Chemical Reaction Networks
The project focuses on the systematic study of mathematical methods that allow the solution of large and complicated reaction networks in which stochastic fluctuation play an essential role. In the macroscopic limit, the dynamics of chemically reacting systems follow the classical equations of reaction kinetics. However, as the number of participating molecules decreases (so-called low copy numbers), stochastic fluctuations come into play, which can be modeled by the chemical master equation (CME). Models for realistic systems from biological or polymer chemistry are high-dimensional on one hand but just contain a rather low-dimensional, yet time-dependent subspace of low copy numbers. In such cases numerical integration in the orthogoal subspace should be based on chemical reation kinetics while the CME is just used in the subspace itself. We aim at developing such hybrid models for biological as well as polymer chemistry systems.
The project is funded through the ITN Nanopoly
- Schütte, Ch. and Wulkow, M. (2010) A Hybrid Galerkin–Monte-Carlo Approach to Higher-Dimensional Population Balances in Polymerization Kinetics. Macromol. React. Eng., 4 (9-10). pp. 562-577.
- Metzner, Ph. and Schütte, Ch. and Vanden-Eijnden, E. (2009) Transition Path Theory for Markov Jump Processes. Mult. Mod. Sim., 7 (3). pp. 1192-1219.