416 research outputs found
Monte Carlo Simulation of Smectic Liquid Crystals and the Electroclinic Effect: the Role of the Molecular Shape
Using Monte Carlo simulation methods, we explore the role of molecular shape
in the phase behavior of liquid crystals and the electroclinic effect. We study
a "bent-rod" mesogen shaped like the letter Z, composed of seven soft spheres
bonded rigidly together with no intra-molecular degrees of freedom. For
strongly angled molecules, we find that steric repulsion alone provides the
driving force for a smectic-C phase, even without intermolecular dipole-dipole
interactions. For weakly angled (nearly rod-like) molecules, we find a stable
smectic-A (SmA) phase and a strong electroclinic effect with a saturation tilt
angle of about 19 degrees. In the SmA phase we find evidence of vortex-like
point defects. We also observe a field-induced nematic-smectic phase
transition.Comment: 10 pages, including 10 postscript figures, uses REVTeX 3.0 and
epsf.st
Order and Frustration in Chiral Liquid Crystals
This paper reviews the complex ordered structures induced by chirality in
liquid crystals. In general, chirality favors a twist in the orientation of
liquid-crystal molecules. In some cases, as in the cholesteric phase, this
favored twist can be achieved without any defects. More often, the favored
twist competes with applied electric or magnetic fields or with geometric
constraints, leading to frustration. In response to this frustration, the
system develops ordered structures with periodic arrays of defects. The
simplest example of such a structure is the lattice of domains and domain walls
in a cholesteric phase under a magnetic field. More complex examples include
defect structures formed in two-dimensional films of chiral liquid crystals.
The same considerations of chirality and defects apply to three-dimensional
structures, such as the twist-grain-boundary and moire phases.Comment: 39 pages, RevTeX, 14 included eps figure
An extremal model for amorphous media plasticity
An extremal model for the plasticity of amorphous materials is studied in a
simple two-dimensional anti-plane geometry. The steady-state is analyzed
through numerical simulations. Long-range spatial and temporal correlations in
local slip events are shown to develop, leading to non-trivial and highly
anisotropic scaling laws. In particular, the plastic strain is shown to
statistically concentrate over a region which tends to align perpendicular to
the displacement gradient. By construction, the model can be seen as giving
rise to a depinning transition, the threshold of which (i.e. the macroscopic
yield stress) also reveal scaling properties reflecting the localization of the
activity.Comment: 4 pages, 5 figure
Cooperative Chiral Order in Copolymers of Chiral and Achiral Units
Polyisocyanates can be synthesized with chiral and achiral pendant groups
distributed randomly along the chains. The overall chiral order, measured by
optical activity, is strongly cooperative and depends sensitively on the
concentration of chiral pendant groups. To explain this cooperative chiral
order theoretically, we map the random copolymer onto the one-dimensional
random-field Ising model. We show that the optical activity as a function of
composition is well-described by the predictions of this theory.Comment: 13 pages, including 3 postscript figures, uses REVTeX 3.0 and
epsf.st
Theory of Chiral Order in Random Copolymers
Recent experiments have found that polyisocyanates composed of a mixture of
opposite enantiomers follow a chiral ``majority rule:'' the chiral order of the
copolymer, measured by optical activity, is dominated by whichever enantiomer
is in the majority. We explain this majority rule theoretically by mapping the
random copolymer onto the random-field Ising model. Using this model, we
predict the chiral order as a function of enantiomer concentration, in
quantitative agreement with the experiments, and show how the sharpness of the
majority-rule curve can be controlled.Comment: 13 pages, including 4 postscript figures, uses REVTeX 3.0 and
epsf.st
Picturing classical and quantum Bayesian inference
We introduce a graphical framework for Bayesian inference that is
sufficiently general to accommodate not just the standard case but also recent
proposals for a theory of quantum Bayesian inference wherein one considers
density operators rather than probability distributions as representative of
degrees of belief. The diagrammatic framework is stated in the graphical
language of symmetric monoidal categories and of compact structures and
Frobenius structures therein, in which Bayesian inversion boils down to
transposition with respect to an appropriate compact structure. We characterize
classical Bayesian inference in terms of a graphical property and demonstrate
that our approach eliminates some purely conventional elements that appear in
common representations thereof, such as whether degrees of belief are
represented by probabilities or entropic quantities. We also introduce a
quantum-like calculus wherein the Frobenius structure is noncommutative and
show that it can accommodate Leifer's calculus of `conditional density
operators'. The notion of conditional independence is also generalized to our
graphical setting and we make some preliminary connections to the theory of
Bayesian networks. Finally, we demonstrate how to construct a graphical
Bayesian calculus within any dagger compact category.Comment: 38 pages, lots of picture
Theory of Chiral Modulations and Fluctuations in Smectic-A Liquid Crystals Under an Electric Field
Chiral liquid crystals often exhibit periodic modulations in the molecular
director; in particular, thin films of the smectic-C* phase show a chiral
striped texture. Here, we investigate whether similar chiral modulations can
occur in the induced molecular tilt of the smectic-A phase under an applied
electric field. Using both continuum elastic theory and lattice simulations, we
find that the state of uniform induced tilt can become unstable when the system
approaches the smectic-A--smectic-C* transition, or when a high electric field
is applied. Beyond that instability point, the system develops chiral stripes
in the tilt, which induce corresponding ripples in the smectic layers. The
modulation persists up to an upper critical electric field and then disappears.
Furthermore, even in the uniform state, the system shows chiral fluctuations,
including both incipient chiral stripes and localized chiral vortices. We
compare these predictions with observed chiral modulations and fluctuations in
smectic-A liquid crystals.Comment: 11 pages, including 9 postscript figures, uses REVTeX 3.0 and
epsf.st
The GHZ/W-calculus contains rational arithmetic
Graphical calculi for representing interacting quantum systems serve a number
of purposes: compositionally, intuitive graphical reasoning, and a logical
underpinning for automation. The power of these calculi stems from the fact
that they embody generalized symmetries of the structure of quantum operations,
which, for example, stretch well beyond the Choi-Jamiolkowski isomorphism. One
such calculus takes the GHZ and W states as its basic generators. Here we show
that this language allows one to encode standard rational calculus, with the
GHZ state as multiplication, the W state as addition, the Pauli X gate as
multiplicative inversion, and the Pauli Z gate as additive inversion.Comment: In Proceedings HPC 2010, arXiv:1103.226
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