Algorithms and Computation for Rare Events in Complex Systems

Pennsylvania State Univ University Park, University Park PA

Investigators

Abstract

The project is concerned with mathematical and computational issues related to the simulation and analysis of equilibria, metastable and transition states and minimum energy paths for complex energy landscapes of practical interests, and associated stochastic dynamics. The research to be carried out is closely motivated by applications in a number of areas of federal strategic interests: the development of effective algorithms and codes is a crucial part of high-performance computing, and numerical methods and software tools to be developed may be potentially useful for effective computational materials and drug design. The principal investigator will carry out interdisciplinary research that encompassing subjects like computational mathematics, physics, information, materials and biological sciences. He will focus on new algorithmic development and analysis which have the potential to significantly improve the usual practice on the modeling and simulation of rare events. He will consider some specific and important applications, including systems of interacting particles and interfaces in geometrically confined and frustrated configurations or deformable geometry which arise in many areas of physics, chemistry and biology (such as formation of nano-clusters, bimolecular conformation, vesicle mediated interactions, and critical nucleation in solid state transformations). He will attempt to draw strong connections with some of the algorithms developed by practitioners implemented in existing software codes such as those for first principle calculation and computational chemistry. Most of the problems involved in the research project are associated with either infinite dimensional spaces such as deterministic or stochastic partial differential equations or finite dimensional spaces with high dimensions (discretization of differential equations or particle systems involving a large number of particles), which lead to many computational challenges. Various mathematical and numerical issues will be studied, ranging from efficient local saddle point search and its robust numerical implementation to rigorous analysis and effective multiscale simulations of relevant dynamics and rare events. It is expected that the progress made during the project will have a broad impact on the community interested in the study of rare events. The project will also contribute to education and training as it will provide students valuable training ground and research experience in an interdisciplinary environment. Much effort will be devoted to promoting active engagement of student participation at all levels and integrating research findings into teaching and training.