Higher order Jordan Osserman Pseudo-Riemannian manifolds

We study the higher order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r,s) for certain values of (r,s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher order Osserman manifolds

The minimal-span channel for rough-wall turbulent flows

Roughness predominantly alters the near-wall region of turbulent flow while the outer layer remains similar with respect to the wall shear stress. This makes it a prime candidate for the minimal-span channel, which only captures the near-wall flow by restricting the spanwise channel width to be of the order of a few hundred viscous units. Recently, Chung et al. (J. Fluid Mech., vol. 773, 2015, pp. 418-431) showed that a minimal-span channel can accurately characterise the hydraulic behaviour of roughness. Following this, we aim to investigate the fundamental dynamics of the minimal-span channel framework with an eye towards further improving performance. The streamwise domain length of the channel is investigated with the minimum length found to be three times the spanwise width or 1000 viscous units, whichever is longer. The outer layer of the minimal channel is inherently unphysical and as such alterations to it can be performed so long as the near-wall flow, which is the same as in a full-span channel, remains unchanged. Firstly, a half-height (open) channel with slip wall is shown to reproduce the near-wall behaviour seen in a standard channel, but with half the number of grid points. Next, a forcing model is introduced into the outer layer of a half-height channel. This reduces the high streamwise velocity associated with the minimal channel and allows for a larger computational time step. Finally, an investigation is conducted to see if varying the roughness Reynolds number with time is a feasible method for obtaining the full hydraulic behaviour of a rough surface. Currently, multiple steady simulations at fixed roughness Reynolds numbers are needed to obtain this behaviour. The results indicate that the non-dimensional pressure gradient parameter must be kept below 0.03-0.07 to ensure that pressure gradient effects do not lead to an inaccurate roughness function. An empirical costing argument is developed to determine the cost in terms of CPU hours of minimal-span channel simulations a priori. This argument involves counting the number of eddy lifespans in the channel, which is then related to the statistical uncertainty of the streamwise velocity. For a given statistical uncertainty in the roughness function, this can then be used to determine the simulation run time. Following this, a finite-volume code with a body-fitted grid is used to determine the roughness function for square-based pyramids using the above insights. Comparisons to experimental studies for the same roughness geometry are made and good agreement is observed.This work was partly funded through the Multi ow program by the European Research Council. Computational time was granted under the Victoria Life Sciences Computational Initiative, which is supported by the Victorian Government, Australia

Radio Sources in Low-Luminosity Active Galactic Nuclei. III. "AGNs" in a Distance-Limited Sample of "LLAGNs"

(abbreviated): This paper presents the results of a high resolution radio imaging survey of all known (96) low-luminosity active galactic nuclei (LLAGNs) at D<19Mpc. We find that almost half of all LINERs and low-luminosity Seyferts have flat-spectrum radio cores when observed at 150mas resolution. Higher (2mas) resolution observations of a flux-limited subsample have provided a 100% (16 of 16) detection rate of pc-scale radio cores, with implied brightness temperatures > 10^8 K. The five LLAGNs with the highest core radio fluxes also have pc-scale `jets.' Compact radio cores are almost exclusively found in massive ellipticals and in type1 nuclei. The core radio power is correlated with the nuclear optical `broad' Halpha luminosity, the nuclear optical `narrow' emission line luminosity and width, and with the galaxy luminosity. In these correlations LLAGNs fall close to the low-luminosity extrapolations of more powerful AGNs. About half of all LLAGNs with multiple epoch data show significant inter-year radio variability. Investigation of a sample of ~150 nearby bright galaxies, most of them LLAGNs, shows that the nuclear (<150mas size) radio power is strongly correlated with both the black hole mass and the galaxy bulge luminosity; linear regression fits to all ~150 galaxies give: log P(2cm) = 1.31 log M_blackhole + 8.77 and log P(2cm) = 1.89 log L_B(bulge) - 0.17. Low accretion rates are implied in both advection- and jet-type models. In brief, all evidence points towards the presence of accreting massive black holes in a large fraction, perhaps all, of LLAGNs.Comment: to appear in A&

