942 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
Size effects and dislocation patterning in two-dimensional bending
We perform atomistic Monte Carlo simulations of bending a Lennard-Jones
single crystal in two dimensions. Dislocations nucleate only at the free
surface as there are no sources in the interior of the sample. When
dislocations reach sufficient density, they spontaneously coalesce to nucleate
grain boundaries, and the resulting microstructure depends strongly on the
initial crystal orientation of the sample. In initial yield, we find a reverse
size effect, in which larger samples show a higher scaled bending moment than
smaller samples for a given strain and strain rate. This effect is associated
with source-limited plasticity and high strain rate relative to dislocation
mobility, and the size effect in initial yield disappears when we scale the
data to account for strain rate effects. Once dislocations coalesce to form
grain boundaries, the size effect reverses and we find that smaller crystals
support a higher scaled bending moment than larger crystals. This finding is in
qualitative agreement with experimental results. Finally, we observe an
instability at the compressed crystal surface that suggests a novel mechanism
for the formation of a hillock structure. The hillock is formed when a high
angle grain boundary, after absorbing additional dislocations, becomes unstable
and folds to form a new crystal grain that protrudes from the free surface.Comment: 15 pages, 8 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
A Graphical Language for Proof Strategies
Complex automated proof strategies are often difficult to extract, visualise,
modify, and debug. Traditional tactic languages, often based on stack-based
goal propagation, make it easy to write proofs that obscure the flow of goals
between tactics and are fragile to minor changes in input, proof structure or
changes to tactics themselves. Here, we address this by introducing a graphical
language called PSGraph for writing proof strategies. Strategies are
constructed visually by "wiring together" collections of tactics and evaluated
by propagating goal nodes through the diagram via graph rewriting. Tactic nodes
can have many output wires, and use a filtering procedure based on goal-types
(predicates describing the features of a goal) to decide where best to send
newly-generated sub-goals.
In addition to making the flow of goal information explicit, the graphical
language can fulfil the role of many tacticals using visual idioms like
branching, merging, and feedback loops. We argue that this language enables
development of more robust proof strategies and provide several examples, along
with a prototype implementation in Isabelle
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