Abstract
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 language | English |
|---|---|
| Pages (from-to) | 748-768 |
| Number of pages | 21 |
| Journal | Journal of Mathematical Chemistry |
| Volume | 45 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2009 Mar 1 |
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Keywords
- Fourth-order parabolic equations
- Geometric flows
- Kirchhoff elastic rods
- Writhe
ASJC Scopus subject areas
- Chemistry(all)
- Applied Mathematics
Cite this
Evolving a Kirchhoff elastic rod without self-intersections. / Lin, Chun-Chi; Schwetlick, Hartmut R.
In: Journal of Mathematical Chemistry, Vol. 45, No. 3, 01.03.2009, p. 748-768.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Evolving a Kirchhoff elastic rod without self-intersections
AU - Lin, Chun-Chi
AU - Schwetlick, Hartmut R.
PY - 2009/3/1
Y1 - 2009/3/1
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
UR - http://www.scopus.com/inward/citedby.url?scp=62949180282&partnerID=8YFLogxK
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 -