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Issue No.12 - Dec. (2012 vol.18)
pp: 2140-2148
Wieland Reich , University of Leipzig
Gerik Scheuermann , University of Leipzig
ABSTRACT
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 & Computer Graphics, vol.18, no. 12, pp. 2140-2148, Dec. 2012, doi:10.1109/TVCG.2012.198
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