Polarization properties and dispersion relations for spiral resonances of a dielectric rod

Dielectric microcavities based on cylindrical and deformed cylindrical shapes have been employed as resonators for microlasers. Such systems support spiral resonances with finite momentum along the cylinder axis. For such modes the boundary conditions do not separate and simple TM and TE polarization states do not exist. We formulate a theory for the dispersion relations and polarization properties of such resonances for an infinite dielectric rod of arbitrary cross-section and then solve for these quantities for the case of a circular cross-section (cylinder). Useful analytic formulas are obtained using the eikonal (Einstein-Brillouin-Keller) method which are shown to be excellent approximations to the exact results from the wave equation. The major finding is that the polarization of the radiation emitted into the far-field is linear up to a polarization critical angle (PCA) at which it changes to elliptical. The PCA always lies between the Brewster and total-internal-reflection angles for the dielectric, as is shown by an analysis based on the Jones matrices of the spiraling rays.Comment: submitted to JOSA

Power-counting theorem for non-local matrix models and renormalisation

Solving the exact renormalisation group equation a la Wilson-Polchinski perturbatively, we derive a power-counting theorem for general matrix models with arbitrarily non-local propagators. The power-counting degree is determined by two scaling dimensions of the cut-off propagator and various topological data of ribbon graphs. As a necessary condition for the renormalisability of a model, the two scaling dimensions have to be large enough relative to the dimension of the underlying space. In order to have a renormalisable model one needs additional locality properties--typically arising from orthogonal polynomials--which relate the relevant and marginal interaction coefficients to a finite number of base couplings. The main application of our power-counting theorem is the renormalisation of field theories on noncommutative R^D in matrix formulation.Comment: 35 pages, 70 figures, LaTeX with svjour macros. v2: proof simplified because a discussion originally designed for \phi^4 on noncommutative R^2 was actually not necessary, see hep-th/0307017. v3: consistency conditions removed because models of interest relate automatically the relevant/marginal interactions to a finite number of base couplings, see hep-th/0401128. v4: integration procedure improved so that the initial cut-off can be directly removed; to appear in Commun. Math. Phy

Limb observations of the Martian atmosphere with Mars Express’ High Resolution Stereo Camera

