TY - JOUR

T1 - Evolving a Kirchhoff elastic rod without self-intersections

AU - Lin, Chun Chi

AU - Schwetlick, Hartmut R.

N1 - Funding Information:
Acknowledgements This work was partially supported by the Taiwan National Science Council Grant 95-2115-M-003-002. We also thank Prof. Tsung-Min Hwang at Department of Mathematics in National Taiwan Normal University for his help with the Matlab codes in the numerical experiment.

PY - 2009/3

Y1 - 2009/3

N2 - 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.

AB - 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.

KW - Fourth-order parabolic equations

KW - Geometric flows

KW - Kirchhoff elastic rods

KW - Writhe

UR - http://www.scopus.com/inward/record.url?scp=62949180282&partnerID=8YFLogxK

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U2 - 10.1007/s10910-008-9383-6

DO - 10.1007/s10910-008-9383-6

M3 - Article

AN - SCOPUS:62949180282

SN - 0259-9791

VL - 45

SP - 748

EP - 768

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

IS - 3

ER -