FE/BE coupling for an acoustic fluid-structure interaction problem. Residual a posteriori error estimates

This is the author's accepted manuscript. The final published article is available from the link below. Copyright © 2011 John Wiley & Sons, Ltd.In this paper, we developed an a posteriori error analysis of a coupling of finite elements and boundary elements for a fluid–structure interaction problem in two and three dimensions. This problem is governed by the acoustic and the elastodynamic equations in time-harmonic vibration. Our methods combined integral equations for the exterior fluid and FEMs for the elastic structure. It is well-known that because of the reduction of the boundary value problem to boundary integral equations, the solution is not unique in general. However, because of superposition of various potentials, we consider a boundary integral equation that is uniquely solvable and avoids the irregular frequencies of the negative Laplacian operator of the interior domain. In this paper, two stable procedures were considered; one is based on the nonsymmetric formulation and the other is based on a symmetric formulation. For both formulations, we derived reliable residual a posteriori error estimates. From the estimators we computed local error indicators that allowed us to develop an adaptive mesh refinement strategy. For the two-dimensional case we performed an adaptive algorithm on triangles, and for the three-dimensional case we used hanging nodes on hexahedrons. Numerical experiments underline our theoretical results.DFG German Research Foundatio

Dual-dual formulation for a contact problem with friction

A variational inequality formulation is derived for some frictional contact problems from linear elasticity. The formulation exhibits a two-fold saddle point structure and is of dual-dual type, involving the stress tensor as primary unknown as well as the friction force on the contact surface by means of a Lagrange multiplier. The approach starts with the minimization of the conjugate elastic potential. Applying Fenchel's duality theory to this dual minimization problem, the connection to the primal minimization problem and a dual saddle point problem is achieved. The saddle point problem possesses the displacement field and the rotation tensor as further unknowns. Introducing the friction force yields the dual-dual saddle point problem. The equivalence and unique solvability of both problems is shown with the help of the variational inequality formulations corresponding to the saddle point formulations, respectively.This work is supported by the German Research Foundation within the priority program 1180 Prediction and Manipulation of Interactions between Structure and Process

Quasi-optimal degree distribution for a quadratic programming problem arising from the p-version finite element method for a one-dimensional obstacle problem

We present a quadratic programming problem arising from the p-version for a finite element method with an obstacle condition prescribed in Gauss-Lobatto points. We show convergence of the approximate solution to the exact solution in the energy norm. We show an a-priori error estimate and derive an a-posteriori error estimate based on bubble functions which is used in an adaptive p-version. Numerical examples show the superiority of the p-version compared with the h-version. © 2013 Elsevier B.V. All rights reserved

Multiscale methods for the solution of the Helmholtz and Laplace equations

This paper presents some numerical results about applications of multiscale techniques to boundary integral equations. The numerical schemes developed here are to some extent based on the results of the papers [6]—[10]. Section 2 deals with a short description of the theory of generalized Petrov-Galerkin methods for elliptic periodic pseudodifferential equations in $\mathbb{R}^n$ covering classical Galerkin schemes, collocation, and other methods. A general setting of multiresolution analysis generated by periodized scaling functions as well as a general stability and convergence theory for such a framework is outlined. The key to the stability analysis is a local principle due to one of the authors. Its applicability relies here on a sufficiently general version of a so-called discrete commutator property of wavelet bases (see [6]). These results establish important prerequisites for developing and analysing methods for the fast solution of the resulting linear systems (Section 2.4). The crucial fact which is exploited by these methods is that the stiffness matrices relative to an appropriate wavelet basis can be approximated well by a sparse matrix while the solution to the perturbed problem still exhibits the same asymptotic accuracy as the solution to the full discrete problem. It can be shown (see [7]) that the amount of the overall computational work which is needed to realize a required accuracy is of the order $\mathcal{O}(N(\log N)^b)$, where $N$ is the number of unknowns and $b \geq 0$ is some real number

Expression of human Kallikrein 14 (KLK14) in breast cancer is associated with higher tumour grades and positive nodal status

Human kallikrein 14 (KLK14) is a steroid hormone-regulated member of the tissue kallikrein family of serine proteases, for which a prognostic and diagnostic value in breast cancer has been suggested. To further characterise the value of KLK14 as a breast tumour marker, we have carefully analysed KLK14 expression in normal breast tissue and breast cancer both on the RNA level by real-time RT-PCR (n=39), and on the protein level (n=127) using a KLK14-specific antibody for immunohistochemistry. We correlated KLK14 protein expression data with available clinico-pathological parameters (mean follow-up time was 55 months) including patient prognosis. KLK14 RNA expression as quantified by real-time RT-PCR was significantly more abundant in breast tumours compared to normal breast tissue (P=0.027), an issue that had not been clarified recently. Concordantly with the RNA data, cytoplasmic KLK14 protein expression was significantly higher in invasive breast carcinomas compared to normal breast tissues (P=0.003). Furthermore, KLK14 protein expression was associated with higher tumour grade (P=0.041) and positive nodal status (P=0.045) but was not significantly associated with shortened disease-free or overall patient survival time in univariate analyses. We conclude that KLK14 is clearly overexpressed in breast cancer in comparison to normal breast tissues and is positively associated with conventional parameters of tumour aggressiveness, but due to a missing association with survival times, the use of KLK14 immunohistochemistry as a prognostic marker in breast cancer is questionable

