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The shrinking figure eight and other solitons for the curve diffusion flow

Journal Article


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Abstract


  • In this article we investigate the dynamics of special solutions to the surface diffusion

    flow of idealised ribbons. This reduces to studying the curve diffusion flow for the

    profile curve of the ribbon.We provide: (1) a complete classification of stationary solutions;

    (2) qualitative results on shrinkers, translators, and rotators; and (3) an explicit parametrisation

    of a shrinking figure eight curve.

Publication Date


  • 2015

Citation


  • Edwards, M., Gerhardt-Bourke, A., McCoy, J., Wheeler, G. & Wheeler, V. (2015). The shrinking figure eight and other solitons for the curve diffusion flow. Journal of Elasticity, 119 (1-2), 191-211.

Scopus Eid


  • 2-s2.0-84939880461

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=4272&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3256

Number Of Pages


  • 20

Start Page


  • 191

End Page


  • 211

Volume


  • 119

Issue


  • 1-2

Place Of Publication


  • Netherlands

Abstract


  • In this article we investigate the dynamics of special solutions to the surface diffusion

    flow of idealised ribbons. This reduces to studying the curve diffusion flow for the

    profile curve of the ribbon.We provide: (1) a complete classification of stationary solutions;

    (2) qualitative results on shrinkers, translators, and rotators; and (3) an explicit parametrisation

    of a shrinking figure eight curve.

Publication Date


  • 2015

Citation


  • Edwards, M., Gerhardt-Bourke, A., McCoy, J., Wheeler, G. & Wheeler, V. (2015). The shrinking figure eight and other solitons for the curve diffusion flow. Journal of Elasticity, 119 (1-2), 191-211.

Scopus Eid


  • 2-s2.0-84939880461

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=4272&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3256

Number Of Pages


  • 20

Start Page


  • 191

End Page


  • 211

Volume


  • 119

Issue


  • 1-2

Place Of Publication


  • Netherlands