Differential Geometry of Polymer Models: Worm-like Chains, Ribbons and Fourier Knots Export

@article{citeulike:6060782, abstract = {We analyze 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 can not 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.}, archivePrefix = {arXiv}, author = {Rappaport, Shay M. and Rabin, Yitzhak}, citeulike-article-id = {6060782}, citeulike-linkout-0 = {http://arxiv.org/abs/cond-mat/0702203}, citeulike-linkout-1 = {http://arxiv.org/pdf/cond-mat/0702203}, day = {8}, eprint = {cond-mat/0702203}, keywords = {wlc}, month = {Feb}, posted-at = {2009-11-03 17:22:02}, priority = {2}, title = {Differential Geometry of Polymer Models: Worm-like Chains, Ribbons and Fourier Knots}, url = {http://arxiv.org/abs/cond-mat/0702203}, year = {2007} }

TY - JOUR ID - citeulike:6060782 L3 - citeulike-article-id:6060782 N2 - We analyze 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 can not 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. TI - Differential Geometry of Polymer Models: Worm-like Chains, Ribbons and Fourier Knots KW - wlc AU - Rappaport, Shay AU - Rabin, Yitzhak PY - 2007/Feb/08/ UR - http://arxiv.org/abs/cond-mat/0702203 ER -