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.

High-resolution terrestrial permian-triassic eventostratigraphic boundary in western Guizhou and eastern Yunnan, southwestern China

The adjoining area of western Guizhou and eastern Yunnan Provinces in southwest China is an ideal place to investigate the feasibility of correlating marine and nonmarine Permian–Triassic boundary (PTB) sequences, as it contains outcrop sections of shallow marine, marginal marine (or paralic), and terrestrial PTB sections, all in close geographic proximity. This paper documents for the first time multiple stratigraphic data from several well-preserved terrestrial PTB sections in the area and attempts to use these data to define, locate, and correlate the PTB in the area. A study of the spores and pollen and vegetation types across the terrestrial PTB sections in the study area suggests three distinct evolutionary stages across the boundary: Stage 1 (Xuanwei Formation) is characterised by Late Permian or Paleozoic-type ferns and pteridosperms (85.0%), with a few gymnosperms (15.0%); stage 2 is marked by an abrupt drop of sporopollen elements of Late Permian aspects, coupled with the appearance of fungal spores and limited Early Triassic palynomorphs; stage 3 (top Xuanwei Formation and Kayitou Formation) is dominated by gymnosperm pollen (58.8%) of clearly Early Triassic aspect, although still retaining limited ferns and pteridosperms. The three biotic stages seem to well correspond with the changing trend of the δ13Corg curves from the same sections, which is characterized by a sharp drop just before the PTB, followed by a short term partial recovery across the boundary, and then succeeded by a gradual decline after the PTB in the Early Triassic. Combining evidence from eventostratigraphic (i.e., the succession of boundary clay beds), biostratigraphic (using both macroplants and palynomorphs), and chemostratigraphic (i.e., organic carbon isotope excursion signals), we propose that a high-resolution PTB succession, closely correlatable to its marine counterpart at the Meishan section in eastern China, is recognisable at the terrestrial PTB sections in the western Guizhou–eastern Yunnan area in southwest China.

Accounting for local government boundary changes in South Australia : valuing assets and liabilities or valuing revenue streams

This paper examines the methodologies adopted in the transfer of assets, liabilities, revenues and expenses resulting from boundary changes associated with municipal amalgamations in South Australia during the late 1990s. It investigates the methods employed for apportioning these financial elements, valuations used and financial settlements required. Significant transfers occurred in only three cases. In two cases, councils used simple, pragmatic methods to apportion assets and liabilities, similar to those used previously in Victoria. In the third case a transfer price was calculated based on the net present value of revenues. This method is quite different from previous methods examined and is appropriate where one council will make significant future gains at another council's loss because of net revenue transfers.

Life crises on land across the Permian–Triassic boundary in South China

The western Guizhou and eastern Yunnan area of southwest China commands a unique and significant position globally in the study of Permian–Triassic boundary (PTB) events as it contains well and continuously exposed PTB sections of marine, non-marine and marginal-marine origin in the same area. By using a range of high-resolution stratigraphic methods including biostratigraphy, eventostratigraphy, chronostratigraphy and chemostratigraphy, not only are the non-marine PTB sections correlated with their marine counterparts in the study area with high-resolution, the non-marine PTB sections of the study area can also be aligned with the PTB Global Stratotype Section and Point (GSSP) at Meishan in eastern China. Plant megafossils (“megaplants”) in the study area indicate a major loss in abundance and diversity across the PTB, and no coal beds and/or seams have been found in the non-marine Lower Triassic although they are very common in the non-marine Upper Permian. The megaplants, however, did not disappear consistently across the whole area, with some elements of the Late Permian Cathaysian Gigantopteris flora surviving the PTB mass extinction and locally even extending up to the Lower Triassic. Palynomorphs exhibit a similar temporal pattern characterized by a protracted stepwise decrease from fern-dominated spores in the Late Permian to pteridosperm and gymnosperm-dominated pollen in the Early Triassic, which was however punctuated by an accelerated loss in both abundance and diversity across the PTB. Contemporaneous with the PTB crisis in the study area was the peculiar prevalence and dominance of some fungi and/or algae species.

The temporal patterns of megaplants and palynomorphs across the PTB in the study area are consistent with the regional trends of plant changes in South China, which also show a long-term decrease in species diversity from the Late Permian Wuchiapingian through the Changhsingian to the earliest Triassic, with about 48% and 77% losses of species occurring respectively in the end-Wuchiapingian and end-Changhsingian. Such consistent patterns, at both local and regional scales, contradict the hypothesis of a regional isochronous extinction of vegetation across the PTB, and hence call into question the notion that the end-Permian mass extinction was a one-hit disaster. Instead, the data from the study area and South China appears more consistent with a scenario that invokes climate change as the main driver for the observed land vegetation changes across the PTB in South China.

