Gower Street
London WC1E 6BT, UK
Tel: +44-(0)20-7679-2727
Fax: +44-(0)20-7380-0986
E-mail: g.heijden@ucl.ac.uk
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Gower Street |
"Many a golden opportunity to remain silent has been squandered by anti-prophets who do not realise that the grounds for declaring something impossible or inconceivable may be undermined by new ideas that cannot be foreseen."
Peter Medawar (1965)
Electrodynamic tethers connect spacecraft to other orbiting bodies and are
designed to use the earth's magnetic field, rather than chemical fuel, for
thrust and drag. Some tethers are spun about their axis for gyroscopic
stability and therefore must resist bending and twisting. Such tethers need
to be described by an elastic rod rather than the traditional string. Of
particular interest are whirling and other instabilities.
[
J. Phys. A paper on the integrability of a rod in a magnetic field (2008)]
[arXiv preprint]
[
J. Phys. A paper on spatial chaos of an EXTENSIBLE rod in a magnetic
field (2009)]
[arXiv preprint]
[
J. Nonl. Sci. paper on magnetically-induced buckling of electrodynamic
space tethers (2010)]
[arXiv preprint]
[
J. Phys. A paper on a Melnikov method and nonintegrability of an
extensible rod in a magnetic field (2011)]
[arXiv preprint]
We study snarling and other twist-induced instabilities of transported
textile yarns in such industrial processes as ring-spinning and texturing.
We are also trying to get a better understanding of the mechanical
properties of textile yarns (such as the twist-stretch coupling) in terms
of the properties of the composing fibres.
[
J. Eng. Math. paper on the snarling instability, 2007]
[
J. Text. Inst. paper on multi-ply textile yarns, 2008]
[
J. Text. Inst. paper on torsional properties of plied yarns, 2010]
The structural support protein collagen is the most abundant protein in
the animal kingdom and helps tissues such as bone and tendon to withstand
stretching. Models of multi-strand plied structures are applied to the
rope-like collagen fibrils recently discovered in UCL's Medicine Department.
[
Biophysical Journal 92, 70-75 (2007)] (nanoscale ropes)
Configurations and bifurcations of rods on or inside surfaces are studied
(i.e., equality or inequality constraints). An example of the latter is a
drill string bouncing inside a borehole. This work is also relevant for
structural problems in molecular biology (for instance, in the
supercoiling and packing of DNA).
[
Arch. Rat. Mech. Anal. 182, 471-511 (2006)] (on
energy-minimising self-contacting rods on a cylinder)
[arXiv preprint]
[
Quart. Appl. Math. 65, 385-402 (2007)] (on end rotation, twist and writhe for large-deformation rods)
[early arXiv preprint]
We study the mechanics of inextensible strips with applications to paper
crumpling, fabric draping as well as general sheet processing. Geometrically
this leads to the study of developable surfaces (surfaces flat in one
direction). As part of this work we solved the long-standing problem of
finding the shape of a Möbius strip.
Our paper `The shape of a Möbius strip' has now appeared in
Nature Materials (2007)
(a preprint can be found here, Supplementary Information here; or read the abstract, or UCL's top story)
See Eugene's page for publicity
Extending this work, we have discovered and described a new triangular buckling pattern of twisted inextensible strips held in tension with edge stress concentration similar to that of the Möbius strip (Proc. R. Soc. A (2010) paper, arXiv preprint):
We have also computed equilibrium shapes of knotted one-sided ribbons such as these (2,5) and (3,7) torus knots:
By contrast, the (2,3) (trefoil) and (4,7) knots look like:
(note that one-sided closed inextensible ribbons need to have an odd number of inflection/switching points (with accompanying singularity in the bending energy density); the (2,3) trefoil knot has these on the outside and therefore looks somewhat different from the usual shape (right), requiring a wider berth to accommodate them; we call it a type II torus knot)
The method for deriving convenient equilibrium equations for general one-dimensional elastic problems (i.e., for geometric variational problems on curves) is discussed in our paper in Physical Review E (2009) [arXiv preprint] Quantum eigenstates of a particle confined to the surface of a Möbius strip (or other one-sided surface) reveal curvature trapping in regions (creases) of high curvature as the strip's width-to-length ratio is increased. This could be important for transport properties of Möbius-type structures in nanoscale devices. See our paper in the Journal of Physics: Condensed Matter (2009) [arXiv preprint] We have also applied our methods to helical ribbons and discovered tension-induced multistability and phase separation (straightening) as observed in cholesterol ribbons. The results may also be relevant for nanobelts and the design of nanoswitches [Physical Review Letters 101, 084301 (2008)] [arXiv preprint]:
How to shed a loop in a kinked helical spring:
Helical nanoribbons of various types of material (SiO2, ZnO, Si/Cr, SiGe/Si,
SiGe/Si/Cr) have been fabricated for use in nano-electromechanical systems
(NEMS) such as nanoinductors, resonators, actuators, etc. Of particular
interest are nanosprings of very low pitch as they allow for a large magnetic
flux density. Such low-pitch springs when pulled may not simply unwind but
instead show a highly nonlinear force-extension response dominated by
sequential multi-loop pop-out.
[J. Mech. Phys. Solids 57, 959-969 (2009)]
[arXiv preprint]
