Elastic tubes and filaments
- Squeezed helical elastica
Lila Bouzar, Martin Michael Müller, Pierre Gosselin, Igor M. Kulić, Hervé Mohrbach
We theoretically study the conformations of a helical semi-flexible filament
confined to a two-dimensional surface. This squeezed helix exhibits a variety of unexpected shapes
resembling circles, waves or spirals depending on the material parameters. We explore the conformation
space in detail and show that the shapes can be understood as the mutual elastic interaction of
conformational quasi-particles. Our theoretical results are potentially useful to
determine the material parameters of such helical filaments in an experimental setting.
Eur. Phys. J. E, 39: 114, 2016. See also arXiv:1606.03611.
- Non-linear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate
Norbert Stoop, Martin Michael Müller
We consider the axial compression of a thin sheet wrapped around a rigid cylindrical substrate. In contrast to the wrinkling-to-fold transitions exhibited in similar systems, we find that the sheet always buckles into a single symmetric fold, while periodic solutions are unstable. Upon further compression, the solution breaks symmetry and stabilizes into a recumbent fold. Using linear analysis and numerics, we theoretically predict the buckling force and energy as a function of the compressive displacement. We compare our theory to experiments employing cylindrical neoprene sheets and find remarkably good agreement.
Int. J. Non-Linear Mech., 75: 115, 2015. See also arXiv:1503.05030.
- Crunching Biofilament Rings
Julien Fierling, Martin Michael Müller, Hervé Mohrbach, Albert Johner, Igor M. Kulić
We discuss a curious example for the collective mechanical behavior of coupled non-linear monomer units entrapped in a circular filament. Within a simple model we elucidate how multistability of monomer units and exponentially large degeneracy of the filament's ground state emerge as a collective feature of the closed filament. Surprisingly, increasing the monomer frustration, i.e., the bending prestrain within the circular filament, leads to a conformational softening of the system. The phenomenon, that we term polymorphic crunching, is discussed and applied to a possible scenario for membrane tube deformation by switchable dynamin or FtsZ filaments. We find an important role of cooperative inter-unit interaction for efficient ring induced membrane fission.
Europhys. Lett., 107(6): 68002, 2014. See also arXiv:1408.6787.
- Confotronic dynamics of tubular filaments
Osman Kahraman, Hervé Mohrbach, Martin Michael Müller, Igor M. Kulić
Tubular lattices are ubiquitous in nature and technology. Microtubules and nanotubes of all
kinds act as important pillars of biological cells and the man-made nano-world. We show that
when prestress is introduced in such structures, localized conformational quasiparticles emerge and
govern the collective shape dynamics of the lattice. When coupled via cooperative interactions these
quasiparticles form larger-scale quasipolymer superstructures exhibiting collective dynamic modes
and giving rise to a hallmark behavior radically different from semiflexible beams.
Soft Matter, 10(16): pp. 2836-2847, 2014. See also arXiv:1312.3106.