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

Mechanism Understanding for NOx storage, release and reduction on Pt doped Ceria based Catalysts

The introduction of increasingly more stringent regulations for tailpipe emissions of lean-burn gasoline and diesel engines presents the need for further optimisation of existing aftertreatment technologies. These legislations focus primarily on the reduction of NOx at low temperature, i.e., during the cold start period of engine operation. High surface area ceria is successfully employed as an excellent support of PGMs in commercial catalytic LNT (Lean NOx Trap) systems for automotive emission control. Platinum supported on ceria shows enhanced NOx storage at low temperatures (150-300 ̊C), together with improved hydrocarbons light-offs. The OSC (Oxygen Storage Capacity) of ceria can be further enhanced using dopants. Their main function is to allow the catalyst to function outside of the normal working temperature range and widen the operating conditions to increase catalyst efficiency. To this end, Samarium was selected as the doping element because of its reported effect on Pt reducibility and the Pt-ceria interaction, which allow for higher storage capacity during lean operation as well as enhanced activation during rich purge. Sm doped catalysts (10 wt.%) were synthesised on a range of ceriabased catalysts with increasing loadings of Pt (0-1 wt.%). The objective of this study was to investigate the effect of the dopant on the performance of the different catalysts, and, to correlate their reactivity with the morphological changes observed on the surface

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