1,066 research outputs found
Deep-Sea Environment
The deep-sea environment is divided into three zones: the abyssopelagic, the abyssobenthic, and the hadal zones. The ocean floor is not a smooth featureless sedimentary plain as has been believed earlier, but instead it is of rough topography with numerous irregularities, deep depressions, many high seamounts, and elongate ridges and trenches, determined largely by tectonic movements and volcanic extrusions. The sea floor is the place of accumulation of solid detrital material of organic or inorganic origin, and it is virtually covered with unconsolidated sediments. These sediments are being deposited on the ocean floor at rates which vary from place to place and are the result of a variety of sources. The sediments are derived from continental areas, coasts, and marine life; the atmosphere, rivers, ocean currents, and ice are the media of transport. The sediments consist of muds of various colors, calcareaous and siliceaous oozes, and a distinctive red clay.
Life does exist, and abundantly in many places, in the abyssal and hadal areas of the oceans. In order for this life to exist it must adapt itself to the characteristics of its environment. Some of these characteristics are poor light, low temperature, high pressure, salinity, low oxygen content, and food
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
Fluctuating Fronts as Correlated Extreme Value Problems: An Example of Gaussian Statistics
In this paper, we view fluctuating fronts made of particles on a
one-dimensional lattice as an extreme value problem. The idea is to denote the
configuration for a single front realization at time by the set of
co-ordinates of the
constituent particles, where is the total number of particles in that
realization at time . When are arranged in the ascending order
of magnitudes, the instantaneous front position can be denoted by the location
of the rightmost particle, i.e., by the extremal value
. Due to interparticle
interactions, at two different times for a single front
realization are naturally not independent of each other, and thus the
probability distribution [based on an ensemble of such front
realizations] describes extreme value statistics for a set of correlated random
variables. In view of the fact that exact results for correlated extreme value
statistics are rather rare, here we show that for a fermionic front model in a
reaction-diffusion system, is Gaussian. In a bosonic front model
however, we observe small deviations from the Gaussian.Comment: 6 pages, 3 figures, miniscule changes on the previous version, to
appear in Phys. Rev.
Contest based on a directed polymer in a random medium
We introduce a simple one-parameter game derived from a model describing the
properties of a directed polymer in a random medium. At his turn, each of the
two players picks a move among two alternatives in order to maximize his final
score, and minimize opponent's return. For a game of length , we find that
the probability distribution of the final score develops a traveling wave
form, , with the wave profile unusually
decaying as a double exponential for large positive and negative . In
addition, as the only parameter in the game is varied, we find a transition
where one player is able to get his maximum theoretical score. By extending
this model, we suggest that the front velocity is selected by the nonlinear
marginal stability mechanism arising in some traveling wave problems for which
the profile decays exponentially, and for which standard traveling wave theory
applies
Extreme statistics for time series: Distribution of the maximum relative to the initial value
The extreme statistics of time signals is studied when the maximum is
measured from the initial value. In the case of independent, identically
distributed (iid) variables, we classify the limiting distribution of the
maximum according to the properties of the parent distribution from which the
variables are drawn. Then we turn to correlated periodic Gaussian signals with
a 1/f^alpha power spectrum and study the distribution of the maximum relative
height with respect to the initial height (MRH_I). The exact MRH_I distribution
is derived for alpha=0 (iid variables), alpha=2 (random walk), alpha=4 (random
acceleration), and alpha=infinity (single sinusoidal mode). For other,
intermediate values of alpha, the distribution is determined from simulations.
We find that the MRH_I distribution is markedly different from the previously
studied distribution of the maximum height relative to the average height for
all alpha. The two main distinguishing features of the MRH_I distribution are
the much larger weight for small relative heights and the divergence at zero
height for alpha>3. We also demonstrate that the boundary conditions affect the
shape of the distribution by presenting exact results for some non-periodic
boundary conditions. Finally, we show that, for signals arising from
time-translationally invariant distributions, the density of near extreme
states is the same as the MRH_I distribution. This is used in developing a
scaling theory for the threshold singularities of the two distributions.Comment: 29 pages, 4 figure
Renormalization flow in extreme value statistics
The renormalization group transformation for extreme value statistics of
independent, identically distributed variables, recently introduced to describe
finite size effects, is presented here in terms of a partial differential
equation (PDE). This yields a flow in function space and gives rise to the
known family of Fisher-Tippett limit distributions as fixed points, together
with the universal eigenfunctions around them. The PDE turns out to handle
correctly distributions even having discontinuities. Remarkably, the PDE admits
exact solutions in terms of eigenfunctions even farther from the fixed points.
In particular, such are unstable manifolds emanating from and returning to the
Gumbel fixed point, when the running eigenvalue and the perturbation strength
parameter obey a pair of coupled ordinary differential equations. Exact
renormalization trajectories corresponding to linear combinations of
eigenfunctions can also be given, and it is shown that such are all solutions
of the PDE. Explicit formulas for some invariant manifolds in the Fr\'echet and
Weibull cases are also presented. Finally, the similarity between
renormalization flows for extreme value statistics and the central limit
problem is stressed, whence follows the equivalence of the formulas for Weibull
distributions and the moment generating function of symmetric L\'evy stable
distributions.Comment: 21 pages, 9 figures. Several typos and an upload error corrected.
Accepted for publication in JSTA
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.
Leadership Statistics in Random Structures
The largest component (``the leader'') in evolving random structures often
exhibits universal statistical properties. This phenomenon is demonstrated
analytically for two ubiquitous structures: random trees and random graphs. In
both cases, lead changes are rare as the average number of lead changes
increases quadratically with logarithm of the system size. As a function of
time, the number of lead changes is self-similar. Additionally, the probability
that no lead change ever occurs decays exponentially with the average number of
lead changes.Comment: 5 pages, 3 figure
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.
In-depth analysis of the Naming Game dynamics: the homogeneous mixing case
Language emergence and evolution has recently gained growing attention
through multi-agent models and mathematical frameworks to study their behavior.
Here we investigate further the Naming Game, a model able to account for the
emergence of a shared vocabulary of form-meaning associations through
social/cultural learning. Due to the simplicity of both the structure of the
agents and their interaction rules, the dynamics of this model can be analyzed
in great detail using numerical simulations and analytical arguments. This
paper first reviews some existing results and then presents a new overall
understanding.Comment: 30 pages, 19 figures (few in reduced definition). In press in IJMP
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