Flow and transport of species are important in many processes in nature and industry. In general, they are modeled by systems consisting of partial differential equations.
Active fields of research are questions concerning the analysis, the numerical analysis, and the numerical simulation of partial differential equations from computational fluid dynamics (CFD). The considered applications include, for example, electrochemical systems, population balance systems and flows in porous media.
Flow through an aortic arch
Turbulent flow around a cylinder, velocity (left) and vorticity (right)
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.
These applications are modeled by population balance systems. Accurate and efficient numerical methods will be developed, in collaboration with partners from academics and industry, which will be in the long term the basis of optimal control methods for the considered processes.
The phenomenon of coagulation occurs in a wide range of applications, e.g., in physics (aggregation of particles, growth of gas bubbles), meteorology (merging of drops in atmospheric clouds, aerosol transport), chemistry (reacting polymers, soot formation) and astrophysics (formation of stars and planets).
Phase transitions and hysteresis are characteristics of energy storage problems. The aim is to formulate and analyse a thermodynamical model which discribes the storage problem.
Today, in medical science digital simulation instruments for processes in the human body are utilized in diagnistics and therapy planning. At WIAS, models for biological tissues, fluids, and their interaction as well as techniques in optimization and optimal control for decision support in biomedicin are devloped.
Thin films play an important role in nature and many areas of technological applications. In particular on micro- and nanoscales technological processes such as dewetting or epitaxial growth are used to design surfaces with specific material properties. Apart from the need to derive mathematical decriptions, analyis and numerical simulation, that serve to accelerate the development of new technologies, it is also exciting to understand material behaviour on these small scales.
Research in this field focuses on mathematical aspects of biological evolution through stochastic modelling. The main areas are the effects of complex fitness landscapes on molecular evolution, the study of sexual selection by stochastic modelling of mating preferences and emerging mating patterns, genealogies of the mathematical seed-bank model and mathematical modelling of controlled evolution under experimental conditions.