Scientific Computing Research Environments for the Mathematical Sciences (SCREMS)

Northwestern University, Evanston IL

Investigators

Abstract

This project incorporates four different applications, which are related through their common need for high-speed computational capabilities. The first project involves the simulation of growing bacterial biofilms. The simulation will couple the extended finite element method with the level set method in order to capture the interaction between the growing biofilm and the surrounding fluid flow. The second project will solve a low Mach number model for deflagrations in stellar envelopes. By filtering out sound waves from the model, significantly larger time steps can be achieved than are possible for full hydrodynamical models, thus making long time computations feasible. The third project will study the role of defects in the break-down of ordered structures. Parallelized Monte-Carlo and Fourier spectral methods will be employed to investigate defect trajectories in two paradigmatic systems, a magnetic system and a dynamical system of coupled oscillators in two dimensions. They exhibit spatially ordered as well as disordered states. The goal is to identify to what extent various statistical measures of the trajectories follow universal power laws. The fourth project will use recently developed importance-sampling methods for simulating rare events that set the performance of optical fiber communication systems. The impact of these projects will be felt across a broad spectrum of disciplines, and will aid in the training and education of several graduate students and postdoctoral research associates. In addition to the scientific areas described above, the training will also include the efficient use of high-performance parallel computing architectures. The study of biofilms will improve our understanding of quourum sensing organisms, and how to treat them. Such organisms are responsible for a number of diseases, including diseases associated with cystic fibrosis and deep burn wounds. The study of deflagrations in stellar envelopes will improve our understanding of the dynamics of novae of white dwarfs and the nature of X-ray bursts from neutron stars. Transitions from ordered patterns to disordered states are observed in many physical systems undergoing phase transitions as well as in dynamical systems like arrays of coupled oscillators, various kinds of fluid flow, and optical systems. Often defects in the patterns are striking features of the disordered states. The research will elucidate the role the defect dynamics play in the break-down of the ordered states. The study of rare events in optical fiber communication systems will lead to the construction of a set of simulation tools capable of predicting the performance of lightwave communication systems.