Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes

We develop a method for generating degree-of-freedom maps for arbitrary order finite element spaces for any cell shape. The approach is based on the composition of permutations and transformations by cell sub-entity. Current approaches to generating degree-of-freedom maps for arbitrary order problems typically rely on a consistent orientation of cell entities that permits the definition of a common local coordinate system on shared edges and faces. However, while orientation of a mesh is straightforward for simplex cells and is a local operation, it is not a strictly local operation for quadrilateral cells and in the case of hexahedral cells not all meshes are orientable. The permutation and transformation approach is developed for a range of element types, including Lagrange, and divergence- and curl-conforming elements, and for a range of cell shapes. The approach is local and can be applied to cells of any shape, including general polytopes and meshes with mixed cell types. A number of examples are presented and the developed approach has been implemented in an open-source finite element library

Nordic Seas polynyas and their role in preconditioning marine productivity during the Last Glacial Maximum.

Arctic and Antarctic polynyas are crucial sites for deep-water formation, which helps sustain global ocean circulation. During glacial times, the occurrence of polynyas proximal to expansive ice sheets in both hemispheres has been proposed to explain limited ocean ventilation and a habitat requirement for marine and higher-trophic terrestrial fauna. Nonetheless, their existence remains equivocal, not least due to the hitherto paucity of sufficiently characteristic proxy data. Here we demonstrate polynya formation in front of the NW Eurasian ice sheets during the Last Glacial Maximum (LGM), which resulted from katabatic winds blowing seaward of the ice shelves and upwelling of warm, sub-surface Atlantic water. These polynyas sustained ice-sheet build-up, ocean ventilation, and marine productivity in an otherwise glacial Arctic desert. Following the catastrophic meltwater discharge from the collapsing ice sheets at ~17.5 ka BP, polynya formation ceased, marine productivity declined dramatically, and sea ice expanded rapidly to cover the entire Nordic Seas

Construction of arbitrary order finite element degree-of-freedom maps on polygonal and polyhedral cell meshes

We develop an approach to generating degree-of-freedom maps for arbitrary order finite element spaces for any cell shape. The approach is based on the composition of permutations and transformations by cell sub-entity. Current approaches to generating degree-of-freedom maps for arbitrary order problems typically rely on a consistent orientation of cell entities that permits the definition of a common local coordinate system on shared edges and faces. However, while orientation of a mesh is straightforward for simplex cells and is a local operation, it is not a strictly local operation for quadrilateral cells and in the case of hexahedral cells not all meshes are orientable. The permutation and transformation approach is developed for a range of element types, including Lagrange, and divergence- and curl-conforming elements, and for a range of cell shapes. The approach is local and can be applied to cells of any shape, including general polytopes and meshes with mixed cell types. A number of examples are presented and the developed approach has been implemented in an open-source finite element library

Effects of Lactobacillus paracasei CNCM I-4034, Bifidobacterium breve CNCM I-4035 and Lactobacillus rhamnosus CNCM I-4036 on Hepatic Steatosis in Zucker Rats

We have previously described the safety and immunomodulatory effects of Lactobacillus paracasei CNCM I-4034, Bifidobacterium breve CNCM I-4035 and Lactobacillus rhamnosus CNCM I-4036 in healthy volunteers. The scope of this work was to evaluate the effects of these probiotic strains on the hepatic steatosis of obese rats. We used the Zucker rat as a genetic model of obesity. Zucker-Leprfa/fa rats received one of three probiotic strains, a mixture of L. paracasei CNCM I-4034 and B. breve CNCM I-4035, or a placebo for 30 days. An additional group of Zucker-lean+/fa rats received a placebo for 30 days. No alterations in intestinal histology, in the epithelial, lamina propria, muscular layers of the ileal or colonic mucosa, or the submucosae, were observed in any of the experimental groups. Triacylglycerol content decreased in the liver of Zucker-Leprfa/fa rats that were fed L. rhamnosus, B. breve, or the mixture of B. breve and L. paracasei. Likewise, the area corresponding to neutral lipids was significantly smaller in the liver of all four groups of Zucker-Leprfa/fa rats that received probiotics than in rats fed the placebo. Zucker-Leprfa/fa rats exhibited significantly greater serum LPS levels than Zucker-lean+/fa rats upon administration of placebo for 30 days. In contrast, all four groups of obese Zucker-Leprfa/fa rats that received LAB strains exhibited serum LPS concentrations similar to those of Zucker-lean+/fa rats. Serum TNF-α levels decreased in the Zucker-Leprfa/fa rats that received B. breve, L. rhamnosus, or the mixture, whereas L. paracasei feeding decreased IL-6 levels in the serum of Zucker-Leprfa/fa rats. In conclusion, the probiotic strains reduced hepatic steatosis in part by lowering serum LPS, and had an anti-inflammatory effect in obese Zucker rats.Part of the research currently in progress in the authors' laboratory is funded by the company Hero Spain, S. A. through the grant #3545 managed by the Fundacion General Empresa-Universidad de Granada