{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T02:22:54Z","timestamp":1776306174221,"version":"3.50.1"},"reference-count":55,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T00:00:00Z","timestamp":1562889600000},"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":[[2019,8,31]]},"abstract":"<jats:p>We introduce variable thickness, viscous vortex filaments. These can model such varied phenomena as underwater bubble rings or the intricate \"chandeliers\" formed by ink dropping into fluid. Treating the evolution of such filaments as an instance of Newtonian dynamics on a Riemannian configuration manifold we are able to extend classical work in the dynamics of vortex filaments through inclusion of viscous drag forces. The latter must be accounted for in low Reynolds number flows where they lead to significant variations in filament thickness and form an essential part of the observed dynamics. We develop and document both the underlying theory and associated practical numerical algorithms.<\/jats:p>","DOI":"10.1145\/3306346.3322962","type":"journal-article","created":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T19:04:08Z","timestamp":1562958248000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":27,"title":["On bubble rings and ink chandeliers"],"prefix":"10.1145","volume":"38","author":[{"given":"Marcel","family":"Padilla","sequence":"first","affiliation":[{"name":"TU Berlin"}]},{"given":"Albert","family":"Chern","sequence":"additional","affiliation":[{"name":"TU Berlin"}]},{"given":"Felix","family":"Kn\u00f6ppel","sequence":"additional","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":[[2019,7,12]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073368.1073380"},{"key":"e_1_2_2_2_1","volume-title":"Khesin","author":"Arnold Vladimir I.","year":"1998","unstructured":"Vladimir I. Arnold and Boris A . Khesin . 1998 . Topological Methods in Hydrodynamics. Springer . Vladimir I. Arnold and Boris A. Khesin. 1998. Topological Methods in Hydrodynamics. Springer."},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0493(1915)43<163:SRROTM>2.0.CO;2"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778853"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0604159103"},{"key":"e_1_2_2_6_1","volume-title":"Vortex Filament Simulation of the Turbulent Coflowing Jet. Phys. Fluids 21, 2","author":"Bernard Peter S.","year":"2009","unstructured":"Peter S. Bernard . 2009. Vortex Filament Simulation of the Turbulent Coflowing Jet. Phys. Fluids 21, 2 ( 2009 ). Peter S. Bernard. 2009. Vortex Filament Simulation of the Turbulent Coflowing Jet. Phys. Fluids 21, 2 (2009)."},{"key":"e_1_2_2_7_1","unstructured":"Danielis Bernoulli. 1738. Hydrodynamica sive de viribus et motibus fluidorum commentarii. Argentorati. For a modern account see also {Grattan-Guinness 2005} and {Darrigol and Frisch 2008}. Danielis Bernoulli. 1738. Hydrodynamica sive de viribus et motibus fluidorum commentarii. Argentorati. For a modern account see also {Grattan-Guinness 2005} and {Darrigol and Frisch 2008}."},{"key":"e_1_2_2_8_1","first-page":"222","article-title":"Note sur le Magn\u00e9tisme de la pile de Volta","volume":"15","author":"Biot Jean-Baptiste","year":"1820","unstructured":"Jean-Baptiste Biot and Nicolas- Pierre-Antoine Savart . 1820 . Note sur le Magn\u00e9tisme de la pile de Volta . Annal. Chimie et Phys. 15 (1820), 222 -- 223 . Jean-Baptiste Biot and Nicolas-Pierre-Antoine Savart. 1820. Note sur le Magn\u00e9tisme de la pile de Volta. Annal. Chimie et Phys. 15 (1820), 222--223.","journal-title":"Annal. Chimie et Phys."},{"key":"e_1_2_2_9_1","volume-title":"Proc. Symp. Comp. Anim. Eurographics Assoc., 87--95","author":"Brochu Tyson","year":"2012","unstructured":"Tyson Brochu , Todd Keeler , and Robert Bridson . 2012 . Linear-Time Smoke Animation with Vortex Sheet Meshes . In Proc. Symp. Comp. Anim. Eurographics Assoc., 87--95 . Tyson Brochu, Todd Keeler, and Robert Bridson. 2012. Linear-Time Smoke Animation with Vortex Sheet Meshes. In Proc. Symp. Comp. Anim. Eurographics Assoc., 87--95."},{"key":"e_1_2_2_10_1","first-page":"171","article-title":"A Mathematical Model Illustrating the Theory of","volume":"1","author":"Burgers J. M.","year":"1948","unstructured":"J. M. Burgers . 