Evolving a Kirchhoff elastic rod without self-intersections

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In this paper we study the problem on how to find an equilibrium state of a Kirchhoff elastic rod by evolving it in a certain way, called a geometric flow. The elastic energy of rods would decrease during the geometric flow. We show that rods remain smooth during the geometric flow as long as they stay embedded, e.g., self-penetrations do no occur. Furthermore, rods would approach an equilibrium configuration asymptotically if self-penetrations are avoided during the flow.
Original languageEnglish
Pages (from-to)748-768
Number of pages21
JournalJournal of Mathematical Chemistry
Issue number3
Publication statusPublished - Mar 2009


  • Writhe
  • Geometric flows
  • Kirchhoff elastic
  • rods
  • Fourth-order parabolic equations


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