A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area
Dallaston, Michael C. & McCue, Scott W. (2016) A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area. Proceedings of the Royal Society A, 472, Article Number:20150629.
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Abstract
Motivated by a problem from fluid mechanics, we consider a generalization of the standard curve shortening flow problem for a closed embedded plane curve such that the area enclosed by the curve is forced to decrease at a prescribed rate. Using formal asymptotic and numerical techniques, we derive possible extinction shapes as the curve contracts to a point, dependent on the rate of decreasing area; we find there is a wider class of extinction shapes than for standard curve shortening, for which initially simple closed curves are always asymptotically circular. We also provide numerical evidence that selfintersection is possible for nonconvex initial conditions, distinguishing between pinchoff and coalescence of the curve interior.
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ID Code:  93810 

Item Type:  Journal Article 
Refereed:  Yes 
Keywords:  curve shortening flow, geometric partial differential equation, extinction behaviour, pinchoff, coalescence, selfsimilar solutions, nonlocal geometric flows, curvature driven flow, HeleShaw flow 
DOI:  10.1098/rspa.2015.0629 
ISSN:  14712946 
Subjects:  Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Algebraic and Differential Geometry (010102) Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Approximation Theory and Asymptotic Methods (010201) 
Divisions:  Current > Schools > School of Mathematical Sciences Current > QUT Faculties and Divisions > Science & Engineering Faculty 
Funding: 

Copyright Owner:  2016 The Authors 
Copyright Statement:  Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/ by/4.0/, which permits unrestricted use, provided the original author and source are credited. 
Deposited On:  16 Mar 2016 00:13 
Last Modified:  17 Mar 2016 04:45 
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