2,976 research outputs found
The effect of shear on persistence in coarsening systems
We analytically study the effect of a uniform shear flow on the persistence
properties of coarsening systems. The study is carried out within the
anisotropic Ohta-Jasnow-Kawasaki (OJK) approximation for a system with
nonconserved scalar order parameter. We find that the persistence exponent
theta has a non-trivial value: theta = 0.5034... in space dimension d=3, and
theta = 0.2406... for d=2, the latter being exactly twice the value found for
the unsheared system in d=1. We also find that the autocorrelation exponent
lambda is affected by shear in d=3 but not in d=2.Comment: 6 page
Facilitated spin models: recent and new results
Facilitated or kinetically constrained spin models (KCSM) are a class of
interacting particle systems reversible w.r.t. to a simple product measure.
Each dynamical variable (spin) is re-sampled from its equilibrium distribution
only if the surrounding configuration fulfills a simple local constraint which
\emph{does not involve} the chosen variable itself. Such simple models are
quite popular in the glass community since they display some of the peculiar
features of glassy dynamics, in particular they can undergo a dynamical arrest
reminiscent of the liquid/glass transitiom. Due to the fact that the jumps
rates of the Markov process can be zero, the whole analysis of the long time
behavior becomes quite delicate and, until recently, KCSM have escaped a
rigorous analysis with the notable exception of the East model. In these notes
we will mainly review several recent mathematical results which, besides being
applicable to a wide class of KCSM, have contributed to settle some debated
questions arising in numerical simulations made by physicists. We will also
provide some interesting new extensions. In particular we will show how to deal
with interacting models reversible w.r.t. to a high temperature Gibbs measure
and we will provide a detailed analysis of the so called one spin facilitated
model on a general connected graph.Comment: 30 pages, 3 figure
Evidence of a Critical time in Constrained Kinetic Ising models
We study the relaxational dynamics of the one-spin facilitated Ising model
introduced by Fredrickson and Andersen. We show the existence of a critical
time which separates an initial regime in which the relaxation is exponentially
fast and aging is absent from a regime in which relaxation becomes slow and
aging effects are present. The presence of this fast exponential process and
its associated critical time is in agreement with some recent experimental
results on fragile glasses.Comment: 20 Pages + 7 Figures, Revte
Three-phase coexistence with sequence partitioning in symmetric random block copolymers
We inquire about the possible coexistence of macroscopic and microstructured
phases in random Q-block copolymers built of incompatible monomer types A and B
with equal average concentrations. In our microscopic model, one block
comprises M identical monomers. The block-type sequence distribution is
Markovian and characterized by the correlation \lambda. Upon increasing the
incompatibility \chi\ (by decreasing temperature) in the disordered state, the
known ordered phases form: for \lambda\ > \lambda_c, two coexisting macroscopic
A- and B-rich phases, for \lambda\ < \lambda_c, a microstructured (lamellar)
phase with wave number k(\lambda). In addition, we find a fourth region in the
\lambda-\chi\ plane where these three phases coexist, with different,
non-Markovian sequence distributions (fractionation). Fractionation is revealed
by our analytically derived multiphase free energy, which explicitly accounts
for the exchange of individual sequences between the coexisting phases. The
three-phase region is reached, either, from the macroscopic phases, via a third
lamellar phase that is rich in alternating sequences, or, starting from the
lamellar state, via two additional homogeneous, homopolymer-enriched phases.
These incipient phases emerge with zero volume fraction. The four regions of
the phase diagram meet in a multicritical point (\lambda_c, \chi_c), at which
A-B segregation vanishes. The analytical method, which for the lamellar phase
assumes weak segregation, thus proves reliable particularly in the vicinity of
(\lambda_c, \chi_c). For random triblock copolymers, Q=3, we find the character
of this point and the critical exponents to change substantially with the
number M of monomers per block. The results for Q=3 in the continuous-chain
limit M -> \infty are compared to numerical self-consistent field theory
(SCFT), which is accurate at larger segregation.Comment: 24 pages, 19 figures, version published in PRE, main changes: Sec.
IIIA, Fig. 14, Discussio
Stability of Quasicrystals Composed of Soft Isotropic Particles
Quasicrystals whose building blocks are of mesoscopic rather than atomic
scale have recently been discovered in several soft-matter systems. Contrary to
metallurgic quasicrystals whose source of stability remains a question of great
debate to this day, we argue that the stability of certain soft-matter
quasicrystals can be directly explained by examining a coarse-grained free
energy for a system of soft isotropic particles. We show, both theoretically
and numerically, that the stability can be attributed to the existence of two
natural length scales in the pair potential, combined with effective three-body
interactions arising from entropy. Our newly gained understanding of the
stability of soft quasicrystals allows us to point at their region of stability
in the phase diagram, and thereby may help control the self-assembly of
quasicrystals and a variety of other desired structures in future experimental
realizations.Comment: Revised abstract, more detailed explanations, and better images of
the numerical minimization of the free energ
Shear Alignment and Instability of Smectic Phases
We consider the shear flow of well-aligned one-component smectic phases, such
as thermotropic smectics and lamellar diblock copolymers, below the critical
region. We show that, as a result of thermal fluctuations of the layers,
parallel () alignment is generically unstable and perpendicular ()
alignment is stable against long-wavelength undulations. We also find,
surprisingly, that both and are stable for a narrow window of values
for the anisotropic viscosity.Comment: To appear in PRL. Revtex, 1 figure
Reactions at polymer interfaces: A Monte Carlo Simulation
Reactions at a strongly segregated interface of a symmetric binary polymer
blend are investigated via Monte Carlo simulations. End functionalized
homopolymers of different species interact at the interface instantaneously and
irreversibly to form diblock copolymers. The simulations, in the framework of
the bond fluctuation model, determine the time dependence of the copolymer
production in the initial and intermediate time regime for small reactant
concentration . The results are compared to
recent theories and simulation data of a simple reaction diffusion model. For
the reactant concentration accessible in the simulation, no linear growth of
the copolymer density is found in the initial regime, and a -law is
observed in the intermediate stage.Comment: to appear in Macromolecule
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
Steady State of microemulsions in shear flow
Steady-state properties of microemulsions in shear flow are studied in the
context of a Ginzburg-Landau free-energy approach. Explicit expressions are
given for the structure factor and the time correlation function at the one
loop level of approximation. Our results predict a four-peak pattern for the
structure factor, implying the simultaneous presence of interfaces aligned with
two different orientations.
Due to the peculiar interface structure a non-monotonous relaxation of the
time correlator is also found.Comment: 5 pages, 3 figure
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