Skip to main content
placeholder image

The mechanics of ribbons and möbius bands

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. M. (2016). The mechanics of ribbons and möbius bands. In The Mechanics of Ribbons and Möbius Bands (pp. 191-212). doi:10.1007/978-94-017-7300-3

International Standard Book Number (isbn) 13


  • 9789401772990

Scopus Eid


  • 2-s2.0-84943312032

Web Of Science Accession Number


Book Title


  • The Mechanics of Ribbons and Möbius Bands

Start Page


  • 191

End Page


  • 212

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. M. (2016). The mechanics of ribbons and möbius bands. In The Mechanics of Ribbons and Möbius Bands (pp. 191-212). doi:10.1007/978-94-017-7300-3

International Standard Book Number (isbn) 13


  • 9789401772990

Scopus Eid


  • 2-s2.0-84943312032

Web Of Science Accession Number


Book Title


  • The Mechanics of Ribbons and Möbius Bands

Start Page


  • 191

End Page


  • 212