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End date: 2009 × Start date: 2000 × DDC: 510 × Has files: Yes × Type: Text × Subject: stability ×

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Now showing 1 - 8 of 8
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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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    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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    An iterative method for the multipliers of periodic delay-differential equations and the analysis of a PDE milling model
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Rott, Oliver; Jarlebring, Elisa
    Locally convergent iterative schemes have turned out to be very useful in the analysis of the characteristic roots of delay-differential equations (DDEs) with constant coefficients. In this work we present a locally convergent iterative scheme for the characteristic multipliers of periodic-coefficient DDEs. The method is an adaption of an iterative method called residual inverse iteration. The possibility to use this method stems from an observation that the characteristic matrix can be expressed with the fundamental solution of a differential equation. We apply the method to a coupled milling model containing a partial and an ordinary differential equation. The conclusion of the numerical results is that the stability diagram of the coupled model differs significantly from the combined stability diagrams for each subsystem
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    A comparison of analytical cutting force models
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Rott, Oliver; Hömberg, Dietmar; Mense, Carsten
    The modeling of dynamic processes in milling and the determination of stable cutting conditions have become increasingly important for the optimization of manufacturing processes. Analytic approaches and time domain simulations based on simplified dynamic systems are used to identify chatter-free machining conditions. Stresses applied to the system are generally estimated by cutting force models. The goal of this paper is to compare the influence of the cutting force models on the stability limits. Numerical simulations of a simplified, generic milling machine model are therefore performed, while varying the cutting force approach. In order to distinguish stable from unstable cutting conditions a numerical stability criterion is used. The resulting stability charts are then investigated and analyzed to show the effect of the different cutting force models.
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    Principle of linearized stability and smooth center manifold theorem for semilinear hyperbolic systems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Lichtner, Mark
    [no abstract available]
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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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    On a thermomechanical milling model
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Chełminski, Krzysztof; Höberg, Dietmar; Rott, Oliver
    This paper deals with a new mathematical model to characterize the interaction between machine and workpiece in a milling process. The model consists of a harmonic oscillator equation for the dynamics of the cutter and a linear thermoelastic workpiece model. The coupling through the cutting force adds delay terms and further nonlinear effects. After a short derivation of the governing equations it is shown that the complete system admits a unique weak solution. A numerical solution strategy is outlined and complemented by numerical simulations of stable and unstable cutting conditions.
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    Spinodal dewetting of thin films with large interfacial slip : implications from the dispersion relation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Rauscher, Markus; Blossey, Ralf; Münch, Andreas; Wagner, Barbara
    We compare the dispersion relations for spinodally dewetting thin liquid films for increasing magnitude of interfacial slip length in the lubrication limit. While the shape of the dispersion relation, in particular the position of the maximum, are equal for no-slip up to moderate slip lengths, the position of the maximum shifts to much larger wavelengths for large slip lengths. Here, we discuss the implications of this fact for recently developed methods to assess the disjoining pressure in spinodally unstable thin films by measuring the shape of the roughness power spectrum. For PS films on OTS covered Si wafers (with slip length $bapprox 1,mu$m) we predict a 20% shift of the position of the maximum of the power spectrum which should be detectable in experiments.