A family of simple and robust finite elements for linear and geometrically nonlinear analysis of laminated composite plates

A family of simple, displacement-based and shear-flexible triangular and quadrilateral flat plate/shell elements for linear and geometrically nonlinear analysis of thin to moderately thick laminate composite plates are introduced and summarized in this paper.

The developed elements are based on the first-order shear deformation theory (FSDT) and von-Karman’s large deflection theory, and total Lagrangian approach is employed to formulate the element for geometrically nonlinear analysis. The deflection and rotation functions of the element boundary are obtained from Timoshenko’s laminated composite beam functions, thus convergence can be ensured theoretically for very thin laminates and shear-locking problem is avoided naturally.

The flat triangular plate/shell element is of 3-node, 18-degree-of-freedom, and the plane displacement interpolation functions of the Allman’s triangular membrane element with drilling degrees of freedom are taken as the in-plane displacements of the element. The flat quadrilateral plate/shell element is of 4-node, 24-degree-of-freedom, and the linear displacement interpolation functions of a quadrilateral plane element with drilling degrees of freedom are taken as the in-plane displacements.

The developed elements are simple in formulation, free from shear-locking, and include conventional engineering degrees of freedom. Numerical examples demonstrate that the elements are convergent, not sensitive to mesh distortion, accurate and efficient for linear and geometric nonlinear analysis of thin to moderately thick laminates.

A new bivalve fauna from the Permian-Triassic boundary section of southwestern China

A new marine bivalve fauna from the continuous Upper Permian Longtan Formation to Lower Triassic Yelang Formation of the Zhongzai section in southwestern China is documented. Four bivalve assemblages spanning the Permian–Triassic boundary are recognized and regionally correlated in South China. The bivalve assemblages changed from elements dominated by Palaeozoic types to those dominated by Mesozoic types. Three new species, Claraia zhongzaiensis sp. nov., Claraia sp. nov. 1 and Claraia sp. nov. 2, are described.

Spectral element modelling of wave propagation with boundary and structural discontinuity reflections

Spectral element method is very efficient in modelling high-frequency stress wave propagation because it works in the frequency domain. It does not need to use very fine meshes in order to capture high frequency wave energy as the time domain methods do, such as finite element method. However, the conventional spectral element method requires a throw-off element to be added to the structural boundaries to act as a conduit for energy to transmit out of the system. This makes the method difficult to model wave reflection at boundaries. To overcome this limitation, imaginary spectral elements are proposed in this study, which are combined with the real structural elements to model wave reflections at structural boundaries. The efficiency and accuracy of this proposed approach is verified by comparing the numerical simulation results with measured results of one dimensional stress wave propagation in a steel bar. The method is also applied to model wave propagation in a steel bar with not only boundary reflection, but also reflections from single and multiple cracks. The reflection and transmission coefficients, which are obtained from the discrete spring model, are adopted to quantify the discontinuities. Experimental tests of wave propagation in a steel bar with one crack of different depths are also carried out. Numerical simulations and experimental results show that the proposed method is effective and reliable in modelling wave propagation in one-dimensional waveguides with reflections from boundary and structural discontinuities. The proposed method can be applied to effectively model stress wave propagation for structural damage detection.

Functional system maps as boundary objects in complex system development

A trend towards the provision of product-service packaging and the proliferation of service businesses introduces both tangible and intangible elements into system design. In this paper, we consider the utility of hierarchical system models as a way of flexibly combining such elements by focusing on requisite functionality. Four cases illustrate how the same approach may be used to clarify the requirements of business or socio-technical systems during system development, operation or reengineering stages. It is suggested that a suitable loosely coupled model has significant utility as a 'boundary object' - a term first coined in the study of museum artefacts. Discussion of such objects requires the use of imagination, which may support innovative system design and development. It is suggested that a well-crafted model has multiple uses - as a foundation for system development, in combining traditional and agile project management strategies and in providing a framework to facilitate the capture and organisation of project knowledge.

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.

