Pattern Formation and Self-Organization

 

Currently, the following topics are under investigation

• Basic mechanisms of pattern formation and their mathematical description
• Localized structures in reaction-diffusion systems
• Pattern formation in nanoscale systems

Localized structures are solutions of nonlinear partial differential equations, which describe e.g. current filaments in gas-discharge systems or localized optical vortices. They are examples of coherent structures, which are stabilized under nonequilibrium conditions. Of special interest are instabilities of localized structures as well as their mutual interactions.

Pattern formation in nanoscale systems is investigated within the German-Chinese Transregio Multilevel Molecular Assembly: Structure, Dynamics and Function. The group is engaged in two projects. One project is devoted to the investigation of pattern formation in Langmuir-Blodgett transfer systems (togehter with Lifeng Chi, WWU Münster). Topic of  the joint project with B. Maier and C. Denz (WWU Münster) is the hydrodynamic interaction of molecular motors.