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  • 1
    Online Resource
    Online Resource
    On the noise-induced passage through an unstable periodic orbit I : two-level model (2003)
    Berlin : WIAS
    Details Availability
    Keywords: Forschungsbericht
    Description / Table of Contents: We consider the problem of stochastic exit from a planar domain, whose boundary is an unstable periodic orbit, and which contains a stable periodic orbit. This problem arises when investigating the distribution of noise-induced phase slips between synchronized oscillators, or when studying stochastic resonance far from the adiabatic limit. We introduce a simple, piecewise linear model equation, for which the distribution of first-passage times can be precisely computed. In particular, we obtain a quantitative description of the phenomenon of cycling: The distribution of first-passage times rotates around the unstable orbit, periodically in the logarithm of the noise intensity, and thus does not converge in the zero-noise limit. We compute explicitly the cycling profile, which is universal in the sense that in depends only on the product of the period of the unstable orbit with its Lyapunov exponent.
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (34 Seiten, 607,96 KB) , Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. no. 864
    URL: http://webdoc.sub.gwdg.de/ebook/serien/e/wias/2003/2003/wias_preprints_864.pdf
    DDC: 510
    Language: English
    Note: Literaturverzeichnis: Seite 31-32
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  • 2
    Online Resource
    Online Resource
    Gibbs properties of the fuzzy Potts model on trees and in mean field (2003)
    Berlin : WIAS
    Details Availability
    Keywords: Forschungsbericht
    Description / Table of Contents: We study Gibbs properties of the fuzzy Potts model in the mean field case (i.e on a complete graph) and on trees. For the mean field case, a complete characterization of the set of temperatures for which non-Gibbsianness happens is given. The results for trees are somewhat less explicit, but we do show for general trees that non-Gibbsianness of the fuzzy Potts model happens exactly for those temperatures where the underlying Potts model has multiple Gibbs measures.
    Type of Medium: Online Resource
    Pages: Online-Resource (29 Seiten, 414,73 KB)
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. no. 878
    URL: http://webdoc.sub.gwdg.de/ebook/serien/e/wias/2003/2003/wias_preprints_878.pdf
    DDC: 530
    Language: English
    Note: Literaturverzeichnis: Seite 25-27
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  • 3
    Online Resource
    Online Resource
    An efficient dual Monte Carlo upper bound for Bermudan style derivatives (2003)
    Berlin : WIAS
    Details Availability
    Keywords: Forschungsbericht
    Description / Table of Contents: Based on a duality approach for Monte Carlo construction of upper bounds for American/Bermudan derivatives (Rogers, Haugh & Kogan), we present a new algorithm for computing dual upper bounds in an efficient way. The method is applied to Bermudan swaptions in the context of a LIBOR market model, where the dual upper bound is constructed from the maximum of still alive swaptions. We give a numerical comparison with Andersen's lower bound method and its dual considered by Andersen & Broadie.
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (21 Seiten, 329,23 KB) , Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. no. 877
    URL: http://webdoc.sub.gwdg.de/ebook/serien/e/wias/2003/2003/wias_preprints_877.pdf
    DDC: 510
    Language: English
    Note: Literaturverzeichnis: Seite 18-19
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  • 4
    Online Resource
    Online Resource
    PID control of laser surface hardening of steel (2003)
    Berlin : WIAS
    Details Availability
    Keywords: Forschungsbericht
    Description / Table of Contents: We discuss control strategies for the laser surface hardening of steel. The goal is to acchieve a prescribed hardening depth avoiding surface melting. Our mathematical model consists of a system of ODEs for the phase volume fractions coupled with the heat equation. The system is solved semi-implicitely using the finite element method. To obtain a uniform hardening depth the first attempt is to use PID control to achieve a constant temperature in the hot spot of the laser beam on the surface. However, the numerical results prove that this is not sufficient. We show that the best strategy is to control the temperature close to the lower boundary of the hardening zone. Then one can compute the optimal temperature in the hot spot of the beam and use it as the set-point for the pyrometer control of the real process.
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (20 Seiten, 528,64 KB) , Illustrationen, Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. no. 876
    URL: http://webdoc.sub.gwdg.de/ebook/serien/e/wias/2003/2003/wias_preprints_876.pdf
    DDC: 530
    Language: English
    Note: Literaturverzeichnis: Seite 18
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  • 5
    Online Resource
    Online Resource
    High order central schemes applied to relativistic multicomponent flows (2003)
    Berlin : WIAS
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    Keywords: Forschungsbericht
    Description / Table of Contents: The dynamics of inviscid multicomponent relativistic fluids may be modelled by the relativistic Euler equations, augmented by one (or more) additional species equation (s). We use high-resolution central schemes to solve these equations. The equilibrium states for each component are coupled in space and time to have a common temperature and velocity. The current schemes can handle strong shocks and the oscillations near the interfaces are negligible, which usually happens in the multicomponent flows. The schemes also guarantee the exact mass conservation for each component and the exact conservation of total momentum and energy in the whole particle system. The central schemes are robust, reliable, compact and easy to implement. Several one- and two-dimensional numerical test cases are included in this paper, which validate the application of these schemes to relativistic multicomponent flows.
