Computational Homology and Fluid Dynamics Workshop
Georgia Tech, Atlanta, GA, USA
March 1-3, 2007
This workshop at the Wardlaw Center at Georgia Tech was intended to bring together a select group of physicists, applied mathematicians and engineers with an interest in characterizing quantitatively structures and dynamics of spatio-temporally chaotic and turbulent fluid flows. In addition to providing a forum for discussing current and future applications of topological techniques, the workshop included tutorial lectures on computational homology and the publicly available software package CHomP. We wanted to give the participants ample opportunity to interact, share ideas, and explore the potential for future collaborations. For this reason, we limited the number and length of the lectures in order to provide adequate time for informal discussions.
Presentations
The following are the talk presentations of people who were attending the Workshop and were willing to share their materials with us. Note that all these materials are Copyright © 2007 by their authors and cannot be used without permission.
Computational Homology Tutorial, Part 1: Introduction to Homology [6.2M]—William D. Kalies (Florida Atlantic University, Department of Mathematical Sciences)
Computational Homology Tutorial, Part 2: The CHomP Software [4.1M]—Marcio Gameiro (Rutgers University, Department of Mathematics)
Computational Homology Tutorial, Part 3: Homological Characterization of Patterns [9.1M]—Thomas Wanner (George Mason University, Department of Mathematical Sciences)
Spatio-Temporal Chaos: Examples from Rayleigh-Benard Convection and Electro Convection [8.3M]—Guenter Ahlers (University of California, Department of Physics)
Quantifying Spatiotemporal Chaos in Rayleigh-Benard Convection: New Insights from Numerics [968K]—Mark Paul (Virginia Tech)
Homological Characterization of Spatiotemporal Patterns [9.5M]—Michael Schatz (Georgia Institute of Technology, School of Physics)
Complex Patterns: Diagnostics and Excitation [2.9M]—Hermann Riecke (Northwestern University)
Estimating the State of Spatiotemporal Chaos: Weather Forecasting, etc [5.6M]—Edward Ott (University of Maryland)
State Estimation for Rayleigh-Benard Convection from Shadowgraph Data [738K]—Brian Hunt (University of Maryland)
Crystalline Chaos and Resonant Structures in Spatially Forced Rayleigh-Benard Convection [11.4M]—Eberhard Bodenschatz (Max Planck Institute for Dynamics and Self-Organization, Goettingen and Cornell University)
Turbulence Structures, Their Control and Unstable Periodic Orbits [26.4M]—Genta Kawahara (Osaka University, Japan)
Homotopy of Exact Coherent States in Shear Flows [3.7M]—Fabian Waleffe (University of Wisconsin)
Turbulence: a Walk on the Wild Side [2.7M]—Predrag Cvitanovic (Georgia Institute of Technology, School of Physics)
Invariant Solutions and the Dynamics of Plane Couette Flow [988K]—John Gibson (Georgia Institute of Technology)
What Can We Learn About Granular Materials from the Geometry and Topology of Force Chain Networks? [7.8M]—Karen Daniels (North Carolina State University)
Photographs
Acknowledgments
This workshop is supported by the Department of Energy, as well as the College of Sciences, the School of Mathematics, the School of Physics and the Vice Provost for Research at the Georgia Institute of Technology, and is related to DARPA's Topological Data Analysis program.
* Workshop logo picture courtsey of Genta Kawahara.