782 research outputs found
Scaling behaviour of lattice animals at the upper critical dimension
We perform numerical simulations of the lattice-animal problem at the upper
critical dimension d=8 on hypercubic lattices in order to investigate
logarithmic corrections to scaling there. Our stochastic sampling method is
based on the pruned-enriched Rosenbluth method (PERM), appropriate to linear
polymers, and yields high statistics with animals comprised of up to 8000
sites. We estimate both the partition sums (number of different animals) and
the radii of gyration. We re-verify the Parisi-Sourlas prediction for the
leading exponents and compare the logarithmic-correction exponents to two
partially differing sets of predictions from the literature. Finally, we
propose, and test, a new Parisi-Sourlas-type scaling relation appropriate for
the logarithmic-correction exponents.Comment: 10 pages, 5 figure
Correlated disordered interactions on Potts models
Using a weak-disorder scheme and real-space renormalization-group techniques,
we obtain analytical results for the critical behavior of various q-state Potts
models with correlated disordered exchange interactions along d1 of d spatial
dimensions on hierarchical (Migdal-Kadanoff) lattices. Our results indicate
qualitative differences between the cases d-d1=1 (for which we find nonphysical
random fixed points, suggesting the existence of nonperturbative fixed
distributions) and d-d1>1 (for which we do find acceptable perturbartive random
fixed points), in agreement with previous numerical calculations by Andelman
and Aharony. We also rederive a criterion for relevance of correlated disorder,
which generalizes the usual Harris criterion.Comment: 8 pages, 4 figures, to be published in Physical Review
Scaling properties in off equilibrium dynamical processes
In the present paper, we analyze the consequences of scaling hypotheses on
dynamic functions, as two times correlations . We show, under general
conditions, that must obey the following scaling behavior , where the scaling variable is
and , two
undetermined functions. The presence of a non constant exponent
signals the appearance of multiscaling properties in the dynamics.Comment: 6 pages, no figure
Distribution of the area enclosed by a 2D random walk in a disordered medium
The asymptotic probability distribution for a Brownian particle wandering in
a 2D plane with random traps to enclose the algebraic area A by time t is
calculated using the instanton technique.Comment: 4 pages, ReVTeX. Phys. Rev. E (March 1999), to be publishe
Frustrated two-dimensional Josephson junction array near incommensurability
To study the properties of frustrated two-dimensional Josephson junction
arrays near incommensurability, we examine the current-voltage characteristics
of a square proximity-coupled Josephson junction array at a sequence of
frustrations f=3/8, 8/21, 0.382 , 2/5, and 5/12.
Detailed scaling analyses of the current-voltage characteristics reveal
approximately universal scaling behaviors for f=3/8, 8/21, 0.382, and 2/5. The
approximately universal scaling behaviors and high superconducting transition
temperatures indicate that both the nature of the superconducting transition
and the vortex configuration near the transition at the high-order rational
frustrations f=3/8, 8/21, and 0.382 are similar to those at the nearby simple
frustration f=2/5. This finding suggests that the behaviors of Josephson
junction arrays in the wide range of frustrations might be understood from
those of a few simple rational frustrations.Comment: RevTex4, 4 pages, 4 eps figures, to appear in Phys. Rev.
Methane in underground air in Gibraltar karst
AbstractLittle is known about the abundance and geochemical behaviour of gaseous methane in the unsaturated zone of karst terrains. The concentrations and δ13C of methane in background atmosphere, soil air and cave air collected at monthly intervals over a 4yr period are reported for St. Michaels Cave, Gibraltar, where the regional climate, surface and cave processes are well documented. Methane concentrations measured in Gibraltar soil are lower than the local background atmosphere average of 1868ppb and fall to <500ppb. The abundance–δ13C relationships in soil air methane lack strong seasonality and suggest mixing between atmosphere and a 12C depleted residue after methanotrophic oxidation. Methane abundances in cave air are also lower than the local background atmosphere average but show strong seasonality that is related to ventilation-controlled annual cycles shown by CO2. Cave air methane abundances are lowest in the CO2-rich air that outflows from cave entrances during the winter and show strong inverse relationship between CH4 abundance and δ13C which is diagnostic of methanotrophy within the cave and unsaturated zone. Anomalies in the soil and cave air seasonal patterns characterised by transient elevated CH4 mixing ratios with δ13C values lower than −47‰ suggests intermittent biogenic input. Dynamically ventilated Gibraltar caves may act as a net sink for atmospheric methane
Mode-Locking in Driven Disordered Systems as a Boundary-Value Problem
We study mode-locking in disordered media as a boundary-value problem.
Focusing on the simplest class of mode-locking models which consists of a
single driven overdamped degree-of-freedom, we develop an analytical method to
obtain the shape of the Arnol'd tongues in the regime of low ac-driving
amplitude or high ac-driving frequency. The method is exact for a scalloped
pinning potential and easily adapted to other pinning potentials. It is
complementary to the analysis based on the well-known Shapiro's argument that
holds in the perturbative regime of large driving amplitudes or low driving
frequency, where the effect of pinning is weak.Comment: 6 pages, 7 figures, RevTeX, Submitte
Replica Symmetry Breaking Instability in the 2D XY model in a random field
We study the 2D vortex-free XY model in a random field, a model for randomly
pinned flux lines in a plane. We construct controlled RG recursion relations
which allow for replica symmetry breaking (RSB). The fixed point previously
found by Cardy and Ostlund in the glass phase is {\it unstable} to RSB.
The susceptibility associated to infinitesimal RSB perturbation in the
high-temperature phase is found to diverge as
when . This provides analytical evidence that RSB occurs
in finite dimensional models. The physical consequences for the glass phase are
discussed.Comment: 8 pages, REVTeX, LPTENS-94/2
Smeared phase transition in a three-dimensional Ising model with planar defects: Monte-Carlo simulations
We present results of large-scale Monte Carlo simulations for a
three-dimensional Ising model with short range interactions and planar defects,
i.e., disorder perfectly correlated in two dimensions. We show that the phase
transition in this system is smeared, i.e., there is no single critical
temperature, but different parts of the system order at different temperatures.
This is caused by effects similar to but stronger than Griffiths phenomena. In
an infinite-size sample there is an exponentially small but finite probability
to find an arbitrary large region devoid of impurities. Such a rare region can
develop true long-range order while the bulk system is still in the disordered
phase. We compute the thermodynamic magnetization and its finite-size effects,
the local magnetization, and the probability distribution of the ordering
temperatures for different samples. Our Monte-Carlo results are in good
agreement with a recent theory based on extremal statistics.Comment: 9 pages, 6 eps figures, final version as publishe
Drag forces on inclusions in classical fields with dissipative dynamics
We study the drag force on uniformly moving inclusions which interact
linearly with dynamical free field theories commonly used to study soft
condensed matter systems. Drag forces are shown to be nonlinear functions of
the inclusion velocity and depend strongly on the field dynamics. The general
results obtained can be used to explain drag forces in Ising systems and also
predict the existence of drag forces on proteins in membranes due to couplings
to various physical parameters of the membrane such as composition, phase and
height fluctuations.Comment: 14 pages, 7 figure
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