MASS CONSERVATION ENHANCEMENT OF FREE BOUNDARY FLOWS IN COMPOSITES MANUFACTURING

Undesirable void formation during the injection phase of the liquid composite molding process can be understood as a consequence of the non-uniformity of the flow front progression, caused by the dual porosity of the fiber perform. Therefore the best examination of the void formation physics can be provided by a mesolevel analysis, where the characteristic dimension is given by the fiber tow diameter. In mesolevel analysis, liquid impregnation along two different scales; inside fiber tows and within the spaces between them; must be considered and the coupling between these flow regimes must be addressed. In such case, it is extremely important to account correctly for the surface tension effects, which can be modeled as capillary pressure applied at the flow front. When continues Galerkin method is used, exploiting elements with velocity components and pressure as nodal variables, strong numerical implementation of such boundary conditions leads to ill-posing of the problem, in terms of the weak classical as well as stabilized formulation. As a consequence, there is an error in mass conservation accumulated especially along the free flow front. This article presents a numerical procedure, which was formulated and implemented in the existing Free Boundary Program in order to significantly reduce this error.

Rare earth elements and stable isotope geochemistry (δ13C and δ18O) of phosphorite deposits in the Gafsa Basin, Tunisia

Rare earth elements (REE) and stable isotope compositions (delta C-13 and delta O-18) of shark teeth and phosphatic coprolites were analyzed from the Lower Maastrichtian layers of the El Haria Formation and two sequences of the Paleocene-Eocene (P/E) Chouabine Formation in the Gafsa Basin (south western of Tunisia) in order to trace the sedimentological, climatic and oceanographic conditions. The REE chemistry and their distribution in the two archives are the same for each of the studied layers indicating that the coprolites and shark teeth experienced the same early diagenetic environments. However major differences occur between the Maastrichtian and the P/E reflecting changes in the depositional conditions. The Early Maastrichtian burial environment tended to be more anoxic with REE derived from reduced FeO. While in the P/E the REE patterns mimic the modern oxic-suboxic seawater, the REE source from remineralisation of organic coating could have more significance. The oxygen isotope compositions of the structural phosphates (delta O-18(PO4)) indicate a stable and warm climate during both studied time intervals. A small offset (-0.4 parts per thousand) in the delta O-18 value between the coprolites and shark teeth show minor thermal gradient between bottom and surface water. The pronounced negative shift of 34%. in delta C-13 values recorded in the upper part of the Chouabine Formation was ascribed to the Paleocene-Eocene boundary. At the same time the lack of negative change in the delta O-18 is explained by the semi-closed situation of the Gafsa Basin, which situation also played an important role in the evolution of the organic matters in the sediment resulting in the exceptional low delta C-13 values. (C) 2008 Elsevier B.V. All rights reserved.

Stable isotope and trace element stratigraphy across the Permian-Triassic transition: A redefinition of the boundary in the Velebit Mountain, Croatia

Stable isotopes of carbonates (delta(13)C(carb), delta(18)O(carb)), organic matter (delta(13)C(org), delta(15)N(org)) and major, trace and rare earth element (REE) compositions of marine carbonate rocks of Late Permian to Early Triassic age were used to establish the position of the Permian-Triassic boundary (PTB) at two continuous sections in the Velebit Mountain, Croatia. The chosen sections - Rizvanusa and Brezimenjaca - are composed of two lithostratigraphic units, the Upper Permian Transitional Dolomite and the overlying Sandy Dolomite. The contact between these units, characterized by the erosional features and sudden occurrence of ooids and siliciclastic grains, was previously considered as the chronostratigraphic PTB. The Sandy Dolomite is characterized by high content of non-carbonate material (up to similar to 30 wt.% insoluble residue), originated from erosion of the uplifted hinterland. A relatively rich assemblage of Permian fossils (including Geinitzina, Globivalvulina, Hemigordius, bioclasts of gastropods, ostracods and brachiopods) was found for the first time in Sandy Dolomite, 5 m above the lithologic boundary in the Rizvanusa section. A rather abrupt negative delta(13)C(carb) excursion in both sections appears in rocks showing no recognizable facies change within the Sandy Dolomite, -2 parts per thousand at Rizvanusa and -1.2 parts per thousand at Brezimenjaca, 11 m and 0.2 m above the lithologic contact, respectively. This level within the lower part of the Sandy Dolomite is proposed as the chemostratigraphic PTB. In the Rizvanusa section, the delta(13)C(org) values decline gradually from similar to-25 parts per thousand in the Upper Permian to similar to-29 parts per thousand in the Lower Triassic. The first negative delta(13)C(org) excursion occurs above the lithologic contact, within the uppermost Permian deposits, and appears to be related to the input of terrigenous material. The release of isotopically light microbial soil-biomass into the shallow-marine water may explain this sudden decrease of delta(13)C(org) values below the PTB. This would support the hypothesis that in the western Tethyan realm the land extinction, triggering a sudden drop of woody vegetation and related land erosion, preceded the marine extinction. The relatively low delta(15)N(org) values at the Permian-Triassic (P-Tr) transition level, close to approximate to 0 parts per thousand, and a secondary negative delta(13)C(org) excursion of -0.5 parts per thousand point to significant terrestrial input and primary contribution of cyanobacteria. The profiles of the concentrations of redox-sensitive elements (Ce, Mn, Fe, V), biogenic or biogenic-scavenged elements (P, Ba, Zn, V), Ce/Ce* values, and normalized trace elements, including Ba/Al, Ba/Fe, Ti/Al, Al/(Al + Fe + Mn) and Mn/Ti show clear excursions at the Transitional Dolomite-Sandy Dolomite lithologic boundary and the chemostratigraphic P-Tr boundary. The stratigraphic variations indicate a major regression phase marking the lithologic boundary, transgressive phases in the latest Permian and a gradual change into shallow/stagnant anoxic marine environment towards the P-Tr boundary level and during the earliest Triassic. (C) 2010 Elsevier B.V. All rights reserved.

