Space-Time Homology of a 2D Vortex
Dr. James Cho
Queen Mary University of London, Princeton University
Abstract: In many areas of research and application, understanding topological properties of continuously deforming scalar, vector, and tensor data spaces is extremely useful. Moreover, when information about persistence across different scales is incorporated, geometric and physical properties of structures in the data can be analyzed directly — rather than via statistical or spectral proxies, as in traditional modalities. Persistent homology can now be efficiently performed via computation, allowing spatially and temporally complex data to be analyzed practically. In this talk, a ‘space-time’ approach to persistent homology is presented, with application to the analysis of a 2D self-straining vortex in an amalgamated (2+1)-space. The global space-time dynamics of vorticity expulsion, disconnection, reconnection, and destruction associated with a vortex at high Reynolds number is discussed, demonstrating the broad utility of the approach for studying realistic data.
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