Special PHYSICAL MATHEMATICS SEMINAR TOPIC: Problems with Multiple Scales: Modeling and Computations SPEAKER: WEINAN E Princeton University ABSTRACT: We will present a general methodology, the heterogeneous multi-scale method (HMM), for efficient numerical computation of problems with multiple scales. Both variational and dynamic problems will be considered. The method relies on an efficient coupling between the macroscopic and microscopic models. In case when the macroscopic model is not explicitly available or invalid, the microscopic solver is used to supply the necessary data for the macroscopic model. Scale separation can be exploited to considerably reduce the complexity of the microscopic solver. Besides unifying several existing multiscale methods such as the {\it ab initio} molecular dynamics, quasi-continuum methods, projective methods for stiff systems, HMM also provides a methodology for designing new methods for a large variety of multiscale problems. We will discuss a framework for the analysis of the stability and accuracy of HMM. We will also discuss applications to problems such as homogenization, complex fluids, molecular dynamics and interfacial dynamics. DATE: THURSDAY, MARCH 7, 2001 TIME: 2:30 PM LOCATION: Building 2, Room 338 Refreshments will be served at 3:30 PM in Room 2-349 Massachusetts Institute of Technology Department of Mathematics Cambridge, MA 02139