687 research outputs found
Probing the tails of the ground state energy distribution for the directed polymer in a random medium of dimension via a Monte-Carlo procedure in the disorder
In order to probe with high precision the tails of the ground-state energy
distribution of disordered spin systems, K\"orner, Katzgraber and Hartmann
\cite{Ko_Ka_Ha} have recently proposed an importance-sampling Monte-Carlo
Markov chain in the disorder. In this paper, we combine their Monte-Carlo
procedure in the disorder with exact transfer matrix calculations in each
sample to measure the negative tail of ground state energy distribution
for the directed polymer in a random medium of dimension .
In , we check the validity of the algorithm by a direct comparison with
the exact result, namely the Tracy-Widom distribution. In dimensions and
, we measure the negative tail up to ten standard deviations, which
correspond to probabilities of order . Our results are
in agreement with Zhang's argument, stating that the negative tail exponent
of the asymptotic behavior
as is directly related to the fluctuation exponent
(which governs the fluctuations
of the ground state energy for polymers of length ) via the simple
formula . Along the paper, we comment on the
similarities and differences with spin-glasses.Comment: 13 pages, 16 figure
Statistics of leaders and lead changes in growing networks
We investigate various aspects of the statistics of leaders in growing
network models defined by stochastic attachment rules. The leader is the node
with highest degree at a given time (or the node which reached that degree
first if there are co-leaders). This comprehensive study includes the full
distribution of the degree of the leader, its identity, the number of
co-leaders, as well as several observables characterizing the whole history of
lead changes: number of lead changes, number of distinct leaders, lead
persistence probability. We successively consider the following network models:
uniform attachment, linear attachment (the Barabasi-Albert model), and
generalized preferential attachment with initial attractiveness.Comment: 28 pages, 14 figures, 1 tabl
On the Role of Global Warming on the Statistics of Record-Breaking Temperatures
We theoretically study long-term trends in the statistics of record-breaking
daily temperatures and validate these predictions using Monte Carlo simulations
and data from the city of Philadelphia, for which 126 years of daily
temperature data is available. Using extreme statistics, we derive the number
and the magnitude of record temperature events, based on the observed Gaussian
daily temperatures distribution in Philadelphia, as a function of the number of
elapsed years from the start of the data. We further consider the case of
global warming, where the mean temperature systematically increases with time.
We argue that the current warming rate is insufficient to measurably influence
the frequency of record temperature events over the time range of the
observations, a conclusion that is supported by numerical simulations and the
Philadelphia temperature data.Comment: 11 pages, 6 figures, 2-column revtex4 format. For submission to
Journal of Climate. Revised version has some new results and some errors
corrected. Reformatted for Journal of Climate. Second revision has an added
reference. In the third revision one sentence that explains the simulations
is reworded for clarity. New revision 10/3/06 has considerable additions and
new results. Revision on 11/8/06 contains a number of minor corrections and
is the version that will appear in Phys. Rev.
On leaders and condensates in a growing network
The Bianconi-Barabasi model of a growing network is revisited. This model,
defined by a preferential attachment rule involving both the degrees of the
nodes and their intrinsic fitnesses, has the fundamental property to undergo a
phase transition to a condensed phase below some finite critical temperature,
for an appropriate choice of the distribution of fitnesses. At high temperature
it exhibits a crossover to the Barabasi-Albert model, and at low temperature,
where the fitness landscape becomes very rugged, a crossover to the recently
introduced record-driven growth process. We first present an analysis of the
history of leaders, the leader being defined as the node with largest degree at
a given time. In the generic finite-temperature regime, new leaders appear
endlessly, albeit on a doubly logarithmic time scale, i.e., extremely slowly.
We then give a novel picture for the dynamics in the condensed phase. The
latter is characterized by an infinite hierarchy of condensates, whose sizes
are non-self-averaging and keep fluctuating forever.Comment: 29 pages, 13 figures, 3 tables. A few minor change
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.
Local Leaders in Random Networks
We consider local leaders in random uncorrelated networks, i.e. nodes whose
degree is higher or equal than the degree of all of their neighbors. An
analytical expression is found for the probability of a node of degree to
be a local leader. This quantity is shown to exhibit a transition from a
situation where high degree nodes are local leaders to a situation where they
are not when the tail of the degree distribution behaves like the power-law
with . Theoretical results are verified by
computer simulations and the importance of finite-size effects is discussed.Comment: 4 pages, 2 figure
Examination of whey de-fatting by enhanced membrane filtration
The largest quantities of by-products of dairy processing originates from the cheese making. Whey proteins are used for animal feeding and human nutrition as well, for example in dry soups, infant formulas, and supplements. The fat components of the whey might impair its use. The aim of our experiments was to investigate the separation of the lipid fraction of whey. The microfiltration is said to be a gentle and energy efficient method for this task. During the measurements 0.2 μm microfiltration membranes were used and the membrane separation was enhanced by vibration, inserting static mixer and air sparging. The de-fatting efficiency, the retention of the whey components, the flux values, and the resistances in different combinations were compared in this paper
Generalised extreme value statistics and sum of correlated variables
We show that generalised extreme value statistics -the statistics of the k-th
largest value among a large set of random variables- can be mapped onto a
problem of random sums. This allows us to identify classes of non-identical and
(generally) correlated random variables with a sum distributed according to one
of the three (k-dependent) asymptotic distributions of extreme value
statistics, namely the Gumbel, Frechet and Weibull distributions. These
classes, as well as the limit distributions, are naturally extended to real
values of k, thus providing a clear interpretation to the onset of Gumbel
distributions with non-integer index k in the statistics of global observables.
This is one of the very few known generalisations of the central limit theorem
to non-independent random variables. Finally, in the context of a simple
physical model, we relate the index k to the ratio of the correlation length to
the system size, which remains finite in strongly correlated systems.Comment: To appear in J.Phys.
Records in a changing world
In the context of this paper, a record is an entry in a sequence of random
variables (RV's) that is larger or smaller than all previous entries. After a
brief review of the classic theory of records, which is largely restricted to
sequences of independent and identically distributed (i.i.d.) RV's, new results
for sequences of independent RV's with distributions that broaden or sharpen
with time are presented. In particular, we show that when the width of the
distribution grows as a power law in time , the mean number of records is
asymptotically of order for distributions with a power law tail (the
\textit{Fr\'echet class} of extremal value statistics), of order
for distributions of exponential type (\textit{Gumbel class}), and of order
for distributions of bounded support (\textit{Weibull class}),
where the exponent describes the behaviour of the distribution at the
upper (or lower) boundary. Simulations are presented which indicate that, in
contrast to the i.i.d. case, the sequence of record breaking events is
correlated in such a way that the variance of the number of records is
asymptotically smaller than the mean.Comment: 12 pages, 2 figure
Shear stress fluctuations in the granular liquid and solid phases
We report on experimentally observed shear stress fluctuations in both
granular solid and fluid states, showing that they are non-Gaussian at low
shear rates, reflecting the predominance of correlated structures (force
chains) in the solidlike phase, which also exhibit finite rigidity to shear.
Peaks in the rigidity and the stress distribution's skewness indicate that a
change to the force-bearing mechanism occurs at the transition to fluid
behaviour, which, it is shown, can be predicted from the behaviour of the
stress at lower shear rates. In the fluid state stress is Gaussian distributed,
suggesting that the central limit theorem holds. The fibre bundle model with
random load sharing effectively reproduces the stress distribution at the yield
point and also exhibits the exponential stress distribution anticipated from
extant work on stress propagation in granular materials.Comment: 11 pages, 3 figures, latex. Replacement adds journal reference and
addresses referee comment
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