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Colloquium: Geometry and optimal packing of twisted columns and filaments

Gregory M. Grason

Gregory M. Grason

  • Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA

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Rev. Mod. Phys. 87, 401 – Published 14 May, 2015

DOI: https://doi.org/10.1103/RevModPhys.87.401

Abstract

This Colloquium presents recent progress in understanding constraints and consequences of close-packing geometry of filamentous or columnar materials possessing nontrivial textures, focusing, in particular, on the common motifs of twisted and toroidal structures. The mathematical framework is presented that relates spacing between linelike, filamentous elements to their backbone orientations, highlighting the explicit connection between the interfilament metric properties and the geometry of non-Euclidean surfaces. The consequences of the hidden connection between packing in twisted filament bundles and packing on positively curved surfaces, like the Thomson problem, are demonstrated for the defect-riddled ground states of physical models of twisted filament bundles. The connection between the “ideal” geometry of fibrations of curved three-dimensional space, including the Hopf fibration, and the non-Euclidean constraints of filament packing in twisted and toroidal bundles is presented, with a focus on the broader dependence of metric geometry on the simultaneous twisting and folding of multifilament bundles.

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Rev. Mod. Phys. 87, 401– Published 14 May, 2015
  • Received 27 October 2014
Article part of CHORUS

© 2015 American Physical Society

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