Introduction: Good knowledge about the aerosol distribution and compositions is essential for the understanding of thermodynamic processes in the Martian atmosphere, which in turn is important for the understanding of the Martian climate and the altitude of the upper boundary of the atmosphere. The last point is of special interest for spacecraft aerobreaking manoeuvres. The Martian atmosphere often shows horizontal layers of haze up to altitudes of about 80 km. These have been described and analysed e.g. by Jaquin et al., 1986, usingViking Orbiter images and by Montmessin et al., 2006, who used SPICAM stellar occultation data. Both showed seasonal and latitudinal changes in the vertical structure of the aerosol distribution and composition. Apart from SPICAM, the High Resolution Stereo Camera (HRSC) is also on board ESA’s robotic spacecraft Mars Express. HRSC was build and is operated by the German Aerospace Center (Neukum et al. 2004; Jaumann et al. 2007). Mars Express is orbiting Mars in an elliptical orbit, with HRSC scanning the surface of Mars, primarily for geological research. In addition to that, HRSC has been used to sample the planetary limb. We examine the HRSC planetary limb data and analyse the seasonal and latitudinal variations of the maximum altitude of the haze layer and of the occurrence of high altitude detached hazes. We make some comparisons with earlier work. In contrast to the SPICAM instrument, HRSC observes the atmosphere during daytime, which makes it possible to compare night and daytime observations. The HRSC Limb Data: HRSC is a push broom scanner with nine line sensors pointing in different directions to facilitate stereoscopic imaging. Four of the sensors have colour filters at 440 nm, 530 nm, 750 nm and 970 nm, respectively. The five other sensors all have filters centred at 650 nm. These panchromatic filters have a much wider bandpass than the four colour filters. The surface observations which are HRSC’s main purpose, are usually take while the spacecraft is nadirtracking near pericentre. Limb observations, however, are mostly made with a pointing of the spacecraft being inertially fixxed in celestial space. This leaves only a small time window to make observations of the limb during descent or ascent. Therefore, usually only a few of the nine sensors can be used for the limb observation. Due to the motion of the spacecraft, the individual image lines are taken at different geographical locations and altitudes. The position of each image pixel above the limb has to be calculated from the spacecraft positioning information (Scholten, pers. comm.). The typical difference in altitude between two neighbouring pixels is between a couple of dozen metres and 150 m. HRSC has been observing the limb occasionally throughout the mission since 2004. So far the northern hemisphere and especially the north polar region, were particularly well covered (Figure 1 and 2). In Figure 2, we give an overview of the available data, sorted by season (LS) and latitude. The channel in which the observations have been made is colourcoded. Most observations were made with the panchromatic channels. There are also many observations with the blue and green sensors and only a few were made in the red and infra red channels. We find the best data coverage in northern spring in the northern most latitudes. For obvious reasons, we do not have any data during polar nights. For most of our actual analysis we sample the five central pixels of the sensor lines. This allows for minimal horizontal averaging. Analysis: As an example, Fig. 3 shows images and profiles for the blue, nadir, and green channels from orbit 6104. Al three images show a continuously bright limb haze until an altitude of about 20 km. At higher altitudes the limb haze becomes darker and stratified consistent with the limb profiles described by Jacquin et al., 1986. As Mars Express progresses along its orbit, the limb observations are made at different locations above the surface. The locations of the three profiles in Fig. 3 are still in close proximity of each other, in fact they overlap, but none the less they show different vertical aerosol distributions. Beginning above the North Polar cap and going southward, we observe less reflectivity above 20 km and more reflectivity below 20 km, hinting at different compositions or amounts of aerosols. It is not possible to obtain and compare profiles at the same location and at the same time with different sensors, but still, averages of profiles over place and season can provide us with information about typical atmospheric conditions. In Fig. 4 we show spectra from the average profiles at three different latitudinal bands between 70�N–90�N, 30�S–30�N, and 90�S– 70�S, on the left, centre, and right, respectively. The different symbols and colours represent the different altitudes at which the spectra were sampled. The size of the symbol increases with the number of averaged profiles. There are very few observations above the South Polar region (compare Fig. 1). In the North (and South) Polar region there is almost no signal above 30 km altitude, while around the equator the limb haze remains bright until altitudes of about 60 km. At the poles, the spectrum at 10 km is reddish. At higher altitudes the spectrum gets whiter, indicating smaller particles or higher ice content. At the low latitudes the spectra are reddish up to 40 km. At 60 km we see a more or less white spectrum. Figure 5 shows the maximum altitude of the aerosols as seen by HRSC, depending on season. During aphelion (LS � 70�) the maximum altitude of the aerosols that are visible with HRSC is around 40 km. During perihelion (LS � 250�) the maximum altitude is around 70 km. Discussion: Figure 1 and 2 show that there are plenty of visual and near infra red HRSC observations of the Martian limb available. These show aerosol distributions that change with season and latitude (Fig. 3 and 4). The plots in Fig. 4 show the spectra of the average limb profiles at several altitudes for three latitudinal bands. Two important distinctions can be made between the equatorial and the polar regions. First, the altitude at which aerosol occur is higher in the equatorial region and second, the composition of the aerosols at different altitudes is different. While the spectrum is white around 20 km altitude above the north pole, it is red at the low latitudes. The seasonal variations of maximum altitude of the aerosols is in good agreement with Jaquin et al. (1986) and with Montmessin et al. (2006). The similarity between Montmessin’s results and ours is likely to be due to the large annual variation of atmospheric dust load compared to the diurnal cycle. A much closer look at the data, is forseen to analyse the daily variation of aerosols in the Martian atmosphere. The CO2 and waterice aerosols are more likely to change their vertical distribution (above the planetary boundary layer) between day and night than the mineral (dust) aerosols. Spectral information would help to discriminate between these components. HRSC can not provide it, because the observation for the different filters take place at different locations and times (see Fig. 3). An alternative is to fit aerosol models to the inverted profiles. Currently, we are preparing this work. Mars Express’ HRSC limb data present a valuable opportunity to analyse Mars daytime atmospheric dust at a high vertical resolution. This work gives a short overview of the available data and analyses some seasonal and latitudinal properties

Dramatic Shape Sensitivity of Directional Emission Patterns from Similarly Deformed Cylindrical Polymer Lasers

Recent experiments on similarly shaped polymer micro-cavity lasers show a dramatic difference in the far-field emission patterns. We show for different deformations of the ellipse, quadrupole and hexadecapole that the large differences in the far-field emission patterns is explained by the differing ray dynamics corresponding to each shape. Analyzing the differences in the appropriate phase space for ray motion, it is shown that the differing geometries of the unstable manifolds of periodic orbits are the decisive factors in determining the far-field pattern. Surprisingly, we find that strongly chaotic ray dynamics is compatible with highly directional emission in the far-field.Comment: 14 pages, 16 figures (eps), RevTeX 4, submitted to JOSA

