Contemporary multiscale and ensemble methods that enable us to understand and model coarse-grained (CG) systems are studied. Since complex systems involve the fluctuating dynamics of many atoms, underlying a CG theory is ultimately a microscopic stochastic model. This suggests that multiscale theory should not only provide governing equations for the coarse-grained state but also a probabilistic accounting of the fine-grained states consistent with the slowly evolving coarse grained one. A traditional starting point for understanding the statistical state of an N-atom system is the Liouville equation (LE). The concepts underlying multiscaling also arise in the design of simulation algorithms. At present, it is not clear whether it is more fruitful to pursue universally applicable techniques or to focus on the development of approaches more tailored to specific classes of rare-event problems.
ASJC Scopus subject areas
- Physical and Theoretical Chemistry
- Surfaces, Coatings and Films
- Materials Chemistry