Vorträge in der Woche 15.05.2023 bis 21.05.2023
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Dienstag, 16.05.2023: Structure-preserving front-tracking methods for the two-phase Navier-Stokes flow
Quan Zhao (Universität Regensburg)
In this talk, I will consider the structure-preserving front-tracking methods for a sharp-interface model of two-phase flow in both the unfitted and fitted mesh approaches, meaning that the volume preservation and energy decay are satisfied on the discrete level. In the unfitted approach, the constructed method is based on an Eulerian weak formulation, while in the fitted approach, the method is devised in the arbitrary Lagrangian-Eulerian (ALE) framework. We compare the numerical results of the two approaches by using the example of a rising bubble.
| Uhrzeit: | 14:15 |
| Ort: | S09, C-Bau, 6. Stock |
| Gruppe: | Oberseminar Numerik |
| Einladender: | Lubich, Prohl |
Dienstag, 16.05.2023: Non-Perturbative Results on the Mass Shell in Nelson-Type Models
Dr. Benjamin Hinrichs (Paderborn)
We consider the infrared problem in translation-invariant Nelson-type models describing a single quantum mechanical particle linearly coupled to a field of scalar bosons at fixed total momentum. Physical examples include the non- and semi-relativistic Nelson models. If the bosons are massless, then the model is infrared divergent and the infimum of the spectrum is not an eigenvalue for any total momentum, i.e., no ground state exists. Applying an appropriate dressing transformation, dependent on the total momentum, one obtains an infrared-renormalized representation of the model, which exhibits a ground state. Previously, this situation has been investigated using perturba tive methods, i.e., for small total momenta and (possibly dependent on the total momentum) small coupling constants. In this talk, we discuss non-perturbative proofs both for the absence of ground states in the usual Fock space representation of Nelson-type models (for all total momenta) and the existence of ground states in the non-equivalent representation (for almost all physically relevant total momenta). We emphasize that our results hold for all values of the coupling constants, due to the non-perturbative nature of their proofs. The talk is based on joint work with Thomas Norman Dam, David Hasler and Oliver Siebert.
| Uhrzeit: | 16:00 |
| Ort: | C4H33 |
| Gruppe: | Oberseminar Mathematical Physics |
| Einladender: | Capel, Keppeler, Lemm, Pickl, Teufel, Tumulka |
Mittwoch, 17.05.2023: About the notion of eigenstates in C*-algebras and some application to quantum mechanics
Danilo Polo (Pontificia Universidad Católica de Chile)
This talk is concerned with the notion of eigenstates of an operator in an abstract C*-algebra. After reviewing some basic and structural results, I will explore the possibility of reinterpreting certain typical concepts of quantum mechanics (dynamical equilibrium states, ground states, gapped states, Fermi surfaces) in terms of (algebraic) eigenstates. Joint work with: Giuseppe De Nittis. https://arxiv.org/abs/2304.02685
| Uhrzeit: | 14:00 |
| Ort: | C4H43 |
| Gruppe: | Oberseminar Mathematical Physics |
| Einladender: | Capel, Keppeler, Lemm, Pickl, Teufel, Tumulka |
Mittwoch, 17.05.2023: Dissipative solutions and Markov selection to the complete stochastic Euler system
Thamsanqa Castern Moyo (TU Clausthal)
We introduce the concept of stochastic measure-valued solutions to the complete Euler system describing the motion of a compressible inviscid fluid subject to stochastic forcing, where the nonlinear terms are described by defect measures. These solutions are weak in the probabilistic sense (probability space is not a given `priori', but part of the solution) and analytical sense (derivatives only exists in the sense distributions). In particular, we show that existence and weak-strong principle (i.e. a weak measure-valued solution coincides with a strong solution provided the later exists) hold true provided they satisfy some form of energy balance. Finally, we show the existence of Markov selection to the associated martingale problem.
| Uhrzeit: | 14:15 |
| Ort: | N12 (E-Bau, Biologie) |
| Gruppe: | Oberseminar Numerik |
| Einladender: | Lubich, Prohl |