104 research outputs found
Self similar Barkhausen noise in magnetic domain wall motion
A model for domain wall motion in ferromagnets is analyzed. Long-range
magnetic dipolar interactions are shown to give rise to self-similar dynamics
when the external magnetic field is increased adiabatically. The power spectrum
of the resultant Barkhausen noise is of the form , where
can be estimated from the critical exponents for interface
depinning in random media.Comment: 7 pages, RevTex. To appear in Phys. Rev. Let
Collective Transport in Arrays of Quantum Dots
(WORDS: QUANTUM DOTS, COLLECTIVE TRANSPORT, PHYSICAL EXAMPLE OF KPZ)
Collective charge transport is studied in one- and two-dimensional arrays of
small normal-metal dots separated by tunnel barriers. At temperatures well
below the charging energy of a dot, disorder leads to a threshold for
conduction which grows linearly with the size of the array. For short-ranged
interactions, one of the correlation length exponents near threshold is found
from a novel argument based on interface growth. The dynamical exponent for the
current above threshold is also predicted analytically, and the requirements
for its experimental observation are described.Comment: 12 pages, 3 postscript files included, REVTEX v2, (also available by
anonymous FTP from external.nj.nec.com, in directory /pub/alan/dotarrays [as
separate files]) [replacement: FIX OF WRONG VERSION, BAD SHAR] March 17,
1993, NEC
Depinning transition and thermal fluctuations in the random-field Ising model
We analyze the depinning transition of a driven interface in the 3d
random-field Ising model (RFIM) with quenched disorder by means of Monte Carlo
simulations. The interface initially built into the system is perpendicular to
the [111]-direction of a simple cubic lattice. We introduce an algorithm which
is capable of simulating such an interface independent of the considered
dimension and time scale. This algorithm is applied to the 3d-RFIM to study
both the depinning transition and the influence of thermal fluctuations on this
transition. It turns out that in the RFIM characteristics of the depinning
transition depend crucially on the existence of overhangs. Our analysis yields
critical exponents of the interface velocity, the correlation length, and the
thermal rounding of the transition. We find numerical evidence for a scaling
relation for these exponents and the dimension d of the system.Comment: 6 pages, including 9 figures, submitted for publicatio
Using force covariance to derive effective stochastic interactions in dissipative particle dynamics
There exist methods for determining effective conservative interactions in
coarse grained particle based mesoscopic simulations. The resulting models can
be used to capture thermal equilibrium behavior, but in the model system we
study do not correctly represent transport properties. In this article we
suggest the use of force covariance to determine the full functional form of
dissipative and stochastic interactions. We show that a combination of the
radial distribution function and a force covariance function can be used to
determine all interactions in dissipative particle dynamics. Furthermore we use
the method to test if the effective interactions in dissipative particle
dynamics (DPD) can be adjusted to produce a force covariance consistent with a
projection of a microscopic Lennard-Jones simulation. The results indicate that
the DPD ansatz may not be consistent with the underlying microscopic dynamics.
We discuss how this result relates to theoretical studies reported in the
literature.Comment: 10 pages, 10 figure
Interface Motion in Random Media at Finite Temperature
We have studied numerically the dynamics of a driven elastic interface in a
random medium, focusing on the thermal rounding of the depinning transition and
on the behavior in the pinned phase. Thermal effects are quantitatively
more important than expected from simple dimensional estimates. For sufficient
low temperature the creep velocity at a driving force equal to the
depinning force exhibits a power-law dependence on , in agreement with
earlier theoretical and numerical predictions for CDW's. We have also examined
the dynamics in the pinned phase resulting from slowly increasing the
driving force towards threshold. The distribution of avalanche sizes
decays as , with , in agreement with
recent theoretical predictions.Comment: harvmac.tex, 30 pages, including 9 figures, available upon request.
SU-rm-94073
Traveling length and minimal traveling time for flow through percolation networks with long-range spatial correlations
We study the distributions of traveling length l and minimal traveling time t
through two-dimensional percolation porous media characterized by long-range
spatial correlations. We model the dynamics of fluid displacement by the
convective movement of tracer particles driven by a pressure difference between
two fixed sites (''wells'') separated by Euclidean distance r. For strongly
correlated pore networks at criticality, we find that the probability
distribution functions P(l) and P(t) follow the same scaling Ansatz originally
proposed for the uncorrelated case, but with quite different scaling exponents.
