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## New concept for quantification of similarity relates entropy and energy of objects: First and Second Law entangled, equivalence of temperature and time proposed

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/06/2009
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When the difference between changes in energy and entropy at a given
temperature is correlated with the ratio between the same changes in energy and
entropy at zero average free energy of an ensemble of similar but distinct
molecule-sized objects, a highly significant linear dependence results from
which a relationship between energy and entropy is derived and the degree of
similarity between the distinctly different members within the group of objects
can be quantified. This fundamental energy-entropy relationship is likely to be
of general interest in physics, most notably in particle physics and cosmology.
We predict a consistent and testable way of classifying mini black holes, to be
generated in future Large Hadron Collider experiments, by their gravitational
energy and area entropy. For any isolated universe we propose absolute
temperature and absolute time to be equivalent, much in the same way as energy
and entropy are for an isolated ensemble of similar objects. According to this
principle, the cosmological constant is the squared product of absolute time
and absolute temperature. The symmetry break into a time component and a
temperature component of the universe takes place when the first irreversible
movement occurs owing to a growing accessed total volume.; Comment: 11 pages text plus 2 pages containing 2 low-res b&w figures (pdf...

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## Diverging probability density functions for flat-top solitary waves

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/06/2009
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We investigate the statistics of flat-top solitary wave parameters in the
presence of weak multiplicative dissipative disorder. We consider first
propagation of solitary waves of the cubic-quintic nonlinear Schr\"odinger
equation (CQNLSE) in the presence of disorder in the cubic nonlinear gain. We
show by a perturbative analytic calculation and by Monte Carlo simulations that
the probability density function (PDF) of the amplitude $\eta$ exhibits
loglognormal divergence near the maximum possible amplitude $\eta_{m}$, a
behavior that is similar to the one observed earlier for disorder in the linear
gain [A. Peleg et al., Phys. Rev. E {\bf 72}, 027203 (2005)]. We relate the
loglognormal divergence of the amplitude PDF to the super-exponential approach
of $\eta$ to $\eta_{m}$ in the corresponding deterministic model with
linear/nonlinear gain. Furthermore, for solitary waves of the derivative CQNLSE
with weak disorder in the linear gain both the amplitude and the group velocity
$\beta$ become random. We therefore study analytically and by Monte Carlo
simulations the PDF of the parameter $p$, where
$p=\eta/(1-\varepsilon_s\beta/2)$ and $\varepsilon_s$ is the self-steepening
coefficient. Our analytic calculations and numerical simulations show that the
PDF of $p$ is loglognormally divergent near the maximum $p$-value.; Comment: 9 pages...

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## Exploring the non-linear density field in the Millennium simulations with tessellations - I. The probability distribution function

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We use the Delaunay Tessellation Field Estimator (DTFE) to study the
one-point density distribution functions of the Millennium (MS) and
Millennium-II (MS-II) simulations. The DTFE technique is based directly on the
particle positions, without requiring any type of smoothing or analysis grid,
thereby providing high sensitivity to all non-linear structures resolved by the
simulations. In order to identify the detailed origin of the shape of the
one-point density probability distribution function (PDF), we decompose the
simulation particles according to the mass of their host FoF halos, and examine
the contributions of different halo mass ranges to the global density PDF. We
model the one-point distribution of the FoF halos in each halo mass bin with a
set of Monte Carlo realizations of idealized NFW dark matter halos, finding
that this reproduces the measurements from the N-body simulations reasonably
well, except for a small excess present in simulation results. This excess
increases with increasing halo mass. We show that its origin lies in
substructure, which becomes progressively more abundant and better resolved in
more massive dark matter halos. We demonstrate that the high density tail of
the one-point distribution function in less massive halos is severely affected
by the gravitational softening length and the mass resolution. In particular...

