Adaptive discontinuous Galerkin methods on polytopic meshes

In this article we consider the application of discontinuous Galerkin finite element methods, defined on agglomerated meshes consisting of general polytopic elements, to the numerical approximation of partial differential equation problems posed on complicated geometries. Here, we assume that the underlying computational domain may be accurately represented by a geometry-conforming fine mesh; the resulting coarse mesh is then constructed based on employing standard graph partitioning algorithms. To improve the accuracy of the computed numerical approximation, we consider the development of goal-oriented adaptation techniques within an automatic mesh refinement strategy. In this setting, elements marked for refinement are subdivided by locally constructing finer agglomerates; should further resolution of the underlying fine mesh T_f be required, then adaptive refinement of T_f will also be undertaken. As an example of the application of these techniques, we consider the numerical approximation of the linear elasticity equations for a homogeneous isotropic material. In particular, the performance of the proposed adaptive refinement algorithm is studied for the computation of the (scaled) effective Young's modulus of a section of trabecular bone

Adaptive discontinuous Galerkin methods on polytopic meshes

In this article we consider the application of discontinuous Galerkin finite element methods, defined on agglomerated meshes consisting of general polytopic elements, to the numerical approximation of partial differential equation problems posed on complicated geometries. Here, we assume that the underlying computational domain may be accurately represented by a geometry-conforming fine mesh; the resulting coarse mesh is then constructed based on employing standard graph partitioning algorithms. To improve the accuracy of the computed numerical approximation, we consider the development of goal-oriented adaptation techniques within an automatic mesh refinement strategy. In this setting, elements marked for refinement are subdivided by locally constructing finer agglomerates; should further resolution of the underlying fine mesh T_f be required, then adaptive refinement of T_f will also be undertaken. As an example of the application of these techniques, we consider the numerical approximation of the linear elasticity equations for a homogeneous isotropic material. In particular, the performance of the proposed adaptive refinement algorithm is studied for the computation of the (scaled) effective Young's modulus of a section of trabecular bone

X-ray studies of monochloroacetamide and benzanilide

The crystal structures of monochloroacetamide and benzanilide have been determined by X-ray diffraction methods. Monochloroacetamide was found to crystallise in the space group P2,1/c, with four molecules in the monoclinic unit cell of dimensions a = 10.276 A b = 5.152 A c = 7.499 A 6 = 98.8° The space group of benzanilide was found to be la with four molecules in the monoclinic unit cell of dimensions a = 23.383 A b = 5.335 A c = 8.027 A 6 = 92.0° Three dimensional intensity data for the monochloroacetamide structure were collected using the multiple film technique, the intensities were measured on a double beam recording microdensitometer. The structure was solved by the interpretation of a three dimensional Patterson Synthesis and was refined using Fourier, difference and least-squares methods. The hydrogen atoms were located in a three dimensional difference synthesis. The carbo-amide plane was found to be planar with the chlorine-carbon bond inclined at 12° to this plane. Three dimensional intensity data for benzanilide were collected using a three circle diffractometer. The structure was solved by the interpretation of Patterson syntheses. Refinement of the structure by the Parameter Shift method showed the structure to be disordered. This fact was substantiated by Weissenberg photographs. The amount of disorder from least-squares refinement was found to be 39%. The structure has been refined in the space groups la and I2/a. In both refinements the N-phenyl bond was found to be rotated by 38° from the amide plane. The C-phenyl bond was found to be rotated by 27° from the amide plane

Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains

The numerical approximation of partial differential equations (PDEs) posed on complicated geometries, which include a large number of small geometrical features or microstructures, represents a challenging computational problem. Indeed, the use of standard mesh generators, employing simplices or tensor product elements, for example, naturally leads to very fine finite element meshes, and hence the computational effort required to numerically approximate the underlying PDE problem may be prohibitively expensive. As an alternative approach, in this article we present a review of composite/agglomerated discontinuous Galerkin finite element methods (DGFEMs) which employ general polytopic elements. Here, the elements are typically constructed as the union of standard element shapes; in this way, the minimal dimension of the underlying composite finite element space is independent of the number of geometrical features. In particular, we provide an overview of hp-version inverse estimates and approximation results for general polytopic elements, which are sharp with respect to element facet degeneration. On the basis of these results, a priori error bounds for the hp-DGFEM approximation of both second-order elliptic and first-order hyperbolic PDEs will be derived. Finally, we present numerical experiments which highlight the practical application of DGFEMs on meshes consisting of general polytopic elements

Statistical Evaluation of Three Distinct Automated Doppler Dealiasing Algorithms Using a Hand-Dealiased Shipborne Radar Dataset

