{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T09:52:02Z","timestamp":1758707522030,"version":"3.41.0"},"reference-count":29,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2014,7,27]],"date-time":"2014-07-27T00:00:00Z","timestamp":1406419200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2014,7,27]]},"abstract":"<jats:p>\n            We give an algorithm which extracts vortex filaments (\"smoke rings\") from a given 3D velocity field. Given a filament strength\n            <jats:italic>h<\/jats:italic>\n            &gt; 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 Schr\u00f6dinger operator. Computationally this amounts to finding the eigenvector belonging to the smallest eigenvalue of a Laplacian type sparse matrix.\n          <\/jats:p>\n          <jats:p>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.<\/jats:p>","DOI":"10.1145\/2601097.2601171","type":"journal-article","created":{"date-parts":[[2014,7,22]],"date-time":"2014-07-22T15:08:20Z","timestamp":1406041700000},"page":"1-8","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":28,"title":["Smoke rings from smoke"],"prefix":"10.1145","volume":"33","author":[{"given":"Steffen","family":"Wei\u00dfmann","sequence":"first","affiliation":[{"name":"TU Berlin"}]},{"given":"Ulrich","family":"Pinkall","sequence":"additional","affiliation":[{"name":"TU Berlin"}]},{"given":"Peter","family":"Schr\u00f6der","sequence":"additional","affiliation":[{"name":"Caltech"}]}],"member":"320","published-online":{"date-parts":[[2014,7,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073368.1073380"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0604159103"},{"key":"e_1_2_2_3_1","first-page":"2","article-title":"Vortex Filament Simulation of the Turbulent Coflowing","volume":"21","author":"Bernard P. S.","year":"2009","unstructured":"Bernard , P. S. 2009 . Vortex Filament Simulation of the Turbulent Coflowing Jet. Phys. Fluids 21 , 2 . Bernard, P. S. 2009. Vortex Filament Simulation of the Turbulent Coflowing Jet. Phys. Fluids 21, 2.","journal-title":"Jet. Phys. Fluids"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.5555\/2421731.2421746"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2007.11.016"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(90)90001-H"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1993.1120"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1137\/090757502"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/2504435.2504442"},{"key":"e_1_2_2_10_1","doi-asserted-by":"crossref","unstructured":"Desbrun M. Kanso E. and \n      Tong Y\n  . \n  2008\n  . Discrete Differential Forms for Computational Modeling. In Discrete Differential Geometry A. I. Bobenko P. Schr\u00f6der J. M. Sullivan and G. M. Ziegler Eds. Vol. \n  38\n   of \n  Oberwolfach Seminars\n  . \n  Birkh\u00e4user Verlag 287--324.  Desbrun M. Kanso E. and Tong Y. 2008. Discrete Differential Forms for Computational Modeling. In Discrete Differential Geometry A. I. Bobenko P. Schr\u00f6der J. M. Sullivan and G. M. Ziegler Eds. Vol. 38 of Oberwolfach Seminars . Birkh\u00e4user Verlag 287--324.","DOI":"10.1007\/978-3-7643-8621-4_16"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366167"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.58.7816"},{"key":"e_1_2_2_13_1","first-page":"12","article-title":"Manifestly Gauge Invariant Discretizations of the Schr\u00f6dinger","volume":"376","author":"Halvorsen T. G.","year":"2012","unstructured":"Halvorsen , T. G. , and Kvaal , S. 2012 . Manifestly Gauge Invariant Discretizations of the Schr\u00f6dinger Operator. Phys. Lett. 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