Veranstaltungen

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Donnerstag, 04.04.2024, 16:00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Prof. Dmitry Turaev, Imperial College London, GB:
4-winged Lorez attractors
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
We show that bifurcations of periodic orbits with multipliers (-1,i,-i) can lead to the birth of pseudohyperbolic Lorenz-like attractors of three different types: one is a discrete analogue of the classical Lorenz attractor, and the other two are new:two- and four-winged Simo angels. These three attractors exist in an orientation-reversing, three-dimensional, quadratic Henon map. This implies the abundance of such attractors in a class of systems with homoclinic tangencies. Our analysis is based on the study of a normal form for this bifurcation, a slow-fast three-dimensional system of differential equations with a Z4-symmetry. The existence of the continuous-time counterparts of the pseudohyperbolic attractors is established for the normal form as a part of an extensive numerical analysis of its bifurcations. In particular, we establish that all three types of continuous-time pseudohyperbolic attractors are born out of a certain Z4-symmetric heteroclinic configurations with three saddles.

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Forschungsseminar Mathematische Modelle der Photonik

Veranstalter
WIAS Berlin
Dienstag, 09.04.2024, 13:30 Uhr (Online Event)
Seminar Materialmodellierung
Cécile Daversin-Catty, Simula Research Laboratory, Norwegen:
Mixed-dimensional coupled finite elements in FEniCS(x) (online talk)
mehr ... Veranstaltungsort
Online Event

Abstrakt
Mixed-dimensional partial differential equations (PDEs) are equations coupling fields defined over distinct domains that may differ in topological dimension. Such PDEs naturally arise in a wide range of fields including geology, bio-medicine, and fracture mechanics. Mixed-dimensional models are also used to impose non-standard conditions through Lagrange multipliers. Finite element discretizations of such PDEs involve nested meshes of possibly heterogeneous topological dimension. The assembly of such systems is non-standard and non-trivial, and requires the design of both generic high level software abstractions and lower level algorithms. The FEniCS project aims at automating the numerical solution of PDE-based models using finite element methods. A core feature is a high-level domain-specific language for finite element spaces and variational forms, close to mathematical syntax. Lately, FEniCS gave way to its successor FEniCSx, including major improvements over the legacy library. An automated framework was developed in core FEniCS legacy libraries to address the challenges characterizing mixed-dimensional problems. These concepts were recently ported to FEniCSx, taking advantage of the underlying upgrades in the library features and design. This talk gives an overview of the abstractions and algorithms involved, and their implementation in the FEniCS project core libraries. The introduced features are illustrated by concrete applications in biomedicine.

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Link on request (dirk.peschka@wias-berlin.de).

Veranstalter
WIAS Berlin
10. – 12. April 2024 (IVW)
Workshop/Konferenz: Leibniz MMS Days 2024
mehr ... Veranstaltungsort
Leibniz-Institut für Verbundwerkstoffe GmbH Kaiserslautern

Veranstalter
Leibniz-Institut fuer Verbundwerkstoffe GmbH IVW
WIAS Berlin
Mittwoch, 10.04.2024, 11:30 Uhr (WIAS-405-406)
Seminar Interacting Random Systems
Heide Langhammer, WIAS Berlin:
tba
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

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Seminar Interacting Random Systems (Hybrid Event)

Veranstalter
WIAS Berlin
Mittwoch, 10.04.2024, 14:15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
M.Sc. Tim Böhnlein, Technische Universität Darmstadt:
Bounded functional calculus and dynamical boundary conditions
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
We consider divergence form operators with complex coefficients on an open subset of Euclidean space. Boundary conditions in the corresponding parabolic problem are dynamical, that is, the time derivative appears on the boundary. As a matter of fact, the elliptic operator and its semigroup act simultaneously in the interior and on (a part of) the boundary. We extrapolate the bounded functional calculus in the Lebesgue scale. In particular, this implies maximal regularity as a starting point to treat nonlinear equations. Our strategy relies on extending a contractivity criterion due to Nittka and a non-linear heat flow method popularized by Carbonaro--Dragičević. This is joint work with Moritz Egert and Joachim Rehberg.

