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

Emplacement of inflated Pāhoehoe flows in the Naude’s Nek Pass, Lesotho remnant, Karoo continental flood basalt province: use of flow-lobe tumuli in understanding flood basalt emplacement

Physical volcanological features are presented for a 710-m-thick section, of the Naude’s Nek Pass, within the lower part of the Lesotho remnant of the Karoo Large Igneous Province. The section consists of inflated pāhoehoe lava with thin, impersistent sedimentary interbeds towards the base. There are seven discreet packages of compound and hummocky pāhoehoe lobes containing flow-lobe tumuli, making up approximately 50% of the section. Approximately 45% of the sequence consists of 14 sheet lobes, between 10 and 52-m-thick. The majority of the sheet lobes are in two packages indicating prolonged periods of lava supply capable of producing thick sheet lobes. The other sheet lobes are as individual lobes or pairs, within compound flows, suggesting brief increases in lava supply rate. We suggest, contrary to current belief, that there is no evidence that compound flows are proximal to source and sheet lobes (simple flows) are distal to source and we propose that the presence of flow-lobe tumuli in compound flows could be an indicator that a flow is distal to source. We use detailed, previously published, studies of the Thakurvadi Formation (Deccan Traps) as an example. We show that the length of a lobe and therefore the sections that are ‘medial or distal to source’ are specific to each individual lobe and are dependent on the lava supply of each eruptive event, and as such flow lobe tumuli can be used as an indicator of relative distance from source

Growth inhibition of oral mutans streptococci and candida by commercial probiotic lactobacilli - an in vitro study

<p>Abstract</p> <p>Background</p> <p>Probiotic bacteria are suggested to play a role in the maintenance of oral health. Such health promoting bacteria are added to different commercial probiotic products. The aim of the study was to investigate the ability of a selection of lactobacilli strains, used in commercially available probiotic products, to inhibit growth of oral mutans streptococci and <it>C. albicans in vitro</it>.</p> <p>Methods</p> <p>Eight probiotic lactobacilli strains were tested for growth inhibition on three reference strains and two clinical isolates of mutans streptococci as well as two reference strains and three clinical isolates of <it>Candida albicans </it>with an agar overlay method.</p> <p>Results</p> <p>At concentrations ranging from 10⁹to 10⁵CFU/ml, all lactobacilli strains inhibited the growth of the mutans streptococci completely with the exception of <it>L. acidophilus </it>La5 that executed only a slight inhibition of some strains at concentrations corresponding to 10⁷and 10⁵CFU/ml. At the lowest cell concentration (10³CFU/ml), only <it>L. plantarum </it>299v and <it>L. plantarum </it>931 displayed a total growth inhibition while a slight inhibition was seen for all five mutans streptococci strains by <it>L. rhamnosus </it>LB21, <it>L. paracasei </it>F19, <it>L. reuteri </it>PTA 5289 and <it>L. reuteri </it>ATCC 55730. All the tested lactobacilli strains reduced candida growth but the effect was generally weaker than for mutans streptococci. The two <it>L. plantarum </it>strains and <it>L. reuteri </it>ATCC 55730 displayed the strongest inhibition on <it>Candida albicans</it>. No significant differences were observed between the reference strains and the clinical isolates.</p> <p>Conclusion</p> <p>The selected probiotic strains showed a significant but somewhat varying ability to inhibit growth of oral mutans streptococci and <it>Candida albicans in vitro</it>.</p

Headache and migraine during pregnancy and puerperium: the MIGRA-study

There is little prospectively gathered data on the course of headaches during pregnancy and postpartum, and the influence of breastfeeding is unclear. This is a large, prospective study, which invited all pregnant women in the catchment area during a defined period. All participants (n = 2,126) filled in questionnaires concerning headache. Among these, a total of 208 women with migraine according to the International Headache Society criteria also filled in detailed headache diaries during pregnancy and the puerperal period. Freedom from earlier headaches during pregnancy was significantly more common than new onset of headache during pregnancy (p < 0.001). This was not influenced by prior use of oral contraceptives. According to the diaries, there was a gradual decrease during pregnancy in the frequency of all headaches and of self-considered migraine. There was also a significant decrease in the duration of headaches (p < 0.001) during pregnancy compared to before. Earlier parity did not influence the course. Apart from a significant increase during the first week postpartum (p < 0.01), the overall occurrence of headaches during puerperium did not differ from the pregnancy period. Compared to pregnancy, there was a postpartum increase in the mean intensity (p < 0.01) and duration (p = 0.050) of headaches, as well as in the mean number of analgesics used (p < 0.001). Breastfeeding did not influence the occurrence of headaches postpartum. These data are of practical value for informing pregnant migraineurs about the typical clinical prospects and for giving advice on breastfeeding

