Vorträge

Vortrag (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.

The presentations aims to give a rather short non-technical introduction in the general concept of a functional calculus including several examples and applications.

The presentation will (mostlikely) make use of the tool 'Zoom'. The audience will not have to do much but simply follow a link the speaker provides everybody with who asks in advance (jan.meichsner@tuhh.de). Members of the institute will get the link via the common email list.