Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The winding of a relaxed elastic line on a cylinder

Author: Gerald S. Manning
Journal: Quart. Appl. Math. 45 (1987), 809-815
MSC: Primary 53A04
DOI: https://doi.org/10.1090/qam/917029
MathSciNet review: 917029
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Abstract: We analyze several cases of the boundary-value problem that determines the path of a relaxed elastic line on a cylinder. A short line with oblique initial tangent deviates from the corresponding helix toward the direction of the axis of the cylinder. A line initially directed along the base circle continues to wind circumferentially if the ratio of its length to the radius of the cylinder does not exceed the critical value $ \pi /{2^{3/2}}$; longer lines deviate from the circle. Infinitely long elastic lines wind in proportion to the logarithm of their arc lengths, as distinct from the direct proportion of a helix. Possible implications for biological structures are discussed.

References [Enhancements On Off] (What's this?)

  • [1] G. S. Manning, Relaxed elastic line on a curved surface, Quart. Appl. Math. 45, 515-527 (1987) MR 910458
  • [2] H. K. Nickerson and G. S. Manning, Intrinsic equations for a relaxed elastic line on an oriented surface, Geom. Dedicat., in press MR 957595
  • [3] J. Darnell, H. Lodish, and D. Baltimore, Molecular cell biology, Scientific American Books, New York, 1986
  • [4] G. S. Manning, Polymer persistence length characterized as a critical length for instability caused by a fluctuating twist, Phys. Rev. A 34, 668-670 (1986)

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DOI: https://doi.org/10.1090/qam/917029
Article copyright: © Copyright 1987 American Mathematical Society

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