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Title:Vortex crystals
Author(s):Aref, Hassan; Newton, Paul K.; Stremler, Mark A.; Tokieda, Tadashi; Vainchtein, Dmitri L.
Subject(s):Vortex crystals
Abstract:Vortex crystals is one name in use for the subject of vortex patterns that move without change of shape or size. Most of what is known pertains to the case of arrays of parallel line vortices moving so as to produce an essentially two-dimensional flow. The possible patterns of points indicating the intersections of these vortices with a plane perpendicular to them have been studied for almost 150 years. Analog experiments have been devised, and experiments with vortices in a variety of fluids have been performed. Some of the states observed are understood analytically. Others have been found computationally to high precision. Our degree of understanding of these patterns varies considerably. Surprising connections to the zeros of 'special functions' arising in classical mathematical physics have been revealed. Vortex motion on two-dimensional manifolds, such as the sphere, the cylinder (periodic strip) and torus (periodic parallelogram) has also been studied, because of the potential applications, and some results are available regarding the problem of vortex crystals in such geometries. Although a large amount of material is available for review, some results are reported here for the first time. The subject seems pregnant with possibilities for further development.
Issue Date:2002-10
Publisher:Department of Theoretical and Applied Mechanics (UIUC)
Series/Report:TAM Reports 1008
Genre:Technical Report
Publication Status:published or submitted for publication
Peer Reviewed:is peer reviewed
Date Available in IDEALS:2007-03-08
Is Version Of:Published as: Hassan Aref, Paul K. Newton, Mark A. Stremler, Tadashi Tokieda, and Dmitri L. Vainchtein. Vortex crystals. Advances in Applied Mechanics, vol. 39: 1-79 (2003). Copyright 2003 Elsevier.

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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.

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