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## The intergalactic medium thermal history at redshift z=1.7--3.2 from the Lyman alpha forest: a comparison of measurements using wavelets and the flux distribution

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We investigate the thermal history of the intergalactic medium (IGM) in the
redshift interval z=1.7--3.2 by studying the small-scale fluctuations in the
Lyman alpha forest transmitted flux. We apply a wavelet filtering technique to
eighteen high resolution quasar spectra obtained with the Ultraviolet and
Visual Echelle Spectrograph (UVES), and compare these data to synthetic spectra
drawn from a suite of hydrodynamical simulations in which the IGM thermal state
and cosmological parameters are varied. From the wavelet analysis we obtain
estimates of the IGM thermal state that are in good agreement with other
recent, independent wavelet-based measurements. We also perform a reanalysis of
the same data set using the Lyman alpha forest flux probability distribution
function (PDF), which has previously been used to measure the IGM
temperature-density relation. This provides an important consistency test for
measurements of the IGM thermal state, as it enables a direct comparison of the
constraints obtained using these two different methodologies. We find the
constraints obtained from wavelets and the flux PDF are formally consistent
with each other, although in agreement with previous studies, the flux PDF
constraints favour an isothermal or inverted IGM temperature-density relation.
We also perform a joint analysis by combining our wavelet and flux PDF
measurements...

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## PDF4LHC recommendations for LHC Run II

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We provide an updated recommendation for the usage of sets of parton
distribution functions (PDFs) and the assessment of PDF and PDF+$\alpha_s$
uncertainties suitable for applications at the LHC Run II. We review
developments since the previous PDF4LHC recommendation, and discuss and compare
the new generation of PDFs, which include substantial information from
experimental data from the Run I of the LHC. We then propose a new prescription
for the combination of a suitable subset of the available PDF sets, which is
presented in terms of a single combined PDF set. We finally discuss tools which
allow for the delivery of this combined set in terms of optimized sets of
Hessian eigenvectors or Monte Carlo replicas, and their usage, and provide some
examples of their application to LHC phenomenology.; Comment: 65 pages, 20 figures, additional benchmark comparison plots available
from http://www.hep.ucl.ac.uk/pdf4lhc/mc2h-gallery/website. v2, accepted for
publication in Journal of Physics G

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## Gravitational fluctuations of the galaxy distribution

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We study the statistical properties of the gravitational field generated by
galaxy distribution observed bythe Sloan Digital Sky Survey (DR7). We
characterize the probability density function of gravitational force
fluctuations and relate its limiting behaviors to the correlation properties of
the underlying density field. In addition, we study whether the PDF converges
to an asymptotic shape within sample volumes. We consider several
volume-limited samples of the Sloan Digital Sky Survey and we compute the
gravitational force probability density function (PDF). The gravitational force
is computed in spheres of varying radius as is its PDF. We find that (i) the
PDF of the force displays features that can be understood in terms of galaxy
two-point correlations and (ii) density fluctuations on the largest scales
probed, i.e. r~100 Mpc/h, still contribute significantly to the amplitude of
the gravitational force. Our main conclusion is that fluctuations in the
gravitational force field generated by galaxy structures are also relevant on
scales ~ 100 Mpc/h. By assuming that the gravitational fluctuations in the
galaxy distribution reflect those in the whole matter distribution, and that
peculiar velocities and accelerations are simply correlated...

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## The role of presumed probability density function in the simulation of non premixed turbulent combustion

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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Flamelet Progress Variable (FPV) combustion models allow the evaluation of
all thermo chemical quantities in a reacting flow by computing only the mixture
fraction Z and a progress variable C. When using such a method to predict a
turbulent combustion in conjunction with a turbulence model, a probability
density function (PDF) is required to evaluate statistical averages (e.g.,
Favre average) of chemical quantities. The choice of the PDF is a compromise
between computational costs and accuracy level. The aim of this paper is to
investigate the influence of the PDF choice and its modeling aspects in the
simulation of non premixed turbulent combustion. Three different models are
considered: the standard one, based on the choice of a beta distribution for Z
and a Dirac distribution for C; a model employing a beta distribution for both
Z and C; a third model obtained using a beta distribution for Z and the
statistical most likely distribution (SMLD) for C. The standard model, although
widely used, doesn't take into account the interaction between turbulence and
chemical kinetics as well as the dependence of the progress variable not only
on its mean but also on its variance. The SMLD approach establishes a
systematic framework to incorporate informations from an arbitrary number of
moments...

