### 摘要

Recently, rod theory has been applied to the mathematical modeling of bacterial fibers and biopolymers (e.g., DNA) to study their mechanical properties and shapes (e.g., supercoiling). In static rod theory, an elastic rod in equilibrium is the critical point of an elastic energy. This induces a natural question of how to find elasticae. In this paper, we focus on how to find the critical points by means of gradient flows. We relate a geometric function of curves to the Isotropic Kirchhoff elastic energy of rods so that the generalized elastic curves are the centerlines of elastic rods in equilibrium. Thus, the variational problem for rods is formulated in curve geometry. This problem turns out to be a generalization of curve-straightening flows, which induce nonlinear fourth-order evolution equations. We establish the long time existence of length-preserving gradient flow for the geometric energy. Furthermore, by studying the asymptotic behavior, we show that the limit curves are the centerlines of the Kirchhoff elastic rods in equilibrium.

原文 | 英語 |
---|---|

頁（從 - 到） | 720-736 |

頁數 | 17 |

期刊 | SIAM Journal on Applied Mathematics |

卷 | 65 |

發行號 | 2 |

DOIs | |

出版狀態 | 已發佈 - 2005 六月 13 |

### ASJC Scopus subject areas

- Applied Mathematics

## 指紋 深入研究「On the geometric flow of kirchhoff elastic rods」主題。共同形成了獨特的指紋。

## 引用此

*SIAM Journal on Applied Mathematics*,

*65*(2), 720-736. https://doi.org/10.1137/S0036139903431713