Sum-factorization techniques in Isogeometric Analysis

The fast assembling of stiffness and mass matrices is a key issue in isogeometric analysis, particularly if the spline degree is increased. We present two algorithms based on the idea of sum factorization, one for matrix assembling and one for matrix-free methods, and study the behavior of their computational complexity in terms of the spline order $p$. Opposed to the standard approach, these algorithms do not apply the idea element-wise, but globally or on macro-elements. If this approach is applied to Gauss quadrature, the computational complexity grows as $p^{d+2}$ instead of $p^{2d+1}$ as previously achieved.Comment: 34 pages, 8 figure

Bacterial degradation of polychlorinted biphenyls in sludge from an industrial sewer lagoon

A laboratory experiment was conducted to determine if polychlorinated biphenyls (PCB's) found in an industrial sewer sludge can be effectively degraded by mutant bacteria. The aerated sludge was inoculated daily with mutant bacteria in order to augment the existing bacteria with bacteria that were considered to be capable of degrading PCB's. The pH, nitrogen, and phosphorus levels were monitored daily to maintain an optimum growing medium for the bacteria. A gas chromatographic method was used to determine the PCB concentrations of the sludge initially and also throughout the experiment. Results and discussion of the bacterial treatment of polychlorinated biphenyls are presented

Exact Maximal Height Distribution of Fluctuating Interfaces

We present an exact solution for the distribution P(h_m,L) of the maximal height h_m (measured with respect to the average spatial height) in the steady state of a fluctuating Edwards-Wilkinson interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h_m,L)=L^{-1/2}f(h_m L^{-1/2}) for all L where the function f(x) is the Airy distribution function that describes the probability density of the area under a Brownian excursion over a unit interval. For the free boundary case, the same scaling holds but the scaling function is different from that of the periodic case. Numerical simulations are in excellent agreement with our analytical results. Our results provide an exactly solvable case for the distribution of extremum of a set of strongly correlated random variables.Comment: 4 pages revtex (two-column), 1 .eps figure include

Towards Precision LSST Weak-Lensing Measurement - I: Impacts of Atmospheric Turbulence and Optical Aberration

The weak-lensing science of the LSST project drives the need to carefully model and separate the instrumental artifacts from the intrinsic lensing signal. The dominant source of the systematics for all ground based telescopes is the spatial correlation of the PSF modulated by both atmospheric turbulence and optical aberrations. In this paper, we present a full FOV simulation of the LSST images by modeling both the atmosphere and the telescope optics with the most current data for the telescope specifications and the environment. To simulate the effects of atmospheric turbulence, we generated six-layer phase screens with the parameters estimated from the on-site measurements. For the optics, we combined the ray-tracing tool ZEMAX and our simulated focal plane data to introduce realistic aberrations and focal plane height fluctuations. Although this expected flatness deviation for LSST is small compared with that of other existing cameras, the fast f-ratio of the LSST optics makes this focal plane flatness variation and the resulting PSF discontinuities across the CCD boundaries significant challenges in our removal of the systematics. We resolve this complication by performing PCA CCD-by-CCD, and interpolating the basis functions using conventional polynomials. We demonstrate that this PSF correction scheme reduces the residual PSF ellipticity correlation below 10^-7 over the cosmologically interesting scale. From a null test using HST/UDF galaxy images without input shear, we verify that the amplitude of the galaxy ellipticity correlation function, after the PSF correction, is consistent with the shot noise set by the finite number of objects. Therefore, we conclude that the current optical design and specification for the accuracy in the focal plane assembly are sufficient to enable the control of the PSF systematics required for weak-lensing science with the LSST.Comment: Accepted to PASP. High-resolution version is available at http://dls.physics.ucdavis.edu/~mkjee/LSST_weak_lensing_simulation.pd

Late gadolinium enhancement and subclinical cardiac dysfunction on cardiac MRI in asymptomatic HIV-positive men