Characterization of insulators and barrier elements for gene therapy

Gene transfer that relies on integrating vectors often suffers from epigenetic or regulatory effects that influence the expression of the therapeutic gene and=or of cellular genes located near the vector integration site in the chromosome. Insulator elements act to block gene activation by enhancers, while chromatin domain boundary or barrier sequences prevent gene-silencing effects. At present, the modes of action of insulator and barriers are poorly understood, and their use in the context of gene therapies remains to be documented. Using combinations of reporter genes coding for indicator fluorescent proteins, we constructed assay systems that allow the quantification of the insulator or barrier activities of genetic elements in individual cells. This presentation will illustrate how these assay systems were used to identify short DNA elements that insulate nearby genes from activation by viral vector elements, and=or that block the propagation of a silent chromatin structure that leads to gene silencing. We will show that some barrier elements do not merely block repressive effects, but that they can act to stabilize and sustain transgene expression. We will illustrate that this may be beneficial when transgenes are introduced into stem or precursor cells using non-viral vectors, where later differentiation may lead to the silencing of the therapeutic gene. We will show that these elements can be used to maintain efficient transgene expression upon the differentiation of murine precursor cells towards myofibers, in a model of cell therapy for muscle dystrophies.

Effect of different surface roughnesses on a turbulent boundary layer

The classical treatment of rough wall turbulent boundary layers consists in determining the effect the roughness has on the mean velocity profile. This effect is usually described in terms of the roughness function delta U+. The general implication is that different roughness geometries with the same delta U+ will have similar turbulence characteristics, at least at a sufficient distance from the roughness elements. Measurements over two different surface geometries (a mesh roughness and spanwise circular rods regularly spaced in the streamwise direction) with nominally the same delta U+ indicate significant differences in the Reynolds stresses, especially those involving the wall-normal velocity fluctuation, over the outer region. The differences are such that the Reynolds stress anisotropy is smaller over the mesh roughness than the rod roughness. The Reynolds stress anisotropy is largest for a smooth wall. The small-scale anisotropy and interniittency exhibit much smaller differences when the Taylor microscale Reynolds number and the Kolmogorov-normalized mean shear are nominally the same. There is nonetheless evidence that the small-scale structure over the three-dimensional mesh roughness conforms more closely with isotropy than that over the rod-roughened and smooth walls.

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

A wavenumber independent boundary element method for an acoustic scattering problem

In this paper we consider the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data, a problem which models, for example, outdoor sound propagation over inhomogeneous. at terrain. To achieve good approximation at high frequencies with a relatively low number of degrees of freedom, we propose a novel Galerkin boundary element method, using a graded mesh with smaller elements adjacent to discontinuities in impedance and a special set of basis functions so that, on each element, the approximation space contains polynomials ( of degree.) multiplied by traces of plane waves on the boundary. We prove stability and convergence and show that the error in computing the total acoustic field is O( N-(v+1) log(1/2) N), where the number of degrees of freedom is proportional to N logN. This error estimate is independent of the wavenumber, and thus the number of degrees of freedom required to achieve a prescribed level of accuracy does not increase as the wavenumber tends to infinity.

