attendance: 56 hrs, self study: 124 hrs

Theory modules in Bachelor, e.g., Mathematical Methods; Quantum Structure of Matter

Computational Fluid Dynamics (CFD I & II) - Deeper understanding of the fundamental equations of fluid dynamics. - Overview of numerical methods for the solution of the fundamental equations of fluid dynamics. - Confrontation with complex problems in fluiddynamics. - To become acquainted with different, widely used CFD models that are used to study complex problems in fluid dynamics. - Ability to apply these CFD models to certain defined problems and to critically evaluate the results of numerical models. Computerorientierte Physik Extension and complement of qualification in theoretical physics through the acquisition of solid and deep knowledge of advanced concepts and methods in theoretical physics. Depending on the selected course the students acquire knowledge in the fields of basis numerical methods of theoretical physics, algorithms and data structures in scientific computing, code debugging. They obtain skills for a confident application of modern methods of theoretical physics such as diagram generation, Molecular Dynamics and Monte Carlo simulations and quantitative analysis of advanced problems of theoretical physics and in further development of the physical intuition. They enhance their competences to effectively deal with sophisticated problems of theoretical physics, to independently develop approaches to current issues of theoretical physics, and to comprehend common concepts and methods of theoretical physics and the natural sciences, in general. Modelling and Simulation The students attending successful the course acquire an advanced understanding of the conceptual design of models in the field of engineering sciences. Special emphasis is on identifying the significant physical processes and the choice of the most efficient modelling type. The interaction of numerical simulations with field measurements and laboratory measurements including the theory of similarity will be discussed. To meet the needs of renewable energy, laser technology, environmental sciences and marine sciences the practical focus is on the modelling and simulation of fluid dynamics in small scales and close to structures.

Computer Physics
Debugging; data structures; algorithms; random numbers; data analysis; percolation; Monte Carlo simulations; finitesize scaling; quantum Monte Carlo; molecular dynamics simulations; event-driven simulations; graphs and algorithms; genetic algorithms; optimization problems.

Density-functional theory
The many-body problem; the Hartree-Fock approximation; Homogeneous electron gas; Hohenberg-Kohn theorems; Kohn-Sham equations; exchange-correlation potentials; pseudopotentials; basis sets.

Machine learning
Unsupervised learning methods; algorithms for clustering, classi cation, component extraction, feature learning, blind source separation and dimensionality reduction; Relations to neural network models; learning in biological systems.

Modelling and Simulation
Advanced fluid dynamics including 3D, transient and compressible processes; Theory of similarity, range of dimensionless numbers; Potential Theory; Numerical Algorithms and possibilities of independent coding of simplest mathematical models; Introduction of a complete chain of Open- Source-CFD-Tools; Contactless  high-resolving measuring techniques in the fluid dynamics.

Signal processing
System properties; Discrete-time signal processing; Statistical signal processing; Adaptive filters.

Computer Physics
- T. H. Cormen, S. Cli ord, C.E. Leiserson, und R.L. Rivest: Introduction to Algorithms. MIT Press, 2001;
- K. Hartmann: Practical guide to computer simulation. World- Scientic, 2009;
- J. M. Thijssen: Computational Physics. Cambridge University Press, 2007;
- M. Newman, G. T. Barkema: Monte Carlo Methods in Statistical Physics. Oxford University Press, 1999.

Density-functional theory
- R. Martin, Electronic Structure, Cambridge University Press (2004);
- F. Bechstedt, Many-body approach to electronic excitations, Springer (2015);
- F. Giustino, Materials modelling using density functional theory, Oxford University Press (2014).

Machine learning
- C. M. Bishop, Pattern Recognition and Machine Learning, Springer 2006;
- D. MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge University Press, 2003.

Modelling and Simulation
- Versteeg, K.H. , Malalasekera, W.: An Introduction to Computational Fluid Dynamics. Prentice Hall, 2nd rev. Ed., 2007

Signal processing
- A. V. Oppenheim, R. W. Schafer, Discrete-Time Signal Processing", Prentice Hall, 2013;
- J. G. Proakis, D. G. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications, Prentice Hall, 2013;
- S. Haykin, Adaptive Filter Theory, Pearson, 2013;
- P. P. Vaidyanathan, Multirate systems and lter banks, Prentice Hall, 1993;
- K.-D. Kammeyer, K. Kroschel, Digitale Signalverarbeitung: Filterung und Spektralanalyse mit MATLAB-Ubungen, Broschiert, 2018;
 

1 exam according to selected course