Applied Mathematics Colloquium

Series: Applied Mathematics Colloquium Series

Smoke Rings from Smoke

Peter Schröder, Professor of Computer Science and Applied and Computational Mathematics, Caltech,

We give an algorithm which extracts vortex filaments ("smoke rings'') from a given 3D velocity field. Given a quality measure h>0, an optimal number of vortex filaments, together with their extent and placement, is given by the zero set of a complex valued function over the domain. This function is the global minimizer of a quadratic energy based on a Schrödinger operator. Computationally this amounts to finding the eigenvector belonging to the smallest eigenvalue of a Laplacian type sparse matrix.

Turning traditional vector field representations of flows, for example, on a regular grid, into a corresponding set of vortex filaments is useful for visualization, analysis of measured flows, hybrid simulation methods, and sparse representations. To demonstrate our method we give examples from each of these.

Joint work with Steffen Weißmann and Ulrich Pinkall of TU Berlin.

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