numerical tools used for the inference of physical properties from the observations. Despite their success, the quality of current spectropolarimetric observations and those expected in the near future presents a challenge to current inversion codes. The pixel-by-pixel strategy of inverting spectropolarimetric data that we currently utilize needs to be surpassed and improved. The inverted physical parameters have to take into account the spatial correlation that is present in the data and that contains valuable physical information. We utilize the concept of sparsity or compressibility to develop an new generation of inversion codes for the Stokes parameters. The inversion code uses numerical optimization techniques based on the idea of proximal algorithms to impose sparsity. In so doing, we allow for the first time to exploit the presence of spatial correlation on the maps of physical parameters. Sparsity also regularizes the solution by reducing the number of unknowns. We compare the results of the new inversion code with pixel-by-pixel inversions, demonstrating the increase in robustness of the solution. We also show how the method can easily compensate for the effect of the telescope point spread function, producing solutions with an enhanced contrast.Comment: 13 pages, 8 figures, accepted for publication in A&

Calabi-Yau Manifolds Over Finite Fields, II

We study zeta-functions for a one parameter family of quintic threefolds defined over finite fields and for their mirror manifolds and comment on their structure. The zeta-function for the quintic family involves factors that correspond to a certain pair of genus 4 Riemann curves. The appearance of these factors is intriguing since we have been unable to `see' these curves in the geometry of the quintic. Having these zeta-functions to hand we are led to comment on their form in the light of mirror symmetry. That some residue of mirror symmetry survives into the zeta-functions is suggested by an application of the Weil conjectures to Calabi-Yau threefolds: the zeta-functions are rational functions and the degrees of the numerators and denominators are exchanged between the zeta-functions for the manifold and its mirror. It is clear nevertheless that the zeta-function, as classically defined, makes an essential distinction between Kahler parameters and the coefficients of the defining polynomial. It is an interesting question whether there is a `quantum modification' of the zeta-function that restores the symmetry between the Kahler and complex structure parameters. We note that the zeta-function seems to manifest an arithmetic analogue of the large complex structure limit which involves 5-adic expansion.Comment: Plain TeX, 50 pages, 4 eps figure

Calabi-Yau Manifolds Over Finite Fields, I

We study Calabi-Yau manifolds defined over finite fields. These manifolds have parameters, which now also take values in the field and we compute the number of rational points of the manifold as a function of the parameters. The intriguing result is that it is possible to give explicit expressions for the number of rational points in terms of the periods of the holomorphic three-form. We show also, for a one parameter family of quintic threefolds, that the number of rational points of the manifold is closely related to as the number of rational points of the mirror manifold. Our interest is primarily with Calabi-Yau threefolds however we consider also the interesting case of elliptic curves and even the case of a quadric in CP_1 which is a zero dimensional Calabi-Yau manifold. This zero dimensional manifold has trivial dependence on the parameter over C but a not trivial arithmetic structure.Comment: 75 pages, 6 eps figure

Short dynamic fibrils in sunspot chromospheres

Sunspot chromospheres display vigorous oscillatory signature when observed in chromospheric diagnostics like the strong Ca II lines and H-alpha. New high-resolution sunspot observations from the Swedish 1-m Solar Telescope show the ubiquitous presence of small-scale periodic jet-like features that move up and down. This phenomenon has not been described before. Their typical width is about 0.3 arcsec and they display clear parabolic trajectories in space-time diagrams. The maximum extension of the top of the jets is lowest in the umbra, a few 100 km, and progressively longer further away from the umbra in the penumbra, with the longest more than 1000 km. These jets resemble dynamic fibrils found in plage regions but at smaller extensions. LTE inversion of spectro-polarimetric Ca II 8542 observations enabled for a comparison of the magnetic field inclination and the properties of these short jets. We find that the most extended of these jets also have longer periods and tend to be located in regions with more horizontal magnetic fields. This is a direct observational confirmation of the mechanism of long-period waves propagating along inclined magnetic fields into the solar chromosphere. This mechanism was identified earlier as the driver of dynamic fibrils in plage, part of the mottles in quiet Sun, and type I spicules at the limb. The sunspot dynamic fibrils that we report here represent a new class of manifestation of this mechanism. They are not the same as the transient penumbral and umbral micro-jets reported earlier.Comment: animations of figures can be found at http://folk.uio.no/rouppe/dfsunspot

