Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations

The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization. We analyse the semi-discrete equations -- a semi-explicit nonlinear DAE -- in terms of the strangeness index and quantify the numerical difficulties in the fully discrete schemes, that are induced by the strangeness of the system. By analyzing the Kronecker index of the difference-algebraic equations, that represent commonly and successfully used time stepping schemes for the Navier--Stokes equations, we show that those time-integration schemes factually remove the strangeness. The theoretical considerations are backed and illustrated by numerical examples.Comment: 28 pages, 2 figure, code available under DOI: 10.5281/zenodo.998909, https://doi.org/10.5281/zenodo.99890

Olfactory function following open rhinoplasty: A 6-month follow-up study

<p>Abstract</p> <p>Background</p> <p>Patients undergoing any type of nasal surgery may experience degrees of postoperative olfactory dysfunction. We sought to investigate "when" the olfactory function recovers to its preoperative levels.</p> <p>Methods</p> <p>In this cohort design, 40 of 65 esthetic open rhinoplasty candidates with equal gender distribution, who met the inclusion criteria, were assessed for their olfactory function using the Smell Identification Test (SIT) with 40 familiar odors in sniffing bottles. All the patients were evaluated for the SIT scores preoperatively and postoperatively (at week 1, week 6, and month 6).</p> <p>Results</p> <p>At postoperative week one, 87.5% of the patients had anosmia, and the rest exhibited at least moderate levels of hyposmia. The anosmia, which was the dominant pattern at postoperative week 1, resolved and converted to various levels of hyposmia, so that no one at postoperative week 6 showed any such complain. At postoperative week six, 85% of the subjects experienced degrees of hyposmia, almost all being mild to moderate. At postoperative six month, the olfactory function had already reverted to the preoperative levels: no anosmia or moderate to severe hyposmia. A repeated ANOVA was indicative of significant differences in the olfactory function at the different time points. According to our post hoc Benfronney, the preoperative scores had a significant difference with those at postoperative week 1, week 6, but not with the ones at month 6.</p> <p>Conclusion</p> <p>Esthetic open rhinoplasty may be accompanied by some degrees of postoperative olfactory dysfunction. Patients need a time interval of 6 weeks to 6 months to fully recover their baseline olfactory function.</p

Limb proportions show developmental plasticity in response to embryo movement

Animals have evolved limb proportions adapted to different environments, but it is not yet clear to what extent these proportions are directly influenced by the environment during prenatal development. The developing skeleton experiences mechanical loading resulting from embryo movement. We tested the hypothesis that environmentally-induced changes in prenatal movement influence embryonic limb growth to alter proportions. We show that incubation temperature influences motility and limb bone growth in West African Dwarf crocodiles, producing altered limb proportions which may, influence post-hatching performance. Pharmacological immobilisation of embryonic chickens revealed that altered motility, independent of temperature, may underpin this growth regulation. Use of the chick also allowed us to merge histological, immunochemical and cell proliferation labelling studies to evaluate changes in growth plate organisation, and unbiased array profiling to identify specific cellular and transcriptional targets of embryo movement. This disclosed that movement alters limb proportions and regulates chondrocyte proliferation in only specific growth plates. This selective targeting is related to intrinsic mTOR (mechanistic target of rapamycin) pathway activity in individual growth plates. Our findings provide new insights into how environmental factors can be integrated to influence cellular activity in growing bones and ultimately gross limb morphology, to generate phenotypic variation during prenatal development

Localization and broadband follow-up of the gravitational-wave transient GW150914

A gravitational-wave (GW) transient was identified in data recorded by the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) detectors on 2015 September 14. The event, initially designated G184098 and later given the name GW150914, is described in detail elsewhere. By prior arrangement, preliminary estimates of the time, significance, and sky location of the event were shared with 63 teams of observers covering radio, optical, near-infrared, X-ray, and gamma-ray wavelengths with ground- and space-based facilities. In this Letter we describe the low-latency analysis of the GW data and present the sky localization of the first observed compact binary merger. We summarize the follow-up observations reported by 25 teams via private Gamma-ray Coordinates Network circulars, giving an overview of the participating facilities, the GW sky localization coverage, the timeline, and depth of the observations. As this event turned out to be a binary black hole merger, there is little expectation of a detectable electromagnetic (EM) signature. Nevertheless, this first broadband campaign to search for a counterpart of an Advanced LIGO source represents a milestone and highlights the broad capabilities of the transient astronomy community and the observing strategies that have been developed to pursue neutron star binary merger events. Detailed investigations of the EM data and results of the EM follow-up campaign are being disseminated in papers by the individual teams

Localization and broadband follow-up of the gravitational-wave transient GW150914

A gravitational-wave transient was identified in data recorded by the Advanced LIGO detectors on 2015 September 14. The event candidate, initially designated G184098 and later given the name GW150914, is described in detail elsewhere. By prior arrangement, preliminary estimates of the time, significance, and sky location of the event were shared with 63 teams of observers covering radio, optical, near-infrared, X-ray, and gamma-ray wavelengths with ground- and space-based facilities. In this Letter we describe the low-latency analysis of the gravitational wave data and present the sky localization of the first observed compact binary merger. We summarize the follow-up observations reported by 25 teams via private Gamma-ray Coordinates Network Circulars, giving an overview of the participating facilities, the gravitational wave sky localization coverage, the timeline and depth of the observations. As this event turned out to be a binary black hole merger, there is little expectation of a detectable electromagnetic signature. Nevertheless, this first broadband campaign to search for a counterpart of an Advanced LIGO source represents a milestone and highlights the broad capabilities of the transient astronomy community and the observing strategies that have been developed to pursue neutron star binary merger events. Detailed investigations of the electromagnetic data and results of the electromagnetic follow-up campaign will be disseminated in the papers of the individual teams

Development, dispersal and recruitment: A paradox for survival among Antarctic fish

At first sight, the life-history strategies adopted by Antarctic fish appear to be a paradox. The majority of fish species are demersal and inhabit the peri-Antarctic islands that are isolated, separated by deep ocean, and subject to the influence of strong currents of the West Wind Drift. In common with Antarctic benthic invertebrates, nearly all of the Antarctic fish have protracted early development but by contrast most Antarctic fish have retained a pelagic larval phase that extends over several months