Entire solutions of hydrodynamical equations with exponential dissipation

We consider a modification of the three-dimensional Navier--Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as \ue ^{|k|/\kd} at high wavenumbers $|k|$. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than \ue ^{-C(k/\kd) \ln (|k|/\kd)} for any $C<1/(2\ln 2)$. The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with $C= C_\star =1/\ln2$. The same behavior with a universal constant $C_\star$ is conjectured for the Navier--Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier--Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.Comment: 29 pages, 3 figures, Comm. Math. Phys., in pres

Host Plant Use by Competing Acacia-Ants: Mutualists Monopolize While Parasites Share Hosts

Protective ant-plant mutualisms that are exploited by non-defending parasitic ants represent prominent model systems for ecology and evolutionary biology. The mutualist Pseudomyrmex ferrugineus is an obligate plant-ant and fully depends on acacias for nesting space and food. The parasite Pseudomyrmex gracilis facultatively nests on acacias and uses host-derived food rewards but also external food sources. Integrative analyses of genetic microsatellite data, cuticular hydrocarbons and behavioral assays showed that an individual acacia might be inhabited by the workers of several P. gracilis queens, whereas one P. ferrugineus colony monopolizes one or more host trees. Despite these differences in social organization, neither of the species exhibited aggressive behavior among conspecific workers sharing a tree regardless of their relatedness. This lack of aggression corresponds to the high similarity of cuticular hydrocarbon profiles among ants living on the same tree. Host sharing by unrelated colonies, or the presence of several queens in a single colony are discussed as strategies by which parasite colonies could achieve the observed social organization. We argue that in ecological terms, the non-aggressive behavior of non-sibling P. gracilis workers — regardless of the route to achieve this social structure — enables this species to efficiently occupy and exploit a host plant. By contrast, single large and long-lived colonies of the mutualist P. ferrugineus monopolize individual host plants and defend them aggressively against invaders from other trees. Our findings highlight the necessity for using several methods in combination to fully understand how differing life history strategies affect social organization in ants

Distinct Occurrence of Proarrhythmic Afterdepolarizations in Atrial Versus Ventricular Cardiomyocytes: Implications for Translational Research on Atrial Arrhythmia

Background: Principal mechanisms of arrhythmia have been derived from ventricular but not atrial cardiomyocytes of animal models despite higher prevalence of atrial arrhythmia (e.g., atrial fibrillation). Due to significant ultrastructural and functional differences, a simple transfer of ventricular proneness toward arrhythmia to atrial arrhythmia is critical. The use of murine models in arrhythmia research is widespread, despite known translational limitations. We here directly compare atrial and ventricular mechanisms of arrhythmia to identify critical differences that should be considered in murine models for development of antiarrhythmic strategies for atrial arrhythmia.Methods and Results: Isolated murine atrial and ventricular myocytes were analyzed by wide field microscopy and subjected to a proarrhythmic protocol during patch-clamp experiments. As expected, the spindle shaped atrial myocytes showed decreased cell area and membrane capacitance compared to the rectangular shaped ventricular myocytes. Though delayed afterdepolarizations (DADs) could be evoked in a similar fraction of both cell types (80% of cells each), these led significantly more often to the occurrence of spontaneous action potentials (sAPs) in ventricular myocytes. Interestingly, numerous early afterdepolarizations (EADs) were observed in the majority of ventricular myocytes, but there was no EAD in any atrial myocyte (EADs per cell; atrial myocytes: 0 ± 0; n = 25/12 animals; ventricular myocytes: 1.5 [0–43]; n = 20/12 animals; p &lt; 0.05). At the same time, the action potential duration to 90% decay (APD90) was unaltered and the APD50 even increased in atrial versus ventricular myocytes. However, the depolarizing L-type Ca2+ current (ICa) and Na+/Ca2+-exchanger inward current (INCX) were significantly smaller in atrial versus ventricular myocytes.Conclusion: In mice, atrial myocytes exhibit a substantially distinct occurrence of proarrhythmic afterdepolarizations compared to ventricular myocytes, since they are in a similar manner susceptible to DADs but interestingly seem to be protected against EADs and show less sAPs. Key factors in the generation of EADs like ICa and INCX were significantly reduced in atrial versus ventricular myocytes, which may offer a mechanistic explanation for the observed protection against EADs. These findings may be of relevance for current studies on atrial level in murine models to develop targeted strategies for the treatment of atrial arrhythmia

Steps toward the power spectrum of matter. II. The biasing correction with sigma_8 normalization

