CRC 1114 aims at methodological developments for the modelling and computational simulation of complex processes involving many (more than two) interacting scales, driven by real-life applications from the bio-, geo-, and material sciences. In its individual projects, mathematicians cooperate with colleagues from the natural sciences to advance both their modelling capabilities and their insight into concrete multiscale phenomena.
Atmospheric dynamics in the mid-latitudes features quasi-stationary atmospheric states (QSAS), also denoted as atmospheric blocking. To obtain a better understanding of the stability of QSAS and to improve predictions of transitions into and out of QSAS, project A08 of CRC1114 aims at mathematically describing and analyzing them as persistent dynamic structures. In particular, we propose to confront geometric trajectory-based with set-oriented transfer-operator-based, Eulerian with Lagrangian, and model-based with data-based approaches. The PhD student working at the Institute of Mathematics will develop a new mathematical framework to unify trajectory-based stability theory for non-autonomous, in particular random, dynamical systems and operator-based approaches for complex coupled systems, using tools from modern ergodic theory. The new mathematical insights will be in strong correspondence with our collaborators in meteorology, deriving by help of advanced learning methods the appropriate mathematical models from meteorological data sets of different complexity, ranging from point vortex models to reanalysis data. The project offers the opportunity to solve cutting-edge problems in ergodic theory and (stochastically driven) dynamical systems, connecting Lyapunov exponents and measures of quasi-stationarity of relevant sets in phase space, and at the same time make the results applicable to the highly challenging physical problem of describing and predicting the rise and decay of QSAS. The third-party funded research project provides an opportunity to do a doctorate.
Completed university degree in mathematics (master’s degree).
• Very good knowledge of dynamical systems, bifurcation theory, ergodic theory and stochastic analysis
• First research experiences in dynamical systems and quasi-stationary phenomena, for example via a Master or Diploma Thesis
• First experiences in the framework of applied math projects, for example via research assistance in a cross-disciplinary research project
• Good knowledge of scientific computing
• Very good knowledge of written and spoken English
• Basic knowledge of discrete mathematics in terms of graph theory and Markov chains
For further information, please contact Frau Dr. Kristine Al Zoukra ([email protected] / 03083852202).
Applications should be sent by e-mail, together with significant documents, indicating the reference codein PDF format (preferably as one document) to Herrn Dr. Maximillian Engel: [email protected] or postal to
Free University of Berlin
Department of Mathematics and Computer Science
SFB 1114: Scale cascades in complex systems
Dr. Maximillian Engel
14195 Berlin (Dahlem)
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