Statistical Mechanics and macroscopic dynamics
The modelling of real-world processes from, e.g., biology, physics or engineering often leads to high-dimensional differential equations with a huge range of spatial and temporal scales. One strategy in dealing with the inherent complexity of the models is to eliminate certain “irrelevant’’ degrees of freedom, while keeping only those variables that are sufficient to describe the system’s effective (i.e., macroscopic) behaviour. Depending on the problem at hand, techniques for multiscale systems involve averaging, homogenization or diffusion approximation or the analysis of low-dimensional free energy profiles.
The research group’s activities include:
- Balanced model reduction for linear and bilinear control systems using singular perturbation methods
- Coarse graining and mesoscale modelling of cellular membranes that are subject to thermal fluctuations
- Optimal prediction and Markovian approxiations of large-scale mechanical systems with random initial data
- Nonequilibrium free energy methods for multiscale diffusions
- C. Hartmann, A. Zueva and B. Schäfer-Bung (2010), Balanced model reduction of bilinear systems with applications to positive systems, submitted to SIAM J. Control Optim.
- J. Latorre, C. Hartmann, Ch. Schütte (2010), Free energy computation by controlled Langevin processes, Procedia Computer Science 1, pp. 1591-1600.