375 research outputs found
Influence of Disorder Strength on Phase Field Models of Interfacial Growth
We study the influence of disorder strength on the interface roughening
process in a phase-field model with locally conserved dynamics. We consider two
cases where the mobility coefficient multiplying the locally conserved current
is either constant throughout the system (the two-sided model) or becomes zero
in the phase into which the interface advances (one-sided model). In the limit
of weak disorder, both models are completely equivalent and can reproduce the
physical process of a fluid diffusively invading a porous media, where
super-rough scaling of the interface fluctuations occurs. On the other hand,
increasing disorder causes the scaling properties to change to intrinsic
anomalous scaling. In the limit of strong disorder this behavior prevails for
the one-sided model, whereas for the two-sided case, nucleation of domains in
front of the invading front are observed.Comment: Accepted for publication in PR
Majority Rule Dynamics in Finite Dimensions
We investigate the long-time behavior of a majority rule opinion dynamics
model in finite spatial dimensions. Each site of the system is endowed with a
two-state spin variable that evolves by majority rule. In a single update
event, a group of spins with a fixed (odd) size is specified and all members of
the group adopt the local majority state. Repeated application of this update
step leads to a coarsening mosaic of spin domains and ultimate consensus in a
finite system. The approach to consensus is governed by two disparate time
scales, with the longer time scale arising from realizations in which spins
organize into coherent single-opinion bands. The consequences of this
geometrical organization on the long-time kinetics are explored.Comment: 8 pages, 2-column revtex format, 11 figures. Version 2: minor changes
in response to referee comments and typos corrected; final version for PR
Reentrant Behavior of the Spinodal Curve in a Nonequilibrium Ferromagnet
The metastable behavior of a kinetic Ising--like ferromagnetic model system
in which a generic type of microscopic disorder induces nonequilibrium steady
states is studied by computer simulation and a mean--field approach. We pay
attention, in particular, to the spinodal curve or intrinsic coercive field
that separates the metastable region from the unstable one. We find that, under
strong nonequilibrium conditions, this exhibits reentrant behavior as a
function of temperature. That is, metastability does not happen in this regime
for both low and high temperatures, but instead emerges for intermediate
temperature, as a consequence of the non-linear interplay between thermal and
nonequilibrium fluctuations. We argue that this behavior, which is in contrast
with equilibrium phenomenology and could occur in actual impure specimens,
might be related to the presence of an effective multiplicative noise in the
system.Comment: 7 pages, 4 figures; Final version to appear in Phys. Rev. E; Section
V has been revise
Statistical physics of the Schelling model of segregation
We investigate the static and dynamic properties of a celebrated model of
social segregation, providing a complete explanation of the mechanisms leading
to segregation both in one- and two-dimensional systems. Standard statistical
physics methods shed light on the rich phenomenology of this simple model,
exhibiting static phase transitions typical of kinetic constrained models,
nontrivial coarsening like in driven-particle systems and percolation-related
phenomena.Comment: 4 pages, 3 figure
Stability of a Nonequilibrium Interface in a Driven Phase Segregating System
We investigate the dynamics of a nonequilibrium interface between coexisting
phases in a system described by a Cahn-Hilliard equation with an additional
driving term. By means of a matched asymptotic expansion we derive equations
for the interface motion. A linear stability analysis of these equations
results in a condition for the stability of a flat interface. We find that the
stability properties of a flat interface depend on the structure of the driving
term in the original equation.Comment: 14 pages Latex, 1 postscript-figur
Dynamics of mesoscopic precipitate lattices in phase separating alloys under external load
We investigate, via three-dimensional atomistic computer simulations, phase
separation in an alloy under external load. A regular two-dimensional array of
cylindrical precipitates, forming a mesoscopic precipitate lattice, evolves in
the case of applied tensile stress by the movement of mesoscopic lattice
defects. A striking similarity to ordinary crystals is found in the movement of
"meso-dislocations", but new mechanisms are also observed. Point defects such
as "meso-vacancies" or "meso-interstitials" are created or annihilated locally
by merging and splitting of precipitates. When the system is subjected to
compressive stress, we observe stacking faults in the mesoscopic
one-dimensional array of plate-like precipitates.Comment: 4 pages, 4 figures, REVTE
Aging classification in glassy dynamics
We study the out of equilibrium dynamics of several models exhibiting aging.
We attempt at identifying various types of aging systems using a phase space
point of view: we introduce a trial classification, based on the overlap
between two replicas of a system, which evolve together until a certain waiting
time, and are then totally decoupled. We investigate in this way two types of
systems, domain growth problems and spin glasses, and we show that they behave
differently.Comment: 18 pages,9 Postscript figures,uses rotate.sty,epsf.st
Coarsening Kinetics of a Two Dimensional O(2) Ginzburg-Landau Model: Effect of Reversible Mode Coupling
We investigate, via numerical simulations, the phase ordering kinetics of a
two- dimensional soft-spin O(2) Ginzburg-Landau model when a reversible mode
cou- pling is included via the conserved conjugate momentum of the spin order
parameter (the model E). Coarsening of the system, when quenched from a dis-
ordered state to zero temperature, is observed to be enhanced by the existence
of the mode coupling terms. The growth of the characteristic length scale L(t)
exhibits an effective super-diffusive growth exponent that can be interpreted
as a positive logarithmic-like correction to a diffusive growth, i.e., L(t) ~
(t ln t)^{1/2}. In order to understand this behavior, we introduced a simple
phenomenological model of coarsening based on the annihilation dynamics of a
vortex-antivortex pair, incorporating the effect of vortex inertia and
logarithmically divergent mobility of the vortex. With a suitable choice of the
parameters, numerical solutions of the simple model can fit the full simulation
results very adequately. The effective growth exponent in the early time stage
is larger due to the effect of the vortex inertia, which crosses over into late
time stage characterized by positive logarithmic correction to a diffusive
growth. We also investigated the non-equilibrium autocorrelation function from
which the so called {\lambda} exponent can be extracted. We get {\lambda} =
1.99(2) which is distinctively larger than the value of {\lambda} = 1.17 for
the purely dissipative model-A dynamics of non-conserved O(2) models.Comment: 19 pages, 8 figure
Coarsening in a Driven Ising Chain with Conserved Dynamics
We study the low-temperature coarsening of an Ising chain subject to
spin-exchange dynamics and a small driving force. This dynamical system reduces
to a domain diffusion process, in which entire domains undergo nearest-neighbor
hopping, except for the shortest domains -- dimers -- which undergo long-range
hopping. This system is characterized by two independent length scales: the
average domain length L(t)~t^{1/2} and the average dimer hopping distance l(t)~
t^{1/4}. As a consequence of these two scales, the density C_k(t) of domains of
length k does not obey scaling. This breakdown of scaling also leads to the
density of short domains decaying as t^{-5/4}, instead of the t^{-3/2} decay
that would arise from pure domain diffusion.Comment: 7 pages, 9 figures, revtex 2-column forma
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