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Tuesday, 18.06.2019, 13:30 (WIAS-406)
Seminar Materialmodellierung
Prof. A. Acharya, Carnegie Mellon University, USA:
Line defect dynamics and solid mechanics
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
Continuum mechanics has been a successful model for studying macroscopic deformations and the forces causing them. The usual framework allows the study of continuous deformations giving way to surfaces of discontinuity, but does not provide an adequate framework for considering the dynamics of the terminating lines of surfaces of discontinuity, were such to occur. It turns out that such terminating lines of surfaces of discontinuity serve as a model of common line defects that arise in a host of materials; dislocations and grain/phase boundary junctions in crystalline and soft matter. I will describe a framework for considering line defect dynamics within continuum mechanics. I will show how the kinematics of line defect dynamics provides a unifying theme for describing the defects mentioned above, resulting in an augmentation of the classical balance laws of continuum mechanics with a microscopic conservation law for topological charge carried by these defect lines. The theory will be illustrated with examples related to dislocation dynamics with inertia, the computation of fields of interfacial defects like the star disclination and grain boundary disconnections.

Further Informations
Seminar Materialmodellierung

Host
WIAS Berlin
Tuesday, 18.06.2019, 15:00 (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Priv.-Doz. Dr. P. Mathë, WIAS Berlin:
The modulus of continuity in Bayesian inverse problems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstract
We shall discuss how the convergence rates of direct and inverse problems are related through the modulus of continuity.

Further Informations
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics

Host
WIAS Berlin
Wednesday, 19.06.2019, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. H. Hron, Palacký University, Olomouc, Czech Republic:
Weighting of densities in Bayes spaces with application to simplicial functional principal component analysis
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Probability density functions (PDFs) can be understood as functional data carrying relative information. As such, standard methods of functional data analysis (FDA) are not appropriate for their statistical processing. They are typically designed in the L2 space (with Lebesgue reference measure), thus cannot be directly applied to densities, as the metrics of L2 does not honor their geometric properties. This has recently motivated the construction of the so-called Bayes Hilbert spaces, which result from the generalization of the Aitchison geometry for compositional data to the in nite dimensional setting. More precisely, if we focus on PDFs restricted to a bounded support (that is mostly used in practical applications), they can be represented with respect to the Lebesgue reference measure using the Bayes space of positive real functions with square-integrable logarithm. The reference measure can be easily changed through the well-known chain rule and interpreted as a weighting technique in Bayes spaces. Moreover, it impacts on the geometry of the Bayes spaces and results in so-called weighted Bayes spaces. The aim of this contribution is to show the e ects of changing the reference measure from the Lebesgue measure to a general probability measure focusing on its practical implications for the Simplicial Functional Principal Component Analysis (SFPCA). A centered log-ratio transformation is proposed to map a weighted Bayes spaces into an unweighted L2 space (i.e. with Lebesgue reference measure), thus it enables to apply standard statistical methods such as SFPCA on PDFs.

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Wednesday, 19.06.2019, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. J. Ginster, Technische Universität Berlin:
Plasticity as the Γ-limit of models for straight, parallel dislocations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Crystal plasticity is the effect of a crystal undergoing a permanent change of shape in response to applied forces. At the atomic scale, dislocations - local defects of the crystalline lattice concentrated on lines - are considered to play a main role in this effect. In this talk, we will derive a macroscopic strain-gradient plasticity theory from two different semi-discrete models for straight, parallel edge dislocations. Firstly, we complement the existing literature by considering a rotationally invariant energy with mixed growth. The main advantage of this formulation is that it does not need the ad-hoc definition of a core-radius. In addition to the Γ-convergence result we present a rigidity result for fields with non-vanishing curl in this setting. Secondly, we will address the fact that most results in the literature are derived under the assumption that the present dislocations are separated on a mesoscopic scale. We will show how to overcome this assumption by an adaption of the ball construction technique which was developed in the context of the Ginzburg--Landau model for superconductivity.

Host
Humboldt-Universität zu Berlin
WIAS Berlin