An Entropy Stable Nodal Discontinuous Galerkin Method for the Two Dimensional Shallow Water Equations on Unstructured Curvilinear Meshes with Discontinuous Bathymetry

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the nonlinear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretisation exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretisation of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem

A Provably Stable Discontinuous Galerkin Spectral Element Approximation for Moving Hexahedral Meshes

We design a novel provably stable discontinuous Galerkin spectral element (DGSEM) approximation to solve systems of conservation laws on moving domains. To incorporate the motion of the domain, we use an arbitrary Lagrangian-Eulerian formulation to map the governing equations to a fixed reference domain. The approximation is made stable by a discretization of a skew-symmetric formulation of the problem. We prove that the discrete approximation is stable, conservative and, for constant coefficient problems, maintains the free-stream preservation property. We also provide details on how to add the new skew-symmetric ALE approximation to an existing discontinuous Galerkin spectral element code. Lastly, we provide numerical support of the theoretical results

Framing Appropriate Accommodations in Terms of Individual Need: Examining the Fit of Four Approaches to Selecting Test Accommodations of English Language Learners

Providing appropriate test accommodations to most English language learners (ELLs) is important to facilitate meaningful inferences about learning. This study compared teacher large-scale test accommodation recommendations to those from a literature- and practitioner-grounded accommodation selection taxonomy. The taxonomy links student-specific needs, strengths and schooling experiences to large-scale test accommodation recommendations that differentially minimize barriers of access for students with different profiles. A blind panel of experts rated four sets of recommendations for each of 114 ELLs. Results found the taxonomy was a significantly better fit for distinguishing accommodations by student need than teacher recommendations. Further, the fit of teacher recommendations showed no difference when the teacher used a structured data collection procedure to gather profile information about each of their ELLs and when they did not, and teachers’ recommendations were not found to differ significantly from a random set of accommodations. Findings are consistent with previous literature that suggests the task of matching specific accommodations to individual needs, rather than the task of identifying individual needs, is where teachers struggle in recommending appropriate test accommodations

Stability of Discontinuous Galerkin Spectral Element Schemes for Wave Propagation when the Coefficient Matrices have Jumps

We use the behavior of the L2 norm of the solutions of linear hyperbolic equations with discontinuous coefficient matrices as a surrogate to infer stability of discontinuous Galerkin spectral element methods (DGSEM). Although the L2 norm is not bounded by the initial data for homogeneous and dissipative boundary conditions for such systems, the L2 norm is easier to work with than a norm that discounts growth due to the discontinuities. We show that the DGSEM with an upwind numerical flux that satisfies the Rankine-Hugoniot (or conservation) condition has the same energy bound as the partial differential equation does in the L2 norm, plus an added dissipation that depends on how much the approximate solution fails to satisfy the Rankine-Hugoniot jump

Sulfate assimilation in eukaryotes: fusions, relocations and lateral transfers

<p>Abstract</p> <p>Background</p> <p>The sulfate assimilation pathway is present in photosynthetic organisms, fungi, and many bacteria, providing reduced sulfur for the synthesis of cysteine and methionine and a range of other metabolites. In photosynthetic eukaryotes sulfate is reduced in the plastids whereas in aplastidic eukaryotes the pathway is cytosolic. The only known exception is <it>Euglena gracilis</it>, where the pathway is localized in mitochondria. To obtain an insight into the evolution of the sulfate assimilation pathway in eukaryotes and relationships of the differently compartmentalized isoforms we determined the locations of the pathway in lineages for which this was unknown and performed detailed phylogenetic analyses of three enzymes involved in sulfate reduction: ATP sulfurylase (ATPS), adenosine 5'-phosphosulfate reductase (APR) and sulfite reductase (SiR).</p> <p>Results</p> <p>The inheritance of ATPS, APR and the related 3'-phosphoadenosine 5'-phosphosulfate reductase (PAPR) are remarkable, with multiple origins in the lineages that comprise the opisthokonts, different isoforms in chlorophytes and streptophytes, gene fusions with other enzymes of the pathway, evidence a eukaryote to prokaryote lateral gene transfer, changes in substrate specificity and two reversals of cellular location of host- and endosymbiont-originating enzymes. We also found that the ATPS and APR active in the mitochondria of <it>Euglena </it>were inherited from its secondary, green algal plastid.</p> <p>Conclusion</p> <p>Our results reveal a complex history for the enzymes of the sulfate assimilation pathway. Whilst they shed light on the origin of some characterised novelties, such as a recently described novel isoform of APR from Bryophytes and the origin of the pathway active in the mitochondria of Euglenids, the many distinct and novel isoforms identified here represent an excellent resource for detailed biochemical studies of the enzyme structure/function relationships.</p