A comparative population-based study of prostate cancer incidence and mortality rates in Singapore, Sweden and Geneva, Switzerland from 1973 to 2006

10.1186/1471-2407-12-222BMC Cancer12-BCMA

Angiopoietin 2 Alters Pancreatic Vascularization in Diabetic Conditions

Islet vascularization, by controlling beta-cell mass expansion in response to increased insulin demand, is implicated in the progression to glucose intolerance and type 2 diabetes. We investigated how hyperglycaemia impairs expansion and differentiation of the growing pancreas. We have grafted xenogenic (avian) embryonic pancreas in severe combined immuno-deficient (SCID) mouse and analyzed endocrine and endothelial development in hyperglycaemic compared to normoglycaemic conditions. 14 dpi chicken pancreases were grafted under the kidney capsule of normoglycaemic or hyperglycaemic, streptozotocin-induced, SCID mice and analyzed two weeks later. Vascularization was analyzed both quantitatively and qualitatively using either in situ hybridization with both mouse- and chick-specific RNA probes for VEGFR2 or immunohistochemistry with an antibody to nestin, a marker of endothelial cells that is specific for murine cells. To inhibit angiopoietin 2 (Ang2), SCID mice were treated with 4 mg/kg IP L1-10 twice/week. In normoglycaemic condition, chicken-derived endocrine and exocrine cells developed well and intragraft vessels were lined with mouse endothelial cells. When pancreases were grafted in hyperglycaemic mice, growth and differentiation of the graft were altered and we observed endothelial discontinuities, large blood-filled spaces. Vessel density was decreased. These major vascular anomalies were associated with strong over-expression of chick-Ang2. To explore the possibility that Ang2 over-expression could be a key step in vascular disorganization induced by hyperglycaemia, we treated mice with L1-10, an Ang-2 specific inhibitor. Inhibition of Ang2 improved vascularization and beta-cell density. this work highligghted an important role of Ang2 in pancreatic vascular defects induced by hyperglycemia

Do Asian breast cancer patients have poorer survival than their western counterparts? A comparison between Singapore and Stockholm

10.1186/bcr2219Breast Cancer Research111-BCRR

Blood-based biomarkers for Alzheimer disease: mapping the road to the clinic.

Biomarker discovery and development for clinical research, diagnostics and therapy monitoring in clinical trials have advanced rapidly in key areas of medicine - most notably, oncology and cardiovascular diseases - allowing rapid early detection and supporting the evolution of biomarker-guided, precision-medicine-based targeted therapies. In Alzheimer disease (AD), breakthroughs in biomarker identification and validation include cerebrospinal fluid and PET markers of amyloid-β and tau proteins, which are highly accurate in detecting the presence of AD-associated pathophysiological and neuropathological changes. However, the high cost, insufficient accessibility and/or invasiveness of these assays limit their use as viable first-line tools for detecting patterns of pathophysiology. Therefore, a multistage, tiered approach is needed, prioritizing development of an initial screen to exclude from these tests the high numbers of people with cognitive deficits who do not demonstrate evidence of underlying AD pathophysiology. This Review summarizes the efforts of an international working group that aimed to survey the current landscape of blood-based AD biomarkers and outlines operational steps for an effective academic-industry co-development pathway from identification and assay development to validation for clinical use.I recieved an honorarium from Roche Diagnostics for my participation in the advisory panel meeting leading to this pape

I Going Away. I Going Home. : Austin Clarke\u27s Leaving this Island Place

Austin Clarke’s “Leaving This Island Place” is one of scores of Caribbean autobiographical works that focus on a bright, young, lower-class islander leaving his/her small island place and setting out on “Eldorado voyages.” The narrative of that journey away from home to Europe or Canada or the United States and the later efforts to return may be said to be the Caribbean story, as suggested in the subtitle of Wilfred Cartey’s study of Caribbean literature, Whispers from the Caribbean: I Going Away, I Going Home, which argues that while in Caribbean literature there is much movement away, there is also a body of literature in which “the notion of ‘away’ and images of movement out are replaced by images of return” (xvi). Traditionally, however, the first autobiographical works, such as George Lamming’s In the Castle of My Skin, V. S. Naipaul’s A House for Mr. Biswas, Merle Hodge’s Crick Crack, Monkey, Jamaica Kincaid’s Annie John, Michelle Cliff’s No Telephone to Heaven, Edwidge Danticat’s Breath, Eyes, Memory, and Elizabeth Nunez’s Beyond the Limbo Silence, have focused on the childhood in the Caribbean and the journey away—or at least the preparation for that journey. Such is the case with Clarke’s “Leaving This Island Place.