MOBAK – Monitoring motorischer Basiskompetenzen von 4- bis 8-jährigen Kindern in der Schweiz: Dokumentation der Items und Skalen

In der vorliegenden Dokumentation sind die Skalen und Items zusammengestellt, welche in der von der Gesundheitsförderung Schweiz (GFCH) geförderten Studie «Monitoring motorischer Basiskompetenzen von 4- bis 8-jährigen Kindern in der Schweiz» (01.12.2019–30.11.2020) verwendet wurden. Diese Studie hat zum Ziel, den motorischen Förderbedarf von 4- bis 8-jährigen Kindern festzustellen und relevante Faktoren zu identifizieren, welche mit der psychischen und physischen Gesundheit der Kinder in Zusammenhang stehen. Kern der Studie bildet die Erfassung der Motorischen Basiskompetenzen (MOBAK; Herrmann, 2018; Herrmann, Seelig, Ferrari & Kühnis, 2019) im 1. Zyklus der Primarschule. Neben einem Monitoring der motorischen Basiskompetenzen im Kindergarten und der ersten Primarschulklasse in den Kantonen Nidwalden und Tessin wurden die Eltern und Lehrpersonen der Kinder mittels Fragebogen befragt. Die Dokumentation der Skalen und Items umfasst die Variablennamen, den zugehörigen Fragetext und die Kodierung, sowie Quellen zu den einzelnen Fragen bzw. Items. Zudem sind Skalen- bzw. Itemkennwerte der psychometrischen Daten aufgeführt.+repphzhbib2020

Drivers and recent trends of hospitalisation costs related to acute pulmonary embolism

BACKGROUND AND AIMS The socio-economic burden imposed by acute pulmonary embolism (PE) on European healthcare systems is largely unknown. We sought to determine temporal trends and identify cost drivers of hospitalisation for PE in Germany. METHODS AND RESULTS We analysed the totality of reimbursed hospitalisation costs in Germany (G-DRG system) in the years 2016-2020. Overall, 484 884 PE hospitalisations were coded in this period. Direct hospital costs amounted to a median of 3572 (IQR, 2804 to 5869) euros, resulting in average total reimbursements of 710 million euros annually. Age, PE severity, comorbidities and in-hospital (particularly bleeding) complications were identified by multivariable logistic regression as significant cost drivers. Use of catheter-directed therapy (CDT) constantly increased (annual change in the absolute proportion of hospitalisations with CDT + 0.40% [95% CI + 0.32% to + 0.47%]; P < 0.001), and it more than doubled in the group of patients with severe PE (28% of the entire population) over time. Although CDT use was overall associated with increased hospitalisation costs, this association was no longer present (adjusted OR 1.02 [0.80-1.31]) in patients with severe PE and shock; this was related, at least in part, to a reduction in the median length of hospital stay (for 14.0 to 8.0 days). CONCLUSIONS We identified current and emerging cost drivers of hospitalisation for PE, focusing on severe disease and intermediate/high risk of an adverse early outcome. The present study may inform reimbursement decisions by policymakers and help to guide future health economic analysis of advanced treatment options for patients with PE

Early microstructural white matter changes in patients with HIV: A diffusion tensor imaging study

Background: Previous studies have reported white matter (WM) brain alterations in asymptomatic patients with human immunodeficiency virus (HIV). Methods: We compared diffusion tensor imaging (DTI) derived WM fractional anisotropy (FA) between HIV-patients with and without mild macroscopic brain lesions determined using standard magnetic resonance imaging (MRI). We furthermore investigated whether WM alterations co-occurred with neurocognitive deficits and depression. We performed structural MRI and DTI for 19 patients and 19 age-matched healthy controls. Regionally-specific WM integrity was investigated using voxel-based statistics of whole-brain FA maps and region-of-interest analysis. Each patient underwent laboratory and neuropsychological tests. Results: Structural MRI revealed no lesions in twelve (HIV-MRN) and unspecific mild macrostructural lesions in seven patients (HIV-MRL). Both analyses revealed widespread FA-alterations in all patients. Patients with HIV-MRL had FA-alterations primarily adjacent to the observed lesions and, whilst reduced in extent, patients with HIV-MRN also exhibited FA-alterations in similar regions. Patients with evidence of depression showed FA-increase in the ventral tegmental area, pallidum and nucleus accumbens in both hemispheres, and patients with evidence of HIV-associated neurocognitive disorder showed widespread FA-reduction. Conclusion: These results show that patients with HIV-MRN have evidence of FA-alterations in similar regions that are lesioned in HIV-MRL patients, suggesting common neuropathological processes. Furthermore, they suggest a biological rather than a reactive origin of depression in HIV-patients