Insights into the regulation of DMSP synthesis in the diatom Thalassiosira pseudonana through APR activity, proteomics and gene expression analyses on cells acclimating to changes in salinity, light and nitrogen

Despite the importance of dimethylsulphoniopropionate (DMSP) in the global sulphur cycle and climate regulation, the biological pathways underpinning its synthesis in marine phytoplankton remain poorly understood. The intracellular concentration of DMSP increases with increased salinity, increased light intensity and nitrogen starvation in the diatom Thalassiosira pseudonana. We used these conditions to investigate DMSP synthesis at the cellular level via analysis of enzyme activity, gene expression and proteome comparison. The activity of the key sulphur assimilatory enzyme, adenosine 5′- phosphosulphate reductase was not coordinated with increasing intracellular DMSP concentration. Under all three treatments coordination in the expression of sulphur assimilation genes was limited to increases in sulphite reductase transcripts. Similarly, proteomic 2D gel analysis only revealed an increase in phosphoenolpyruvate carboxylase following increases in DMSP concentration. Our findings suggest that increased sulphur assimilation might not be required for increased DMSP synthesis, instead the availability of carbon and nitrogen substrates may be important in the regulation of this pathway. This contrasts with the regulation of sulphur metabolism in higher plants, which generally involves upregulation of several sulphur assimilatory enzymes. In T. pseudonana changes relating to sulphur metabolism were specific to the individual treatments and, given that little coordination was seen in transcript and protein responses across the three growth conditions, different patterns of regulation might be responsible for the increase in DMSP concentration seen under each treatment

H3 histamine receptor-mediated activation of protein kinase calpha inhibits the growth of cholangiocarcinoma in vitro and in vivo

Histamine regulates functions via four receptors (HRH1, HRH2, HRH3, and HRH4). The D-myo-inositol 1,4,5-trisphosphate (IP(3))/Ca(2+)/protein kinase C (PKC)/mitogen-activated protein kinase pathway regulates cholangiocarcinoma growth. We evaluated the role of HRH3 in the regulation of cholangiocarcinoma growth. Expression of HRH3 in intrahepatic and extrahepatic cell lines, normal cholangiocytes, and human tissue arrays was measured. In Mz-ChA-1 cells stimulated with (R)-(alpha)-(-)-methylhistamine dihydrobromide (RAMH), we measured (a) cell growth, (b) IP(3) and cyclic AMP levels, and (c) phosphorylation of PKC and mitogen-activated protein kinase isoforms. Localization of PKC alpha was visualized by immunofluorescence in cell smears and immunoblotting for PKC alpha in cytosol and membrane fractions. Following knockdown of PKC alpha, Mz-ChA-1 cells were stimulated with RAMH before evaluating cell growth and extracellular signal-regulated kinase (ERK)-1/2 phosphorylation. In vivo experiments were done in BALB/c nude mice. Mice were treated with saline or RAMH for 44 days and tumor volume was measured. Tumors were excised and evaluated for proliferation, apoptosis, and expression of PKC alpha, vascular endothelial growth factor (VEGF)-A, VEGF-C, VEGF receptor 2, and VEGF receptor 3. HRH3 expression was found in all cells. RAMH inhibited the growth of cholangiocarcinoma cells. RAMH increased IP(3) levels and PKC alpha phosphorylation and decreased ERK1/2 phosphorylation. RAMH induced a shift in the localization of PKC alpha expression from the cytosolic domain into the membrane region of Mz-ChA-1 cells. Silencing of PKC alpha prevented RAMH inhibition of Mz-ChA-1 cell growth and ablated RAMH effects on ERK1/2 phosphorylation. In vivo, RAMH decreased tumor growth and expression of VEGF and its receptors; PKC alpha expression was increased. RAMH inhibits cholangiocarcinoma growth by PKC alpha-dependent ERK1/2 dephosphorylation. Modulation of PKC alpha by histamine receptors may be important in regulating cholangiocarcinoma growth. (Mol Cancer Res 2009;7(10):1704-13