Transforming the World
In the course of the current COVID-19 situation, we have decided to take some precautions and organize the semester program online. In particular, it will be possible to present and attend the lectures of the kick-off conference via an online platform, where we strive to making interactive discussions as engaging as possible.
Scope of the Semester
Since the early works of Lagrange and Hamilton for classical mechanics and Rayleigh and Helmholtz for dissipative processes, energetic variational methods for fluids and solids have been developed extensively. The relation to underlying microscopic stochastic models was pioneered by Onsager leading to his celebrated reciprocal relations. However, most systematic developments concerned either purely conservative Hamiltonian systems or purely dissipative gradient systems. In the last two decades, a unification of these two extremes was addressed by developing concepts for systems combining both systems. More recently, these topics evolved into mathematical theories such as GENERIC and port-Hamiltonian structures. Corresponding thermodynamical structures are advantageous from the modeling point-of-view and for the design of efficient numerical schemes. However, different communities have developed own languages and specific mathematical methods that are not always accessible for non-experts.
This Thematic Einstein Semester will bring together scientists from different communities to develop synergies between the different approaches. The mathematical community could contribute (to) the structural analysis of flowing systems concerning, for example, the geometry of thermodynamic systems, functional analytical frameworks for partial differential equations, description of bulk-interface coupling, connection to microscopic/stochastic models, construction of structure-preserving numerical schemes, model reduction or modular modeling. Communication with applied material research communities in mathematics, physics and engineering will cover diverse material systems such as, for example, reactive flows, porous medium flow, hydrogels, electrolytes, colloidal and non-colloidal suspensions, nematic materials, and beyond, where thermodynamic descriptions play an important role.
Thursday 3 pm-4.30 pm CET ( UTC + 1)
The seminar is held online in Zoom. In order to receive the Zoom-links to attend the talks, please register using the button below.
Next seminar: December 10, 2020
Speaker: Martin Kružík (Czech Technical University)
Title of the talk: Equilibrium for multiphase solids with Eulerian interfaces
Abstract: We describe a general phase-field model for hyperelastic multiphase materials. The model features an elastic energy functional that depends on the phase-field variable and a surface energy term that depends in turn on the elastic deformation, as it measures interfaces in the deformed configuration. We prove the existence of energy minimizing equilibrium states and Γ-convergence of diffuse-interface approximations to the sharp-interface limit.
This is a joint work with D. Grandi, E. Mainini and U. Stefanelli.
November 23–25, 2020
Scope: This workshop is devoted to recent aspects regarding the analysis of mathematical problems arising in the continuum mechanics of solids.
It features 20 presentations by invited speakers and will be held as an online format. Registration is required and open till November 20, 2020.
In particular, please note that the links to the online-presentation sessions will be available for registered participants, only.
More details soon.
Info: Jointly organized with SPP 2171, SFB 1114, SPP 1984
More details soon.
October 26–30, 2020
Scope: For this conference, we combine daily invited presentations (40 minutes including discussion) with other interactive discussion formats. In particular, we have parallel discussion sessions that are supposed to create the interactive discussion type of a poster presentation. We also have moderated discussion sessions (round table) on given topics, where we discuss promising research topics in the field of energetic- variational mathematical methods with the participants of the conference. The talks on Friday Oct 30 are organized in cooperation with the DFG CRC 910. All parts of the conference (invited talks, discussions and round table) are available online. If you plan to contribute a talk or a discussion contribution, please indicate this during the registration procedure (and we will provide additional information & extended abstract template afterwards).
October 12–23, 2020
Scope: The course will give an in-depth background on the topics of the Thematic Einstein Semester Energy-based Mathematical Methods for Reactive Multiphase Flows. In particular, the focus is on evolutionary systems whose mathematical formulation exhibits advantageous structures such as port-Hamiltonian, gradient, or GENERIC (General Equations for Non-Equilibrium Reversible Irreversible Coupling) structures.