A new method to determine the bias parameter of galaxies relative to matter is suggested. The method is based on the assumption that gravity is the dominating force which determines the formation of the structure in the Universe. Due to gravitational instability the galaxy formation is a threshold process: in low-density environments galaxies do not form and matter remains in primordial form. We investigate the influence of the presence of void and clustered populations to the power spectrum of matter and galaxies. The power spectrum of galaxies is similar to the power spectrum of matter; the fraction of total matter in the clustered population determines the difference between amplitudes of fluctuations of matter and galaxies, i.e. the bias factor. To determine the fraction of matter in voids and clustered population we perform numerical simulations. The fraction of matter in galaxies at the present epoch is found using a calibration through the sigma_8 parameter.Comment: LaTex (sty files added), 31 pages, 4 PostScript figures embedded, Astrophysical Journal (accepted

Keck-Nirspec Infrared OH Lines: Oxygen Abundances in Metal-Poor Stars Down to [Fe/H] = -2.9

Infrared OH lines at 1.5 - 1.7 um in the H band were obtained with the NIRSPEC high-resolution spectrograph at the 10m Keck Telescope for a sample of seven metal-poor stars. Detailed analyses have been carried out, based on optical high-resolution data obtained with the FEROS spectrograph at ESO. Stellar parameters were derived by adopting infrared flux method effective temperatures, trigonometric and/or evolutionary gravities and metallicities from FeII lines. We obtain that the sample stars with metallicities [Fe/H] < -2.2 show a mean oxygen abundance [O/Fe] ~ 0.54, for a solar oxygen abundance of epsilon(O) = 8.87, or [O/Fe] ~ 0.64 if epsilon(O) = 8.77 is assumed.Comment: To be published in ApJ 575 (August 10

Chemical Abundances from Inversions of Stellar Spectra: Analysis of Solar-Type Stars with Homogeneous and Static Model Atmospheres

Spectra of late-type stars are usually analyzed with static model atmospheres in local thermodynamic equilibrium (LTE) and a homogeneous plane-parallel or spherically symmetric geometry. The energy balance requires particular attention, as two elements which are particularly difficult to model play an important role: line blanketing and convection. Inversion techniques are able to bypass the difficulties of a detailed description of the energy balance. Assuming that the atmosphere is in hydrostatic equilibrium and LTE, it is possible to constrain its structure from spectroscopic observations. Among the most serious approximations still implicit in the method is a static and homogeneous geometry. In this paper, we take advantage of a realistic three-dimensional radiative hydrodynamical simulation of the solar surface to check the systematic errors incurred by an inversion assuming a plane-parallel horizontally-homogeneous atmosphere. The thermal structure recovered resembles the spatial and time average of the three-dimensional atmosphere. Furthermore, the abundances retrieved are typically within 10% (0.04 dex) of the abundances used to construct the simulation. The application to a fairly complete dataset from the solar spectrum provides further confidence in previous analyses of the solar composition. There is only a narrow range of one-dimensional thermal structures able to fit the absorption lines in the spectrum of the Sun. With our carefully selected dataset, random errors are about a factor of two smaller than systematic errors. A small number of strong metal lines can provide very reliable results. We foresee no major difficulty in applying the technique to other similar stars, and obtaining similar accuracies, using spectra with a resolving power about 50,000 and a signal-to-noise ratio as low as 30.Comment: 65 pages, figures included; uses aastex; to appear in The Astrophysical Journa

Emerging Concepts for Pelvic Organ Prolapse Surgery: What is Cure?

The objective of this review is to discuss emerging concepts in pelvic organ prolapse, in particular, “What is cure?” In a post-trial data analysis of the CARE (Colpopexy and Urinary Reduction Efforts) trial, treatment success varied tremendously depending on the definition used (19.2%–97.2%). Definitions that included the absence of vaginal bulge symptoms had the strongest relationships with the patients’ assessment of overall improvement and treatment success. As demonstrated by this study, there are several challenges in defining cure in prolapse surgery. Additionally, the symptoms of prolapse are variable. The degree of prolapse does not correlate directly with symptoms. There are many surgical approaches to pelvic organ prolapse. Multiple ways to quantify prolapse are used. There is a lack of standardized definition of cure. The data on prolapse surgery outcomes are heterogeneous. The goal of surgical repair is to return the pelvic organs to their original anatomic positions. Ideally, we have four main goals: no anatomic prolapse, no functional symptoms, patient satisfaction, and the avoidance of complications. The impact of transvaginal mesh requires thoughtful investigation. The driving force should be patient symptoms in defining cure of prolapse