3,250 research outputs found
Quantum Buckling
We study the mechanical buckling of a two dimensional membrane coated with a
thin layer of superfluid. It is seen that a singularity (vortex or anti-vortex
defect) in the phase of the quantum order parameter, distorts the membrane
metric into a negative conical singularity surface, irrespective of the defect
sign. The defect-curvature coupling and the observed instability is in striking
contrast with classical elasticity where, the in-plane strain induced by
positive (negative) disclinations is screened by a corresponding positive
(negative) conical singularity surface. Defining a dimensionless ratio between
superfluid stiffness and membrane bending modulus, we derive conditions under
which the quantum buckling instability occurs. An ansatz for the resulting
shape of the buckled membrane is analytically and numerically confirmed
The geometry of thresholdless active flow in nematic microfluidics
"Active nematics" are orientationally ordered but apolar fluids composed of
interacting constituents individually powered by an internal source of energy.
When activity exceeds a system-size dependent threshold, spatially uniform
active apolar fluids undergo a hydrodynamic instability leading to spontaneous
macroscopic fluid flow. Here, we show that a special class of spatially
non-uniform configurations of such active apolar fluids display laminar (i.e.,
time-independent) flow even for arbitrarily small activity. We also show that
two-dimensional active nematics confined on a surface of non-vanishing Gaussian
curvature must necessarily experience a non-vanishing active force. This
general conclusion follows from a key result of differential geometry:
geodesics must converge or diverge on surfaces with non-zero Gaussian
curvature. We derive the conditions under which such curvature-induced active
forces generate "thresholdless flow" for two-dimensional curved shells. We then
extend our analysis to bulk systems and show how to induce thresholdless active
flow by controlling the curvature of confining surfaces, external fields, or
both. The resulting laminar flow fields are determined analytically in three
experimentally realizable configurations that exemplify this general
phenomenon: i) toroidal shells with planar alignment, ii) a cylinder with
non-planar boundary conditions, and iii) a "Frederiks cell" that functions like
a pump without moving parts. Our work suggests a robust design strategy for
active microfluidic chips and could be tested with the recently discovered
"living liquid crystals".Comment: The rewritten paper has several changes, principally: 1. A separate
section III for two-dimensional curved systems, illustrated with an new
example. 2. Remarks about the relevance of the frozen director approximation
in the case of weak nematic order; and 3. A separate Supplemental Material
document, containing material previously in the Appendix, along with
additional materia
Dualities and non-Abelian mechanics
Dualities are mathematical mappings that reveal unexpected links between
apparently unrelated systems or quantities in virtually every branch of
physics. Systems that are mapped onto themselves by a duality transformation
are called self-dual and they often exhibit remarkable properties, as
exemplified by an Ising magnet at the critical point. In this Letter, we unveil
the role of dualities in mechanics by considering a family of so-called twisted
Kagome lattices. These are reconfigurable structures that can change shape
thanks to a collapse mechanism easily illustrated using LEGO. Surprisingly,
pairs of distinct configurations along the mechanism exhibit the same spectrum
of vibrational modes. We show that this puzzling property arises from the
existence of a duality transformation between pairs of configurations on either
side of a mechanical critical point. This critical point corresponds to a
self-dual structure whose vibrational spectrum is two-fold degenerate over the
entire Brillouin zone. The two-fold degeneracy originates from a general
version of Kramers theorem that applies to classical waves in addition to
quantum systems with fermionic time-reversal invariance. We show that the
vibrational modes of the self-dual mechanical systems exhibit non-Abelian
geometric phases that affect the semi-classical propagation of wave packets.
Our results apply to linear systems beyond mechanics and illustrate how
dualities can be harnessed to design metamaterials with anomalous symmetries
and non-commuting responses.Comment: See http://home.uchicago.edu/~vitelli/videos.html for Supplementary
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