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- ItemHausdorff metric BV discontinuity of sweeping processes(Bristol : IOP Publ., 2016) Klein, Olaf; Recupero, VincenzoSweeping processes are a class of evolution differential inclusions arising in elastoplasticity and were introduced by J.J. Moreau in the early seventies. The solution operator of the sweeping processes represents a relevant example of rate independent operator. As a particular case we get the so called play operator, which is a typical example of a hysteresis operator. The continuity properties of these operators were studied in several works. In this note we address the continuity with respect to the strict metric in the space of functions of bounded variation with values in the metric space of closed convex subsets of a Hilbert space. We provide counterexamples showing that for all BV-formulations of the sweeping process the corresponding solution operator is not continuous when its domain is endowed with the strict topology of BV and its codomain is endowed with the L1-topology. This is at variance with the play operator which has a BV-extension that is continuous in this case.
- ItemOn forward and inverse uncertainty quantification for models involving hysteresis operators(Les Ulis : EDP Sciences, 2020) Klein, Olaf; Davino, Daniele; Visone, CiroParameters within hysteresis operators modeling real world objects have to be identified from measurements and are therefore subject to corresponding errors. To investigate the influence of these errors, the methods of Uncertainty Quantification (UQ) are applied. Results of forward UQ for a play operator with a stochastic yield limit are presented. Moreover, inverse UQ is performed to identify the parameters in the weight function in a Prandtl-Ishlinskiĭ operator and the uncertainties of these parameters.
- ItemOn forward and inverse uncertainty quantification for models involving hysteresis operators(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Klein, Olaf; Davino, Daniele; Visone, CiroParameters within hysteresis operators modeling real world objects have to be identified from measurements and are therefore subject to corresponding errors. To investigate the influence of these errors, the methods of Uncertainty Quantification (UQ) are applied.