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## Evolution of the cosmological density distribution function

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/01/2000
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We present a new calculation for the evolution of the 1-point Probability
Distribution Function (PDF) of the cosmological density field based on an exact
statistical treatment. Using the Chapman-Kolmogorov equation and second-order
Eulerian perturbation theory we propagate the initial density distribution into
the nonlinear regime. Our calculations yield the moment generating function,
allowing a straightforward derivation of the skewness of the PDF to second
order. We find a new dependency on the initial perturbation spectrum. We
compare our results with other approximations to the 1-pt PDF, and with N-body
simulations. We find that our distribution accurately models the evolution of
the 1-pt PDF of dark matter.; Comment: 7 pages, 7 figures, accepted for publication in MNRAS

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## Oscillatory dynamics of the classical Nonlinear Schrodinger equation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We study numerically the statistical properties of the modulation instability
(MI) developing from condensate solution seeded by weak, statistically
homogeneous in space noise, in the framework of the classical (integrable)
one-dimensional Nonlinear Schrodinger (NLS) equation. We demonstrate that in
the nonlinear stage of the MI the moments of the solutions amplitudes oscillate
with time around their asymptotic values very similar to sinusoidal law. The
amplitudes of these oscillations decay with time $t$ as $t^{-3/2}$, the phases
contain the nonlinear phase shift that decays as $t^{-1/2}$, and the period of
the oscillations is equal to $\pi$. The asymptotic values of the moments
correspond to Rayleigh probability density function (PDF) of waves amplitudes
appearance. We show that such behavior of the moments is governed by
oscillatory-like, decaying with time, fluctuations of the PDF around the
Rayleigh PDF; the time dependence of the PDF turns out to be very similar to
that of the moments. We study how the oscillations that we observe depend on
the initial noise properties and demonstrate that they should be visible for a
very wide variety of statistical distributions of noise.; Comment: 7 pages, 5 figures

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## Probability density function of turbulent velocity fluctuation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/03/2002
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The probability density function (PDF) of velocity fluctuations is studied
experimentally for grid turbulence in a systematical manner. At small distances
from the grid, where the turbulence is still developing, the PDF is
sub-Gaussian. At intermediate distances, where the turbulence is fully
developed, the PDF is Gaussian. At large distances, where the turbulence has
decayed, the PDF is hyper-Gaussian. The Fourier transforms of the velocity
fluctuations always have Gaussian PDFs. At intermediate distances from the
grid, the Fourier transforms are statistically independent of each other. This
is the necessary and sufficient condition for Gaussianity of the velocity
fluctuations. At small and large distances, the Fourier transforms are
dependent.; Comment: 7 pages, 8 figures in a PS file, to appear in Physical Review E

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## Single or combined location measurements of the same parameter without prior probability. (Altern. title, Parametric inference as useful illusion; Part 1)

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Physics - Data Analysis, Statistics and Probability#Mathematics - General Mathematics#62A01 (Primary) 62G99, 62F99 (Secondary)

Motivation. This version is based solely on the calculus of probability,
excluding any statistical principle. "Location measurement" means the pdf of
the error is known. When the datum is obtained, intuition suggests something
like a pdf for the parameter; here we attempt a critical examination of its
meaning.
Summary. In default of prior probability the parameter is not defined as a
random variable, hence there can be no genuine prior-free parametric inference.
Nevertheless prior-free predictive inference regarding any future datum is
generated directly from the datum of a location measurement. Such inference
turns out as if obtained from a certain pdf ("fiducial") indirectly associated
with the parameter. This false pdf can expedite predictive inference, but is
inappropriate in the analysis of combined measurements (unless they all are
location measurements of the same parameter). Also it has the same distribution
as the ostensible Bayesian posterior from a uniform "prior". However, if any of
these spurious entities is admitted in the analysis, inconsistent results
follow. When we combine measurements, we find that the quantisation errors,
inevitable in data recording, must be taken into consideration. These errors
cannot be folded into predictive inference in an exact sense; that is...

