EXC 2044 - T09: Multiscale processes and effective behaviour

Basic data for this project

Description

Many processes in physics, engineering and life sciences involve multiple spatial and temporal scales, where the underlying geometry and dynamics on the smaller scales typically influence the emerging structures on the coarser ones. A unifying theme running through this research topic is to identify the relevant spatial and temporal scales governing the processes under examination. This is achieved, e.g., by establishing sharp scaling laws, by rigorously deriving effective scale-free theories and by developing novel approximation algorithms which balance various parameters arising in multiscale methods. In optimisation and design problems, multiple scales can either emerge as optimal structures, or they can be a priori present in the system that one wants to control. In the first case, the main challenge is to characterise emergence of multiple scales and to develop numerical methods that can identify the highly complex optimisers. In the second case, the challenge is to analytically or numerically approximate the macroscopic system behaviour with sufficiently high efficiency such that it can form part of each step in an iterative optimisation.