277 research outputs found
Fast and Accurate Coarsening Simulation with an Unconditionally Stable Time Step
We present Cahn-Hilliard and Allen-Cahn numerical integration algorithms that
are unconditionally stable and so provide significantly faster
accuracy-controlled simulation. Our stability analysis is based on Eyre's
theorem and unconditional von Neumann stability analysis, both of which we
present. Numerical tests confirm the accuracy of the von Neumann approach,
which is straightforward and should be widely applicable in phase-field
modeling. We show that accuracy can be controlled with an unbounded time step
Delta-t that grows with time t as Delta-t ~ t^alpha. We develop a
classification scheme for the step exponent alpha and demonstrate that a class
of simple linear algorithms gives alpha=1/3. For this class the speed up
relative to a fixed time step grows with the linear size of the system as N/log
N, and we estimate conservatively that an 8192^2 lattice can be integrated 300
times faster than with the Euler method.Comment: 14 pages, 6 figure
Dynamical Scaling: the Two-Dimensional XY Model Following a Quench
To sensitively test scaling in the 2D XY model quenched from
high-temperatures into the ordered phase, we study the difference between
measured correlations and the (scaling) results of a Gaussian-closure
approximation. We also directly compare various length-scales. All of our
results are consistent with dynamical scaling and an asymptotic growth law , though with a time-scale that depends on the
length-scale in question. We then reconstruct correlations from the
minimal-energy configuration consistent with the vortex positions, and find
them significantly different from the ``natural'' correlations --- though both
scale with . This indicates that both topological (vortex) and
non-topological (``spin-wave'') contributions to correlations are relevant
arbitrarily late after the quench. We also present a consistent definition of
dynamical scaling applicable more generally, and emphasize how to generalize
our approach to other quenched systems where dynamical scaling is in question.
Our approach directly applies to planar liquid-crystal systems.Comment: 10 pages, 10 figure
Phase Ordering of 2D XY Systems Below T_{KT}
We consider quenches in non-conserved two-dimensional XY systems between any
two temperatures below the Kosterlitz-Thouless transition. The evolving systems
are defect free at coarse-grained scales, and can be exactly treated.
Correlations scale with a characteristic length at late
times. The autocorrelation decay exponent, ,
depends on both the initial and the final state of the quench through the
respective decay exponents of equilibrium correlations, . We also discuss time-dependent quenches.Comment: LATeX 11 pages (REVTeX macros), no figure
Anisotropic Coarsening: Grain Shapes and Nonuniversal Persistence
We solve a coarsening system with small but arbitrary anisotropic surface
tension and interface mobility. The resulting size-dependent growth shapes are
significantly different from equilibrium microcrystallites, and have a
distribution of grain sizes different from isotropic theories. As an
application of our results, we show that the persistence decay exponent depends
on anisotropy and hence is nonuniversal.Comment: 4 pages (revtex), 2 eps figure
Perceived stigma among patients receiving antiretroviral treatment: A prospective randomised trial comparing an m-DOT strategy with standardof- care in Kenya
HIV and AIDS remain highly stigmatised. Modified directly observed therapy (m-DOT) supports antiretroviral treatment (ART) adherence but little is known about its association with perceived stigma in resource-constrained settings. In 2003, 234 HIV-infected adults enrolled in a two-arm randomised trial comparing a health centre-based m-DOT strategy with standard self-administration of ART. Data on perceived stigma were collected using Berger’s HIV stigma scale prior to starting ART and after 12 months. Thiswas a secondary analysis to examine whether perceived stigma was related to treatment delivery. Perceived stigma scores declined after 12 months of treatment from a mean of 44.9 (sd=7.6) to a mean of 41.4 (sd=7.7), (t=6.14,
Unraveling critical dynamics: The formation and evolution of topological textures
We study the formation of topological textures in a nonequilibrium phase
transition of an overdamped classical O(3) model in 2+1 dimensions. The phase
transition is triggered through an external, time-dependent effective mass,
parameterized by quench timescale \tau. When measured near the end of the
