The wall effect in cavity flow

A non-linear theory for the calculation of the flow field of an oblique flat plate under blockage condition is given using the techniques of integral equations. Numerical results are obtained with the aid of a high speed digital computer for the plate situated mid-channel at values of the angle of attack from 50 to 90° and the channel width-chord ratio from 3 to 20. Also obtained are results for the plate situated at two different off-center positions for a channel width-chord ratio 5 and angles of attack less than 30°

Automatic generation of simplified weakest preconditions for integrity constraint verification

Given a constraint $c$ assumed to hold on a database $B$ and an update $u$ to be performed on $B$, we address the following question: will $c$ still hold after $u$ is performed? When $B$ is a relational database, we define a confluent terminating rewriting system which, starting from $c$ and $u$, automatically derives a simplified weakest precondition $wp(c,u)$ such that, whenever $B$ satisfies $wp(c,u)$, then the updated database $u(B)$ will satisfy $c$, and moreover $wp(c,u)$ is simplified in the sense that its computation depends only upon the instances of $c$ that may be modified by the update. We then extend the definition of a simplified $wp(c,u)$ to the case of deductive databases; we prove it using fixpoint induction

Sizes and Kinematics of Extended Narrow-Line Regions in Luminous Obscured AGN Selected by Broadband Images

To study the impact of active galactic nuclei (AGN) feedback on the galactic ISM, we present Magellan long-slit spectroscopy of 12 luminous nearby type 2 AGN (L_bol~10^{45.0-46.5} erg/s, z~0.1). These objects are selected from a parent sample of spectroscopically identified AGN to have high [OIII]{\lambda}5007 and WISE mid-IR luminosities and extended emission in the SDSS r-band images, suggesting the presence of extended [OIII]{\lambda}5007 emission. We find spatially resolved [OIII] emission (2-35 kpc from the nucleus) in 8 out of 12 of these objects. Combined with samples of higher luminosity type 2 AGN, we confirm that the size of the narrow-line region (R_NLR) scales with the mid-IR luminosity until the relation flattens at ~10 kpc. Nine out of 12 objects in our sample have regions with broad [OIII] linewidths (w_80>600 km/s), indicating outflows. We define these regions as the kinematically-disturbed region (KDR). The size of the KDR (R_KDR) is typically smaller than R_NLR by few kpc but also correlates strongly with the AGN mid-IR luminosity. Given the unknown density in the gas, we derive a wide range in the energy efficiency {\eta}=dot{E}/L_bol=0.01%-30%. We find no evidence for an AGN luminosity threshold below which outflows are not launched. To explain the sizes, velocity profiles, and high occurrence rates of the outflows in the most luminous AGN, we propose a scenario in which energy-conserving outflows are driven by AGN episodes with ~10^8-year durations. Within each episode the AGN flickers on shorter timescales, with a cadence of ~10^6 year active phases separated by ~10^7 years.Comment: 32 pages, 21 figures, ApJ in revie

Karhunen-Lo\`eve expansion for a generalization of Wiener bridge

We derive a Karhunen-Lo\`eve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u)\,d B_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2\,d u =1$. This process is an important limit process in the theory of goodness-of-fit tests. We formulate two special cases with the function $g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$.Comment: 25 pages, 1 figure. The appendix is extende

An intracardiac electrogram model to bridge virtual hearts and implantable cardiac devices

Virtual heart models have been proposed to enhance the safety of implantable cardiac devices through closed loop validation. To communicate with a virtual heart, devices have been driven by cardiac signals at specific sites. As a result, only the action potentials of these sites are sensed. However, the real device implanted in the heart will sense a complex combination of near and far-field extracellular potential signals. Therefore many device functions, such as blanking periods and refractory periods, are designed to handle these unexpected signals. To represent these signals, we develop an intracardiac electrogram (IEGM) model as an interface between the virtual heart and the device. The model can capture not only the local excitation but also far-field signals and pacing afterpotentials. Moreover, the sensing controller can specify unipolar or bipolar electrogram (EGM) sensing configurations and introduce various oversensing and undersensing modes. The simulation results show that the model is able to reproduce clinically observed sensing problems, which significantly extends the capabilities of the virtual heart model in the context of device validation

ALMA Observations of a Candidate Molecular Outflow in an Obscured Quasar

We present Atacama Large Millimeter/Submillimeter Array (ALMA) CO (1-0) and CO (3-2) observations of SDSS J135646.10+102609.0, an obscured quasar and ultra-luminous infrared galaxy (ULIRG) with two merging nuclei and a known 20-kpc-scale ionized outflow. The total molecular gas mass is M_{mol} ~ 9^{+19}_{-6} x 10^8 Msun, mostly distributed in a compact rotating disk at the primary nucleus (M_{mol} ~ 3 x 10^8 Msun) and an extended tidal arm (M_{mol} ~ 5 x 10^8 Msun). The tidal arm is one of the most massive molecular tidal features known; we suggest that it is due to the lower chance of shock dissociation in this elliptical/disk galaxy merger. In the spatially resolved CO (3-2) data, we find a compact (r ~ 0.3 kpc) high velocity (v ~ 500 km/s) red-shifted feature in addition to the rotation at the N nucleus. We propose a molecular outflow as the most likely explanation for the high velocity gas. The outflowing mass of M_{mol} ~ 7 x 10^7 Msun and the short dynamical time of t_{dyn} ~ 0.6 Myr yield a very high outflow rate of \dot{M}_{mol} ~ 350 Msun/yr and can deplete the gas in a million years. We find a low star formation rate (< 16 Msun/yr from the molecular content and < 21 Msun/yr from the far-infrared spectral energy distribution decomposition) that is inadequate to supply the kinetic luminosity of the outflow (\dot{E} ~ 3 x 10^43 erg/s). Therefore, the active galactic nucleus, with a bolometric luminosity of 10^46 erg/s, likely powers the outflow. The momentum boost rate of the outflow (\dot{p}/(Lbol/c) ~ 3) is lower than typical molecular outflows associated with AGN, which may be related to its compactness. The molecular and ionized outflows are likely two distinct bursts induced by episodic AGN activity that varies on a time scale of 10^7 yr.Comment: 16 pages, 7 figures, ApJ accepte

On the variational interpretation of the discrete KP equation

We study the variational structure of the discrete Kadomtsev-Petviashvili (dKP) equation by means of its pluri-Lagrangian formulation. We consider the dKP equation and its variational formulation on the cubic lattice ${\mathbb Z}^{N}$ as well as on the root lattice $Q(A_{N})$. We prove that, on a lattice of dimension at least four, the corresponding Euler-Lagrange equations are equivalent to the dKP equation.Comment: 24 page

Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization

In this article, we study an analog of the Bj\"orling problem for isothermic surfaces (that are more general than minimal surfaces): given a real analytic curve $\gamma$ in ${\mathbb R}^3$, and two analytic non-vanishing orthogonal vector fields $v$ and $w$ along $\gamma$, find an isothermic surface that is tangent to $\gamma$ and that has $v$ and $w$ as principal directions of curvature. We prove that solutions to that problem can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is sampled along $\gamma$, and passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.Comment: 29 pages, some figure

Comment on Bress et al. Effect of Intensive Versus Standard Blood Pressure Treatment According to Baseline Prediabetes Status: A Post Hoc Analysis of a Randomized Trial. Diabetes Care 2017;40:1401-1408.

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