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

Chapter


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


  • 2016

Citation


  • Edwards, M., Gerhardt-Bourke, A., McCoy, J., Wheeler, G. & Wheeler, V. (2016). The shrinking figure eight and other solitons for the curve diffusion flow. In R. Fosdick & E. Fried (Eds.), The Mechanics of Ribbons and Möbius Bands (pp. 191-211). Switzerland: Springer Netherlands.

Book Title


  • The Mechanics of Ribbons and Möbius Bands

Start Page


  • 191

End Page


  • 211

Place Of Publication


  • Switzerland

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


  • 2016

Citation


  • Edwards, M., Gerhardt-Bourke, A., McCoy, J., Wheeler, G. & Wheeler, V. (2016). The shrinking figure eight and other solitons for the curve diffusion flow. In R. Fosdick & E. Fried (Eds.), The Mechanics of Ribbons and Möbius Bands (pp. 191-211). Switzerland: Springer Netherlands.

Book Title


  • The Mechanics of Ribbons and Möbius Bands

Start Page


  • 191

End Page


  • 211

Place Of Publication


  • Switzerland