11,438 research outputs found
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
Velocity Distribution of Topological Defects in Phase-Ordering Systems
The distribution of interface (domain-wall) velocities in a
phase-ordering system is considered. Heuristic scaling arguments based on the
disappearance of small domains lead to a power-law tail,
for large v, in the distribution of . The exponent p is
given by , where d is the space dimension and 1/z is the growth
exponent, i.e. z=2 for nonconserved (model A) dynamics and z=3 for the
conserved case (model B). The nonconserved result is exemplified by an
approximate calculation of the full distribution using a gaussian closure
scheme. The heuristic arguments are readily generalized to conserved case
(model B). The nonconserved result is exemplified by an approximate calculation
of the full distribution using a gaussian closure scheme. The heuristic
arguments are readily generalized to systems described by a vector order
parameter.Comment: 5 pages, Revtex, no figures, minor revisions and updates, to appear
in Physical Review E (May 1, 1997
Vortex annihilation in the ordering kinetics of the O(2) model
The vortex-vortex and vortex-antivortex correlation functions are determined
for the two-dimensional O(2) model undergoing phase ordering. We find
reasonably good agreement with simulation results for the vortex-vortex
correlation function where there is a short-scaled distance depletion zone due
to the repulsion of like-signed vortices. The vortex-antivortex correlation
function agrees well with simulation results for intermediate and long-scaled
distances. At short-scaled distances the simulations show a depletion zone not
seen in the theory.Comment: 28 pages, REVTeX, submitted to Phys. Rev.
Phase Ordering Dynamics of the O(n) Model - Exact Predictions and Numerical Results
We consider the pair correlation functions of both the order parameter field
and its square for phase ordering in the model with nonconserved order
parameter, in spatial dimension and spin dimension .
We calculate, in the scaling limit, the exact short-distance singularities of
these correlation functions and compare these predictions to numerical
simulations. Our results suggest that the scaling hypothesis does not hold for
the model. Figures (23) are available on request - email
[email protected]: 23 pages, Plain LaTeX, M/C.TH.93/2
Phase Ordering Kinetics with External Fields and Biased Initial Conditions
The late-time phase-ordering kinetics of the O(n) model for a non-conserved
order parameter are considered for the case where the O(n) symmetry is broken
by the initial conditions or by an external field. An approximate theoretical
approach, based on a `gaussian closure' scheme, is developed, and results are
obtained for the time-dependence of the mean order parameter, the pair
correlation function, the autocorrelation function, and the density of
topological defects [e.g. domain walls (), or vortices ()]. The
results are in qualitative agreement with experiments on nematic films and
related numerical simulations on the two-dimensional XY model with biased
initial conditions.Comment: 35 pages, latex, no figure
A volumetric Penrose inequality for conformally flat manifolds
We consider asymptotically flat Riemannian manifolds with nonnegative scalar
curvature that are conformal to , and so that
their boundary is a minimal hypersurface. (Here, is open
bounded with smooth mean-convex boundary.) We prove that the ADM mass of any
such manifold is bounded below by , where is the
Euclidean volume of and is the volume of the Euclidean
unit -ball. This gives a partial proof to a conjecture of Bray and Iga
\cite{brayiga}. Surprisingly, we do not require the boundary to be outermost.Comment: 7 page
Corrections to Scaling in Phase-Ordering Kinetics
The leading correction to scaling associated with departures of the initial
condition from the scaling morphology is determined for some soluble models of
phase-ordering kinetics. The result for the pair correlation function has the
form C(r,t) = f_0(r/L) + L^{-\omega} f_1(r/L) + ..., where L is a
characteristic length scale extracted from the energy. The
correction-to-scaling exponent \omega has the value \omega=4 for the d=1
Glauber model, the n-vector model with n=\infty, and the approximate theory of
Ohta, Jasnow and Kawasaki. For the approximate Mazenko theory, however, \omega
has a non-trivial value: omega = 3.8836... for d=2, and \omega = 3.9030... for
d=3. The correction-to-scaling functions f_1(x) are also calculated.Comment: REVTEX, 7 pages, two figures, needs epsf.sty and multicol.st
Reply to a Comment
Reply to the Comment by F. Corberi, E. Lipiello and M. Zannetti
(cond-mat/0211609)
do testicular seminoma and nonseminoma share the same etiology evidence from an age period cohort analysis of incidence trends in eight european countries
The incidence of the two main clinical subentities of testicular germ cell cancer (seminoma and nonseminoma) is increasing throughout Europe. Most studies have revealed little variation in risk factors between the two subtypes. This study compared generation-specific trends in eight European countries, hypothesizing that similar temporal pattern by birth cohort implied that seminoma and nonseminoma had a largely comparable etiology. The results are presented using the age-period-cohort model and the nonidentifiability problem highlighted by partitioning the age, period, and cohort effects in terms of their linear and curvature component parts, assuming a priori that cohort effects predominated. Despite uniform overall increases by calendar period, declining rates of nonseminoma but not pure seminoma were observed in the majority of countries during the 1990s. The subtype trends were, however, largely analogous on a birth cohort scale. Notable observations were a decline in rates of both subtypes among recent birth cohorts in Switzerland and a short-term wartime effect in several countries, involving an attenuation of increasing risk of both subtypes in men born in 1940 to 1945. Departures from the steady increases in testicular cancer over time were likely to occur for nonseminomas some years ahead of seminoma on a period scale. The importance of birth cohort coincided with the view that given a short time interval of susceptibility to exposures earlier in life and a biologically constant time to diagnosis, all temporal changes in rate-limiting exposures should appear as generational effects. Trends in seminoma and nonseminoma conform to largely the same temporal patterns on this scale, implying that they share important etiologic factors
Non-equilibrium Phase-Ordering with a Global Conservation Law
In all dimensions, infinite-range Kawasaki spin exchange in a quenched Ising
model leads to an asymptotic length-scale
at because the kinetic coefficient is renormalized by the broken-bond
density, . For , activated kinetics recovers the
standard asymptotic growth-law, . However, at all temperatures,
infinite-range energy-transport is allowed by the spin-exchange dynamics. A
better implementation of global conservation, the microcanonical Creutz
algorithm, is well behaved and exhibits the standard non-conserved growth law,
, at all temperatures.Comment: 2 pages and 2 figures, uses epsf.st
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