489 research outputs found

### Multiscaling to Standard Scaling Crossover in the Bray-Humayun Model for Phase Ordering Kinetics

The Bray-Humayun model for phase ordering dynamics is solved numerically in
one and two space dimensions with conserved and non conserved order parameter.
The scaling properties are analysed in detail finding the crossover from
multiscaling to standard scaling in the conserved case. Both in the
nonconserved case and in the conserved case when standard scaling holds the
novel feature of an exponential tail in the scaling function is found.Comment: 21 pages, 10 Postscript figure

### Lifshitz-Slyozov Scaling For Late-Stage Coarsening With An Order-Parameter-Dependent Mobility

The coarsening dynamics of the Cahn-Hilliard equation with order-parameter
dependent mobility, $\lambda(\phi) \propto (1-\phi^2)^\alpha$, is addressed at
zero temperature in the Lifshitz-Slyozov limit where the minority phase
occupies a vanishingly small volume fraction. Despite the absence of bulk
diffusion for $\alpha>0$, the mean domain size is found to grow as $\propto t^{1/(3+\alpha)}$, due to subdiffusive transport of the order parameter
through the majority phase. The domain-size distribution is determined
explicitly for the physically relevant case $\alpha = 1$.Comment: 4 pages, Revtex, no figure

### Glassy dynamics near zero temperature

We numerically study finite-dimensional spin glasses at low and zero
temperature, finding evidences for (i) strong time/space heterogeneities, (ii)
spontaneous time scale separation and (iii) power law distributions of flipping
times. Using zero temperature dynamics we study blocking, clustering and
persistence phenomena

### Scaling and Crossover in the Large-N Model for Growth Kinetics

The dependence of the scaling properties of the structure factor on space
dimensionality, range of interaction, initial and final conditions, presence or
absence of a conservation law is analysed in the framework of the large-N model
for growth kinetics. The variety of asymptotic behaviours is quite rich,
including standard scaling, multiscaling and a mixture of the two. The
different scaling properties obtained as the parameters are varied are
controlled by a structure of fixed points with their domains of attraction.
Crossovers arising from the competition between distinct fixed points are
explicitely obtained. Temperature fluctuations below the critical temperature
are not found to be irrelevant when the order parameter is conserved. The model
is solved by integration of the equation of motion for the structure factor and
by a renormalization group approach.Comment: 48 pages with 6 figures available upon request, plain LaTe

### 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 $L
\sim (t/\ln[t/t_0])^{1/2}$, though with a time-scale $t_0$ 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 $L$. 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

### Non-trivial exponents in the zero temperature dynamics of the 1D Ising and Potts models

URL: http://www-spht.cea.fr/articles/T94/069International audienceWe consider the Glauber dynamics of the $q$-state Potts model in one dimension at zero temperature. Starting with a random initial configuration, we measure the density $r_t$ of spins which have never flipped from the beginning of the simulation until time $t.$ We find that for large $t,$ the density $r_t$ has a power law decay $\left(r_t \sim t^{-\theta} \right)$ where the exponent $\theta$ varies with $q.$ Our simulations lead to $\theta \simeq .37$ for $q=2,$ $\theta \simeq .53$ for $q=3$ and $\theta \longrightarrow 1$ as $ q \longrightarrow \infty .

### The Effect of Shear on Phase-Ordering Dynamics with Order-Parameter-Dependent Mobility: The Large-n Limit

The effect of shear on the ordering-kinetics of a conserved order-parameter
system with O(n) symmetry and order-parameter-dependent mobility
\Gamma({\vec\phi}) \propto (1- {\vec\phi} ^2/n)^\alpha is studied analytically
within the large-n limit. In the late stage, the structure factor becomes
anisotropic and exhibits multiscaling behavior with characteristic length
scales (t^{2\alpha+5}/\ln t)^{1/2(\alpha+2)} in the flow direction and (t/\ln
t)^{1/2(\alpha+2)} in directions perpendicular to the flow. As in the \alpha=0
case, the structure factor in the shear-flow plane has two parallel ridges.Comment: 6 pages, 2 figure

### Survival Probability of a Ballistic Tracer Particle in the Presence of Diffusing Traps

We calculate the survival probability P_S(t) up to time t of a tracer
particle moving along a deterministic trajectory in a continuous d-dimensional
space in the presence of diffusing but mutually noninteracting traps. In
particular, for a tracer particle moving ballistically with a constant velocity
c, we obtain an exact expression for P_S(t), valid for all t, for d<2. For d
\geq 2, we obtain the leading asymptotic behavior of P_S(t) for large t. In all
cases, P_S(t) decays exponentially for large t, P_S(t) \sim \exp(-\theta t). We
provide an explicit exact expression for the exponent \theta in dimensions d
\leq 2, and for the physically relevant case, d=3, as a function of the system
parameters.Comment: RevTeX, 4 page

### 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]

### Interface fluctuations, bulk fluctuations and dimensionality in the off-equilibrium response of coarsening systems

The relationship between statics and dynamics proposed by Franz, Mezard,
Parisi and Peliti (FMPP) for slowly relaxing systems [Phys.Rev.Lett. {\bf 81},
1758 (1998)] is investigated in the framework of non disordered coarsening
systems. Separating the bulk from interface response we find that for statics
to be retrievable from dynamics the interface contribution must be
asymptotically negligible. How fast this happens depends on dimensionality.
There exists a critical dimensionality above which the interface response
vanishes like the interface density and below which it vanishes more slowly. At
$d=1$ the interface response does not vanish leading to the violation of the
FMPP scheme. This behavior is explained in terms of the competition between
curvature driven and field driven interface motion.Comment: 11 pages, 3 figures. Significantly improved version of the paper with
new results, new numerical simulations and new figure

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