Numerical optimization design of advanced transonic wing configurations

A computationally efficient and versatile technique for use in the design of advanced transonic wing configurations has been developed. A reliable and fast transonic wing flow-field analysis program, TWING, has been coupled with a modified quasi-Newton method, unconstrained optimization algorithm, QNMDIF, to create a new design tool. Fully three-dimensional wing designs utilizing both specified wing pressure distributions and drag-to-lift ration minimization as design objectives are demonstrated. Because of the high computational efficiency of each of the components of the design code, in particular the vectorization of TWING and the high speed of the Cray X-MP vector computer, the computer time required for a typical wing design is reduced by approximately an order of magnitude over previous methods. In the results presented here, this computed wave drag has been used as the quantity to be optimized (minimized) with great success, yielding wing designs with nearly shock-free (zero wave drag) pressure distributions and very reasonable wing section shapes

A Bose-Einstein Approach to the Random Partitioning of an Integer

Consider N equally-spaced points on a circle of circumference N. Choose at random n points out of $N$ on this circle and append clockwise an arc of integral length k to each such point. The resulting random set is made of a random number of connected components. Questions such as the evaluation of the probability of random covering and parking configurations, number and length of the gaps are addressed. They are the discrete versions of similar problems raised in the continuum. For each value of k, asymptotic results are presented when n,N both go to infinity according to two different regimes. This model may equivalently be viewed as a random partitioning problem of N items into n recipients. A grand-canonical balls in boxes approach is also supplied, giving some insight into the multiplicities of the box filling amounts or spacings. The latter model is a k-nearest neighbor random graph with N vertices and kn edges. We shall also briefly consider the covering problem in the context of a random graph model with N vertices and n (out-degree 1) edges whose endpoints are no more bound to be neighbors

Simulating radiative shocks in nozzle shock tubes

We use the recently developed Center for Radiative Shock Hydrodynamics (CRASH) code to numerically simulate laser-driven radiative shock experiments. These shocks are launched by an ablated beryllium disk and are driven down xenon-filled plastic tubes. The simulations are initialized by the two-dimensional version of the Lagrangian Hyades code which is used to evaluate the laser energy deposition during the first 1.1ns. The later times are calculated with the CRASH code. This code solves for the multi-material hydrodynamics with separate electron and ion temperatures on an Eulerian block-adaptive-mesh and includes a multi-group flux-limited radiation diffusion and electron thermal heat conduction. The goal of the present paper is to demonstrate the capability to simulate radiative shocks of essentially three-dimensional experimental configurations, such as circular and elliptical nozzles. We show that the compound shock structure of the primary and wall shock is captured and verify that the shock properties are consistent with order-of-magnitude estimates. The produced synthetic radiographs can be used for comparison with future nozzle experiments at high-energy-density laser facilities.Comment: submitted to High Energy Density Physic

Predictions for the First Parker Solar Probe Encounter

We examine Alfv\'en Wave Solar atmosphere Model (AWSoM) predictions of the first Parker Solar Probe (PSP) encounter. We focus on the 12-day closest approach centered on the 1st perihelion. AWSoM (van der Holst et al., 2014) allows us to interpret the PSP data in the context of coronal heating via Alfv\'en wave turbulence. The coronal heating and acceleration is addressed via outward-propagating low-frequency Alfv\'en waves that are partially reflected by Alfv\'en speed gradients. The nonlinear interaction of these counter-propagating waves results in a turbulent energy cascade. To apportion the wave dissipation to the electron and anisotropic proton temperatures, we employ the results of the theories of linear wave damping and nonlinear stochastic heating as described by Chandran et al. (2011). We find that during the first encounter, PSP was in close proximity to the heliospheric current sheet (HCS) and in the slow wind. PSP crossed the HCS two times, namely at 2018/11/03 UT 01:02 and 2018/11/08 UT 19:09 with perihelion occuring on the south of side of the HCS. We predict the plasma state along the PSP trajectory, which shows a dominant proton parallel temperature causing the plasma to be firehose unstable.Comment: 16 pages, 5 figures; accepted for publication in the Astrophysical Journal Letter

Investigation on the influence of nematophagous fungi as feed additive on nematode infection risk of sheep and goats on pasture

