454 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
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
Modeling Smectic Layers in Confined Geometries: Order Parameter and Defects
We identify problems with the standard complex order parameter formalism for
smectic-A (SmA) liquid crystals, and discuss possible alternative descriptions
of smectic order. In particular, we suggest an approach based on the real
smectic density variation rather than a complex order parameter. This approach
gives reasonable numerical results for the smectic layer configuration and
director field in sample geometries, and can be used to model smectic liquid
crystals under nanoscale confinement for technological applications.Comment: 8 page
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
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
Emergence of hexatic and long-range herringbone order in two-dimensional smectic liquid crystals : A Monte Carlo study
Using a high resolution Monte Carlo simulation technique based on
multi-histogram method and cluster-algorithm, we have investigated critical
properties of a coupled XY model, consists of a six-fold symmetric hexatic and
a three-fold symmetric herringbone field, in two dimensions. The simulation
results demonstrate a series of novel continues transitions, in which both
long-range hexatic and herringbone orderings are established simultaneously. It
is found that the specific-heat anomaly exponents for some regions in coupling
constants space are in excellent agreement with the experimentally measured
exponents extracted from heat-capacity data near the smecticA-hexaticB
transition of two-layer free standing film
The Role of Bilayer Tilt Difference in Equilibrium Membrane Shapes
Lipid bilayer membranes below their main transition have two tilt order
parameters, corresponding to the two monolayers. These two tilts may be
strongly coupled to membrane shape but only weakly coupled to each other. We
discuss some implications of this observation for rippled and saddle phases,
bilayer tubules, and bicontinuous phases. Tilt difference introduces a length
scale into the elastic theory of tilted fluid membranes. It can drive an
instability of the flat phase; it also provides a simple mechanism for the
spontaneous breaking of inversion symmetry seen in some recent experiments.Comment: Latex file; .ps available at
http://dept.physics.upenn.edu/~nelson/saddle.p
Tilt Texture Domains on a Membrane and Chirality induced Budding
We study the equilibrium conformations of a lipid domain on a planar fluid
membrane where the domain is decorated by a vector field representing the tilt
of the stiff fatty acid chains of the lipid molecules, while the surrounding
membrane is fluid and structureless. The inclusion of chirality in the bulk of
the domain induces a novel budding of the membrane, which preempts the budding
induced by a decrease in interfacial tension.Comment: 5 pages, 3 figure
A lambda calculus for quantum computation with classical control
The objective of this paper is to develop a functional programming language
for quantum computers. We develop a lambda calculus for the classical control
model, following the first author's work on quantum flow-charts. We define a
call-by-value operational semantics, and we give a type system using affine
intuitionistic linear logic. The main results of this paper are the safety
properties of the language and the development of a type inference algorithm.Comment: 15 pages, submitted to TLCA'05. Note: this is basically the work done
during the first author master, his thesis can be found on his webpage.
Modifications: almost everything reformulated; recursion removed since the
way it was stated didn't satisfy lemma 11; type inference algorithm added;
example of an implementation of quantum teleportation adde
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