3,284 research outputs found
Global Stationary Phase and the Sign Problem
We present a computational strategy for reducing the sign problem in the
evaluation of high dimensional integrals with non-positive definite weights.
The method involves stochastic sampling with a positive semidefinite weight
that is adaptively and optimally determined during the course of a simulation.
The optimal criterion, which follows from a variational principle for analytic
actions S(z), is a global stationary phase condition that the average gradient
of the phase Im(S) along the sampling path vanishes. Numerical results are
presented from simulations of a model adapted from statistical field theories
of classical fluids.Comment: 9 pages, 3 figures, submitted for publicatio
Orientational phase transitions in the hexagonal phase of a diblock copolymer melt under shear flow
We generalize the earlier theory by Fredrickson [J. Rheol. v.38, 1045 (1994)]
to study the orientational behaviour of the hexagonal phase of diblock
copolymer melt subjected to steady shear flow. We use symmetry arguments to
show that the orientational ordering in the hexagonal phase is a much weaker
effect than in the lamellae. We predict the parallel orientation to be stable
at low and the perpendicular orientation at high shear rates. Our analysis
reproduces the experimental results by Tepe et al. [Macromolecules v.28, 3008
(1995)] and explains the difficulties in experimental observation of the
different orientations in the hexagonal phase.Comment: 21 pages, 6 eps figures, submitted to Physical Review
Surface states in nearly modulated systems
A Landau model is used to study the phase behavior of the surface layer for
magnetic and cholesteric liquid crystal systems that are at or near a Lifshitz
point marking the boundary between modulated and homogeneous bulk phases. The
model incorporates surface and bulk fields and includes a term in the free
energy proportional to the square of the second derivative of the order
parameter in addition to the usual term involving the square of the first
derivative. In the limit of vanishing bulk field, three distinct types of
surface ordering are possible: a wetting layer, a non-wet layer having a small
deviation from bulk order, and a different non-wet layer with a large deviation
from bulk order which decays non-monotonically as distance from the wall
increases. In particular the large deviation non-wet layer is a feature of
systems at the Lifshitz point and also those having only homogeneous bulk
phases.Comment: 6 pages, 7 figures, submitted to Phys. Rev.
Interfaces of Modulated Phases
Numerically minimizing a continuous free-energy functional which yields
several modulated phases, we obtain the order-parameter profiles and
interfacial free energies of symmetric and non-symmetric tilt boundaries within
the lamellar phase, and of interfaces between coexisting lamellar, hexagonal,
and disordered phases. Our findings agree well with chevron, omega, and
T-junction tilt-boundary morphologies observed in diblock copolymers and
magnetic garnet films.Comment: 4 page
Simple model with facilitated dynamics for granular compaction
A simple lattice model is used to study compaction in granular media. As in
real experiments, we consider a series of taps separated by large enough
waiting times. The relaxation of the density exhibits the characteristic
inverse logarithmic law. Moreover, we have been able to identify analytically
the relevant time scale, leading to a relaxation law independent of the
specific values of the parameters. Also, an expression for the asymptotic
density reached in the compaction process has been derived. The theoretical
predictions agree fairly well with the results from the Monte Carlo simulation.Comment: 15 pages, 4 figures, REVTeX file; no changes except for
single-spacing to save paper (previous version 22 pages
What do we learn from the shape of the dynamical susceptibility of glass-formers?
We compute analytically and numerically the four-point correlation function
that characterizes non-trivial cooperative dynamics in glassy systems within
several models of glasses: elasto-plastic deformations, mode-coupling theory
(MCT), collectively rearranging regions (CRR), diffusing defects and
kinetically constrained models (KCM). Some features of the four-point
susceptibility chi_4(t) are expected to be universal. at short times we expect
an elastic regime characterized by a t or sqrt{t} growth. We find both in the
beta, and the early alpha regime that chi_4 sim t^mu, where mu is directly
related to the mechanism responsible for relaxation. This regime ends when a
maximum of chi_4 is reached at a time t=t^* of the order of the relaxation time
of the system. This maximum is followed by a fast decay to zero at large times.
The height of the maximum also follows a power-law, chi_4(t^*) sim t^{*lambda}.
The value of the exponents mu and lambda allows one to distinguish between
different mechanisms. For example, freely diffusing defects in d=3 lead to mu=2
and lambda=1, whereas the CRR scenario rather predicts either mu=1 or a
logarithmic behaviour depending on the nature of the nucleation events, and a
logarithmic behaviour of chi_4(t^*). MCT leads to mu=b and lambda =1/gamma,
where b and gamma are the standard MCT exponents. We compare our theoretical
results with numerical simulations on a Lennard-Jones and a soft-sphere system.
Within the limited time-scales accessible to numerical simulations, we find
that the exponent mu is rather small, mu < 1, with a value in reasonable
agreement with the MCT predictions.Comment: 26 pages, 6 figure
Interfaces in Diblocks: A Study of Miktoarm Star Copolymers
We study AB miktoarm star block copolymers in the strong segregation
limit, focussing on the role that the AB interface plays in determining the
phase behavior. We develop an extension of the kinked-path approach which
allows us to explore the energetic dependence on interfacial shape. We consider
a one-parameter family of interfaces to study the columnar to lamellar
transition in asymmetric stars. We compare with recent experimental results. We
discuss the stability of the A15 lattice of sphere-like micelles in the context
of interfacial energy minimization. We corroborate our theory by implementing a
numerically exact self-consistent field theory to probe the phase diagram and
the shape of the AB interface.Comment: 12 pages, 11 included figure
Negative emotional stimuli reduce contextual cueing but not response times in inefficient search
In visual search, previous work has shown that negative stimuli narrow the focus of attention and speed reaction times (RTs). This paper investigates these two effects by first asking whether negative emotional stimuli narrow the focus of attention to reduce the learning of a display context in a contextual cueing task and, second, whether exposure to negative stimuli also reduces RTs in inefficient search tasks. In Experiment 1, participants viewed either negative or neutral images (faces or scenes) prior to a contextual cueing task. In a typical contextual cueing experiment, RTs are reduced if displays are repeated across the experiment compared with novel displays that are not repeated. The results showed that a smaller contextual cueing effect was obtained after participants viewed negative stimuli than when they viewed neutral stimuli. However, in contrast to previous work, overall search RTs were not faster after viewing negative stimuli (Experiments 2 to 4). The findings are discussed in terms of the impact of emotional content on visual processing and the ability to use scene context to help facilitate search
Cutoff for the East process
The East process is a 1D kinetically constrained interacting particle system,
introduced in the physics literature in the early 90's to model liquid-glass
transitions. Spectral gap estimates of Aldous and Diaconis in 2002 imply that
its mixing time on sites has order . We complement that result and show
cutoff with an -window.
The main ingredient is an analysis of the front of the process (its rightmost
zero in the setup where zeros facilitate updates to their right). One expects
the front to advance as a biased random walk, whose normal fluctuations would
imply cutoff with an -window. The law of the process behind the
front plays a crucial role: Blondel showed that it converges to an invariant
measure , on which very little is known. Here we obtain quantitative
bounds on the speed of convergence to , finding that it is exponentially
fast. We then derive that the increments of the front behave as a stationary
mixing sequence of random variables, and a Stein-method based argument of
Bolthausen ('82) implies a CLT for the location of the front, yielding the
cutoff result.
Finally, we supplement these results by a study of analogous kinetically
constrained models on trees, again establishing cutoff, yet this time with an
-window.Comment: 33 pages, 2 figure
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