1,137 research outputs found
Universal distribution of threshold forces at the depinning transition
We study the distribution of threshold forces at the depinning transition for
an elastic system of finite size, driven by an external force in a disordered
medium at zero temperature. Using the functional renormalization group (FRG)
technique, we compute the distribution of pinning forces in the quasi-static
limit. This distribution is universal up to two parameters, the average
critical force, and its width. We discuss possible definitions for threshold
forces in finite-size samples. We show how our results compare to the
distribution of the latter computed recently within a numerical simulation of
the so-called critical configuration.Comment: 12 pages, 7 figures, revtex
Renormalization group study of the two-dimensional random transverse-field Ising model
The infinite disorder fixed point of the random transverse-field Ising model
is expected to control the critical behavior of a large class of random quantum
and stochastic systems having an order parameter with discrete symmetry. Here
we study the model on the square lattice with a very efficient numerical
implementation of the strong disorder renormalization group method, which makes
us possible to treat finite samples of linear size up to . We have
calculated sample dependent pseudo-critical points and studied their
distribution, which is found to be characterized by the same shift and width
exponent: . For different types of disorder the infinite disorder
fixed point is shown to be characterized by the same set of critical exponents,
for which we have obtained improved estimates: and
. We have also studied the scaling behavior of the magnetization
in the vicinity of the critical point as well as dynamical scaling in the
ordered and disordered Griffiths phases
Chemical fracture and distribution of extreme values
When a corrosive solution reaches the limits of a solid sample, a chemical
fracture occurs. An analytical theory for the probability of this chemical
fracture is proposed and confirmed by extensive numerical experiments on a two
dimensional model. This theory follows from the general probability theory of
extreme events given by Gumbel. The analytic law differs from the Weibull law
commonly used to describe mechanical failures for brittle materials. However a
three parameters fit with the Weibull law gives good results, confirming the
empirical value of this kind of analysis.Comment: 7 pages, 5 figures, to appear in Europhysics Letter
Statistics of Lead Changes in Popularity-Driven Systems
We study statistical properties of the highest degree, or most popular, nodes
in growing networks. We show that the number of lead changes increases
logarithmically with network size N, independent of the details of the growth
mechanism. The probability that the first node retains the lead approaches a
finite constant for popularity-driven growth, and decays as N^{-phi}(ln
N)^{-1/2}, with phi=0.08607..., for growth with no popularity bias.Comment: 4 pages, 4 figures, 2 column revtex format. Minor changes in response
to referee comments. For publication in PR
Extreme events driven glassy behaviour in granular media
Motivated by recent experiments on the approach to jamming of a weakly forced
granular medium using an immersed torsion oscillator [Nature 413 (2001) 407],
we propose a simple model which relates the microscopic dynamics to macroscopic
rearrangements and accounts for the following experimental facts: (1) the
control parameter is the spatial amplitude of the perturbation and not its
reduced peak acceleration; (2) a Vogel-Fulcher-Tammann-like form for the
relaxation time. The model draws a parallel between macroscopic rearrangements
in the system and extreme events whose probability of occurrence (and thus the
typical relaxation time) is estimated using extreme-value statistics. The range
of validity of this description in terms of the control parameter is discussed
as well as the existence of other regimes.Comment: 7 pages, to appear in Europhys. Let
Correlator Bank Detection of GW chirps. False-Alarm Probability, Template Density and Thresholds: Behind and Beyond the Minimal-Match Issue
The general problem of computing the false-alarm rate vs. detection-threshold
relationship for a bank of correlators is addressed, in the context of
maximum-likelihood detection of gravitational waves, with specific reference to
chirps from coalescing binary systems. Accurate (lower-bound) approximants for
the cumulative distribution of the whole-bank supremum are deduced from a class
of Bonferroni-type inequalities. The asymptotic properties of the cumulative
distribution are obtained, in the limit where the number of correlators goes to
infinity. The validity of numerical simulations made on small-size banks is
extended to banks of any size, via a gaussian-correlation inequality. The
result is used to estimate the optimum template density, yielding the best
tradeoff between computational cost and detection efficiency, in terms of
undetected potentially observable sources at a prescribed false-alarm level,
for the simplest case of Newtonian chirps.Comment: submitted to Phys. Rev.
Partially asymmetric exclusion models with quenched disorder
We consider the one-dimensional partially asymmetric exclusion process with
random hopping rates, in which a fraction of particles (or sites) have a
preferential jumping direction against the global drift. In this case the
accumulated distance traveled by the particles, x, scales with the time, t, as
x ~ t^{1/z}, with a dynamical exponent z > 0. Using extreme value statistics
and an asymptotically exact strong disorder renormalization group method we
analytically calculate, z_{pt}, for particlewise (pt) disorder, which is argued
to be related to the dynamical exponent for sitewise (st) disorder as
z_{st}=z_{pt}/2. In the symmetric situation with zero mean drift the particle
diffusion is ultra-slow, logarithmic in time.Comment: 4 pages, 3 figure
Anomalous diffusion in disordered multi-channel systems
We study diffusion of a particle in a system composed of K parallel channels,
where the transition rates within the channels are quenched random variables
whereas the inter-channel transition rate v is homogeneous. A variant of the
strong disorder renormalization group method and Monte Carlo simulations are
used. Generally, we observe anomalous diffusion, where the average distance
travelled by the particle, []_{av}, has a power-law time-dependence
[]_{av} ~ t^{\mu_K(v)}, with a diffusion exponent 0 \le \mu_K(v) \le 1.
In the presence of left-right symmetry of the distribution of random rates, the
recurrent point of the multi-channel system is independent of K, and the
diffusion exponent is found to increase with K and decrease with v. In the
absence of this symmetry, the recurrent point may be shifted with K and the
current can be reversed by varying the lane change rate v.Comment: 16 pages, 7 figure
Beam Dynamics in High Intensity Cyclotrons Including Neighboring Bunch Effects: Model, Implementation and Application
Space charge effects, being one of the most significant collective effects,
play an important role in high intensity cyclotrons. However, for cyclotrons
with small turn separation, other existing effects are of equal importance.
Interactions of radially neighboring bunches are also present, but their
combined effects has not yet been investigated in any great detail. In this
paper, a new particle in cell based self-consistent numerical simulation model
is presented for the first time. The model covers neighboring bunch effects and
is implemented in the three-dimensional object-oriented parallel code
OPAL-cycl, a flavor of the OPAL framework. We discuss this model together with
its implementation and validation. Simulation results are presented from the
PSI 590 MeV Ring Cyclotron in the context of the ongoing high intensity upgrade
program, which aims to provide a beam power of 1.8 MW (CW) at the target
destination
Synchronization of random walks with reflecting boundaries
Reflecting boundary conditions cause two one-dimensional random walks to
synchronize if a common direction is chosen in each step. The mean
synchronization time and its standard deviation are calculated analytically.
Both quantities are found to increase proportional to the square of the system
size. Additionally, the probability of synchronization in a given step is
analyzed, which converges to a geometric distribution for long synchronization
times. From this asymptotic behavior the number of steps required to
synchronize an ensemble of independent random walk pairs is deduced. Here the
synchronization time increases with the logarithm of the ensemble size. The
results of this model are compared to those observed in neural synchronization.Comment: 10 pages, 7 figures; introduction changed, typos correcte
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