Laplace operators with eigenfunctions whose nodal set is a knot

We prove that, given any knot $\gamma$ in a compact 3-manifold M, there exists a Riemannian metric on M such that there is a complex-valued eigenfunction u of the Laplacian, corresponding to the first nontrivial eigenvalue, whose nodal set $u^{-1}(0)$ has a connected component given by $\gamma$. Higher dimensional analogs of this result will also be considered.Comment: 16 page

Dislocations of arbitrary topology in Coulomb eigenfunctions

For any finite link $L$ in $\mathbb{R}^3$ we prove the existence of a high-energy complex-valued eigenfunction of the hydrogen atom such that its nodal set contains a union of connected components diffeomorphic to $L$. This problem goes back to Berry, who constructed such eigenfunctions in the case where $L$ is the trefoil knot or the Hopf link and asked the question about the general result.Comment: 10 page

South polar dynamics of the Venusian atmosphere from VIRTIS/Venus Express mapping in the thermal range

We report on measurements of Venus cloud velocities from VIRTIS/Venus Express observations of the south polar region of Venus. Cloud tracking has been performed using a method of automated digital correlation. Tracking has been performed on pairs of monochromatic VIRTIS images selected mainly in the 5 μm window, but also at 1.74, 2.3, 3.93 micrometers. Wind measurements from vector retrievals based on automated feature tracking show high variability, indicating the presence of important transient motions. The time-averaged zonal winds indicate different day and night side regimes. On the day side both the zonal wind component (u) and the meridional one (v) are approximately uniform between 84S and 76S, with u ∼ −40 m/s and v ∼ −10 m/s. On the night side the zonal wind decreases poleward, from a maximum at 76S. The meridional wind is smaller than on the day side and appears to change sign from poleward to equatorward at 76S. The cold collar boundary appears to be a transition region not only for the temperature, but for the winds as well. In this region wave motions are also apparent, with amplitudes on the order of 40 m/s for u′ and 10 m/s for v′

Characterization of Atmospheric Waves at the Upper Clouds in the Polar Region of Venus

Non solar-fixed waves at the cloud tops of the southern polar region of Venus are studied in the winds measured with 3.9 and 5.0 μm images taken by the instrument VIRTIS-M onboard Venus Express. Wavenumbers 1, 2 and 3 are detected, with wave amplitudes ranging from 3.6 to 8.0 m/s. The evolution of the phase has been studied in 16 orbits, finding in a subset of orbits wavenumbers 1 and 2 propagating in different directions (zonal wind), and a westward progression with a phase velocity of approximately 5.7 m/s for the wavenumber 1 in the meridional wind. Finally, a new set of analytical solutions to the atmospheric waves is obtained for the planet Venus, and these are used to characterize the found waves in terms of the horizontal wavelength and phase velocity

Rehabilitación edificio para la Colombiana de Capitalización

Trabajo de gradoEl proyecto empieza a partir de un mapeo colectivo realizado en el centro histórico de la ciudad de Bogotá, donde encontramos diferentes falencias con respecto a los componentes sociales y de paisaje, en este caso poco espacio público para la sociedad. Como punto de partida se plantea un diseño urbano destinado netamente a la población que constantemente hace uso de espacios no aptos para presentaciones, para demostraciones de talentos y aptitudes, actualmente el centro tiene un movimiento artístico regados, se quiere lograr juntar estos talentos en un solo lugar en donde tengan el aprecio del resto de sociedad y tengan un reconocimiento mayor. El proyecto a trabajar es el EDIFICIO PARA LA COLOMBIANA DE CAPITALIZACIÓN, ubicado en la Carrera 10 # 15 – 11, el edificio actualmente funciona en su primer nivel como comercio y de segundo en adelante como uso de oficinas, la intervención de este es fundamentada con el amarre directo del espacio público propuesto y desde luego su uso, en primer nivel se eliminara la barrera que existía entre lo privado y público, de acuerdo a esto se genera de cierta manera una planta libre en donde se promocionara y se mostrara el arte de la población que caracteriza el centro.PregradoArquitect