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (29 Seiten, 4,46 MB) , Illustrationen, Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. no. 875
    URL: http://webdoc.sub.gwdg.de/ebook/serien/e/wias/2003/2003/wias_preprints_875.pdf
    DDC: 530
    Language: English
    Note: Literaturverzeichnis: Seite 25-27
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  • 6
    Online Resource
    Online Resource
    On modeling acoustic waves in saturated poroelastic media (2003)
    Berlin : WIAS
    Details Availability
    Keywords: Forschungsbericht
    Description / Table of Contents: In this paper we present a comparison of the linear wave analysis for four models of poroelastic materials. As shown in a paper by Wilmanski (Arch. Mech. 2002) a nonlinear thermodynamical construction of a two-component model of such materials requires a dependence on the porosity gradient. In the linear version this dependence may or may not be present (WIAS-Preprint No. 868). Consequently, we may work with the model without a dependence on this gradient which is identical with Biot's model or we can use the so-called full model. In both cases we can construct simplified models without a coupling between partial stresses introduced by Biot. These simplified models have the advantage that their application to, for instance, surface wave analysis yields much simpler mathematical problems. In the present work we show that such a simplification for granular materials leads to a good qualitative agreement of all four models in ranges of porosity and Poisson's ratio commonly appearing in geotechnical applications. Quantitative differences depend on the mode of propagation and vary between 10% and 20%. We illustrate the analysis with a numerical example corresponding to data for sands ...
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (24 Seiten, 566,30 KB) , Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. no. 874
    URL: http://webdoc.sub.gwdg.de/ebook/serien/e/wias/2003/2003/wias_preprints_874.pdf
    DDC: 530
    Language: English
    Note: Literaturverzeichnis: Seite 21-22
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  • 7
    Online Resource
    Online Resource
    Transient conductive radiative heat transfer : discrete existence and uniqueness for a finite volume scheme (2003)
    Berlin : WIAS
    Details Availability
    Keywords: Forschungsbericht
    Type of Medium: Online Resource
    Pages: 1 Online-Resource (30 Seiten, 310,26 KB) , Illustrationen
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. no. 871
    URL: http://webdoc.sub.gwdg.de/ebook/serien/e/wias/2003/2003/wias_preprints_871.pdf
    DDC: 510
    Language: English
    Note: Literaturverzeichnis: Seite 27-28
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  • 8
    Online Resource
    Online Resource
    Finite element method for epitaxial growth with thermodynamic boundary conditions (2003)
    Berlin : WIAS
    Details Availability
    Keywords: Forschungsbericht
    Description / Table of Contents: We develop an adaptive finite element method for island dynamics in epitaxial growth. We study a step-flow model, which consists of an adatom (adsorbed atom) diffusion equation on terraces of different height, thermodynamic boundary conditions on terrace boundaries including anisotropic line tension, and the normal velocity law for the motion of such boundaries determined by a two-sided flux, together with the one-dimensional (possibly anisotropic) ``surface'' diffusion of edge-adatoms along the step-edges. The problem is solved using two independent meshes: a two-dimensional mesh for the adatom diffusion and a one-dimensional mesh for the boundary evolution. A penalty method is used in order to incorporate the boundary conditions. The evolution of the terrace boundaries includes both the weighted/anisotropic mean curvature flow and the weighted/anisotropic surface diffusion. Its governing equation is solved by a semi-implicit front-tracking method using parametric finite elements.
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (19 Seiten, 1,54 MB) , Illustrationen, Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. no. 873
    URL: http://webdoc.sub.gwdg.de/ebook/serien/e/wias/2003/2003/wias_preprints_873.pdf
    DDC: 530
    Language: English
    Note: Literaturverzeichnis: Seite 17
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  • 9
    Online Resource
    Online Resource
    Global behavior and asymptotic reduction of a chemical kinetics system with continua of equlibria (2003)
    Berlin : WIAS
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    Keywords: Forschungsbericht ; Störungstheorie ; Asymptotische Methode
    Description / Table of Contents: We consider a model chemical kinetics system describing the dynamics of species concentrations taking part in a consecutive-competitive reaction in a continuously stirred tank reactor. Corresponding dynamical system has a continua of equilibria. The solution of the system tends to a particular equilibrium depending on the initial conditions. Global behavior of the system and its reductions via invariant manifold theory and the boundary function methods are studied.
    Type of Medium: Online Resource
    Pages: 1 Online-Resource (20 Seiten, 267,48 KB) , Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. no. 870
    URL: http://webdoc.sub.gwdg.de/ebook/serien/e/wias/2003/2003/wias_preprints_870.pdf
    DDC: 540
    Language: English
    Note: Literaturverzeichnis Seite 17-18
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  • 10
    Online Resource
    Online Resource
    On jump conditions at phase boundaries for ordered and disordered phases (2003)
    Berlin : WIAS
    Details Availability
    Keywords: Forschungsbericht
    Description / Table of Contents: This is a study on jump conditions across the interface between two adjacent phases. The interface behaves as a free boundary, and in sharp interface models jump conditions are used to determine the values of thermodynamic fields at the free boundaries. In this study the jump conditions are derived from balance equations for singular surfaces that do not have singular lines, i.e. triple junctions are not considered here. At first we present the most general form of jump conditions to give a general framework, from where we consider various special cases with a focus on the influence of mechanical fields on the interfacial processes. The special cases include the Hoffmann/Cahn capillarity vector theory and jump conditions for interfaces where order/disorder transitions are involved. Furthermore we discuss interfacial chemical reaction laws, and in particular the creation and annihilation of vacancies at a liquid/solid interface.
    Type of Medium: Online Resource
    Pages: 1 Online-Resource (40 Seiten, 457,73 KB) , Illustration
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. no. 869
    URL: http://webdoc.sub.gwdg.de/ebook/serien/e/wias/2003/2003/wias_preprints_869.pdf
    DDC: 510
    Language: English
    Note: Literaturverzeichnis Seite 36-38
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