Shape Analysis and Non-Linear PDEs
Dienstag, 16.10.18, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Asymptotic rigidity of layered structures and its applications in homogenization theory
Dienstag, 23.10.18, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Rigidity results in elasticity are powerful statements that allow to derive global properties of a deformation from local ones. The classical Liouville theorem states that every local isometry of a domain corresponds to a rigid body motion. If connectedness of the set fails, clearly, global rigidity can no longer be true. \nIn this talk, I will present a new type of asymptotic rigidity lemma, which shows that if an elastic body contains sufficiently stiff connected components arranged into fine parallel layers, then macroscopic rigidity up to horizontal shearing prevails in the limit of vanishing layer thickness. The optimal scaling between layer thickness and stiffness can be identified using suitable bending constructions. This result constitutes a useful tool for proving homogenization results of variational problems modeling high-contrast bilayered composites. We will finally utilize it to characterize the homogenized Gamma-limits of two models inspired by nonlinear elasticity and finite crystal plasticity. \n\nThis is joint work with Fabian Christowiak (Universität Regensburg).\n
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Dienstag, 30.10.18, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Phasenfeldmethoden zur Querschnittsoptimierung eines Pflanzenstiels
Dienstag, 6.11.18, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Strain-gradient plasticity with cross-hardening
Dienstag, 27.11.18, 15:00-16:00, Raum 226, Hermann-Herder-Str. 10
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Dienstag, 18.12.18, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
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Dienstag, 22.1.19, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
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Dienstag, 29.1.19, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Numerical Approximation of the Stochastic Cahn-Hilliard Equation Near the Sharp Interface Limit
Donnerstag, 31.1.19, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
I discuss a stable time discretization of the stochastic\nCahn-Hilliard equation with an additive noise term \(\bvarepsilon^{\bgamma}\n\bdot{W}\), where \(\bgamma >0\), and \(\bvarepsilon>0\) is the interfacial\nwidth parameter. For sufficiently small noise (i.e., for \(\bgamma\) sufficiently\nlarge) and sufficiently small time-steps \(k \bleq k_0(\bgamma)\), I detail\narguments which lead to strong error estimates where the\nparameter \(\bvarepsilon\) only enters polynomially -- avoiding Gronwall's lemma.\n
Effective theories for heterogeneous multilayers
Dienstag, 5.2.19, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
We will report on recent advances in deriving effective theories for thin sheets consisting of multiple layers with (slightly) mismatching equilibria in various energy regimes. Moreover, we will investigate optimal energy configurations and identify a critical energy scaling for their generic shape.\n