Double-period zero-order metal gratings as effective selective absorbers

W.-C. Tan, J. Roy Sambles, and T. W. Preist, Physical Review B, Vol. 61, pp. 13177-13182 (2000). "Copyright © 2000 by the American Physical Society."The electromagnetic response of a zero-order metal grating having a primary deep short-period component and a shallow long-period component is modeled. It is found that such a metal grating has an unusual surface-plasmon-polariton band structure and exhibits strong selective absorption of incident radiation. This opens up potential for designing metal surfaces with specific optical response features

Study of the production of Λb0\Lambda_b^0 and B‾0\overline{B}^0 hadrons in pppp collisions and first measurement of the Λb0→J/ψpK−\Lambda_b^0\rightarrow J/\psi pK^- branching fraction

The product of the $\Lambda_b^0$ ($\overline{B}^0$) differential production cross-section and the branching fraction of the decay $\Lambda_b^0\rightarrow J/\psi pK^-$ ($\overline{B}^0\rightarrow J/\psi\overline{K}^*(892)^0$) is measured as a function of the beauty hadron transverse momentum, $p_{\rm T}$, and rapidity, $y$. The kinematic region of the measurements is $p_{\rm T}<20~{\rm GeV}/c$ and $2.0<y<4.5$. The measurements use a data sample corresponding to an integrated luminosity of $3~{\rm fb}^{-1}$ collected by the LHCb detector in $pp$ collisions at centre-of-mass energies $\sqrt{s}=7~{\rm TeV}$ in 2011 and $\sqrt{s}=8~{\rm TeV}$ in 2012. Based on previous LHCb results of the fragmentation fraction ratio, $f_{\Lambda_B^0}/f_d$, the branching fraction of the decay $\Lambda_b^0\rightarrow J/\psi pK^-$ is measured to be \begin{equation*} \mathcal{B}(\Lambda_b^0\rightarrow J/\psi pK^-)= (3.17\pm0.04\pm0.07\pm0.34^{+0.45}_{-0.28})\times10^{-4}, \end{equation*} where the first uncertainty is statistical, the second is systematic, the third is due to the uncertainty on the branching fraction of the decay $\overline{B}^0\rightarrow J/\psi\overline{K}^*(892)^0$, and the fourth is due to the knowledge of $f_{\Lambda_b^0}/f_d$. The sum of the asymmetries in the production and decay between $\Lambda_b^0$ and $\overline{\Lambda}_b^0$ is also measured as a function of $p_{\rm T}$ and $y$. The previously published branching fraction of $\Lambda_b^0\rightarrow J/\psi p\pi^-$, relative to that of $\Lambda_b^0\rightarrow J/\psi pK^-$, is updated. The branching fractions of $\Lambda_b^0\rightarrow P_c^+(\rightarrow J/\psi p)K^-$ are determined.Comment: 29 pages, 19figures. All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-032.htm

Constraints on the Physical Properties of GW190814 through Simulations Based on DECam Follow-up Observations by the Dark Energy Survey

On 2019 August 14, the LIGO and Virgo Collaborations detected gravitational waves from a black hole and a 2.6 solar mass compact object, possibly the first neutron star–black hole merger. In search of an optical counterpart, the Dark Energy Survey (DES) obtained deep imaging of the entire 90% confidence level localization area with Blanco/DECam 0, 1, 2, 3, 6, and 16 nights after the merger. Objects with varying brightness were detected by the DES Pipeline, and we systematically reduced the candidate counterparts through catalog matching, light-curve properties, host-galaxy photometric redshifts, Southern Astrophysical Research spectroscopic follow-up observations, and machine-learning-based photometric classification. All candidates were rejected as counterparts to the merger. To quantify the sensitivity of our search, we applied our selection criteria to full light-curve simulations of supernovae and kilonovae as they would appear in the DECam observations. Because the source class of the merger was uncertain, we utilized an agnostic, three-component kilonova model based on tidally disrupted neutron star (NS) ejecta properties to quantify our detection efficiency of a counterpart if the merger included an NS. We find that, if a kilonova occurred during this merger, configurations where the ejected matter is greater than 0.07 solar masses, has lanthanide abundance less than 10−8.56, and has a velocity between 0.18c and 0.21c are disfavored at the 2σ level. Furthermore, we estimate that our background reduction methods are capable of associating gravitational wave signals with a detected electromagnetic counterpart at the 4σ level in 95% of future follow-up observations