Talks

Since most of you couldn't attend my master thesis defense due to the university closure, I would like to use this talk to present you some results of my master thesis "Many-body localization: A spectral theoretic investigation of spin chains". Spin chains are a class of quantum-mechanical models well-suited to study many-body localization (MBL) phenomena due to their one-dimensional structure. After a brief introduction to one-particle (Anderson) localization and spectral properties of infinite-dimensional operators, we will see possible definitions and manifestations of MBL. The proofs of MBL for two specific spin chains will be sketched, illustrating how one-particle and many-body techniques can be combined. Furthermore, I would like to use this talk to properly present myself in case you wondered who that person in the guest office was.

Since I am new to the institute, I want to use this talk to introduce myself to you, and talk a little bit about my master thesis.

For the thesis I studied the approximability of the inverse of finite element matrices, i.e. matrices which are gained from the discretization of elliptic PDE's with the finite element method, by hierarchical matrices. So, after introducing myself, i will give an overview about the construction of the approximation and the error analysis.

supervision by Prof. Ernst Brinkmeyer (retired 2013, hence not hosted by him)

no maths topic

Talk (PDF, 219KB)

For a regular coupled cell network, we define an index of integer tuples for its associated lattice of synchrony subspaces, and use this index for identifying equivalent synchrony subspaces to be merged to each other. Based on this equivalence, the initial lattice of synchrony subspaces can be reduced to a lattice of synchrony subspaces which corresponds to a simple eigenvalue case discussed in previous work. The result is a reduced lattice of synchrony subspaces, which affords a well-defined non-negative integer index that can be used for bifurcation analysis in regular coupled cell networks.

After only two weeks of being able to get to know you in person, I will use this talk to introduce myself and talk about present and past work. My presentation will be divided into three parts. After shortly introducing myself (1), I'll cover the following topics related to my masters thesis (2) and my PhD research (3).

2. Amplitude dynamics of resonant Rossby wave triads in Nambu form:
Non-linear interactions play a fundamental role in the redistribution of energy amongst Rossby waves. For weakly interacting waves, geometric constraints govern the dynamics of forced and unforced resonant Rossby wave triads. These constraints allow to cast the dynamical equations in Nambu formulation.

3. How Semi-Implicit Spectral Deferred Correction (SISDC) can improve Numerical Weather Prediction (NWP) models and climate projections:
The multitude of time scales associated with atmospheric waves (e.g. Rossby-, gravity-, sound-waves) poses difficulties in modeling the full governing equations. The CFL condition usually requires the adaption of the time step to the fastest waves to prevent instabilities. However, the fastest waves (i.e. sound waves) in general transport a negligible amount of energy and therefore have minimal impact on the dynamics. By treating the fastest waves implicitly, instabilities can be prevented despite a CFL-number > 1. Using SISDC to integrate the linearized Boussinesq equations has proven to be valuable alternative to implicit-explicit Runge-Kutta and diagonally implicit Runge-Kutta methods. Applying SISDC to the full compressible governing equations may improve cost and accuracy of state of the art NWP models.