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## Parton distributions with LHC data

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We present the first determination of parton distributions of the nucleon at
NLO and NNLO based on a global data set which includes LHC data: NNPDF2.3. Our
data set includes, besides the deep inelastic, Drell-Yan, gauge boson
production and jet data already used in previous global PDF determinations, all
the relevant LHC data for which experimental systematic uncertainties are
currently available: ATLAS and LHCb W and Z lepton rapidity distributions from
the 2010 run, CMS W electron asymmetry data from the 2011 run, and ATLAS
inclusive jet cross-sections from the 2010 run. We introduce an improved
implementation of the FastKernel method which allows us to fit to this extended
data set, and also to adopt a more effective minimization methodology. We
present the NNPDF2.3 PDF sets, and compare them to the NNPDF2.1 sets to assess
the impact of the LHC data. We find that all the LHC data are broadly
consistent with each other and with all the older data sets included in the
fit. We present predictions for various standard candle cross-sections, and
compare them to those obtained previously using NNPDF2.1, and specifically
discuss the impact of ATLAS electroweak data on the determination of the
strangeness fraction of the proton. We also present collider PDF sets...

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## Extracting the Pair Distribution Function of Liquids and Liquid-Vapor Surfaces by Grazing Incidence X-ray Diffraction Mode

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/07/2008
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We show that the structure factor $S(q)$ of water can be obtained from X-ray
synchrotron experiments at grazing angle of incidence (in reflection mode) by
using a liquid surface diffractometer. The corrections used to obtain $S(q)$
self-consistently are described. Applying these corrections to scans at
different incident beam angles (above the critical angle) collapses the
measured intensities into a single master curve, without fitting parameters,
which within a scale factor yields $S(q)$. Performing the measurements below
the critical angle for total reflectivity yields the structure factor of the
top most layers of the water/vapor interface. Our results indicate water
restructuring at the vapor/water interface. We also introduce a new approach to
extract $g(r)$, the pair distribution function (PDF), by expressing the PDF as
a linear sum of Error functions whose parameters are refined by applying a
non-linear least square fit method. This approach enables a straightforward
determination of the inherent uncertainties in the PDF. Implications of our
results to previously measured and theoretical predictions of the PDF are also
discussed.

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## Shock generated vorticity in the interstellar medium and the origin of the stellar initial mass function

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/07/2009
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The main observational evidence for turbulence in the interstellar medium
(ISM) and molecular clouds is the power-law energy spectrum for velocity
fluctuations, E(k) \propto k^{\alpha}. The Kolmogorov scaling exponent,
\alpha=-5/3, is typical. At the same time, the observed probability
distribution function (PDF) of gas densities in both the ISM as well as in
molecular clouds is a log-normal distribution, which is similar to the initial
mass function (IMF) that describes the distribution of stellar masses. We
examine the density and velocity structure of interstellar gas traversed by
curved shock waves in the kinematic limit. We demonstrate mathematically that
just a few passages of curved shock waves generically produces a log-normal
density PDF. This explains the ubiquity of the log-normal PDF in many different
numerical simulations. We also show that subsequent interaction with a
spherical blast wave generates a power-law density distribution at high
densities, qualitatively similar to the Salpeter power-law for the IMF.
Finally, we show that a focused shock produces a downstream flow with energy
spectrum exponent \alpha=-2. Subsequent shock passages reduce this slope,
achieving \alpha \approx -5/3 after a few passages. Subsequent dissipation of
energy piled up at the small scales will act to maintain the spectrum very near
to the Kolomogorov value. Therefore...