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Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Montag, 15.04.2024, 14:00 Uhr (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Anthony Nouy, Centrale Nantes, Frankreich:
tba
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Veranstalter
WIAS Berlin
Dienstag, 16.04.2024, 10:15 Uhr (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Apala Majumdar, University of Strathclyde, GB:
Solution landscapes in the Landau-de Gennes theory for nematic liquid crystals: Analysis, computations and applications
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
Nematic liquid crystals are classical examples of partially ordered materials that combine fluidity with the order of crystalline solids. They are the working material of a range of electro-optic devices i.e. in the liquid crystal display industry and more recently, they are used in sensors, actuators, elastomers, security applications and pathological studies. We review the celebrated Landau-de Gennes theory for nematic liquid crystals and focus on the modelling of nematics confined to thin quasi-2D systems, with reference to 2D polygons. We perform asymptotic analysis in certain distinguished limits, encoded in terms of geometrical, material and temperature-dependent parameters, accompanied by exhaustive numerical studies of solution landscapes that include stable and unstable solution branches for these systems. There are several numerical challenges associated with the numerical computation of the unstable solution branches and their unstable directions, for which we use the powerful High-Index Shrinking Optimisation Dimer Method. In the last leg of the talk, we discuss the mathematical modelling of some recent experiments on nematic shells and doped bent-core liquid crystals, to illustrate the synergistic links between theory, experiment and novel applications.

All collaborations will be acknowledged throughout the talk.

Veranstalter
WIAS Berlin

Mittwoch, 17.04.2024, 14:15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Pierluigi Colli, Università di Pavia, Italien:
Curvature effects in pattern formation: Analysis and control of a sixth-order Cahn--Hilliard equation
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
In this talk, the well-posedness and optimal control are discussed for a sixth-order Cahn--Hilliard system, which represents a higher-order variant of the well-known Cahn--Hilliard equation. In our system, the evolution equation is complemented with a source term, where the control variable enters as a distributed mass regulator. The presence of further spatial derivatives in the sixth-order formulation enables the model to capture curvature effects, for a more accurate description of isothermal phase separation dynamics in complex materials systems. A well-posedness result for the initial-boundary value problem is shown when assuming a smooth double-well potential as part of the free energy. Then, the related optimal control problem is addressed. Existence of optimal controls is established, and the first-order necessary optimality conditions are characterized via a suitable variational inequality involving the solution to the adjoint problem. These results have been obtained in a recent collaboration with G. Gilardi (University of Pavia), A. Signori (Polytechnic of Milan) and J. Sprekels (WIAS Berlin).

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Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Veranstalter
Humboldt-Universität zu Berlin
Montag, 22.04.2024, 13:30 Uhr (WIAS-ESH)
Berlin Oberseminar: Optimization, Control and Inverse Problems
Dr. Johannes Royset, USC, University of Southern California, CA, USA:
TBA
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Veranstalter
WIAS Berlin
Mittwoch, 24.04.2024, 11:30 Uhr (WIAS-405-406)
Seminar Interacting Random Systems
Julia Hörmann, WIAS Berlin:
tba
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Weitere Informationen
Seminar Interacting Random Systems (Hybrid Event)

Veranstalter
WIAS Berlin
Mittwoch, 22.05.2024, 14:15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Jürgen Sprekels, WIAS Berlin:
Necessary and sufficient optimality conditions in the sparse optimal control of singular Allen--Cahn systems with dynamic boundary conditions
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Weitere Informationen
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
1. Juli 2024 (WIAS-ESH)
Workshop/Konferenz: Developments in Computational Finance - Honoring John Schoenmakers on the occasion of his retirement
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Veranstalter
WIAS Berlin