Winds and cloud morphology in the southern polar region of Venus

Spinning on average 60 times faster than the surface, the atmosphere of Venus is superrotational, a state in which the averaged angular momentum is much greater than that corresponding to co-rotation with the solid globe. The rapid mean flow, which is main- tained by momentum transports in the deep atmo- sphere, presents a puzzle to the atmospheric and plan- etary sciences[1]. After previous missions revealed a bright polar feature at the north pole[9, 10], the Venus Express spacecraft discovered a fast-rotating counter- part at the southern polar region[6], which has been identified as a vortex[2]. The southern polar vortex can be observed at 5.0 μm as a bright, highly vari- able structure which is ∼ 15 K warmer than the sur- rounding air[6]. Although the Venus superrotation has been measured by tracking cloud features at UV and infrared wavelengths[7, 4, 8, 5], the winds in the po- lar region remain poorly constrained. Characterizing the zonal and meridional circulation in this region, as well as their variability, is crucial for understanding the mechanisms that maintain superrotation. In partic- ular, mean zonal winds are necessary to understand the nature of the polar vortex, how it is connected with the general circulation of the atmosphere, and to diagnose momentum transports. Winds at 45 and 65 km can be detected from cloud motion monitoring by the VIRTIS-M subsection on- board the Venus Express (VEX) spacecraft. Our ob- jective is to provide direct wind measurements at cloud tops and in the lower cloud level, in order to help in- terpret the VEX observations concerning the meso- spheric wind regime and temperature fields. In par- ticular, we present direct measurements of the zonal and meridional winds at both altitudes. For this work we selected nadir-pointing, high- spatial resolution VIRTIS data cubes obtained from apocenter in order to minimize the geometric distortion of the polar region. On average these contain lat- itudes extending from the pole to 70S. Since the VIR- TIS field of view is rectangular, lower latitudes are also present but cannot be observed over full latitude circles. Cloud tracking has been performed using the method of digital correlation described in a previous article[3]. VEX orbits were selected so as to have in each one at least one pair of images suitable for track- ing, i.e., with a considerable spatial overlap. Tracking has been performed on pairs of monochromatic im- ages at wavelengths of 1.74 μm, 2.3 μm, 3.93 μm and 5 μm. In the data cubes obtained with longer integration times (3s) the long-wavelength range of the spectrum, above 4.3 μm, is saturated. In those cases we se- lected the 3.93 μm radiance map instead of the one at 5 μm. The monochromatic radiance maps are first ex- tracted from data cubes that have undergone the stan- dard VIRTIS calibration procedures. The maps are then projected onto a polar stereographic grid and the wind retrieval procedure is applied. A total of 20 lat- itude bins, separated by 1 degree were used. For the analysis of transient motions the spatial averaging was done in 72 longitude bins at 5 degree intervals. In order to evaluate the variability over the time scale of one orbit, we have computed the orbital aver- ages, i.e., averages of all measurements coming from one given orbit. These orbital averages are only ap- proximations to temporal averages, since they do not cover one full rotation. The differences between same- orbit averages are apparent in both day and night side averages. Some notable features indicating different day and night side regimes are also apparent in the or- bit averages, and the boundary of the cold collar ap- pears to be a transition latitude. Moreover, the vari- ability that can be observed from orbit to orbit and be- tween series of observations from the same orbit indi- cates that departures from this mean flow are large and a persistent feature of the global circulation

Reducing the rare event: lessons from the implementation of a ventilator bundle.

The ventilator-associated event (VAE) is a potentially avoidable complication of mechanical ventilation (MV) associated with poor outcomes. Although rare, VAEs and other nosocomial events are frequently targeted for quality improvement efforts consistent with the creed to 'do no harm'. In October 2016, VA Greater Los Angeles (GLA) was in the lowest-performing decile of VA medical centres on a composite measure of quality, owing to GLA's relatively high VAE rate. To decrease VAEs, we sought to reduce average MV duration of patients with acute respiratory failure to less than 3 days by 1 July 2017. In our first intervention (period 1), intensive care unit (ICU) attending physicians trained residents to use an existing ventilator bundle order set; in our second intervention (period 2), we updated the order set to streamline order entry and incorporate new nurse-driven and respiratory therapist (RT)-driven spontaneous awakening trial (SAT) and spontaneous breathing trial (SBT) protocols. In period 1, the proportion of eligible patients with SAT and SBT orders increased from 29.9% and 51.2% to 67.4% and 72.6%, respectively, with sustained improvements through December 2017. Mean MV duration decreased from 7.2 days at baseline to 5.5 days in period 1 and 4.7 days in period 2; statistical process control charts revealed no significant differences, but the difference between baseline and period 2 MV duration was statistically significant at p=0.049. Bedside audits showed RTs consistently performed indicated SBTs, but there were missed opportunities for SATs due to ICU staff concerns about the SAT protocol. The rarity of VAEs, small population of ventilated patients and infrequent use of sedative infusions at GLA may have decreased the opportunity to achieve staff acceptance and use of the SAT protocol. Quality improvement teams should consider frequency of targeted outcomes when planning interventions; rare events pose challenges in implementation and evaluation of change

