Statistics and Topology of Fluctuating Ribbons

Kavli Affiliate: L. Mahadevan

| First 5 Authors: Ee Hou Yong, Farisan Dary, Luca Giomi, L. Mahadevan,

| Summary:

Ribbons are a class of slender structures whose length, width, and thickness
are widely separated from each other. This scale separation gives a ribbon
unusual mechanical properties in athermal macroscopic settings, e.g. it can
bend without twisting, but cannot twist without bending. Given the ubiquity of
ribbon-like biopolymers in biology and chemistry, here we study the statistical
mechanics of microscopic inextensible, fluctuating ribbons loaded by forces and
torques. We show that these ribbons exhibit a range of topologically and
geometrically complex morphologies exemplified by three phases – a
twist-dominated helical phase (HT), a writhe-dominated helical phase (HW), and
an entangled phase – that arise as the applied torque and force is varied.
Furthermore, the transition from HW to HT phases is characterized by the
spontaneous breaking of parity symmetry and the disappearance of perversions
that characterize chirality reversals. This leads to a universal response curve
of a topological quantity, the link, as a function of the applied torque that
is similar to magnetization curves in second-order phase transitions.

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