Am Mittwoch, 30. November, finden in der FernUniversität drei Vorträge statt. Interessierte sind herzlich willkommen.
Beim „Hagen-Wuppertal Analysis-Treffen“ finden am Mittwoch, 30. November, drei Vorträge statt. Interessierte sind in die FernUniversität in Hagen, TGZ-Gebäude, Universitätsstr. 11, 58097 Hagen, Raum „Ellipse“ im Erdgeschoss, eingeladen.
- 14.30 Uhr Hanno Gottschalk (Bergische Universität Wuppertal):
„Optimal Reliability for Fatigue Life“
Mechanical components fail under cyclic loading due to fatigue of the materials. This process is highly stochastic as the time to the formation of mesoscopic cracks is subject to a statistical scatter of one order of magniture in lab experiments. In this talk, the probabilistic crack formation is modeled by spatio-temporal point processes with intensity depending locally on the mechanical load situation. This allows to compute failure probabilities at a given number of load cycles. A survey is given about experimental calibration and validation of these models, numerical implementation and their applications to gas turbine design. In mechanical design, reliability is one of the main design objectives. The mathematical quest thus is to find a shape for the component such that the failure probability is minimized. This optimization task can be understood as an optimal control problem with the elasticity PDE as the state equation and the boundary of the shape as control parameter. A proof for the existence of optimal shapes within certain regularity classes of the boundary is given using strong solutions and uniform Schauder estimates.
- 15.30 Uhr Delio Mugnolo (FernUniversität in Hagen):
„The Airy equation on a quantum graph”
The Airy equation is a one-dimensional partial differential equation of first order in time and third order in space; it is mostly relevant as the linear part of the classical KdV equation. An explicit formula for the Airy equation on the line is known and shows that the solution is given by a unitary group with dispersive features. Little is known about different geometrical settings, but unitary group generation cannot be expected on bounded and semibounded intervals. I am going to show how the theory of Krein spaces can be used to fully characterize self-adjoint extensions on a star graph. Even when self-adjointness fails, the Airy equation can be well-posed under infinitely many transition conditions in the nodes: I am going to discuss how to pick correct ones based on known invariant quantities of the Airy equation. If time allows, I will also briefly discuss existence of solitons for the KdV equation. This is joint work with Diego Noja (Milano) and Christian Seifert (Hamburg).
(16.30 Uhr Kaffeepause)
- 17.00 Uhr Ben Schweizer (TU Dortmund):
„Resonance phenomena of small objects and the construction of meta-materials with astonishing properties”
We know resonance effects from daily life: In a classical instrument, vibrations of some part of the instrument are amplified by resonance in the sound body. Typically, the resonator has a size that is related to the frequency: the larger the instrument, the lower the tone. In this talk we discuss resonators for light and sound waves that are small in size, much smaller than the wave-length. The assembly of many small resonators can act as a meta-material with astonishing properties: As a sound absorber or as a material with negative index. Our first example are small Helmholtz resonators, we investigate their frequency and the behavior of the corresponding meta-material. The second example are split-ring resonators for Maxwell’s equations and the negative refraction of light. We conclude with some comments on negative index cloaks: These resonators lead to the invisibility of small objects in their vicinity.
Veranstalter sind Prof. Dr. Werner Kirsch, Prof. Dr. Wolfgang Spitzer und Prof. Dr. Delio Mugnolo (FernUniversität).