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Start date: 2000 × End date: 2009 × WGL Institute: WIAS ×

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Now showing 1 - 10 of 415
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    New results on the stability of quasi-static paths of a single particle system with Coulomb friction and persistent contact
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Schmid, Florian; Martins, J.A.C.; Rebrova, Natalia
    In this paper we announce some new mathematical results on the stability of quasi-static paths of a single particle linearly elastic system with Coulomb friction and persistent normal contact with a flat obstacle.A quasi-static path is said to be stable at some value of the load parameter if, for some finite interval of the load parameter thereafter, the dynamic solutions behave continuously with respect to the size of the initial perturbations (as in Lyapunov stability) and to the smallness of the rate of application of the external forces, $varepsilon$ (as in singular perturbation problems). In this paper we prove sufficient conditions for stability of quasi-static paths of a single particle linearly elastic system with Coulomb friction and persistent normal contact with a flat obstacle. The present system has the additional difficulty of its non-smoothness: the friction law is a multivalued operator and the dynamic evolutions of this system may have discontinuous accelerations.
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    A jump-diffusion Libor model and tits robust calibration
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Belomestrny, Denis; Schoenmakers, John G.M.
    In this paper we propose a jump-diffusion Libor model with jumps in a high-dimensional space and test a stable non-parametric calibration algorithm which takes into account a given local covariance structure. The algorithm returns smooth and simply structured Lévy densities, and penalizes the deviation from the Libor market model. In practice, the procedure is FFT based, thus fast, easy to implement, and yields good results, particularly in view of the ill-posedness of the underlying inverse problem.
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    Simulationsbasierte Regelung der Laserhärtung von Stahl
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Alder, Holger; Hömberg, Dietmar; Weiss, Wolf
    Bei der Oberflaechenhärtung mit Hilfe von Laserstrahlen ist eine konstante Einhärtetiefe erwünscht, wobei gleichzeitig Anschmelzungen vermieden werden sollen. Um Anschmelzungen zu verhindern, kann die Temperatur im Auftreffpunkt des Lasers gemessen werden und die Laserleistung entsprechend geregelt werden. Eine konstante Temperatur fährt bei geometrisch komplizierten Bauteilen jedoch nicht zu einer konstanten Einhärtetiefe. In dieser Arbeit wird ein Verfahren aufgezeigt, wobei durch numerische Simulationen eine nichtkonstante Oberflächentemperatur berechnet wird, die eine konstante Einhärtetiefe liefert. Die berechnete Oberflächentemperatur kann als Solltemperatur im realen Prozess benutzt werden.
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    An optimisation method in inverse acoustic scattering by an elastic obstacle
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Elschner, Johannes; Hsiao, George C.; Rathsfeld, Andreas
    We consider the interaction between an elastic body and a compressible inviscid fluid, which occupies the unbounded exterior domain. The inverse problem of determining the shape of such an elastic scatterer from the measured far field pattern of the scattered fluid pressure field is of central importance in detecting and identifying submerged objects. Following a method proposed by Kirsch and Kress, we approximate the acoustic and elastodynamic wave by potentials over auxiliary surfaces, and we reformulate the inverse problem as an optimisation problem. The objective function to be minimised is the sum of three terms. The first is the deviation of the approximate far field pattern from the measured one, the second is a regularisation term, and the last a control term for the transmission condition. We prove that the optimisation problem has a solution and that, for the regularisation parameter tending to zero, the minimisers tend to a solution of the inverse problem. In contrast to a numerical method from a previous paper, the presented method does require neither a direct solution method nor an additional treatment of possible Jones modes.
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    Optimal control of static plasticity with linear kinematic hardening
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Griesse, Roland; Meyer, Christian
    An optimal control problem for the static problem of infinitesimal elastoplasticity with linear kinematic hardening is considered. The variational inequality arising on the lower-level is regularized using a Yosida-type approach, and an optimal control problem for the so-called viscoplastic model is obtained. Existence of a global optimizer is proved for both the regularized and original problems, and strong convergence of the solutions is established
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    Error estimates for space-time discretizations of a rate-independent variational inequality
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Mielke, Alexander; Paoli, Laetitia; Petrov, Adrien; Stefanelli, Ulisse
    This paper deals with error estimates for space-time discretizations in the context of evolutionary variational inequalities of rate-independent type. After introducing a general abstract evolution problem, we address a fully-discrete approximation and provide a priori error estimates. The application of the abstract theory to a semilinear case is detailed. In particular, we provide explicit space-time convergence rates for the isothermal Souza-Auricchio model for shape-memory alloys.
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    Constrained Delaunay tetrahedral mesh generation and refinement
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Hang, Si
    A it constrained Delaunay tetrahedralization of a domain in $mathbbR^3$ is a tetrahedralization such that it respects the boundaries of this domain, and it has properties similar to those of a Delaunay tetrahedralization. Such objects have various applications such as finite element analysis, computer graphics rendering, geometric modeling, and shape analysis. This article is devoted to presenting recent developments on constrained Delaunay tetrahedralizations of piecewise linear domains. The focus is for the application of numerically solving partial differential equations using finite element or finite volume methods. We survey various related results and detail two core algorithms that have provable guarantees and are amenable to practical implementation. We end this article by listing a set of open questions.
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    A milling model with thermal effects including the dynamics of machine and work piece
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Rott, Oliver; Rasper, Patrick; Hömberg, Dietmar; Uhlmann, Eckart
    This paper deals with the development of a new mathematical model that characterizes the structure-process interaction for a complex milling system. The structure is divided into a work piece and a machine part, which are represented by different models. While the machine dynamics is characterized by a standard multi-body system, the work piece is described as a linear thermo-elastic continuum. The coupling of both parts is carried out by an empirical process model permitting an estimate of heat and coupling forces occurring during milling. This work reports the derivation of the governing equations emphasizing the coupling and summarizes the numerical algorithms being applied to solve the coupled equation system. The results of numerical simulations that show the dynamics of the complex thermo-mechanical system are presented at the end.
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    Stochastic spectral and Fourier-wavelet methods for vector Gaussian random fields
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2005) Kurbanmuradov, Orazgeldi; Sabelfeld, Karl
    Randomized Spectral Models (RSM) and Randomized Fourier-Wavelet Models (FWM) for simulation of homogeneous Gaussian random fields based on spectral representations and plane wave decomposition of random fields are developed. Extensions of FWM to vector random processes are constructed. Convergence of the constructed Fourier-Wavelet models (in the sense of finite-dimensional distributions) under some general conditions on the spectral tensor is given. A comparative analysis of RSM and FWM is made by calculating Eulerian and Lagrangian statistical characteristics of a 3D isotropic incompressible random field through an ensemble and space averaging
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    Rescaled stable generalised Fleming-Viot processes : Flickering random measures
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Birkner, Matthias; Blath, Jochen
    We show how Donnelly and Kurtz' (modified) lookdown construction for measure-valued processes can be used to analyse the longterm- and scaling properties of spatially stable generalised $Lambda$-Fleming Viot processes, exhibiting a rare ``natural'' example of a scaling family converging in f.d.d. sense, but not in any of Skorohod's topologies on path space. This completes results of Fleischmann and Wachtel (2004) about the spatial Neveu process and complements results of Dawson and Hochberg (1982) about the classical Fleming Viot process. The lookdown construction provides an elegant machinery and clear intuition to describe the path properties of the family in terms of a ``flicker effect'', clarifying ``what can go wrong.''