Ribbon crystals.

Ribbon crystals.

A repetitive crystal-like pattern is spontaneously formed upon the twisting of straight ribbons. The pattern is akin to a tessellation with isosceles triangles, and it can easily be demonstrated with ribbons cut from an overhead transparency. We give a general description of developable ribbons usin...

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Autores principales: Jakob Bohr, Steen Markvorsen
Formato: article
Lenguaje:EN
Publicado: Public Library of Science (PLoS) 2013
Materias:
Medicine
R
Science
Q
Acceso en línea:https://doaj.org/article/325711421c57465bbbab6553555828f0
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spelling oai:doaj.org-article:325711421c57465bbbab6553555828f02021-11-18T08:52:36ZRibbon crystals.1932-620310.1371/journal.pone.0074932https://doaj.org/article/325711421c57465bbbab6553555828f02013-01-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/pmid/24098360/pdf/?tool=EBIhttps://doaj.org/toc/1932-6203A repetitive crystal-like pattern is spontaneously formed upon the twisting of straight ribbons. The pattern is akin to a tessellation with isosceles triangles, and it can easily be demonstrated with ribbons cut from an overhead transparency. We give a general description of developable ribbons using a ruled procedure where ribbons are uniquely described by two generating functions. This construction defines a differentiable frame, the ribbon frame, which does not have singular points, whereby we avoid the shortcomings of the Frenet-Serret frame. The observed spontaneous pattern is modeled using planar triangles and cylindrical arcs, and the ribbon structure is shown to arise from a maximization of the end-to-end length of the ribbon, i.e. from an optimal use of ribbon length. The phenomenon is discussed in the perspectives of incompatible intrinsic geometries and of the emergence of long-range order.Jakob BohrSteen MarkvorsenPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 8, Iss 10, p e74932 (2013)
institution DOAJ
collection DOAJ
language EN
topic Medicine
R
Science
Q
spellingShingle Medicine
R
Science
Q
Jakob Bohr
Steen Markvorsen
Ribbon crystals.
description A repetitive crystal-like pattern is spontaneously formed upon the twisting of straight ribbons. The pattern is akin to a tessellation with isosceles triangles, and it can easily be demonstrated with ribbons cut from an overhead transparency. We give a general description of developable ribbons using a ruled procedure where ribbons are uniquely described by two generating functions. This construction defines a differentiable frame, the ribbon frame, which does not have singular points, whereby we avoid the shortcomings of the Frenet-Serret frame. The observed spontaneous pattern is modeled using planar triangles and cylindrical arcs, and the ribbon structure is shown to arise from a maximization of the end-to-end length of the ribbon, i.e. from an optimal use of ribbon length. The phenomenon is discussed in the perspectives of incompatible intrinsic geometries and of the emergence of long-range order.
format article
author Jakob Bohr
Steen Markvorsen
author_facet Jakob Bohr
Steen Markvorsen
author_sort Jakob Bohr
title Ribbon crystals.
title_short Ribbon crystals.
title_full Ribbon crystals.
title_fullStr Ribbon crystals.
title_full_unstemmed Ribbon crystals.
title_sort ribbon crystals.
publisher Public Library of Science (PLoS)
publishDate 2013
url https://doaj.org/article/325711421c57465bbbab6553555828f0
work_keys_str_mv AT jakobbohr ribboncrystals
AT steenmarkvorsen ribboncrystals
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