Optimal Control Realizations of Lagrangian Systems with Symmetry

A new relation among a class of optimal control systems and Lagrangian systems with symmetry is discussed. It will be shown that a family of solutions of optimal control systems whose control equation are obtained by means of a group action are in correspondence with the solutions of a mechanical Lagrangian system with symmetry. This result also explains the equivalence of the class of Lagrangian systems with symmetry and optimal control problems discussed in \cite{Bl98}, \cite{Bl00}. The explicit realization of this correspondence is obtained by a judicious use of Clebsch variables and Lin constraints, a technique originally developed to provide simple realizations of Lagrangian systems with symmetry. It is noteworthy to point out that this correspondence exchanges the role of state and control variables for control systems with the configuration and Clebsch variables for the corresponding Lagrangian system. These results are illustrated with various simple applications

Is the sky the limit? Performance of the revamped Swedish 1-m Solar Telescope and its blue- and red-beam re-imaging systems

We demonstrate that for data recorded with a solar telescope that uses adaptive optics and/or post-processing to compensate for many low- and high-order aberrations, the RMS granulation contrast is directly proportional to the Strehl ratio calculated from the residual (small-scale) wavefront error. We demonstrate that the wings of the high-order compensated PSF for SST are likely to extend to a radius of not more than about 2 arcsec, consistent with earlier conclusions drawn from straylight compensation of sunspot images. We report on simultaneous measurements of seeing and solar granulation contrast averaged over 2 sec time intervals at several wavelengths from 525 nm to 853.6 nm on the red-beam (CRISP beam) and wavelengths from 395 nm to 484 nm on the blue-beam (CHROMIS beam). These data were recorded with the Swedish 1-m Solar Telescope (SST) that has been revamped with an 85-electrode adaptive mirror and a new tip-tilt mirror, both of which were polished to exceptionally high optical quality. The highest 2-sec average image contrast measured in April 2015 through 0.3-0.9 nm interference filters at 525 nm, 557 nm, 630 nm and 853.5 nm with compensation only for the diffraction limited point spread function of SST is 11.8%, 11.8%, 10.2% and 7.2% respectively. Similarly, the highest 2-sec contrast measured at 395 nm, 400 nm and 484 nm in May 2016 through 0.37-1.3 nm filters is 16%, 16% and 12.5% respectively. The granulation contrast observed with SST compares favorably with that of other telescopes. Simultaneously with the above wideband red-beam data, we also recorded narrow-band continuum images with the CRISP imaging spectropolarimeter. We find that contrasts measured with CRISP are entirely consistent with the corresponding wide-band contrasts, demonstrating that any additional image degradation by the CRISP etalons and telecentric optical system is marginal or even insignificant.Comment: In press in Astronomy & Astrophysic

Real-time multiframe blind deconvolution of solar images

The quality of images of the Sun obtained from the ground are severely limited by the perturbing effect of the turbulent Earth's atmosphere. The post-facto correction of the images to compensate for the presence of the atmosphere require the combination of high-order adaptive optics techniques, fast measurements to freeze the turbulent atmosphere and very time consuming blind deconvolution algorithms. Under mild seeing conditions, blind deconvolution algorithms can produce images of astonishing quality. They can be very competitive with those obtained from space, with the huge advantage of the flexibility of the instrumentation thanks to the direct access to the telescope. In this contribution we leverage deep learning techniques to significantly accelerate the blind deconvolution process and produce corrected images at a peak rate of ~100 images per second. We present two different architectures that produce excellent image corrections with noise suppression while maintaining the photometric properties of the images. As a consequence, polarimetric signals can be obtained with standard polarimetric modulation without any significant artifact. With the expected improvements in computer hardware and algorithms, we anticipate that on-site real-time correction of solar images will be possible in the near future.Comment: 16 pages, 12 figures, accepted for publication in A&

Metabasin dynamics and local structure in supercooled water

We employ the Distance Matrix method to investigate metabasin dynamics in supercooled water. We find that the motion of the system consists in the exploration of a finite region of configuration space (enclosing several distinct local minima), named metabasin, followed by a sharp crossing to a different metabasin. The characteristic time between metabasin transitions is comparable to the structural relaxation time, suggesting that these transitions are relevant for the long time dynamics. The crossing between metabasins is accompanied by very rapid diffusional jumps of several groups of dynamically correlated particles. These particles form relatively compact clusters and act as cooperative relaxing units responsible for the density relaxation. We find that these mobile particles are often characterized by an average coordination larger than four, i.e. are located in regions where the tetrahedral hydrogen bond network is distorted