23 research outputs found
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
Local scale invariance as dynamical space-time symmetry in phase-ordering kinetics
The scaling of the spatio-temporal response of coarsening systems is studied
through simulations of the 2D and 3D Ising model with Glauber dynamics. The
scaling functions agree with the prediction of local scale invariance,
extending dynamical scaling to a space-time dynamical symmetry.Comment: Latex, 4 pages, 4 figure
Reproductive decisionmaking in the context of HIV/AIDS in Ndola, Zambia
Family planning (FP) programs are increasingly being considered as a logical focal point for STD and HIV/AIDS prevention services because they serve large numbers of women at risk, address the sensitive issue of sexual behavior and fertility control, and the methods for preventing unwanted pregnancy and disease can be the same. FP programs, by providing contraceptive methods, are currently one of the few sources of assistance in the sub-Saharan African region for preventing perinatal transmission of HIV, while the promotion of barrier methods contributes to the prevention of heterosexual transmission. Given this potential, research is needed to understand how the HIV epidemic influences reproductive decision-making. The Africa OR/TA II Project undertook an exploratory study of women and men’s attitudes and experiences regarding reproductive decision-making in a setting of high HIV prevalence in Ndola, Zambia. The objectives, as described in this report, were to examine perceptions of risk by men and women living in a high HIV prevalence setting, how these perceptions are related to decisions about childbearing and contraceptive use, and to identify opportunities for FP programs to expand services to address HIV prevention
Comment on ``Phase ordering in chaotic map lattices with conserved dynamics''
Angelini, Pellicoro, and Stramaglia [Phys. Rev. E {\bf 60}, R5021 (1999),
cond-mat/9907149] (APS) claim that the phase ordering of two-dimensional
systems of sequentially-updated chaotic maps with conserved ``order parameter''
does not belong, for large regions of parameter space, to the expected
universality class. We show here that these results are due to a slow crossover
and that a careful treatment of the data yields normal dynamical scaling.
Moreover, we construct better models, i.e. synchronously-updated coupled map
lattices, which are exempt from these crossover effects, and allow for the
first precise estimates of persistence exponents in this case.Comment: 3 pages, to be published in Phys. Rev.
Theory of Phase Ordering Kinetics
The theory of phase ordering dynamics -- the growth of order through domain
coarsening when a system is quenched from the homogeneous phase into a
broken-symmetry phase -- is reviewed, with the emphasis on recent developments.
Interest will focus on the scaling regime that develops at long times after the
quench. How can one determine the growth laws that describe the time-dependence
of characteristic length scales, and what can be said about the form of the
associated scaling functions? Particular attention will be paid to systems
described by more complicated order parameters than the simple scalars usually
considered, e.g. vector and tensor fields. The latter are needed, for example,
to describe phase ordering in nematic liquid crystals, on which there have been
a number of recent experiments. The study of topological defects (domain walls,
vortices, strings, monopoles) provides a unifying framework for discussing
coarsening in these different systems.Comment: To appear in Advances in Physics. 85 pages, latex, no figures. For a
hard copy with figures, email [email protected]
Random Walks in Logarithmic and Power-Law Potentials, Nonuniversal Persistence, and Vortex Dynamics in the Two-Dimensional XY Model
The Langevin equation for a particle (`random walker') moving in
d-dimensional space under an attractive central force, and driven by a Gaussian
white noise, is considered for the case of a power-law force, F(r) = -
Ar^{-sigma}. The `persistence probability', P_0(t), that the particle has not
visited the origin up to time t, is calculated. For sigma > 1, the force is
asymptotically irrelevant (with respect to the noise), and the asymptotics of
P_0(t) are those of a free random walker. For sigma < 1, the noise is
(dangerously) irrelevant and the asymptotics of P_0(t) can be extracted from a
weak noise limit within a path-integral formalism. For the case sigma=1,
corresponding to a logarithmic potential, the noise is exactly marginal. In