No abstract availabl

Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains

The numerical approximation of partial differential equations (PDEs) posed on complicated geometries, which include a large number of small geometrical features or microstructures, represents a challenging computational problem. Indeed, the use of standard mesh generators, employing simplices or tensor product elements, for example, naturally leads to very fine finite element meshes, and hence the computational effort required to numerically approximate the underlying PDE problem may be prohibitively expensive. As an alternative approach, in this article we present a review of composite/agglomerated discontinuous Galerkin finite element methods (DGFEMs) which employ general polytopic elements. Here, the elements are typically constructed as the union of standard element shapes; in this way, the minimal dimension of the underlying composite finite element space is independent of the number of geometrical features. In particular, we provide an overview of hp-version inverse estimates and approximation results for general polytopic elements, which are sharp with respect to element facet degeneration. On the basis of these results, a priori error bounds for the hp-DGFEM approximation of both second-order elliptic and first-order hyperbolic PDEs will be derived. Finally, we present numerical experiments which highlight the practical application of DGFEMs on meshes consisting of general polytopic elements

Adverse prognostic and predictive significance of low DNA-dependent protein kinase catalytic subunit (DNA-PKcs) expression in early-stage breast cancers

Background: DNA-dependent protein kinase catalytic subunit (DNA-PKcs), a serine threonine kinase belonging to the PIKK family (phosphoinositide 3-kinase-like-family of protein kinase), is a critical component of the non-homologous end joining (NHEJ) pathway required for the repair of DNA double strand breaks. DNA-PKcs may be involved in breast cancer pathogenesis. Methods: We evaluated clinicopathological significance of DNA-PKcs protein expression in 1161 tumours and DNA-PKcs mRNA expression in 1950 tumours. We correlated DNA-PKcs to other markers of aggressive phenotypes, DNA repair, apoptosis and cell cycle regulation. Results: Low DNA-PKcs protein expression was associated with higher tumour grade, higher mitotic index, tumour de-differentiation and tumour type (ps<0.05). Absence of BRCA1, low XRCC1/SMUG1/APE1/Polβ were also more likely in low DNA-PKcs expressing tumours (ps<0.05). Low DNA-PKcs protein expression was significantly associated with worse breast cancer specific survival (BCCS) in univariate and multivariate analysis (ps<0.01). At the mRNA level, low DNA-PKcs was associated with PAM50.Her2 and PAM50.LumA molecular phenotypes (ps<0.01) and poor BCSS. In patients with ER positive tumours who received endocrine therapy, low DNA-PKcs (protein and mRNA) was associated with poor survival. In ER negative patients, low DNA-PKcs mRNA remains significantly associated with adverse outcome. Conclusions: Our study suggests that low DNA-PKcs expression may have prognostic and predictive significance in breast cancers

Marshall Space Flight Center and the Open-Source Radar Software Revolution

No abstract availabl

Marine integrons containing novel integrase genes, attachment sites, attI, and associated gene cassettes in polluted sediments from Suez and Tokyo Bays

In order to understand the structure and biological significance of integrons and associated gene cassettes in marine polluted sediments, metagenomic DNAs were extracted from sites at Suez and Tokyo Bays. PCR amplicons containing new integrase genes, intI, linked with novel gene cassettes, were recovered and had sizes from 1.8 to 2.5 kb. This approach uncovered, for the first time, the structure and diversity of both marine integron attachment site, attI, and the first gene cassette, the most efficiently expressed integron-associated gene cassette. The recovered 13 and 20 intI phylotypes, from Suez and Tokyo Bay samples, respectively, showed a highly divergence, suggesting a difference in integron composition between the sampling sites. Some intI phylotypes showed similarity with that from Geobacter metallireducens, belonging to Deltaproteobacteria, the dominant class in both sampling sites, as determined by 16S rRNA gene analysis. Thirty distinct families of putative attI site, as determined by the presence of an attI-like simple site, were recovered. A total of 146 and 68 gene cassettes represented Suez and Tokyo Bay unsaturated cassette pools, respectively. Gene cassettes, including a first cassette, from both sampling sites encoded two novel families of glyoxalase/bleomycin antibiotic-resistance protein. Gene cassettes from Suez Bay encoded proteins similar to haloacid dehalogenases, protein disulfide isomerases and death-on-curing and plasmid maintenance system killer proteins. First gene cassettes from Tokyo Bay encoded a xenobiotic-degrading protein, cardiolipin synthetase, esterase and WD40-like β propeller protein. Many of the first gene cassettes encoded proteins with no ascribable function but some of them were duplicated and possessed signal functional sites, suggesting efficient adaptive functions to their bacterial sources. Thus, each sampling site had a specific profile of integrons and cassette types consistent with the hypothesis that the environment shapes the genome