WPC1. Colloid-enhanced flow of contaminants in porous media

Experimental evidence shows that the transport of contaminants in porous media is strongly enhanced by the attachment of contaminants to colloids. We must derive, analyze and discretize efficient multi-scale models to explain these phenomena and to further exploit them in environmental technologies.

WPC2. Electrowetting: modeling, analysis, and simulation

In microfluidics, tiny amounts of liquids may be manipulated (drop transport, splitting & coalescence) by applying electric fields without the need for any tear-and-wear-elements such as valves, pumps etc. We shall derive and analyze new models for electrowetting, taking in particular different mass densities of the involved fluids into account. For appropriate quasi-stationary model versions, optimal control of droplet motion may be studied as well.

WPC3.  Level Set Methods for Multilayer Geological Folding                     Link EURAXESS

Singularity formation in the bending shapes of multilayers can be predicted by geometry, and are observed in actual geological formations, but lead to significantproblems in variational formulations involving bending energy and friction terms. Further work is needed to develop more sophisticated models for geological deformation and to establish a consistent variational formulation of rock folding which will predict the complex folding patterns observed in practice.

WPC4.  Non linear systems in some technology problems

Micromagnetism is essentially a theoretical formalism which enables the prediction of magnetisation structures such as domain walls and the investigation of magnetisation reversal mechanisms in bulk magnetic materials.  It has applications in the area of recording media. Our project research bears on the magnetization in thin ferromagnetic films, and in particular, compactness for the two-dimensional approximation of the micromagnetic energy. Moreover we shall study the application of this type of technique to nonlinear optics.

WPC5. Reduced order plasticity models for the real-time control for hot rolling of steel

In production lines of steel plates, there is currently still a considerable amount of energy and material wasted due to difficulties with the optimal shape-formation of the plates. Siemens plans to employ one ESR who will derive and implement a reduced order model based algorithm for the real time control of steel plate production. It is planned to implement the results of this research in algorithms for the control of steel mills.

WPC6.  Models with a not controllable linearized control system and  Computational aspects of interfaces

For many equations or systems considered in this project to model porous media, one can act on them by using suitable controls. A practical important question is the problem of controllability: can one steer the control system from a first given state to a desired state? One knows many tools to study the controllability of such control systems if they are linear. From the controllability of the linearized control systems at some equilibrium one can deduce the local controllability around this equilibrium. However, in many important cases, associated to free boundary problems, the linearized control system is not controllable. The computational aspects of such type of problems will be also studied: a first part will be related to the study of interfaces in direct problems of computational electromagnetics, faced in the form of material discontinuities, for instance the edges of conductors or metal sheets for shielding. A second part will be related to the evaluation of modelling errors.

WPC7. Control and stabilization of flows in networked transportation systems

Optimal control and stabilization of flow of gas, water and traffic in networked pipe- and road-systems, respectively, is one of the major challenges in Civil Engineering and Applied Mathematics. Such systems are used along the links (pipes, roads) while nodal conditions are to be applied at the multiple nodes (joints) and boundary conditions at the intake-nodes. Control instruments are to be modelled via nonlinear and non-homogenous nodal conditions at simple and multiple nodes. The first goal is to fully understand the reachability and stabilizability properties under constraints both in the states and the controls. The second goal is to derive sensitivities, including shock-sensitivities, in order to apply real-time capable algorithms for the numerical treatment of optimal controls for systems of realistic size.