TY - JOUR
T1 - Evolving a Kirchhoff elastic rod without self-intersections
AU - Lin, C C
AU - Schwetlick, Hartmut R
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 - Writhe
KW - Geometric flows
KW - Kirchhoff elastic
KW - rods
KW - Fourth-order parabolic equations
UR - http://www.scopus.com/inward/record.url?scp=62949180282&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1007/s10910-008-9383-6
U2 - 10.1007/s10910-008-9383-6
DO - 10.1007/s10910-008-9383-6
M3 - Article
SN - 0259-9791
VL - 45
SP - 748
EP - 768
JO - Journal of Mathematical Chemistry
JF - Journal of Mathematical Chemistry
IS - 3
ER -