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
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U2 - 10.1007/s10910-008-9383-6
DO - 10.1007/s10910-008-9383-6
M3 - Article
AN - SCOPUS:62949180282
VL - 45
SP - 748
EP - 768
JO - Journal of Mathematical Chemistry
JF - Journal of Mathematical Chemistry
SN - 0259-9791
IS - 3
ER -