Background: HIV is associated with an increased risk of cardiovascular disease (CVD) and related clinical events. While traditional risk factors play an important role in the pathology of cardiovascular disease, HIV infection and its sequelae of immune activation and inflammation may have significant effects on the myocardium before becoming clinically evident. Cardiac MRI (CMR) can be used to detect the pattern of these subclinical changes. This will lead to a better understanding of risk factors contributing to cardiovascular disease prior to it becoming clinically significant in HIV-positive patients. Methods: Prospective cohort study of 127 asymptomatic HIV-positive men on ART compared to 35 matched controls. Baseline demographics, HIV parameters, 12-lead ECG, routine biochemistry, and traditional cardiovascular risk factors were recorded. Images were acquired on a 3T Achieva Philips MRI scanner with 5 channel phase array cardiac coil and weight-based IV gadolinium was given at 0.15 mmol/kg dose with post-contrast inversion recovery imaging after 10 minutes. Results: 6/127 (4.7%) of asymptomatic HIV-positive men had late gadolinium enhancement (LGE) on MRI verses 1/35 (2.9%) in the control group. In 3/6 (50%) of cases this was in a classical infarction pattern with subendocardial involvement. 3/6 (50%) were consistent with prior myocarditis. There was no significant difference in mean LVEF (66.93% vs 65.18%), LVMI (60.05g/m2 vs 55.94g/m2) or posterolateral wall thickness (8.28 mm and 8.16 mm) between cases and controls respectively. There was significantly more diastolic dysfunction, E:A ratio < 1, found in the HIV-positive group, 18% vs 7% of controls (p = 0.037). Framingham risk did not predict either of these outcomes. Conclusions: There is an increased incidence of LGE detected on CMR in this asymptomatic HIV-positive cohort. Two distinct pathological processes were identifed as causing these changes, myocardial infarction and myocarditis. These findings were independent of traditional cardiac risk factors, duration of HIV infection and ART therapy. Sub clinical cardiac dysfunction may be underreported in other cardiac evaluation studies. The true impact of other potential risk factors may also be underestimated, highlighting the need for the development of more complex prediction models

A parallel multigrid solver for multi-patch Isogeometric Analysis

Isogeometric Analysis (IgA) is a framework for setting up spline-based discretizations of partial differential equations, which has been introduced around a decade ago and has gained much attention since then. If large spline degrees are considered, one obtains the approximation power of a high-order method, but the number of degrees of freedom behaves like for a low-order method. One important ingredient to use a discretization with large spline degree, is a robust and preferably parallelizable solver. While numerical evidence shows that multigrid solvers with standard smoothers (like Gauss Seidel) does not perform well if the spline degree is increased, the multigrid solvers proposed by the authors and their co-workers proved to behave optimal both in the grid size and the spline degree. In the present paper, the authors want to show that those solvers are parallelizable and that they scale well in a parallel environment.Comment: The first author would like to thank the Austrian Science Fund (FWF) for the financial support through the DK W1214-04, while the second author was supported by the FWF grant NFN S117-0

The mass and density of the dwarf planet (225088) 2007 OR10

The satellite of (225088) 2007 OR10 was discovered on archival Hubble Space Telescope images and along with new observations with the WFC3 camera in late 2017 we have been able to determine the orbit. The orbit's notable eccentricity, e$\approx$0.3, may be a consequence of an intrinsically eccentric orbit and slow tidal evolution, but may also be caused by the Kozai mechanism. Dynamical considerations also suggest that the moon is small, D$_{eff}$ $<$ 100 km. Based on the newly determined system mass of 1.75x10$^{21}$ kg, 2007 OR10 is the fifth most massive dwarf planet after Eris, Pluto, Haumea and Makemake. The newly determined orbit has also been considered as an additional option in our radiometric analysis, provided that the moon orbits in the equatorial plane of the primary. Assuming a spherical shape for the primary this approach provides a size of 1230$\pm$50 km, with a slight dependence on the satellite orbit orientation and primary rotation rate chosen, and a bulk density of 1.75$\pm$0.07 g cm$^{-3}$ for the primary. A previous size estimate that assumed an equator-on configuration (1535$^{+75}_{-225}$ km) would provide a density of 0.92$^{+0.46}_{-0.14}$ g cm$^{-3}$, unexpectedly low for a 1000 km-sized dwarf planet.Comment: Accepted for publication in Icaru