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.
- Gerald S. Manning, Relaxed elastic line on a curved surface, Quart. Appl. Math. 45 (1987), no. 3, 515–527. MR 910458, DOI https://doi.org/10.1090/S0033-569X-1987-0910458-8
- H. K. Nickerson and Gerald S. Manning, Intrinsic equations for a relaxed elastic line on an oriented surface, Geom. Dedicata 27 (1988), no. 2, 127–136. MR 957595, DOI https://doi.org/10.1007/BF00151344
J. Darnell, H. Lodish, and D. Baltimore, Molecular cell biology, Scientific American Books, New York, 1986
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)
G. S. Manning, Relaxed elastic line on a curved surface, Quart. Appl. Math. 45, 515–527 (1987)
H. K. Nickerson and G. S. Manning, Intrinsic equations for a relaxed elastic line on an oriented surface, Geom. Dedicat., in press
J. Darnell, H. Lodish, and D. Baltimore, Molecular cell biology, Scientific American Books, New York, 1986
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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Article copyright:
© Copyright 1987
American Mathematical Society