A high-wavenumber boundary-element method for an acoustic scattering problem

In this paper we show stability and convergence for a novel Galerkin boundary element method approach to the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data. This problem models, for example, outdoor sound propagation over inhomogeneous flat terrain. To achieve a good approximation with a relatively low number of degrees of freedom we employ a graded mesh with smaller elements adjacent to discontinuities in impedance, and a special set of basis functions for the Galerkin method so that, on each element, the approximation space consists of polynomials (of degree $\nu$) multiplied by traces of plane waves on the boundary. In the case where the impedance is constant outside an interval $[a,b]$, which only requires the discretization of $[a,b]$, we show theoretically and experimentally that the $L_2$ error in computing the acoustic field on $[a,b]$ is ${\cal O}(\log^{\nu+3/2}|k(b-a)| M^{-(\nu+1)})$, where $M$ is the number of degrees of freedom and $k$ is the wavenumber. This indicates that the proposed method is especially commendable for large intervals or a high wavenumber. In a final section we sketch how the same methodology extends to more general scattering problems.

Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

A high frequency boundary element method for scattering by convex polygons with impedance boundary conditions

We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions. Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy. Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem, we propose a novel Galerkin boundary element method, with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon. Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.

A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity

We propose a discontinuous-Galerkin-based immersed boundary method for elasticity problems. The resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous Galerkin approximation. Special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non-homogeneous essential and natural boundary conditions. The role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension. Finally, extensive two- and three-dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions. (C) 2009 Elsevier B.V. All rights reserved.

A discontinuous-Galerkin-based immersed boundary method

A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of user-defined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous-Galerkin approximation and impose the Dirichlet boundary conditions strongly. By virtue of relaxing the continuity constraint at those elements. boundary locking is avoided and optimal-order convergence is achieved. This is shown through numerical experiments in reaction-diffusion problems. Copyright (c) 2008 John Wiley & Sons, Ltd.

Dynamic stationary response of reinforced plates by the boundary element method

A direct version of the boundary element method (BEM) is developed to model the stationary dynamic response of reinforced plate structures, such as reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary fundamental solutions of thin plates and plane stress state are used to transform the governing partial differential equations into boundary integral equations (BIEs). Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state ( membrane) and for the out-of-plane state ( bending). These uncoupled systems are joined to formamacro-element, in which membrane and bending effects are present. The association of these macro-elements is able to simulate thin-walled structures, including reinforced plate structures. In the present formulation, the BIE is discretized by continuous and/or discontinuous linear elements. Four displacement integral equations are written for every boundary node. Modal data, that is, natural frequencies and the corresponding mode shapes of reinforced plates, are obtained from information contained in the frequency response functions (FRFs). A specific example is presented to illustrate the versatility of the proposed methodology. Different configurations of the reinforcements are used to simulate simply supported and clamped boundary conditions for the plate structures. The procedure is validated by comparison with results determined by the finite element method (FEM).

Hadronic matrix elements in lattice QCD

The lattice formulation of Quantum ChromoDynamics (QCD) has become a reliable tool providing an ab initio calculation of low-energy quantities. Despite numerous successes, systematic uncertainties, such as discretisation effects, finite-size effects, and contaminations from excited states, are inherent in any lattice calculation. Simulations with controlled systematic uncertainties and close to the physical pion mass have become state-of-the-art. We present such a calculation for various hadronic matrix elements using non-perturbatively O(a)-improved Wilson fermions with two dynamical light quark flavours. The main topics covered in this thesis are the axial charge of the nucleon, the electro-magnetic form factors of the nucleon, and the leading hadronic contributions to the anomalous magnetic moment of the muon. Lattice simulations typically tend to underestimate the axial charge of the nucleon by 5 − 10%. We show that including excited state contaminations using the summed operator insertion method leads to agreement with the experimentally determined value. Further studies of systematic uncertainties reveal only small discretisation effects. For the electro-magnetic form factors of the nucleon, we see a similar contamination from excited states as for the axial charge. The electro-magnetic radii, extracted from a dipole fit to the momentum dependence of the form factors, show no indication of finite-size or cutoff effects. If we include excited states using the summed operator insertion method, we achieve better agreement with the radii from phenomenology. The anomalous magnetic moment of the muon can be measured and predicted to very high precision. The theoretical prediction of the anomalous magnetic moment receives contribution from strong, weak, and electro-magnetic interactions, where the hadronic contributions dominate the uncertainties. A persistent 3σ tension between the experimental determination and the theoretical calculation is found, which is considered to be an indication for physics beyond the Standard Model. We present a calculation of the connected part of the hadronic vacuum polarisation using lattice QCD. Partially twisted boundary conditions lead to a significant improvement of the vacuum polarisation in the region of small momentum transfer, which is crucial in the extraction of the hadronic vacuum polarisation.