Best Paper Award

Visualization of Discontinuous Vector Field Topology

Egzon Miftari, Daniel Durstewitz, Filip Sadlo

Room: Plenary-1

2023-10-24T04:55:00ZGMT-0600Change your timezone on the schedule page
Exemplar figure, described by caption below
Topological analysis of vector field with discontinuity (transparent gray) exhibiting repelling sliding flow (red LIC). Qualitatively different equivalence streamsets (white) are separated by stable (blue) and unstable (red) manifolds. Equitrices (violet) separate streamsets of different dimensionality.
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Discontinuous vector field topology, equivalence in non-unique flow, non-smooth dynamical systems


This paper extends the concept and the visualization of vector field topology to vector fields with discontinuities. We address the non-uniqueness of flow in such fields by introduction of a time-reversible concept of equivalence. This concept generalizes streamlines to streamsets and thus vector field topology to discontinuous vector fields in terms of invariant streamsets. We identify respective novel critical structures as well as their manifolds, investigate their interplay with traditional vector field topology, and detail the application and interpretation of our approach using specifically designed synthetic cases and a simulated case from physics.