Singularities of the inertial flow map gradient
Günther T, Theisel H (2016)
Publication Type: Conference contribution
Publication year: 2016
Publisher: Eurographics Association
Pages Range: 69-76
Conference Proceedings Title: VMV 2016 - Vision, Modeling and Visualization
Event location: Bayreuth
ISBN: 9783038680253
DOI: 10.2312/vmv.20161344
Abstract
Inertial particles are finite-sized objects that are carried by flows, for example sand particles in air. In contrast to massless tracer particles, the trajectories of inertial particles can intersect in space-time. When this occurs, the inertial flow map gradient becomes singular. This has an impact on visualization concepts that require the flow map gradient to be invertible. An example are influence curves, which allow to move inertial particles backward in time and thereby avoid the numerically ill-posed inertial backward integration. In this paper, we show that singularities of the inertial flow map gradient can act as poles for influence curves, i.e., as structures that influence curves cannot cross. Influence curves thereby decay into disconnected pieces. We extract singularities in space-time and propose a simple approach to extract influence curves even when they are spatially disconnected. We demonstrate the extraction techniques and discuss the role of singularities in a number of 2D vector fields.
Authors with CRIS profile
Involved external institutions
Otto-von-Guericke-Universität Magdeburg
Germany (DE)
Eidgenössische Technische Hochschule Zürich (ETHZ) / Swiss Federal Institute of Technology in Zurich
Switzerland (CH)
Germany (DE)
Eidgenössische Technische Hochschule Zürich (ETHZ) / Swiss Federal Institute of Technology in Zurich
Switzerland (CH)
How to cite
APA:
Günther, T., & Theisel, H. (2016). Singularities of the inertial flow map gradient. In Dieter Fellner (Eds.), VMV 2016 - Vision, Modeling and Visualization (pp. 69-76). Bayreuth, DE: Eurographics Association.
MLA:
Günther, Tobias, and Holger Theisel. "Singularities of the inertial flow map gradient." Proceedings of the 21st International Symposium on Vision, Modeling and Visualization, VMV 2016, Bayreuth Ed. Dieter Fellner, Eurographics Association, 2016. 69-76.
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