Gastrointestinal nematodes in small ruminants cause high economic losses. Thus on most farms anthelmintic treatment is required. In response to increasing problems with anthelmintic resistance, biological control, for example the use of nematophagous fungi, has received significant attention. The aim of this study was to investigate the effect of Duddingtonia flagrans orally applied to small ruminants on natural infection with gastrointestinal nematodes in a field study in Northern Germany. 20 goats and 20 sheep were fed daily for 3 months with 5x105 spores of D. flagrans per kg bodyweight. Differences in body weight, faecal egg count and larval development in faeces and on pasture in comparison with same-sized control groups were analysed. After 3 months the control goats showed significantly higher mean faecal egg count than the fungus-fed group. No significant difference was found between the two sheep groups. The maximum in larval reduction in faeces was 81.3 % in the sheep groups and 67.9 % in the goat groups (not significant). At the end of the study the body weight gain in the fungus-treated groups was 1.7 kg higher in goats and 0.7 kg higher in sheep than in the control groups (not significant). Regarding the first-year-grazing goats only, the bodyweights revealed significant differences (p<0.05). No statistically significant differences were observed in pasture larval counts. In the study presented here, no clear effect of fungus could be observed. A modified feeding regimen, perhaps with permanent release boluses or feed blocks, may improve the efficacy. Furthermore, it seems that climatic conditions during the study period could have influenced the results and displayed how sensitive the fungus application may be on such parameters

Semilinear mixed problems on Hilbert complexes and their numerical approximation

Arnold, Falk, and Winther recently showed [Bull. Amer. Math. Soc. 47 (2010), 281-354] that linear, mixed variational problems, and their numerical approximation by mixed finite element methods, can be studied using the powerful, abstract language of Hilbert complexes. In another recent article [arXiv:1005.4455], we extended the Arnold-Falk-Winther framework by analyzing variational crimes (a la Strang) on Hilbert complexes. In particular, this gave a treatment of finite element exterior calculus on manifolds, generalizing techniques from surface finite element methods and recovering earlier a priori estimates for the Laplace-Beltrami operator on 2- and 3-surfaces, due to Dziuk [Lecture Notes in Math., vol. 1357 (1988), 142-155] and later Demlow [SIAM J. Numer. Anal., 47 (2009), 805-827], as special cases. In the present article, we extend the Hilbert complex framework in a second distinct direction: to the study of semilinear mixed problems. We do this, first, by introducing an operator-theoretic reformulation of the linear mixed problem, so that the semilinear problem can be expressed as an abstract Hammerstein equation. This allows us to obtain, for semilinear problems, a priori solution estimates and error estimates that reduce to the Arnold-Falk-Winther results in the linear case. We also consider the impact of variational crimes, extending the results of our previous article to these semilinear problems. As an immediate application, this new framework allows for mixed finite element methods to be applied to semilinear problems on surfaces.Comment: 22 pages; v2: major revision, particularly sharpening of error estimates in Section

The effects of dietary fibre type on satiety-related hormones and voluntary food intake in dogs

Depending on type and inclusion level, dietary fibre may increase and maintain satiety and postpone the onset of hunger. This 7-week study evaluated the effect of fibre fermentability on physiological satiety-related metabolites and voluntary food intake (VFI) in dogs. Sixteen healthy adult dogs were fed a low-fermentable fibre (LFF) diet containing 8·5 % cellulose or a high-fermentable fibre (HFF) diet containing 8·5 % sugarbeet pulp and 2 % inulin. Large intestinal fibre degradation was evaluated by apparent faecal digestibility of nutrients and faecal SCFA and NH3 concentrations. Postprandial blood samples were obtained to determine postprandial plasma glucose, insulin, total peptide tyrosine–tyrosine (PYY), total glucagon-like peptide-1 (GLP-1) and total ghrelin concentrations. At the end of the study, the dogs were given a single meal of a dry dog food to determine VFI. Dogs fed the HFF diet had a significantly higher large intestinal fibre degradation and production of SCFA compared with the dogs fed the LFF diet. The HFF-fed dogs tended (P = 0·058) to show a lower VFI at the end of the study. No treatment effects were found for postprandial plasma glucose, PYY, GLP-1 and ghrelin responses. The concentrations of these metabolites could not be related to the observed difference in VFI. The inclusion of fermentable fibre in canine diets may contribute to the prevention or mitigation of obesity through its effects on satiety. The underlying mechanisms require further investigatio