1948 . A Mathematical Model Illustrating the Theory of Turbulence. Adv. Appl. Math. 1 (1948), 171 -- 199 . J. M. Burgers. 1948. A Mathematical Model Illustrating the Theory of Turbulence. Adv. Appl. Math. 1 (1948), 171--199.","journal-title":"Turbulence. Adv. Appl. Math."},{"key":"e_1_2_2_11_1","volume-title":"Oeuvres Compl\u00e8tes d'Augustin Cauchy.","author":"Cauchy Augustin-Louis","year":"1815","unstructured":"Augustin-Louis Cauchy . 1815. Th\u00e9orie de la Propagation des Ondes a la Surface d'un Fluide Pesant d'une Profondeur Ind\u00e9finie . In Oeuvres Compl\u00e8tes d'Augustin Cauchy. Vol. 1 . Imprimerie Royale. Presented to the French Academy in 1815 (publ. 1827). Augustin-Louis Cauchy. 1815. Th\u00e9orie de la Propagation des Ondes a la Surface d'un Fluide Pesant d'une Profondeur Ind\u00e9finie. In Oeuvres Compl\u00e8tes d'Augustin Cauchy. Vol. 1. Imprimerie Royale. Presented to the French Academy in 1815 (publ. 1827)."},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1017\/jfm.2018.795"},{"key":"e_1_2_2_13_1","doi-asserted-by":"crossref","unstructured":"M. Cheng J. Lou and T. T. Lim. 2013. Motion of a Bubble Ring in a Viscous Fluid. Phys. Fluids 25 6 (2013) 067104:1--19. M. Cheng J. Lou and T. T. Lim. 2013. Motion of a Bubble Ring in a Viscous Fluid. Phys. Fluids 25 6 (2013) 067104:1--19.","DOI":"10.1063\/1.4811407"},{"key":"e_1_2_2_14_1","doi-asserted-by":"crossref","unstructured":"Stephen Childress. 2009. An Introduction to Theoretical Fluid Dynamics. AMS. Stephen Childress. 2009. An Introduction to Theoretical Fluid Dynamics. AMS.","DOI":"10.1090\/cln\/019"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(90)90001-H"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1993.1120"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/2767003"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925899"},{"key":"e_1_2_2_19_1","first-page":"14","article-title":"From Newton's Mechanics to Euler's Equations. Phy","volume":"237","author":"Darrigol O.","year":"2008","unstructured":"O. Darrigol and U. Frisch . 2008 . From Newton's Mechanics to Euler's Equations. Phy . D: Nonl. Phenom. 237 , 14 -- 17 (2008), 1855--1869. O. Darrigol and U. Frisch. 2008. From Newton's Mechanics to Euler's Equations. Phy. D: Nonl. Phenom. 237, 14--17 (2008), 1855--1869.","journal-title":"D: Nonl. Phenom."},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1140\/epjh\/e2014-50016-6"},{"key":"e_1_2_2_21_1","doi-asserted-by":"crossref","unstructured":"Sylvestre Gallot Dominique Hulin and Jacques Lafontaine. 2004. Riemannian Geometry (3<sup>rd<\/sup> ed.). Springer. Sylvestre Gallot Dominique Hulin and Jacques Lafontaine. 2004. Riemannian Geometry (3<sup>rd<\/sup> ed.). Springer.","DOI":"10.1007\/978-3-642-18855-8"},{"issue":"89","key":"e_1_2_2_22_1","first-page":"271","article-title":"A Difference Method for Numerical Calculation of Discontinuous Solutions of the Equations of Hydrodynamics","volume":"47","author":"Godunov S. K.","year":"1959","unstructured":"S. K. Godunov . 1959 . A Difference Method for Numerical Calculation of Discontinuous Solutions of the Equations of Hydrodynamics . Mat. Sb. (N.S.) 47 ( 89 ), 3 (1959), 271 -- 306 . S. K. Godunov. 1959. A Difference Method for Numerical Calculation of Discontinuous Solutions of the Equations of Hydrodynamics. Mat. Sb. (N.S.) 47(89), 3 (1959), 271--306.","journal-title":"Mat. Sb. (N.S.)"},{"key":"e_1_2_2_23_1","doi-asserted-by":"crossref","unstructured":"Ivor Grattan-Guinness (Ed.). 2005. Landmark Writings in Western Mathematics 1640--1940. Elsevier Chapter Daniel Bernoulli: Hydrodynamica (G. K. Mikhailov) 131--142. Ivor Grattan-Guinness (Ed.). 2005. Landmark Writings in Western Mathematics 1640--1940. Elsevier Chapter Daniel Bernoulli: Hydrodynamica (G. K. Mikhailov) 131--142.","DOI":"10.1016\/B978-044450871-3\/50090-5"},{"key":"e_1_2_2_24_1","volume-title":"Syvert Paul N\u00f8rsett, and Gerhard Wanner","author":"Hairer Ernst","year":"1993","unstructured":"Ernst Hairer , Syvert Paul N\u00f8rsett, and Gerhard Wanner . 1993 . Solving Ordinary Differential Equations I: Nonstiff Problems ( 2 nd ed.). Springer . Ernst Hairer, Syvert Paul N\u00f8rsett, and Gerhard Wanner. 