Gert van der Heijden

Centre for Nonlinear Dynamics and its Applications

Department of Civil, Environmental and Geomatic Engineering

University College London

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


"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)

Call for papers:
8th European Nonlinear Dynamics Conference (ENOC 2014), 6-11 July 2014, Vienna
including a Minisymposium on Nonlinear Dynamics in Biological Systems (MS-13)

Recent event:
Symposium on Mechanics of Slender Structures (MoSS 2012), 23-25 July 2012, Harbin, P.R. China

Recent event:
7th European Nonlinear Dynamics Conference (ENOC 2011), 24-29 July 2011, Rome
including a Minisymposium on Nonlinear Dynamics of Biological Systems (MS-13)

EPSRC grant awarded on the project `A chiral theory of DNA supercoiling'
(as part of this there is a PhD studentship available at Imperial College London)
(position filled)

EPSRC-funded DTA studentship available on the project `Collagen: a nanoscale rope made of twisted bundles of fibres' (position filled)
(read more)

Recent event:
Workshop `Nonlinear Dynamics of Chemical and Biochemical Reaction Networks'
28 May 2008
(check here for more information)

EPSRC-funded 2-year postdoc position available! (position filled)
(read more)

Call for Papers (closed)
Symposium on Mechanics of Slender Structures (MoSS 2008), 23-25 July 2008, UMBC

Call for Papers (closed)
for a Special Issue on 'Nonlinear Mechanics and Dynamics of Macromolecules' of the International Journal of Non-Linear Mechanics

Recent event:
Workshop `Nonlinear Dynamics of Biological Filaments'
1 June 2007
(check here for more information)

Latest news (August 2004):
EPSRC-funded 3-year postdoc position available! (position filled)
(read more)

Event:
Workshop `Modern Trends in Theoretical and Applied Mechanics'
23-24 April 2003
(view the flyer or click here to read more)
group picture

Curriculum Vitae

Research Interests:

Generally the geometrically exact description and analysis of slender structures in constrained environments
  • Nonlinear mechanics of slender elastic structures, both 1D (rods, strings) and 2D (strips, ribbons): post-buckling behaviour, large deformations, (multi-pulse) localisation, statical and dynamical stability, bifurcation, constrained deformation (self-contact and surface contact), interaction, discontinuities (kinks), writhing, whirling, transport, ply formation, multi-strand structures, boundary layers, topological properties such as link and writhe. Applications both in engineering (pipe lay, twisted cables, (electrodynamic) space tethers, drill strings, wire rope, rotated and transported textile yarn, nanotube junctions) and in biology (supercoiled DNA, deformations under screened electrostatic interactions, cholesterol ribbons, plied proteins, collagen fibres). Read more in the research overview article (dated 2007). For prize-winning experiments on rods, by former student Geoff Goss, click here.
  • Constrained variational calculus, conjugate point theory, variational inequalities, non-smooth mechanical systems
  • Hamiltonian mechanics, integrability, Melnikov theory
  • Computational (numerical as well as analytical) dynamical systems: normal forms, (homoclinic) bifurcations
  • Numerical continuation and bifurcation analysis, computer software
  • Nonlinear rotordynamics, coupled oscillators, chaotic dynamics

Publications

Highlights in pictures (old)

 

Some current research projects:

  • Statical and dynamical behaviour of electrodynamic space tethers:

  • 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]

    As a spin-off, in this ZAMP paper we give the first correct proof that the nonsymmetric top, and hence the anisotropic rod, is chaotic

     

  • Writhing instabilities of transported textile yarns in spinning and texturing:

  • 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]

     

     

  • Collagen nanofibres and fibrillogenesis:

  • 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)

     

  • Variational analysis of rods subject to surface constraints - from drill strings to DNA packing:

  • 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]

     

  • Two-strand plies with applications to DNA supercoiling:

  • We have developed a general theory of elastic two-strand structures. The strands are assumed to have circular cross-section and to be in continuous (frictionless) contact, but we make no assumption about the shape of the contact curve, i.e., the axis of the ply is free to adopt any configuration under the action of end loads. Local interaction between the rods is also incorporated and we are applying the theory to study DNA supercoiling (both open braided DNA and closed minicircles) due to chiral DNA-DNA interactions.

