340 research outputs found
Breakdown of Scaling in the Nonequilibrium Critical Dynamics of the Two-Dimensional XY Model
The approach to equilibrium, from a nonequilibrium initial state, in a system
at its critical point is usually described by a scaling theory with a single
growing length scale, , where z is the dynamic exponent
that governs the equilibrium dynamics. We show that, for the 2D XY model, the
rate of approach to equilibrium depends on the initial condition. In
particular, if no free vortices are present in the
initial state, while if free vortices are
present.Comment: 4 pages, 3 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
Heterocyst placement strategies to maximize growth of cyanobacterial filaments
Under conditions of limited fixed-nitrogen, some filamentous cyanobacteria
develop a regular pattern of heterocyst cells that fix nitrogen for the
remaining vegetative cells. We examine three different heterocyst placement
strategies by quantitatively modelling filament growth while varying both
external fixed-nitrogen and leakage from the filament. We find that there is an
optimum heterocyst frequency which maximizes the growth rate of the filament;
the optimum frequency decreases as the external fixed-nitrogen concentration
increases but increases as the leakage increases. In the presence of leakage,
filaments implementing a local heterocyst placement strategy grow significantly
faster than filaments implementing random heterocyst placement strategies. With
no extracellular fixed-nitrogen, consistent with recent experimental studies of
Anabaena sp. PCC 7120, the modelled heterocyst spacing distribution using our
local heterocyst placement strategy is qualitatively similar to experimentally
observed patterns. As external fixed-nitrogen is increased, the spacing
distribution for our local placement strategy retains the same shape while the
average spacing between heterocysts continuously increases.Comment: This is an author-created, un-copyedited version of an article
accepted for publication in Physical Biology. IOP Publishing Ltd is not
responsible for any errors or omissions in this version of the manuscript or
any version derived from it. The definitive publisher-authenticated version
will be available onlin
Stress-free Spatial Anisotropy in Phase-Ordering
We find spatial anisotropy in the asymptotic correlations of two-dimensional
Ising models under non-equilibrium phase-ordering. Anisotropy is seen for
critical and off-critical quenches and both conserved and non-conserved
dynamics. We argue that spatial anisotropy is generic for scalar systems
(including Potts models) with an anisotropic surface tension. Correlation
functions will not be universal in these systems since anisotropy will depend
on, e.g., temperature, microscopic interactions and dynamics, disorder, and
frustration.Comment: 4 pages, 4 figures include
Area-preserving dynamics of a long slender finger by curvature: a test case for the globally conserved phase ordering
A long and slender finger can serve as a simple ``test bed'' for different
phase ordering models. In this work, the globally-conserved,
interface-controlled dynamics of a long finger is investigated, analytically
and numerically, in two dimensions. An important limit is considered when the
finger dynamics are reducible to the area-preserving motion by curvature. A
free boundary problem for the finger shape is formulated. An asymptotic
perturbation theory is developed that uses the finger aspect ratio as a small
parameter. The leading-order approximation is a modification of ``the Mullins
finger" (a well-known analytic solution) which width is allowed to slowly vary
with time. This time dependence is described, in the leading order, by an
exponential law with the characteristic time proportional to the (constant)
finger area. The subleading terms of the asymptotic theory are also calculated.
Finally, the finger dynamics is investigated numerically, employing the
Ginzburg-Landau equation with a global conservation law. The theory is in a
very good agreement with the numerical solution.Comment: 8 pages, 4 figures, Latex; corrected typo
Previous reproductive history and post-natal family planning among HIV-infected women in Ukraine
BACKGROUND: Ukraine has the highest antenatal HIV prevalence in Europe. The national prevention of mother-to-child transmission (MTCT) programme has reduced the MTCT rate, but less attention has been given to the prevention of unintended pregnancy among HIV-positive women. Our objectives were to describe the reproductive health, condom use and family planning (FP) practices of HIV-positive childbearing Ukrainian women and to identify factors associated with different methods of post-natal contraception.
METHODS: HIV-infected childbearing women, diagnosed before or during pregnancy, were enrolled prospectively in a post-natal cohort study in four regional HIV/AIDS centres in Ukraine from December 2007. Logistic regression models were used to identify factors associated with post-natal FP practices.
RESULTS: Data were available for 371 women enrolled by March 2009; 82% (n = 303) were married or cohabiting, 27% (97 of 363) reported a current HIV-negative sexual partner and 69% were diagnosed with HIV during their most recent pregnancy. Overall, 21% (75 of 349) of women were not using contraception post-natally (of whom 80% reported no current sexual activity), 50% (174 of 349) used condoms, 20% (74 of 349) relied solely/partially on coitus interruptus and 4% used hormonal methods or intrauterine device. Among married/cohabiting women, consistent use of condoms in the previous pregnancy [AOR 1.96 (95%CI 1.06ā3.62)], having an HIV-positive partner [AOR 0.42 (0.20ā0.87)], current sexual activity [AOR 4.53 (1.19ā17.3)] and study site were significantly associated with post-natal condom use; 16% of those with HIV-negative partners did not use condoms. Risk factors for non-use of FP were lack of affordability [AOR 6.34 (1.73ā23.2)] and inconsistent use of condoms in the previous pregnancy [AOR 7.25 (1.41ā37.2)].
CONCLUSIONS: More than 40% of HIV-positive women in this population are at risk of unintended pregnancy and the one in six women in HIV-discordant couples not using barrier methods risk transmitting HIV to their partners. Our study results are limited by the observational nature of the data and the potential for both measured and unmeasured confounding
Floating Phase in 2D ANNNI Model
We investigate whether the floating phase (where the correlation length is
infinite and the spin-spin correlation decays algebraically with distance)
exists in the temperature() - frustration parameter () phase diagram
of 2D ANNNI model. To identify this phase, we look for the region where (i)
finite size effect is prominent and (ii) some relevant physical quantity
changes somewhat sharply and this change becomes sharper as the system size
increases. For , the low temperature phase is ferromagnetic and
we study energy and magnetization. For , the low temperature
phase is antiphase and we study energy, layer magnetization, length of domain
walls running along the direction of frustration, number of domain-intercepts
that are of length 2 along the direction of frustration, and the number of
domain walls that do not touch the upper and/or lower boundary. In agreement
with some previous studies, our final conclusion is that, the floating phase
exists, if at all, only along a line.Comment: 9 pages, 17 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
Glassy timescale divergence and anomalous coarsening in a kinetically constrained spin chain
We analyse the out of equilibrium behavior of an Ising spin chain with an
asymmetric kinetic constraint after a quench to a low temperature T. In the
limit T\to 0, we provide an exact solution of the resulting coarsening process.
The equilibration time exhibits a `glassy' divergence \teq=\exp(const/T^2)
(popular as an alternative to the Vogel-Fulcher law), while the average domain
length grows with a temperature dependent exponent, \dbar ~ t^{T\ln 2}. We show
that the equilibration time \teq also sets the timescale for the linear
response of the system at low temperatures.Comment: 4 pages, revtex, includes two eps figures. Proof of energy barrier
hierarchy added. Version to be published in Phys Rev Let
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