Thin-Film Sparse Boundary Array Design for Passive Acoustic Mapping During Ultrasound Therapy

A new 2-D hydrophone array for ultrasound therapy monitoring is presented, along with a novel algorithm for passive acoustic mapping using a sparse weighted aperture. The array is constructed using existing polyvinylidene fluoride (PVDF) ultrasound sensor technology, and is utilized for its broadband characteristics and its high receive sensitivity. For most 2-D arrays, high-resolution imagery is desired, which requires a large aperture at the cost of a large number of elements. The proposed array's geometry is sparse, with elements only on the boundary of the rectangular aperture. The missing information from the interior is filled in using linear imaging techniques. After receiving acoustic emissions during ultrasound therapy, this algorithm applies an apodization to the sparse aperture to limit side lobes and then reconstructs acoustic activity with high spatiotemporal resolution. Experiments show verification of the theoretical point spread function, and cavitation maps in agar phantoms correspond closely to predicted areas, showing the validity of the array and methodology.

Effect of boundary conditions on yield properties of human femoral trabecular bone

Trabecular bone plays an important mechanical role in bone fractures and implant stability. Homogenized nonlinear finite element (FE) analysis of whole bones can deliver improved fracture risk and implant loosening assessment. Such simulations require the knowledge of mechanical properties such as an appropriate yield behavior and criterion for trabecular bone. Identification of a complete yield surface is extremely difficult experimentally but can be achieved in silico by using micro-FE analysis on cubical trabecular volume elements. Nevertheless, the influence of the boundary conditions (BCs), which are applied to such volume elements, on the obtained yield properties remains unknown. Therefore, this study compared homogenized yield properties along 17 load cases of 126 human femoral trabecular cubic specimens computed with classical kinematic uniform BCs (KUBCs) and a new set of mixed uniform BCs, namely periodicity-compatible mixed uniform BCs (PMUBCs). In stress space, PMUBCs lead to 7–72 % lower yield stresses compared to KUBCs. The yield surfaces obtained with both KUBCs and PMUBCs demonstrate a pressure-sensitive ellipsoidal shape. A volume fraction and fabric-based quadric yield function successfully fitted the yield surfaces of both BCs with a correlation coefficient R2≥0.93. As expected, yield strains show only a weak dependency on bone volume fraction and fabric. The role of the two BCs in homogenized FE analysis of whole bones will need to be investigated and validated with experimental results at the whole bone level in future studies.

Finite volume effects in chiral perturbation theory with twisted boundary conditions

We study the effects of a finite cubic volume with twisted boundary conditions on pseudoscalar mesons. We apply Chiral Perturbation Theory in the p-regime and introduce the twist by means of a constant vector field. The corrections of masses, decay constants, pseudoscalar coupling constants and form factors are calculated at next-to-leading order. We detail the derivations and compare with results available in the literature. In some case there is disagreement due to a different treatment of new extra terms generated from the breaking of the cubic invariance. We advocate to treat such terms as renormalization terms of the twisting angles and reabsorb them in the on-shell conditions. We confirm that the corrections of masses, decay constants, pseudoscalar coupling constants are related by means of chiral Ward identities. Furthermore, we show that the matrix elements of the scalar (resp. vector) form factor satisfies the Feynman–Hellman Theorem (resp. the Ward–Takahashi identity). To show the Ward–Takahashi identity we construct an effective field theory for charged pions which is invariant under electromagnetic gauge transformations and which reproduces the results obtained with Chiral Perturbation Theory at a vanishing momentum transfer. This generalizes considerations previously published for periodic boundary conditions to twisted boundary conditions. Another method to estimate the corrections in finite volume are asymptotic formulae. Asymptotic formulae were introduced by Lüscher and relate the corrections of a given physical quantity to an integral of a specific amplitude, evaluated in infinite volume. Here, we revise the original derivation of Lüscher and generalize it to finite volume with twisted boundary conditions. In some cases, the derivation involves complications due to extra terms generated from the breaking of the cubic invariance. We isolate such terms and treat them as renormalization terms just as done before. In that way, we derive asymptotic formulae for masses, decay constants, pseudoscalar coupling constants and scalar form factors. At the same time, we derive also asymptotic formulae for renormalization terms. We apply all these formulae in combination with Chiral Perturbation Theory and estimate the corrections beyond next-to-leading order. We show that asymptotic formulae for masses, decay constants, pseudoscalar coupling constants are related by means of chiral Ward identities. A similar relation connects in an independent way asymptotic formulae for renormalization terms. We check these relations for charged pions through a direct calculation. To conclude, a numerical analysis quantifies the importance of finite volume corrections at next-to-leading order and beyond. We perform a generic Analysis and illustrate two possible applications to real simulations.