Research objectives

Crowded transport can be observed on various scales in life and social sciences. Examples include the motion of charged particles through ion channels, the flow of large pedestrian crowds or the collective behavior of animals like fish or bird. Crowding is generally caused by limitations of the physical domain or aggregation phenomena, hence multiscale effects appear naturally in this context. The common denominator of crowding processes is the fact that the size of the particles plays an important role in the transportation and should not be neglected in the mathematical modeling.

The research objectives of the New Frontiers group include general modeling approaches of crowded transport on different scales and their efficient numerical simulation. A main focus of the modeling is the systematic translation of finite size effects for different methods and scales as well as the consistent coupling of models in multiscale phenomena. Efficient numerical simulations are a further key issue of the project, since the transportation equations for crowded motion are in general highly nonlinear and require the development of flexible discretization techniques to capture the versatile behavior of the derived models in a reliable manner.