Veranstaltungen
- 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).
Weitere Informationen
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Veranstalter
Humboldt-Universität zu Berlin
- Mittwoch, 17.04.2024, 10:00 Uhr (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Dr. Gil Kur, ETH Zürich, Switzerland:
Connections between minimum norm interpolation and local theory of Banach spaces
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Weitere Informationen
Der Vortrag findet auch via Zoom statt: https://zoom.us/j/159082384
Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Dienstag, 16.04.2024, 15:00 Uhr (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Maalvladedon Ganet Some, University of Ghana, Republik Ghana:
Stochastic optimal control of a prosumer in a district heating system
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
We consider networks of residential heating systems in which several prosumers satisfy their heating and hot water demand using solar thermal collectors and services of a central producer. Overproduction of heat can either be stored in a local thermal storage or sold to the network. Our focus is the minimization of the prosumers expected total cost from purchasing and selling thermal energy and running the system. This decision making problem under uncertainty about the future production and consumption of thermal energy is formulated as a stochastic optimal control problem and solved with dynamic programming techniques. We present numerical results for the value function and the optimal control.
Weitere Informationen
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715
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 - Montag, 15.04.2024, 14:30 Uhr (WIAS-406)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Anthony Nouy, Ecole Centrale de Nantes, Frankreich:
Moment methods for some optimal transport problems and parameter-dependent equations
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstrakt
Most optimal transport (OT) solvers are currently based on an approximation of underlying measures by discrete measures. Another route is to approximate moments of measures, when these are determinate. Here, we show that many common OT problems can be formulated as generalized moment problems [1]. These include the computation of Lp Wasserstein or Gromov-Wasserstein distances and the corresponding barycenters. For measures supported on compact semi-algebraic sets, a practical numerical approach then consists in truncating moment sequences up to a certain order, and using the polynomial sums-of-squares hierarchy. The approach is proved to converge. It allows to extract a posteriori relevant information on the measures, such as their supports that can be estimated using Christoffel-Darboux kernels. In a second part of this talk, we present how these moment methods can be used for the solution of parameter-dependent hyperbolic equations, by using weak formulations on measure-valued solutions [2]. These methods can be used to directly approximate the solution as a function of the parameter, or to construct reduced order models by interpolation in Wasserstein spaces.These are joint works with Olga Mula and Clément Cardoen, Swann Marx and Nicolas Seguin.
References:
[1] O. Mula and A. Nouy. Moment-SoS methods for optimal transport problems, arXiv:2211.10742, 2022.
[2] C. Cardoen, S. Marx, A. Nouy, and N. Seguin. A moment approach for entropy solutions of parameter-dependent hyperbolic conservation laws, 2024.
Veranstalter
WIAS Berlin
