The design of this CRC’s Research Areas is guided by structural similarities in the application problems we intend to investigate. The individual research areas address three structurally different problem classes.
Research Area A: Efficient modelling of macro scales
We aim to predict large-scale/longtime features of the considered processes accurately, while accounting for smaller space and shorter time scales only to the extent necessary to achieve this goal. This entails, e.g., a progressive shift to probabilistic, averaged, or – more generally – set-based reduced representations at the smaller scales.
A01 - Coupling a multiscale stochastic precipitation model to large scale atmospheric flow dynamics (Rust, Névir, Koltai)
A02 - Multiscale data and asymptotic model assimilation for atmospheric flows (Reich, Klein)
A04 - Efficient calculation of slow and stationary scales in molecular dynamics (Noé, Weikl)
A05 - Probing scales in equilibrated systems by optimal nonequilibrium forcing (Hartmann, Schütte, Weber)
A07 - Langevin dynamics of particles in membranes (Gräser, Kornhuber, Delle Site)
Research Area B: Uniform meso scale behavior in scaling cascades
We consider processes involving a discrete or continuous range of scales all of which contribute collectively to the processes’ target features. Scale interactions are structurally similar across at least part of the scale range so that asymmetric representations of the larger and smaller scales, as in Research Area A, are not an option.
B01 - Fault networks and scaling properties of deformation accumulation (Oncken, Rosenau, Kornhuber, Mielke)
B03 - Multilevel coarse graining of multiscale problems (Koksch, Netz, Schütte)
B05 - Origin of scaling cascades in protein dynamics (Keller, Weber, Heyne)
B06 - Data-driven and tensor-based analysis of multiscale systems (Eisert, Klus)
B07 - Selfsimilar structures in turbulent flows and the construction of LES closures (Kutyniok, Klein, Vercauteren)
Research Area C: Bridging the micro-macro scale range
We are interested in processes in which a determining part of the physics arises at the smallest scales only, and we study how the smallest and largest scales communicate across the scale range.
C01 - Adaptive coupling of scales in molecular dynamics and beyond to fluid dynamics (Delle Site, Höfling, Klein)
C02 - Interface dynamics: Bridging stochastic and hydrodynamic descriptions (Netz, Mielke)
C03 - Multiscale modelling and simulation for spatiotemporal master equations (Höfling, Noé, Schütte)
C05 - Effective models for materials and interfaces with multiple scales (Mielke)
C06 - Multiscale structure of atmospheric vortices (Hege, Klein, Pfahl, Schielicke)
C08 - Stochastic spatial coagulation particle processes (Patterson)
C09 - Dynamics of rock dehydration on multiple scales (Thomas, John)