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Analysis of Streamline Separation at Infinity Using Time-Discrete Markov Chains
Dec. 2012 (vol. 18 no. 12)
pp. 2140-2148
Wieland Reich, University of Leipzig
Gerik Scheuermann, University of Leipzig
Existing methods for analyzing separation of streamlines are often restricted to a finite time or a local area. In our paper we introduce a new method that complements them by allowing an infinite-time-evaluation of steady planar vector fields. Our algorithm unifies combinatorial and probabilistic methods and introduces the concept of separation in time-discrete Markov-Chains. We compute particle distributions instead of the streamlines of single particles. We encode the flow into a map and then into a transition matrix for each time direction. Finally, we compare the results of our grid-independent algorithm to the popular Finite-Time-Lyapunov-Exponents and discuss the discrepancies.
Index Terms:
Vectors,Eigenvalues and eigenfunctions,Markov processes,Transmission line matrix methods,Sparse matrices,Approximation methods,Topology,uncertainty,Vector field topology,flow visualization,feature extraction
Citation:
Wieland Reich, Gerik Scheuermann, "Analysis of Streamline Separation at Infinity Using Time-Discrete Markov Chains," IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 12, pp. 2140-2148, Dec. 2012, doi:10.1109/TVCG.2012.198
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