48 research outputs found
Hamiltonian flows on null curves
The local motion of a null curve in Minkowski 3-space induces an evolution
equation for its Lorentz invariant curvature. Special motions are constructed
whose induced evolution equations are the members of the KdV hierarchy. The
null curves which move under the KdV flow without changing shape are proven to
be the trajectories of a certain particle model on null curves described by a
Lagrangian linear in the curvature. In addition, it is shown that the curvature
of a null curve which evolves by similarities can be computed in terms of the
solutions of the second Painlev\'e equation.Comment: 14 pages, v2: final version; minor changes in the expositio
Forceless Sadowsky strips are spherical
© 2018 American Physical Society. We show that thin rectangular ribbons, defined as energy-minimizing 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
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
Linkage Mechanisms Governed by Integrable Deformations of Discrete Space Curves
A linkage mechanism consists of rigid bodies assembled by joints which can be
used to translate and transfer motion from one form in one place to another. In
this paper, we are particularly interested in a family of spacial linkage
mechanisms which consist of -copies of a rigid body joined together by
hinges to form a ring. Each hinge joint has its own axis of revolution and
rigid bodies joined to it can be freely rotated around the axis. The family
includes the famous threefold symmetric Bricard6R linkage also known as the
Kaleidocycle, which exhibits a characteristic "turning over" motion. We can
model such a linkage as a discrete closed curve in with a
constant torsion up to sign. Then, its motion is described as the deformation
of the curve preserving torsion and arc length. We describe certain motions of
this object that are governed by the semi-discrete mKdV equations, where
infinitesimally the motion of each vertex is confined in the osculating plane