Tätigkeitsprofil:

The position is within the Math+ project "Anisotropic microfluids -- fluctuations, control, effective models and their numerics “.

Here, we study anisotropic microfluids and the effect of stochastic fluctuations in electrokinetic flows. This is of interest in so-called lab-on-chip devices, where laboratory functions should be integrated and automized on small chips. A possible way of establishing a precise reliable microfluidic control is via flows induced via electric fields in anisotropic media. It turns out that such devices are prone to random fluctuations, which can influence the system quite heavily.

We establish new results concerning the analysis of stochastically driven anisotropic fluids, design novel numerical simulation and optimal control schemes, and provide new means for risk management. This project mainly focuses on the analysis and optimal control of the underlying SPDE and the associated numerical implementation. As a simplified model for the underlying phenomena, we are going to consider the Ericksen—Leslie model with stochastic fluctuations and investigate it in terms of existence of solutions and their approximation, the associated large deviation principle and the simulation of the occurrence of rare events, as well as model simplifications and associated a posteriori error estimate. This will mainly rely on the construction of optimal control strategies associated to the large deviation principle of the system.

The project is a collaboration between WIAS (Research Group “Nonlinear Optimization and Inverse Poblems” – PI Robert Lasarzik) and TU Berlin (PI Benjamin Gess and Sandra May).

Anforderungsprofil:

We are looking for: a highly motivated researcher with at least 3 years of research experience (possibly as part of the PhD) in a field related to mathematical analysis of partial differential equations (PDEs), calculus of variations, optimal control, who is willing to engage in innovative and interdisciplinary research questions. Good communication skills in English and/or German are expected.

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