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

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

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

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

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

Measurement of triple gauge-boson couplings at 172 GeV

The triple gauge-boson couplings, Awp, Aw and Abp, have been measured using 34 semileptonically and 54 hadronically decaying WW candidate events. The events were selected in the data recorded during 1996 with the ALEPH detector at 172 GeV, corresponding to an integrated luminosity of 10.65 pb^-1. The triple gauge-boson couplings have been measured using optimal observables constructed from kinematic information of WW events. The results are in agreement with the Standard Model expectation

Determination of sin2 θeff w using jet charge measurements in hadronic Z decays

The electroweak mixing angle is determined with high precision from measurements of the mean difference between forward and backward hemisphere charges in hadronic decays of the Z. A data sample of 2.5 million hadronic Z decays recorded over the period 1990 to 1994 in the ALEPH detector at LEP is used. The mean charge separation between event hemispheres containing the original quark and antiquark is measured for bb̄ and cc̄ events in subsamples selected by their long lifetimes or using fast D*'s. The corresponding average charge separation for light quarks is measured in an inclusive sample from the anticorrelation between charges of opposite hemispheres and agrees with predictions of hadronisation models with a precision of 2%. It is shown that differences between light quark charge separations and the measured average can be determined using hadronisation models, with systematic uncertainties constrained by measurements of inclusive production of kaons, protons and A's. The separations are used to measure the electroweak mixing angle precisely as sin2 θeff w = 0.2322 ± 0.0008(exp. stat.) ±0.0007(exp. syst.) ± 0.0008(sep.). The first two errors are due to purely experimental sources whereas the third stems from uncertainties in the quark charge separations

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

Measurement of the W mass by direct reconstruction in e+e−e^+ e^- collisions at 172 GeV

The mass of the W boson is obtained from reconstructed invariant mass distributions in W-pair events. The sample of W pairs is selected from 10.65~pb$^{-1}$ collected with the ALEPH detector at a mean centre-of-mass energy of 172.09 \GEV. The invariant mass distribution of simulated events are fitted to the experimental distributions and the following W masses are obtained: $WW \to q\overline{q}q\overline{q } m_W = 81.30 +- 0.47(stat.) +- 0.11(syst.) GeV/c^2$, $WW \to l\nu q\overline{q}(l=e,\mu) m_W = 80.54 +- 0.47(stat.) +- 0.11(syst.) GeV/c^2$, $WW \to \tau\nu q\overline{q} m_W = 79.56 +- 1.08(stat.) +- 0.23(syst.) GeV/C62$. The statistical errors are the expected errors for Monte Carlo samples of the same integrated luminosity as the data. The combination of these measurements gives: $m_W = 80.80 +- 0.11(syst.) +- 0.03(LEP energy) GeV/^2$