Energy-variational Methods for Innovative Materials

The group contributes primarily to the following application oriented research topics of WIAS:

Mathematical models and computational techniques are nowadays utilized in medical sciences for noninvasive diagnostic, diseases characterization, therapy planning, and treatment monitoring. The research at WIAS focuses on efficient and robust models for biological tissues and fluids, on the usage of advanced mathematical models in data assimilation and medical imaging applications, as well as on techniques in optimization, machine learning, and optimal control for decision support in biomedicine. [>> more]

This research topic focusses on modeling complex material systems with different phases including multiphase and interfacial flows, damage and fatigue modeling, topology optimization and complex materials. Physical phenomena modelled involve fluid flow, diffuse transport and (visco)elastic deformation in the context of phase separation and phase transitions. Applications range from biology to physics and engineering. [>> more]

Industrial processes are currently experiencing their fourth revolution. The entire production process is connected and equipped with sensor technology, which makes huge amounts of data available. Workers are not only supported by technical visualization and information processing, but parts of the decision-making processes are even carried out independently with the help of AI systems. The large amount of data and the fully automated process pose new challenges for mathematics, but offer unprecedented opportunities for optimization algorithms, not only in the optimization of individual production steps, but across the entire value chain. [>> more]

The behavior of electrochemical systems is widely investigated with continuum physics models. Applications range from single crystal electrochemistry to lithium batteries and fuel cells, from biological nano-pores to electrolysis and corrosion science, and further. [>> more]