Tendril perversion

This article is about the geometric phenomenon. For the pornographic genre, see tentacle erotica.
A tendril of Bryonia dioica exhibiting tendril perversion
Cucurbita pepo exhibiting tendril perversion
A telephone handset cord exhibiting tendril perversion
GIF video showing two different types of tendril perversion

Tendril perversion is a geometric phenomenon sometimes observed in helical structures in which the direction of the helix transitions between left-handed and right-handed.[1] [2] Such a reversal of chirality is commonly seen in helical plant tendrils and telephone handset cords.[3]

The phenomenon was known to Charles Darwin,[4] who wrote in 1865,

A tendril ... invariably becomes twisted in one part in one direction, and in another part in the opposite direction ... This curious and symmetrical structure has been noticed by several botanists, but has not been sufficiently explained.[5]

The term "tendril perversion" was coined by Alain Goriely and Michael Tabor in 1998 based on the word perversion found in 19th-century science literature.[6][7] "Perversion" is a transition from one chirality to another and was known to James Clerk Maxwell, who attributed it to topologist J. B. Listing.[4][8]

Tendril perversion can be viewed as an example of spontaneous symmetry breaking, in which the strained structure of the tendril adopts a configuration of minimum energy while preserving zero overall twist.[2]

Tendril perversion has been studied both experimentally and theoretically. Gerbode et al. have made experimental studies of the coiling of cucumber tendrils.[9][10] A detailed study of a simple model of the physics of tendril perversion was made by McMillen and Goriely in the early 2000s.[2] Liu et al. showed in 2014 that "the transition from a helical to a hemihelical shape, as well as the number of perversions, depends on the height to width ratio of the strip's cross-section."[3]

Generalized tendril perversions were put forward by Silva et al., to include perversions that can be intrinsically produced in elastic filaments, leading to a multiplicity of geometries and dynamical properties.[11]

  1. ^ Goriely, Alain (2017). The mathematics and mechanics of biological growth. New York: Springer. ISBN 978-0-387-87709-9. OCLC 989037743.
  2. ^ a b c McMillen; Goriely (2002). "Tendril Perversion in Intrinsically Curved Rods". Journal of Nonlinear Science. 12 (3): 241. Bibcode:2002JNS....12..241M. CiteSeerX 10.1.1.140.352. doi:10.1007/s00332-002-0493-1. S2CID 18480860.
  3. ^ a b Liu, J.; Huang, J.; Su, T.; Bertoldi, K.; Clarke, D. R. (2014). "Structural Transition from Helices to Hemihelices". PLOS ONE. 9 (4): e93183. Bibcode:2014PLoSO...993183L. doi:10.1371/journal.pone.0093183. PMC 3997338. PMID 24759785.
  4. ^ a b Alain Goriely (2013). "Inversion, Rotation, and Perversion in Mechanical Biology: From Microscopic Anisotropy to Macroscopic Chirality" (PDF). p. 9.
  5. ^ Charles Darwin, "On the movements and habits of climbing plants", Journal of the Linnean Society, 1865.
  6. ^ Goriely, Alain; Tabor, Michael (1998-02-16). "Spontaneous Helix Hand Reversal and Tendril Perversion in Climbing Plants". Physical Review Letters. 80 (7). American Physical Society (APS): 1564–1567. Bibcode:1998PhRvL..80.1564G. doi:10.1103/physrevlett.80.1564. ISSN 0031-9007.
  7. ^ McMillen; Goriely (2002). "Tendril Perversion in Intrinsically Curved Rods". Journal of Nonlinear Science. 12 (3): 241. Bibcode:2002JNS....12..241M. CiteSeerX 10.1.1.140.352. doi:10.1007/s00332-002-0493-1. S2CID 18480860.
  8. ^ James Clerk Maxwell (1873). A Treatise of Electricity and Magnetism. Oxford: Clarendon Press. The operation of passing from one system to the other is called by Listing, Perversion. The reflection of an object in a mirror image is a perverted image of the object.
  9. ^ Gerbode, S. J.; Puzey, J. R.; McCormick, A. G.; Mahadevan, L. (2012). "How the Cucumber Tendril Coils and Overwinds". Science. 337 (6098): 1087–91. Bibcode:2012Sci...337.1087G. doi:10.1126/science.1223304. PMID 22936777. S2CID 17405225.
  10. ^ Geraint Jones (30 August 2012). "Scientists unwind the secrets of climbing plants' tendrils". The Guardian.
  11. ^ Silva, Pedro E. S.; Trigueiros, Joao L.; Trindade, Ana C.; Simoes, Ricardo; Dias, Ricardo G.; Godinho, Maria Helena; Abreu, Fernao Vistulo de (2016-03-30). "Perversions with a twist". Scientific Reports. 6: 23413. Bibcode:2016NatSR...623413S. doi:10.1038/srep23413. PMC 4812244. PMID 27025549.