1993. Solving Ordinary Differential Equations I: Nonstiff Problems (2nd ed.). Springer.","edition":"2"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2018.09.015"},{"key":"e_1_2_2_26_1","volume-title":"Zum Unit\u00e4tsproblem der Physik. Sitzungsber. Preuss. Akad. Wiss. Berlin","author":"Kaluza Theodor","year":"1921","unstructured":"Theodor Kaluza . 1921. Zum Unit\u00e4tsproblem der Physik. Sitzungsber. Preuss. Akad. Wiss. Berlin ( 1921 ), 966--972. English translation in Theodor Kaluza. 1921. Zum Unit\u00e4tsproblem der Physik. Sitzungsber. Preuss. Akad. Wiss. Berlin (1921), 966--972. English translation in"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01397481"},{"key":"e_1_2_2_28_1","volume-title":"Powers","author":"Lauga Eric","year":"2009","unstructured":"Eric Lauga and Thomas R . Powers . 2009 . The Hydrodynamics of Swimming Microorganisms. Rep. Prog. Phys . 72 (2009), 096601:1--36. Eric Lauga and Thomas R. Powers. 2009. The Hydrodynamics of Swimming Microorganisms. Rep. Prog. Phys. 72 (2009), 096601:1--36."},{"key":"e_1_2_2_29_1","doi-asserted-by":"crossref","unstructured":"Randall J. LeVeque. 2002. Finite-Volume Methods for Hyperbolic Problems. Cam. U. P. Randall J. LeVeque. 2002. Finite-Volume Methods for Hyperbolic Problems. Cam. U. P.","DOI":"10.1017\/CBO9780511791253"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2017.2665551"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112089000662"},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112088003076"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112091001702"},{"key":"e_1_2_2_35_1","first-page":"1","article-title":"Coadjoint Orbits","volume":"7","author":"Marsden Jerrold","year":"1983","unstructured":"Jerrold Marsden and Alan Weinstein . 1983 . Coadjoint Orbits , Vortices and Clebsch Variables for Incompressible Fluids. Phy. D: Nonl. Phenom. 7 , 1 -- 3 (1983), 305--323. Jerrold Marsden and Alan Weinstein. 1983. Coadjoint Orbits, Vortices and Clebsch Variables for Incompressible Fluids. Phy. D: Nonl. Phenom. 7, 1--3 (1983), 305--323.","journal-title":"Vortices and Clebsch Variables for Incompressible Fluids. Phy. D: Nonl. Phenom."},{"key":"e_1_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1017\/S002211209100304X"},{"key":"e_1_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10958-012-1100-0"},{"key":"e_1_2_2_38_1","volume-title":"The Motion of a Vortex Filament with Axial Flow. Phil. Tr. R. Soc. Lond. A 272, 1226","author":"Moore Derek William","year":"1972","unstructured":"Derek William Moore and Philip Geoffrey Saffman . 1972. The Motion of a Vortex Filament with Axial Flow. Phil. Tr. R. Soc. Lond. A 272, 1226 ( 1972 ), 403--429. Derek William Moore and Philip Geoffrey Saffman. 1972. The Motion of a Vortex Filament with Axial Flow. Phil. Tr. R. Soc. Lond. A 272, 1226 (1972), 403--429."},{"key":"e_1_2_2_39_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112068000601"},{"key":"e_1_2_2_40_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185608"},{"key":"e_1_2_2_41_1","first-page":"431","article-title":"Visual Simulation of Multiple Fluids in Computer Graphics","volume":"33","author":"Ren Bo","year":"2018","unstructured":"Bo Ren , Xu-Yun Yang , Ming C. Lin , Nils Thuerey , Matthias Teschner , and Chenfeng Li . 2018 . Visual Simulation of Multiple Fluids in Computer Graphics : A State-of-the-Art Report. J. Comp. Sc. Tech. 33 , 3 (2018), 431 -- 451 . Bo Ren, Xu-Yun Yang, Ming C. Lin, Nils Thuerey, Matthias Teschner, and Chenfeng Li. 2018. Visual Simulation of Multiple Fluids in Computer Graphics: A State-of-the-Art Report. J. Comp. Sc. Tech. 33, 3 (2018), 431--451.","journal-title":"A State-of-the-Art Report. J. Comp. Sc. Tech."},{"key":"e_1_2_2_42_1","first-page":"246","article-title":"On the Formation of Rotating Rings by Air and Liquids under certain Conditions of","volume":"26","author":"Rogers William B.","year":"1858","unstructured":"William B. Rogers . 1858 . On the Formation of Rotating Rings by Air and Liquids under certain Conditions of Discharge. Am. J. Sc. A. 26 , 77 (1858), 246 -- 258 . William B. Rogers. 1858. On the Formation of Rotating Rings by Air and Liquids under certain Conditions of Discharge. Am. J. Sc. A. 26, 77 (1858), 246--258.","journal-title":"Discharge. Am. J. Sc. A."