Hans Herrmann (ETH Zürich)

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14 juin 2013 11:00 » 12:00 — Bureau d’Etudes

Packing of wires in cavities and growing surfaces

We investigate the morphologies and maximum packing density of thin wires packed into spherical cavities.
Using simulations and experiments with nylon lines, we find that ordered as well as disordered structures emerge,
depending on the amount of internal torsion. We find that the highest packing densities are achieved in a low torsion
packing for large systems, but in a high torsion packing for small systems. An analysis of both situations is given
in terms of energetics and comparison is made to analytical models of DNA packing in viral capsids. In two dimensions
we also find different morphologies and present the associated morphological phase diagram based on experiments
with metallic wires and confirmed by numerical simulations using discrete elements. During crumpling, the number
of loops increases according to a power-law with different exponents in each morphology. Furthermore,
we observe a power-law divergence of the structure’s bulk. We also investigate the morphology of thin discs and rings
growing in circumferential direction. Recent analytical results suggest that this growth produces symmetric excess cones (e-cones).
We study the stability of such solutions considering self-contact and bending stress. Contrary to what was assumed
in previous analytical solutions, beyond a critical growth factor, no symmetric e-cone solution is energetically minimal any more.
Instead, we obtain skewed e-cone solutions having lower energy, characterized by a skewness angle and repetitive spiral winding
with increasing growth. These results are generalized to discs with varying thickness and rings with holes of different radii.
Experiments with cardboard confirm the simulations.

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