235 research outputs found
A formula for the minimal coordination number of a parallel bundle
An exact formula for the minimal coordination numbers of the parallel packed
bundle of rods is presented based on an optimal thickening scenario. Hexagonal
and square lattices are considered.Comment: 12 pages, 4 figures, to appear in J. Chem. Phy
Writhe formulas and antipodal points in plectonemic DNA configurations
The linking and writhing numbers are key quantities when characterizing the
structure of a piece of supercoiled DNA. Defined as double integrals over the
shape of the double-helix, these numbers are not always straightforward to
compute, though a simplified formula exists. We examine the range of
applicability of this widely-used simplified formula, and show that it cannot
be employed for plectonemic DNA. We show that inapplicability is due to a
hypothesis of Fuller theorem that is not met. The hypothesis seems to have been
overlooked in many works.Comment: 20 pages, 7 figures, 47 reference
Forceless Sadowsky strips are spherical
We show that thin rectangular ribbons, defined as energy-minimising
configurations of the Sadowsky functional for narrow developable elastic
strips, have a propensity to form spherical shapes in the sense that forceless
solutions lie on a sphere. This has implications for ribbonlike objects in
(bio)polymer physics and nanoscience that cannot be described by the classical
wormlike chain model. A wider class of functionals with this property is
identified.Comment: 15 pages, 4 figure
Cascade unlooping of a low-pitch helical spring under tension
We study the force vs extension behaviour of a helical spring made of a thin
torsionally-stiff anisotropic elastic rod. Our focus is on springs of very low
helical pitch. For certain parameters of the problem such a spring is found not
to unwind when pulled but rather to form hockles that pop-out one by one and
lead to a highly non-monotonic force-extension curve. Between abrupt loop
pop-outs this curve is well described by the planar elastica whose relevant
solutions are classified. Our results may be relevant for tightly coiled
nanosprings in future micro- and nano(electro)mechanical devices.Comment: 20 pages, 15 figure
Tension-induced multistability in inextensible helical ribbons
We study the non-monotonic force-extension behaviour of helical ribbons using
a new model for inextensible elastic strips. Unlike previous rod models our
model predicts hysteresis behaviour for low-pitch ribbons of arbitrary material
properties. Associated with it is a first-order transition between two
different helical states as observed in experiments with cholesterol ribbons.
Numerical solutions show non-uniform uncoiling with hysteresis also occurring
under controlled tension. They furthermore reveal a new uncoiling scenario in
which a ribbon of very low pitch shears under tension and successively releases
a sequence of almost planar loops. Our results may be relevant for nanoscale
devices such as force probes.Comment: 11 pages, 6 figure
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