Multiscale Analysis of Nonlinear Systems Using Computational Topology
Computational Homology in Fluids: M. Schatz, K. Mischaikow. This effort focused on characterizing both the structure and dynamics of complex spatio-temporal flows that arise in thermal convection. Microstructure Characterization: T. Wanner, K. Mischaikow. We extended our previous work on studying the time evolution of patterns associated with phase separation in conserved concentration fields. Probabilistic Homology Validation: W. Kalies, T. Wanner, K. Mischaikow. Our above mentioned work on microstructure characterization is based on numerically studying the homology of certain sublevel sets of a function, whose evolution is described by deterministic or stochastic evolution equations. Computational Homology and Dynamics: W. Kalies, T. Wanner, K. Mischaikow. Topological methods can be used to rigorously describe the dynamics of nonlinear systems. We are approaching this problem from several perspectives and through a variety of systems. Stress Networks in Polycrystals: T. Wanner. Together with E. Fuller (NIST) and D. Saylor (FDA) we have characterized stress networks in polycrystals. This part of the project is aimed at developing homological metrics which can aid in distinguishing not only microstructures, but also derived mechanical response fields. Microstructure-Controlled Drug Release: K. Mischaikow, T. Wanner. This part of the project is concerned with the development of topological metrics in the context of controlled drug delivery systems, such as drug-eluting stents. We are particularly interested in developing metrics which can be used to link the processing stage to the resulting microstructure, and ultimately to the achieved system response in terms of drug release profiles. Microstructure of Fuel Cells: W. Kalies, K. Mischaikow. In collaboration with P. Voorhees (Northwestern Univ.) and M. Gameiro (Rutgers) we have been using our computational homology software to analyze the topological structure of the void, metal and ceramic components of a Solid Oxide Fuel Cell.
- Research Organization:
- Georgia Tech Research Corporation, Atlanta GA
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- FG02-05ER25711
- OSTI ID:
- 1057064
- Country of Publication:
- United States
- Language:
- English
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Multiscale analysis of nonlinear systems using computational homology
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