},{"key":"e_1_2_2_43_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1930.0078"},{"key":"e_1_2_2_44_1","doi-asserted-by":"crossref","unstructured":"P. G. Saffman. 1992. Vortex Dynamics. Cam. U. P. P. G. Saffman. 1992. Vortex Dynamics. Cam. U. P.","DOI":"10.1017\/CBO9780511624063"},{"key":"e_1_2_2_45_1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.fl.24.010192.001315"},{"key":"e_1_2_2_46_1","volume-title":"Breakup and Deformation of a Droplet Falling in a Miscible Solution. Phys. R. E 93, 6","author":"Shimokawa Michiko","year":"2016","unstructured":"Michiko Shimokawa , Ryosei Mayumi , Taiki Nakamura , Toshiya Takami , and Hidetsugu Sakaguchi . 2016. Breakup and Deformation of a Droplet Falling in a Miscible Solution. Phys. R. E 93, 6 ( 2016 ), 062214:1--9. Michiko Shimokawa, Ryosei Mayumi, Taiki Nakamura, Toshiya Takami, and Hidetsugu Sakaguchi. 2016. Breakup and Deformation of a Droplet Falling in a Miscible Solution. Phys. R. E 93, 6 (2016), 062214:1--9."},{"key":"e_1_2_2_47_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2008.05.022"},{"key":"e_1_2_2_48_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1721114"},{"key":"e_1_2_2_49_1","volume-title":"A Treatise on the Motion of Vortex Rings","author":"Thomson J. J.","unstructured":"J. J. Thomson . 1883. A Treatise on the Motion of Vortex Rings . Macmillan , London . J. J. Thomson. 1883. A Treatise on the Motion of Vortex Rings. Macmillan, London."},{"key":"e_1_2_2_50_1","first-page":"239","article-title":"On the Formation of Vortex Rings by Drops falling into Liquids, and some allied Phenomena","volume":"39","author":"Thomson J. J.","year":"1886","unstructured":"J. J. Thomson and H. F. Newall . 1886 . On the Formation of Vortex Rings by Drops falling into Liquids, and some allied Phenomena . Proc. R. Soc. Lond. 39 , 239 -- 241 (1886), 417--436. J. J. Thomson and H. F. Newall. 1886. On the Formation of Vortex Rings by Drops falling into Liquids, and some allied Phenomena. Proc. R. Soc. Lond. 39, 239--241 (1886), 417--436.","journal-title":"Proc. R. Soc. Lond."},{"key":"e_1_2_2_51_1","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1080\/14786446408643694","article-title":"LXV. On a New Vareity of the Cohesion-Figures of Liquids","volume":"27","author":"Tomlinson Charles","year":"1864","unstructured":"Charles Tomlinson . 1864 . LXV. On a New Vareity of the Cohesion-Figures of Liquids . Lon. Edin. Dub. Phil. M. J. Sc. 27 , 184 (1864), 425 -- 432 . Charles Tomlinson. 1864. LXV. On a New Vareity of the Cohesion-Figures of Liquids. Lon. Edin. Dub. Phil. M. J. Sc. 27, 184 (1864), 425--432.","journal-title":"Lon. Edin. Dub. Phil. M. J. Sc."},{"key":"e_1_2_2_52_1","volume-title":"Proc. R. Soc. Lond. A 239","author":"Turner J. S.","year":"1957","unstructured":"J. S. Turner . 1957 . Buoyant Vortex Rings . Proc. R. Soc. Lond. A 239 , 1216 (1957), 61--75. J. S. Turner. 1957. Buoyant Vortex Rings. Proc. R. Soc. Lond. A 239, 1216 (1957), 61--75."},{"key":"e_1_2_2_53_1","doi-asserted-by":"publisher","DOI":"10.1515\/crll.1858.55.25"},{"key":"e_1_2_2_54_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778852"},{"key":"e_1_2_2_55_1","volume-title":"Linear and Nonlinear Waves","author":"Whitham G. B.","unstructured":"G. B. Whitham . 1974. Linear and Nonlinear Waves . Wiley . G. B. Whitham. 1974. Linear and Nonlinear Waves. Wiley."},{"key":"e_1_2_2_56_1","doi-asserted-by":"publisher","DOI":"10.1017\/S002211207100260X"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3306346.3322962","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3306346.3322962","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T00:25:44Z","timestamp":1750206344000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3306346.3322962"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,12]]},"references-count":55,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,8,31]]}},"alternative-id":["10.1145\/3306346.3322962"],"URL":"https:\/\/doi.org\/10.1145\/3306346.3322962","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,12]]},"assertion":[{"value":"2019-07-12","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}