180 research outputs found
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
Movi
Nuts and bolts of supersymmetry
A topological mechanism is a zero elastic-energy deformation of a mechanical
structure that is robust against smooth changes in system parameters. Here, we
map the nonlinear elasticity of a paradigmatic class of topological mechanisms
onto linear fermionic models using a supersymmetric field theory introduced by
Witten and Olive. Heuristically, this approach consists of taking the square
root of a non-linear Hamiltonian and generalizes the standard procedure of
obtaining two copies of Dirac equation from the square root of the linear Klein
Gordon equation. Our real space formalism goes beyond topological band theory
by incorporating non-linearities and spatial inhomogeneities, such as domain
walls, where topological states are typically localized. By viewing the two
components of the real fermionic field as site and bond displacements
respectively, we determine the relation between the supersymmetry
transformations and the Bogomolny-Prasad-Sommerfield (BPS) bound saturated by
the mechanism. We show that the mechanical constraint, which enforces a BPS
saturated kink into the system, simultaneously precludes an anti-kink. This
mechanism breaks the usual kink-antikink symmetry and can be viewed as a
manifestation of the underlying supersymmetry being half-broken.Comment: 14 pages, 5 figure
Non-reciprocal phase transitions
Out of equilibrium, the lack of reciprocity is the rule rather than the
exception. Non-reciprocal interactions occur, for instance, in networks of
neurons, directional growth of interfaces, and synthetic active materials.
While wave propagation in non-reciprocal media has recently been under intense
study, less is known about the consequences of non-reciprocity on the
collective behavior of many-body systems. Here, we show that non-reciprocity
leads to time-dependent phases where spontaneously broken symmetries are
dynamically restored. The resulting phase transitions are controlled by
spectral singularities called exceptional points. We describe the emergence of
these phases using insights from bifurcation theory and non-Hermitian quantum
mechanics. Our approach captures non-reciprocal generalizations of three
archetypal classes of self-organization out of equilibrium: synchronization,
flocking and pattern formation. Collective phenomena in these non-reciprocal
systems range from active time-(quasi)crystals to exceptional-point enforced
pattern-formation and hysteresis. Our work paves the way towards a general
theory of critical phenomena in non-reciprocal matter.Comment: Supplementary movies at
https://home.uchicago.edu/~vitelli/videos.htm
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