this case, P_0(t) decays as a power-law, P_0(t) \sim t^{-theta}, with an
exponent theta that depends continuously on the ratio of the strength of the
potential to the strength of the noise. This case, with d=2, is relevant to the
annihilation dynamics of a vortex-antivortex pair in the two-dimensional XY
model. Although the noise is multiplicative in the latter case, the relevant
Langevin equation can be transformed to the standard form discussed in the
first part of the paper. The mean annihilation time for a pair initially
separated by r is given by t(r) \sim r^2 ln(r/a) where a is a microscopic
cut-off (the vortex core size). Implications for the nonequilibrium critical
dynamics of the system are discussed and compared to numerical simulation
results.Comment: 10 pages, 1 figur
The Chiral Phase Transition in Dissipative Dynamics
Numerical simulations of the chiral phase transition in the (3+1)dimensional
O(4)-model are presented. The evolutions of the chiral field follow purely
dissipative dynamics, starting from random chirally symmetric initial
configurations down to the true vacuum with spontaneously broken symmetry. The
model stabilizes topological textures which are formed together with domains of
disoriented chiral condensate (DCC) during the roll-down phase. The classically
evolving field acts as source for the emission of pions and mesons.
The exponents of power laws for the growth of angular correlations and for
emission rates are extracted. Fluctuations in the abundance ratios for neutral
and charged pions are compared with those for uncorrelated sources as potential
signature for the chiral phase transition after heavy-ion collisions. It is
found that the presence of stabilizing textures (baryons and antibaryons)
prevents sufficiently rapid growth of DCC-domain size, so observability of
anomalous tails in the abundance ratios is unlikely. However, the transient
formation of growing DCC domains causes sizable broadening of the distributions
as compared to the statistical widths of generic sources.Comment: 28 pages, 8 figure
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
DCC Dynamics in (2+1)D-O(3) model
The dynamics of symmetry-breaking after a quench is numerically simulated on
a lattice for the (2+1)-dimensional O(3) model. In addition to the standard
sigma-model with temperature-dependent Phi^4-potential the energy functional
includes a four-derivative current-current coupling to stabilize the size of
the emerging extended topological textures. The total winding number can be
conserved by constraint. As a model for the chiral phase transition during the
cooling phase after a hadronic collision this allows to investigate the
interference of 'baryon-antibaryon' production with the developing disoriented
aligned domains. The growth of angular correlations, condensate, average
orientation is studied in dependence of texture size, quench rate, symmetry
breaking. The classical dissipative dynamics determines the rate of energy
emitted from the relaxing source for each component of the 3-vector field which
provides a possible signature for domains of Disoriented Chiral Condensate. We
find that the 'pions' are emitted in two distinct pulses; for sufficiently
small lattice size the second one carries the DCC signal, but it is strongly
suppressed as compared to simultaneous 'sigma'-meson emission. We compare the
resulting anomalies in the distributions of DCC pions with probabilities
derived within the commonly used coherent state formalism.Comment: 27 pages, 17 figures; several minor insertions in the text; two
references adde
Ordering dynamics of the driven lattice gas model
The evolution of a two-dimensional driven lattice-gas model is studied on an
L_x X L_y lattice. Scaling arguments and extensive numerical simulations are
used to show that starting from random initial configuration the model evolves
via two stages: (a) an early stage in which alternating stripes of particles
and vacancies are formed along the direction y of the driving field, and (b) a
stripe coarsening stage, in which the number of stripes is reduced and their
average width increases. The number of stripes formed at the end of the first
stage is shown to be a function of L_x/L_y^\phi, with \phi ~ 0.2. Thus,
depending on this parameter, the resulting state could be either single or
multi striped. In the second, stripe coarsening stage, the coarsening time is
found to be proportional to L_y, becoming infinitely long in the thermodynamic
limit. This implies that the multi striped state is thermodynamically stable.
The results put previous studies of the model in a more general framework