New Measurements of Venus Winds with Ground-Based Doppler Velocimetry at CFHT

operations with observations from the ground using various techniques and spectral domains (Lellouch and Witasse, 2008). We present an analysis of Venus Doppler winds at cloud tops based on observations made at the Canada France Hawaii 3.6-m telescope (CFHT) with the ESPaDOnS visible spectrograph. These observations consisted of high-resolution spectra of Fraunhofer lines in the visible range (0.37-1.05 μm) to measure the winds at cloud tops using the Doppler shift of solar radiation scattered by cloud top particles in the observer's direction (Widemann et al., 2007, 2008). The observations were made during 19-20 February 2011 and were coordinated with Visual Monitoring Camera (VMC) observations by Venus Express. The complete optical spectrum was collected over 40 spectral orders at each point with 2-5 seconds exposures, at a resolution of about 80000. The observations included various points of the dayside hemisphere at a phase angle of 67°, between +10° and -60° latitude, in steps of 10° , and from +70° to -12° longitude relative to sub-Earth meridian in steps of 12°. The Doppler shift measured in scattered solar light on Venus dayside results from two instantaneous motions: (1) a motion between the Sun and Venus upper cloud particles; (2) a motion between the observer and Venus clouds. The measured Doppler shift, which results from these two terms combined, varies with the planetocentric longitude and latitude and is minimum at meridian ΦN = ΦSun - ΦEarth where the two components subtract to each other for a pure zonal regime. Due to the need for maintaining a stable velocity reference during the course of acquisition using high resolution spectroscopy, we measure relative Doppler shifts to ΦN. The main purpose of our work is to provide variable wind measurements with respect to the background atmosphere, complementary to simultaneous measurements made with the VMC camera onboard the Venus Express. We will present first results from this work, comparing with previous results by the CFHT/ESPaDOnS and VLT-UVES spectrographs (Machado et al., 2012), with Galileo fly-by measurements and with VEx nominal mission observations (Peralta et al., 2007, Luz et al., 2011). Acknowledgements: The authors acknowledge support from FCT through projects PTDC/CTE-AST/110702/2009 and PEst-OE/FIS/UI2751/2011. PM and TW also acknowledge support from the Observatoire de Paris. Lellouch, E., and Witasse, O., A coordinated campaign of Venus ground-based observations and Venus Express measurements, Planetary and Space Science 56 (2008) 1317-1319. Luz, D., et al., Venus's polar vortex reveals precessing circulation, Science 332 (2011) 577-580. Machado, P., Luz, D. Widemann, T., Lellouch, E., Witasse, O, Characterizing the atmospheric dynamics of Venus from ground-based Doppler velocimetry, Icarus, submitted. Peralta J., R. Hueso, A. Sánchez-Lavega, A reanalysis of Venus winds at two cloud levels from Galileo SSI images, Icarus 190 (2007) 469-477. Widemann, T., Lellouch, E., Donati, J.-F., 2008, Venus Doppler winds at Cloud Tops Observed with ESPaDOnS at CFHT, Planetary and Space Science, 56, 1320-1334

Dynamics of Venus’ southern polar vortex from over two years of VIRTIS/Venus Express observations

Recently, the results of an initial study of the southern polar region of Venus, using measurements from the VIRTIS instrument from the Venus Express Mission, revealed it to be in constant dynamic change, with the southern polar vortex displaced from the rotational geometry of the planet. Here, we place these results in the context of measurements taken over a two year period. We examine the dynamics of the southern polar region based on measurements of winds at the 45 and 65 km levels, detected from cloud motion monitoring by the VIRTIS instrument. The wind velocity components were determined by an automatic cloud-tracking technique based on evaluating the similarity between pairs of images of cloud structures at a specific atmospheric altitude, separated by a short time interval. The images were obtained at infrared wavelengths of 1.74 and 2.3 μm, for the night side, and 3.9 and 5.0 μm, for both the day and night sides. These wavelengths are sensitive to radiation originating from levels close to the base and to the top of the cloud deck, respectively. The technique assumes that the clouds are passive tracers of the atmospheric mass flow, and that the cloud structure does not change substantially between the two images. Our objectives have been 1) to provide horizontal maps of direct wind measurements at cloud tops and in the lower cloud level with a high spatial resolution; 2) to characterize the southern polar vortex as to its motion, rotation rate and dynamical stability; 3) to constrain the contribution of the circumpolar circulation to the angular momentum budget; and 4) to provide valuable information for Venus climate modelling, for the planning of future probe or balloon missions, and to examine the Venus polar vortex in the context of other planetary vortices. The circulation in the southern polar region is dominated by the zonal flow, which is much stronger than the meridional circulation. The latitudinal profiles show a relatively smooth variation and the vertical shear between the 45-km and 65-km levels is on the order of 5–10 ms−1. The horizontal structure of the zonal and meridional wind components indicate that wavenumber-2 thermal tides are likely to be present