The Constraint Interpretation of Physical Emergence

I develop a variant of the constraint interpretation of the emergence of purely physical (non-biological) entities, focusing on the principle of the non-derivability of actual physical states from possible physical states (physical laws) alone. While this is a necessary condition for any account of emergence, it is not sufficient, for it becomes trivial if not extended to types of constraint that specifically constitute physical entities, namely, those that individuate and differentiate them. Because physical organizations with these features are in fact interdependent sets of such constraints, and because such constraints on physical laws cannot themselves be derived from physical laws, physical organization is emergent. These two complementary types of constraint are components of a complete non-reductive physicalism, comprising a non-reductive materialism and a non-reductive formalism

Real fake? Appropriating mobility via Schengen visa in the context of biometric border controls

Although the majority of illegalised migrants in the European Union are so-called ‘visa overstayers’ who enter with a Schengen visa only to become ‘illegal’ once it has expired, this mode of illegalised migration has only received scarce attention in border and migration studies so far. This article takes the introduction of biometric technologies in the Schengen visa regime as an opportunity to compensate for this neglect by asking: How do migrants appropriate Schengen visa in the context of biometric border controls? Drawing on the autonomy of migration approach (AoM), it investigates the visa regime from the perspective of mobility in order to elaborate on one set of practices of appropriation that involves the provision of falsified or manipulated supporting documents upon which the decision to issue a biometric visa is based. The article draws on this example to develop a conception of the notion of appropriation that addresses the two central criticisms that have been raised against the AoM. Besides contributing to the development of the AoM, the article thus introduces a concept in debates on migrant agency that highlights, better than existing concepts, the intricate intertwinement of migrants’ practices with the actors, means and methods of mobility control

Predictions for the future of kallikrein-related peptidases in molecular diagnostics

Kallikrein-related peptidases (KLKs) form a cancer-related ensemble of serine proteases. This multigene family hosts the most widely used cancer biomarker that is PSA-KLK3, with millions of tests performed annually worldwide. The present report provides an overview of the biomarker potential of the extended KLK family (KLK1-KLK15) in various disease settings and envisages approaches that could lead to additional KLK-driven applications in future molecular diagnostics. Particular focus is given on the inclusion of KLKs into multifaceted cancer biomarker panels that provide enhanced diagnostic, prognostic and/or predictive accuracy in several human malignancies. Such panels have been described so far for prostate, ovarian, lung and colorectal cancers. The role of KLKs as biomarkers in non-malignant disease settings, such as Alzheimer’s disease and multiple sclerosis, is also commented upon. Predictions are given on the challenges and future directions regarding clinically oriented KLK research

Non-Invasive Quantification of White and Brown Adipose Tissues and Liver Fat Content by Computed Tomography in Mice

OBJECTIVES: Obesity and its distribution pattern are important factors for the prediction of the onset of diabetes in humans. Since several mouse models are suitable to study the pathophysiology of type 2 diabetes the aim was to validate a novel computed tomograph model (Aloka-Hitachi LCT-200) for the quantification of visceral, subcutaneous, brown and intrahepatic fat depots in mice. METHODS: Different lean and obese mouse models (C57BL/6, B6.V-Lep(ob), NZO) were used to determine the most adequate scanning parameters for the detection of the different fat depots. The data were compared with those obtained after preparation and weighing the fat depots. Liver fat content was determined by biochemical analysis. RESULTS: The correlations between weights of fat tissues on scale and weights determined by CT were significant for subcutaneous (r(2) = 0.995), visceral (r(2) = 0.990) and total white adipose tissue (r(2) = 0.992). Moreover, scans in the abdominal region, between lumbar vertebrae L4 to L5 correlated with whole-body fat distribution allowing experimenters to reduce scanning time and animal exposure to radiation and anesthesia. Test-retest reliability and measurements conducted by different experimenters showed a high reproducibility in the obtained results. Intrahepatic fat content estimated by CT was linearly related to biochemical analysis (r(2) = 0.915). Furthermore, brown fat mass correlated well with weighted brown fat depots (r(2) = 0.952). In addition, short-term cold-expose (4 °C, 4 hours) led to alterations in brown adipose tissue attributed to a reduction in triglyceride content that can be visualized as an increase in Hounsfield units by CT imaging. CONCLUSION: The 3D imaging of fat by CT provides reliable results in the quantification of total, visceral, subcutaneous, brown and intrahepatic fat in mice. This non-invasive method allows the conduction of longitudinal studies of obesity in mice and therefore enables experimenters to investigate the onset of complex diseases such as diabetes and obesity

Sobolev spaces on non-Lipschitz subsets of Rn with application to boundary integral equations on fractal screens

We study properties of the classical fractional Sobolev spaces on non-Lipschitz subsets of Rn. We investigate the extent to which the properties of these spaces, and the relations between them, that hold in the well-studied case of a Lipschitz open set, generalise to non-Lipschitz cases. Our motivation is to develop the functional analytic framework in which to formulate and analyse integral equations on non-Lipschitz sets. In particular we consider an application to boundary integral equations for wave scattering by planar screens that are non-Lipschitz, including cases where the screen is fractal or has fractal boundary