    Below are three ideal shapes with hard-core contact only, i.e., without electrostatic forces: a link, a knot and a braid. In each case we verify that the contact pressure is everywhere positive, meaning that the shapes are physical: the strands are naturally in contact and would require a force to be pulled apart.

    4link 9knot braid

     

  • Twisted strips - states of an inextensible sheet:

  • 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.

    animated Escher Escher Lk=3/2 animated Moebius Nature Materials cover

    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):

    strip buckling strip computed

    We have also computed equilibrium shapes of knotted one-sided ribbons such as these (2,5) and (3,7) torus knots:

    (2,5) torus knot (3,7) torus knot

    By contrast, the (2,3) (trefoil) and (4,7) knots look like:

    (2,3) torus knot (4,7) torus knot common trefoil knot

    (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]:

    stretched helix

    How to shed a loop in a kinked helical spring:

    stretched helix

    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]

 

Research students, postdocs and visitors:

present:
  • Colin Taylor (EPSRC-funded PhD student on 4-year EngD in Molecular Modelling and Materials Science, started in October 2009; bundle models for collagen and other biofilaments)
  • Eugene Starostin (EPSRC Research Fellow, Jul. 2005 - Sep. 2009 - Sep. 2012; writhing structures, geometry and mechanics of strips, plies and bundles, applications to biofilaments, DNA supercoiling)
  • Anthony Korte (EPSRC Research Fellow, Apr. 2008 - Apr. 2010; HFSP, Apr. 2010 - Mar. 2013; quantum eigenstates and transport properties of Möbius-type nanostructures, curvature trapping, buckling and instabilities of twisted strips; chiral effects in DNA supercoiling)
  • Caifa Guo (College of Aerospace and Materials Engineering, National University of Defense Technology, Changsha, China; PhD student funded by the China Scholarship Council, Oct. 2011 - Sep. 2013; bifurcation and stability of electrodynamic space tethers)
past:
  • Mark Peletier (EPSRC Visiting Fellow, 6 weeks 2002; global energy minimisers, constrained rods, Link-Twist-Writhe)
  • Geoff Goss (part-time PhD student, finished Sep. 2003; thesis title: Snap buckling, writhing and loop formation in twisted rods [PDF file, 7.8 MB])
  • Juan Valverde (Royal Society Visiting Research Fellow, Seville, Jul.-Dec. 2004; buckling of conducting rods in a magnetic field, instabilities of whirling electrodynamic space tethers)
  • Qiguo Sun (Royal Society KC Wong China Fellow, Nov. 2005 - Oct. 2006; fluid-structure interactions in whirling tether and rotor systems)
  • Kazuyuki Yagasaki (London Mathematical Society, Mar. 2006; multi-pulse homoclinic orbits, spatial chaos)
  • Pedro Ribeiro (on sabbatical leave from the University of Porto, Jan. - Aug. 2007)
  • Barrie Fraser (EPSRC Visiting Fellow, periodically, 2005 - 2008; instabilities in whirling and transported rods and textile yarns)
  • David Sinden (EPSRC-funded PhD student, 2004-2008; thesis title: Integrability, localisation and bifurcation of an elastic conducting rod in a uniform magnetic field; now a Research Assistant in UCL's Department of Mechanical Engineering)
  • David Lane (EPSRC-funded PhD student, 2006-2010; thesis title: Stability of discontinuous elastic rods with applications to nanotube junctions
  • Qiguo Sun (Royal Society China-UK 1 Year Networking grant, periodically, Apr. 2009 - Aug. 2010; control of space tethers)

 

Teaching:

 

Further professional activities:

 

Other interests:

 

Useful links:

 


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