We relate these changes in dynamical behavior to the main morphological
difference between correlated and uncorrelated clusters, namely, the
compactness of their backbones. Our simulations reveal that the dynamical
scaling exponents for correlated geometries take values intermediate between
the uncorrelated and homogeneous limiting cases
Avalanches and Correlations in Driven Interface Depinning
We study the critical behavior of a driven interface in a medium with random
pinning forces by analyzing spatial and temporal correlations in a lattice
model recently proposed by Sneppen [Phys. Rev. Lett. {\bf 69}, 3539 (1992)].
The static and dynamic behavior of the model is related to the properties of
directed percolation. We show that, due to the interplay of local and global
growth rules, the usual method of dynamical scaling has to be modified. We
separate the local from the global part of the dynamics by defining a train of
causal growth events, or "avalanche", which can be ascribed a well-defined
dynamical exponent where is the
roughness exponent of the interface. We observe that the avalanche size
distribution obeys a power-law decay with an exponent .Comment: 7 pages, (5 figures available upon request), REVTeX, RUB-TP3-93-0
Depinning with dynamic stress overshoots: A hybrid of critical and pseudohysteretic behavior
A model of an elastic manifold driven through a random medium by an applied
force F is studied focussing on the effects of inertia and elastic waves, in
particular {\it stress overshoots} in which motion of one segment of the
manifold causes a temporary stress on its neighboring segments in addition to
the static stress. Such stress overshoots decrease the critical force for
depinning and make the depinning transition hysteretic. We find that the steady
state velocity of the moving phase is nevertheless history independent and the
critical behavior as the force is decreased is in the same universality class
as in the absence of stress overshoots: the dissipative limit which has been
studied analytically. To reach this conclusion, finite-size scaling analyses of
a variety of quantities have been supplemented by heuristic arguments.
If the force is increased slowly from zero, the spectrum of avalanche sizes
that occurs appears to be quite different from the dissipative limit. After
stopping from the moving phase, the restarting involves both fractal and
bubble-like nucleation. Hysteresis loops can be understood in terms of a
depletion layer caused by the stress overshoots, but surprisingly, in the limit
of very large samples the hysteresis loops vanish. We argue that, although
there can be striking differences over a wide range of length scales, the
universality class governing this pseudohysteresis is again that of the
dissipative limit. Consequences of this picture for the statistics and dynamics
of earthquakes on geological faults are briefly discussed.Comment: 43 pages, 57 figures (yes, that's a five followed by a seven), revte
Collective Particle Flow through Random Media
A simple model for the nonlinear collective transport of interacting
particles in a random medium with strong disorder is introduced and analyzed. A
finite threshold for the driving force divides the behavior into two regimes
characterized by the presence or absence of a steady-state particle current.
Below this threshold, transient motion is found in response to an increase in
the force, while above threshold the flow approaches a steady state with motion
only on a network of channels which is sparse near threshold. Some of the
critical behavior near threshold is analyzed via mean field theory, and
analytic results on the statistics of the moving phase are derived. Many of the
results should apply, at least qualitatively, to the motion of magnetic bubble
arrays and to the driven motion of vortices in thin film superconductors when
the randomness is strong enough to destroy the tendencies to lattice order even
on short length scales. Various history dependent phenomena are also discussed.Comment: 63 preprint pages plus 6 figures. Submitted to Phys Rev
Pattern Formation in Interface Depinning and Other Models: Erratically Moving Spatial Structures
We study erratically moving spatial structures that are found in a driven
interface in a random medium at the depinning threshold. We introduce a
bond-disordered variant of the Sneppen model and study the effect of extremal
dynamics on the morphology of the interface. We find evidence for the formation
of a structure which moves along with the growth site. The time average of the
structure, which is defined with respect to the active spot of growth, defines
an activity-centered pattern. Extensive Monte Carlo simulations show that the
pattern has a tail which decays slowly, as a power law. To understand this sort
of pattern formation, we write down an approximate integral equation involving
the local interface dynamics and long-ranged jumps of the growth spot. We
clarify the nature of the approximation by considering a model for which the
integral equation is exactly derivable from an extended master equation.
Improvements to the equation are considered by adding a second coupled equation
which provides a self-consistent description. The pattern, which defines a
one-point correlation function, is shown to have a strong effect on ordinary
space-fixed two-point correlation functions. Finally we present evidence that
this sort of pattern formation is not confined to the interface problem, but is
generic to situations in which the activity at succesive time steps is
correlated, as for instance in several other extremal models. We present
numerical results for activity-centered patterns in the Bak-Sneppen model of
evolution and the Zaitsev model of low-temperature creep.Comment: RevTeX, 18 pages, 19 eps-figures, To appear in Phys. Rev.
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