A Bramble-Pasciak conjugate gradient method for discrete Stokes equations with random viscosity

We study the iterative solution of linear systems of equations arising from stochastic Galerkin finite element discretizations of saddle point problems. We focus on the Stokes model with random data parametrized by uniformly distributed random variables and discuss well-posedness of the variational formulations. We introduce a Bramble-Pasciak conjugate gradient method as a linear solver. It builds on a non-standard inner product associated with a block triangular preconditioner. The block triangular structure enables more sophisticated preconditioners than the block diagonal structure usually applied in MINRES methods. We show how the existence requirements of a conjugate gradient method can be met in our setting. We analyze the performance of the solvers depending on relevant physical and numerical parameters by means of eigenvalue estimates. For this purpose, we derive bounds for the eigenvalues of the relevant preconditioned sub-matrices. We illustrate our findings using the flow in a driven cavity as a numerical test case, where the viscosity is given by a truncated Karhunen-Lo\`eve expansion of a random field. In this example, a Bramble-Pasciak conjugate gradient method with block triangular preconditioner outperforms a MINRES method with block diagonal preconditioner in terms of iteration numbers.Comment: 19 pages, 1 figure, submitted to SIAM JU

Supernova neutrino physics with xenon dark matter detectors: A timely perspective

Dark matter detectors that utilize liquid xenon have now achieved tonne-scale targets, giving them sensitivity to all flavours of supernova neutrinos via coherent elastic neutrino-nucleus scattering. Considering for the first time a realistic detector model, we simulate the expected supernova neutrino signal for different progenitor masses and nuclear equations of state in existing and upcoming dual-phase liquid xenon experiments. We show that the proportional scintillation signal (S2) of a dual-phase detector allows for a clear observation of the neutrino signal and guarantees a particularly low energy threshold, while the backgrounds are rendered negligible during the supernova burst. XENON1T (XENONnT and LZ; DARWIN) experiments will be sensitive to a supernova burst up to 25 (35; 65) kpc from Earth at a significance of more than 5 sigma, observing approximately 35 (123; 704) events from a 27 Msun supernova progenitor at 10 kpc. Moreover, it will be possible to measure the average neutrino energy of all flavours, to constrain the total explosion energy, and to reconstruct the supernova neutrino light curve. Our results suggest that a large xenon detector such as DARWIN will be competitive with dedicated neutrino telescopes, while providing complementary information that is not otherwise accessible.Comment: 19 pages, 9 figures. Minor revisions compared to original version. Matches version published in Phys. Rev.

Silicon Whisker and Carbon Nanofiber Composite Anode

Phase II Objectives: Demonstrate production levels of grams per batch; Achieve full cell anode capacity of greater than 1,000 mAh/g at a charge rate of 10 (C/10) and 0 degree C; Establish a full cell cycle life of over 300 cycles; Display an operating temperature of negative 30 degrees C to plus 30 degrees C; Demonstrate a rate capability of C/5 or higher; Deliver to NASA three 2.5 Ah cells (energy density greater than 220 Wh/kg); Exhibit the safety features of the anode and full cells; Design a 1 kWh prismatic battery pack

Cleaning the USNO-B Catalog through automatic detection of optical artifacts

The USNO-B Catalog contains spurious entries that are caused by diffraction spikes and circular reflection halos around bright stars in the original imaging data. These spurious entries appear in the Catalog as if they were real stars; they are confusing for some scientific tasks. The spurious entries can be identified by simple computer vision techniques because they produce repeatable patterns on the sky. Some techniques employed here are variants of the Hough transform, one of which is sensitive to (two-dimensional) overdensities of faint stars in thin right-angle cross patterns centered on bright (<13 \mag) stars, and one of which is sensitive to thin annular overdensities centered on very bright (<7 \mag) stars. After enforcing conservative statistical requirements on spurious-entry identifications, we find that of the 1,042,618,261 entries in the USNO-B Catalog, 24,148,382 of them (2.3 \percent) are identified as spurious by diffraction-spike criteria and 196,133 (0.02 \percent) are identified as spurious by reflection-halo criteria. The spurious entries are often detected in more than 2 bands and are not overwhelmingly outliers in any photometric properties; they therefore cannot be rejected easily on other grounds, i.e., without the use of computer vision techniques. We demonstrate our method, and return to the community in electronic form a table of spurious entries in the Catalog.Comment: published in A

The Error is the Feature: how to Forecast Lightning using a Model Prediction Error

Despite the progress within the last decades, weather forecasting is still a challenging and computationally expensive task. Current satellite-based approaches to predict thunderstorms are usually based on the analysis of the observed brightness temperatures in different spectral channels and emit a warning if a critical threshold is reached. Recent progress in data science however demonstrates that machine learning can be successfully applied to many research fields in science, especially in areas dealing with large datasets. We therefore present a new approach to the problem of predicting thunderstorms based on machine learning. The core idea of our work is to use the error of two-dimensional optical flow algorithms applied to images of meteorological satellites as a feature for machine learning models. We interpret that optical flow error as an indication of convection potentially leading to thunderstorms and lightning. To factor in spatial proximity we use various manual convolution steps. We also consider effects such as the time of day or the geographic location. We train different tree classifier models as well as a neural network to predict lightning within the next few hours (called nowcasting in meteorology) based on these features. In our evaluation section we compare the predictive power of the different models and the impact of different features on the classification result. Our results show a high accuracy of 96% for predictions over the next 15 minutes which slightly decreases with increasing forecast period but still remains above 83% for forecasts of up to five hours. The high false positive rate of nearly 6% however needs further investigation to allow for an operational use of our approach.Comment: 10 pages, 7 figure

A Photometric Study of the Young Stellar Population Throughout the lambda Orionis Star-Forming Region

We present VRI photometry of 320,917 stars with 11 < R < 18 throughout the lambda Orionis star-forming region. We statistically remove the field stars and identify a representative PMS population throughout the interior of the molecular ring. The spatial distribution of this population shows a concentration of PMS stars around lambda Ori and in front of the B35 dark cloud. Few PMS stars are found outside these pockets of high stellar density, suggesting that star formation was concentrated in an elongated cloud extending from B35 through lambda Ori to the B30 cloud. We find a lower limit for the global stellar mass of about 500 Mo. We find that the global ratio of low- to high-mass stars is similar to that predicted by the field initial mass function, but this ratio varies strongly as a function of position in the star-forming region. Locally, the star-formation process does not produce a universal initial mass function. We construct a history of the star-forming complex. This history incorporates a recent supernova to explain the distribution of stars and gas today.Comment: 42 pages, 11 figures; to appear in the Astronomical Journa