Energy-based mathematical methods for reactive multiphase flows

**Outline: ** The online student compact course takes place from Oct 12—23, 2020 and will give an in-depth background on the topics of the Thematic Einstein Semester. This will include topics in variational thermomechanics and applications, modeling by Port-Hamiltonian systems and GENERIC, analytical and numerical methods. We will have 4x 45minutes lectures each weekday during this compact course and time for interactive discussions and dedicated time slots, where students can present their interests/research.

** Participation: ** We welcome everyone interested in the course to join and participate. Lectures will be given by researchers from Berlin and guests of the Thematic Einstein Semester on topics related to analysis, modeling, numerics, optimization, control, model reduction using energetic variational methods. The lecturers will present problems which can lead to projects to be solved by small groups of students during the TES BMS semester and presented at a final workshop.

Even if you just want to take part in the student compact course, please register so we can estimate the number of participants. If you are interested to take part in one of the projects of the TES BMS Semester, please indicate this during the registration.

**Contact: **If you have questions, please feel free to contact us using tesenergy@wias-berlin.de.

**NOTE: The time table for Wednesday – Friday, October 14–16, was slightly modified. You can find the updated version below.**

Time | Monday | Tuesday |
---|---|---|

10:00–10:45 | Modelling via energy and entropy functionals: Bulk GENERIC, Part I (M. Thomas) | Variational structures for the analysis of PDE systems, Part I (A. Mielke) |

10:45–11:05 | Lagrangian-Eulerian reduction of GENERIC systems (A. Zafferi) | Separately Global Solutions to Rate-Independent Systems (P. Pelech) |

11:05–11:20 | Coffee break | Coffee break |

11:20–12:05 | Modelling via energy and entropy functionals: Bulk GENERIC, Part II (M. Thomas) | Variational structures for the analysis of PDE systems, Part II (A. Mielke) |

12:05–12:30 | Discussion | Discussion |

12:30–14:00 | Lunch break | Lunch break |

14:00–14:20 | Exergetic Port-Hamiltonian Systems - a tutorial (M. Lohmayer) | Relative energy in viscoelastic phase separation (A. Brunk) |

14:20–15:05 | Port-Hamiltonian systems, Lecture I (V. Mehrmann) | Basics of classical thermodynamics: a systems perspective (A. van der Schaft) |

15:05–15:20 | Coffee break | Coffee break |

15:20–16:05 | Port-Hamiltonian systems, Lecture II (V. Mehrmann) | Introduction to algebraic constraints in port-Hamiltonian systems (A. van der Schaft) |

16:05–16:30 | Discussion | Discussion |

**Note**: All times are with respect to Central European Summer Time (CEST = UTC + 2)

Time | Wednesday | Thursday | Friday |
---|---|---|---|

10:00–10:45 | Formal asymptotics for multiscale problems, Part I (R. Klein/ B. Wagner) | Evolutionary Γ-convergence for multiscale problems, Part I (M. Liero) | Entropy methods for diffusion equations, Part I (A. Jüngel) |

10:45–11:05 | Dynamic phase-field fracture in visco-elastic materials (S. Tornquist) | Coarse-graining for gradient systems with applications to reaction systems (A. Stephan) | Discrete-to-continuum limit of transport costs (L. Portinale) |

11:05–11:25 | Coffee break | Coffee break | Coffee break |

11:25–12:10 | Formal asymptotics for multiscale problems, Part II (R. Klein/ B. Wagner) | Evolutionary Γ-convergence for multiscale problems, Part II (M. Liero) | Entropy methods for diffusion equations, Part II (A. Jüngel) |

12:10–12:40 | Discussion | Discussion | Discussion |

12:40–14:20 | Lunch break | Lunch break | Lunch break |

14:20–15:05 | Formal asymptotics for multiscale problems, Part III (R. Klein/ B. Wagner) | Variational structures and particle systems, Part I (D.R.M. Renger) | Variational structures and particle systems, Part III (D.R.M. Renger) |

15:05–15:25 | Coffee break | Coffee break | Coffee break |

15:25–16:10 | Formal asymptotics for multiscale problems, Part IV (R. Klein/ B. Wagner) | Variational structures and particle systems, Part II (D.R.M. Renger) | Variational structures and particle systems, Part IV (D.R.M. Renger) |

16:10–16:40 | Discussion | Discussion | Discussion |

**Note**: All times are with respect to Central European Summer Time (CEST = UTC + 2)

Time | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|

10:00–10:45 | Modeling via energy and entropy functionals: Bulk-interface coupling, Part III (M. Thomas) | Port-Hamiltonian differential-algebraic systems, Lecture III (V. Mehrmann) | Structure preserving discretization methods for port-Hamiltonian systems, Lecture V (V. Mehrmann) | Optional project discussion | Discrete gradient methods for the preservation or dissipation of energy in evolutionary equations, Part I (E. Celledoni) |

10:45–11:05 | Project teaser | Project teaser | Project teaser | Project teaser | Project teaser |

11:05–11:20 | Coffee break | Coffee break | Coffee break | Coffee break | Coffee break |

11:20–12:05 | Modeling via energy and entropy functionals: Bulk-interface coupling, Part IV (M. Thomas) | Port-Hamiltonian differential-algebraic systems, Lecture IV (V. Mehrmann) | Structure preserving discretization methods for port-Hamiltonian systems in energy transport networks, Lecture VI (V. Mehrmann) | Optional project discussion | Discrete gradient methods for the preservation or dissipation of energy in evolutionary equations, Part II (E. Celledoni) |

12:05–12:30 | Discussion | Discussion | Discussion | Discussion | Discussion |

12:30–14:00 | Lunch break | Lunch break | Lunch break | Lunch break | Lunch break |

14:00–14:20 | Project teaser | Project teaser | Project teaser | Project teaser | Project teaser |

14:20–15:05 | Evolutionary Γ-convergence for multiscale problems, Part III (M. Liero) | Fluid-structure interaction, Part I (D. Peschka, L. Heltai) | Fluid-structure interaction, Part III (D. Peschka, L. Heltai) | Model reduction, control, and optimization, Lecture VII (V. Mehrmann) | Optional project discussion |

15:05–15:20 | Coffee break | Coffee break | Coffee break | Coffee break | Coffee break |

15:20–16:05 | Evolutionary Γ-convergence for multiscale problems, Part IV (M. Liero) | Fluid-structure interaction, Part II (D. Peschka, L. Heltai) | Fluid-structure interaction, Part IV (D. Peschka, L. Heltai) | Model reduction, control, and optimization, Lecture VIII (V. Mehrmann) | Optional project discussion |

16:05–16:30 | Discussion | Discussion | Discussion | Discussion | Discussion |

**Note**: All times are with respect to Central European Summer Time (CEST = UTC + 2)