transition the texture separation and the texture width scale respectively as
\tau^(0.39 \pm 0.02) and \tau^(0.46 \pm 0.04), significantly larger than
\tau^(0.25) predicted from the Kibble-Zurek mechanism. We show that
Kibble-Zurek scaling is recovered at very early times but that by the end of
the transition the power-laws result instead from a competition between the
length scale determined at freeze-out and the ordering dynamics of a textured
system. In the context of phase ordering these results suggest that the
multiple length scales characteristic of the late-time ordering of a textured
system derive from the critical dynamics of a single nonequilibrium correlation
length. In the context of defect formation these results imply that significant
evolution of the defect network can occur before the end of the phase
transition. Therefore a quantitative understanding of the defect network at the
end of the phase transition generally requires an understanding of both
critical dynamics and the interactions among topological defects.Comment: 12 pages, revtex, 9 figures in eps forma
The Energy-Scaling Approach to Phase-Ordering Growth Laws
We present a simple, unified approach to determining the growth law for the
characteristic length scale, , in the phase ordering kinetics of a system
quenched from a disordered phase to within an ordered phase. This approach,
based on a scaling assumption for pair correlations, determines
self-consistently for purely dissipative dynamics by computing the
time-dependence of the energy in two ways. We derive growth laws for conserved
and non-conserved models, including two-dimensional XY models and
systems with textures. We demonstrate that the growth laws for other systems,
such as liquid-crystals and Potts models, are determined by the type of
topological defect in the order parameter field that dominates the energy. We
also obtain generalized Porod laws for systems with topological textures.Comment: LATeX 18 pages (REVTeX macros), one postscript figure appended,
REVISED --- rearranged and clarified, new paragraph on naive dimensional
analysis at end of section I
Corrections to Scaling in the Phase-Ordering Dynamics of a Vector Order Parameter
Corrections to scaling, associated with deviations of the order parameter
from the scaling morphology in the initial state, are studied for systems with
O(n) symmetry at zero temperature in phase-ordering kinetics. Including
corrections to scaling, the equal-time pair correlation function has the form
C(r,t) = f_0(r/L) + L^{-omega} f_1(r/L) + ..., where L is the coarsening length
scale. The correction-to-scaling exponent, omega, and the correction-to-scaling
function, f_1(x), are calculated for both nonconserved and conserved order
parameter systems using the approximate Gaussian closure theory of Mazenko. In
general, omega is a non-trivial exponent which depends on both the
dimensionality, d, of the system and the number of components, n, of the order
parameter. Corrections to scaling are also calculated for the nonconserved 1-d
XY model, where an exact solution is possible.Comment: REVTeX, 20 pages, 2 figure
Anisotropic dynamical scaling in a spin model with competing interactions
Results are presented for the kinetics of domain growth of a two-dimensional
Ising spin model with competing interactions quenched from a disordered to a
striped phase. The domain growth exponent are and for
single-spin-flip and spin-exchange dynamics, as found in previous simulations.
However the correlation functions measured in the direction parallel and
transversal to the stripes are different as suggested by the existence of
different interface energies between the ground states of the model. In the
case of single-spin-flip dynamics an anisotropic version of the
Ohta-Jasnow-Kawasaki theory for the pair scaling function can be used to fit
our data.Comment: 4 pages, REVTeX fil
Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet
We study the low-temperature behaviour of the classical Heisenberg
antiferromagnet with nearest neighbour interactions on the pyrochlore lattice.
Because of geometrical frustration, the ground state of this model has an
extensive number of degrees of freedom. We show, by analysing the effects of
small fluctuations around the ground-state manifold, and from the results of
Monte Carlo and molecular dynamics simulations, that the system is disordered
at all temperatures, T, and has a finite relaxation time, which varies as 1/T
for small T.Comment: 4 pages revtex; 3 figures automatically include
- …