TY - JOUR
T1 - Differential geometry of polymer models
T2 - Worm-like chains, ribbons and Fourier knots
AU - Rappaport, S. M.
AU - Rabin, Y.
PY - 2007/4/27
Y1 - 2007/4/27
N2 - We analyse several continuum models of polymers: worm-like chains, ribbons and Fourier knots. We show that the torsion of worm-like chains diverges and conclude that such chains cannot be described by the Frenet - Serret (FS) equation of space curves. While the same holds for ribbons as well, their rate of twist is finite and, therefore, they can be described by the generalized FS equation of stripes. Finally, Fourier knots have finite curvature and torsion and, therefore, are sufficiently smooth to be described by the FS equation of space curves.
AB - We analyse several continuum models of polymers: worm-like chains, ribbons and Fourier knots. We show that the torsion of worm-like chains diverges and conclude that such chains cannot be described by the Frenet - Serret (FS) equation of space curves. While the same holds for ribbons as well, their rate of twist is finite and, therefore, they can be described by the generalized FS equation of stripes. Finally, Fourier knots have finite curvature and torsion and, therefore, are sufficiently smooth to be described by the FS equation of space curves.
UR - http://www.scopus.com/inward/record.url?scp=34548484163&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/40/17/003
DO - 10.1088/1751-8113/40/17/003
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AN - SCOPUS:34548484163
SN - 1751-8113
VL - 40
SP - 4455
EP - 4466
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 17
ER -