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## A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov-Poisson equations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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The Vlasov-Poisson equations describe the evolution of a collisionless
plasma, represented through a probability density function (PDF) that
self-interacts via an electrostatic force. One of the main difficulties in
numerically solving this system is the severe time-step restriction that arises
from parts of the PDF associated with moderate-to-large velocities. The
dominant approach in the plasma physics community for removing these time-step
restrictions is the so-called particle-in-cell (PIC) method, which discretizes
the distribution function into a set of macro-particles, while the electric
field is represented on a mesh. Several alternatives to this approach exist,
including fully Lagrangian, fully Eulerian, and so-called semi-Lagrangian
methods. The focus of this work is the semi-Lagrangian approach, which begins
with a grid-based Eulerian representation of both the PDF and the electric
field, then evolves the PDF via Lagrangian dynamics, and finally projects this
evolved field back onto the original Eulerian mesh. In particular, we develop
in this work a method that discretizes the 1+1 Vlasov-Poisson system via a
high-order discontinuous Galerkin (DG) method in phase space, and an operator
split, semi-Lagrangian method in time. Second-order accuracy in time is
relatively easy to achieve via Strang operator splitting. With additional work...

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## Craig's XY-distribution and the statistics of Lagrangian power in two-dimensional turbulence

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We examine the probability distribution function (pdf) of energy injection
rate (power) in numerical simulations of stationary two--dimensional (2D)
turbulence in the Lagrangian frame. The simulation is designed to mimic an
electromagnetically driven fluid layer, a well-documented system for generating
two--dimensional turbulence in the laboratory. In our simulations, the forcing
and velocity fields are close to Gaussian. On the other hand, the measured PDF
of injected power is very sharply peaked at zero, suggestive of a singularity
there, with tails which are exponential but asymmetric. Large positive
fluctuations are more probable than large negative fluctuations. It is this
asymmetry of the tails, which leads to a net positive mean value for the energy
input despite the most probable value being zero. The main features of the
power distribution are well described by Craig's XY distribution for the PDF of
the product of two correlated normal variables. We show that the power
distribution should exhibit a logarithmic singularity at zero and decay
exponentially for large absolute values of the power. We calculate the
asymptotic behavior and express the asymmetry of the tails in terms of the
correlation coefficient of the force and velocity. We compare the measured pdfs
with the theoretical calculations and briefly discuss how the power pdf might
change with other forcing mechanisms.; Comment: 9 pages...

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## Evaluate the Word Error Rate of Binary Block Codes with Square Radius Probability Density Function

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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The word error rate (WER) of soft-decision-decoded binary block codes rarely
has closed-form. Bounding techniques are widely used to evaluate the
performance of maximum-likelihood decoding algorithm. But the existing bounds
are not tight enough especially for low signal-to-noise ratios and become
looser when a suboptimum decoding algorithm is used. This paper proposes a new
concept named square radius probability density function (SR-PDF) of decision
region to evaluate the WER. Based on the SR-PDF, The WER of binary block codes
can be calculated precisely for ML and suboptimum decoders. Furthermore, for a
long binary block code, SR-PDF can be approximated by Gamma distribution with
only two parameters that can be measured easily. Using this property, two
closed-form approximative expressions are proposed which are very close to the
simulation results of the WER of interesting.; Comment: I tried to fix the problem that figures cannot be displayed in
Version1~3, but it doesnot work. Some new results about decoding threshold is
added in version 4 and a pdf is included which is compile in my PC. Figures
can displayed

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## Density probability distribution in one-dimensional polytropic gas dynamics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/02/1998
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We discuss the generation and statistics of the density fluctuations in
highly compressible polytropic turbulence, based on a simple model and
one-dimensional numerical simulations. Observing that density structures tend
to form in a hierarchical manner, we assume that density fluctuations follow a
random multiplicative process. When the polytropic exponent $\gamma$ is equal
to unity, the local Mach number is independent of the density, and our
assumption leads us to expect that the probability density function (PDF) of
the density field is a lognormal. This isothermal case is found to be singular,
with a dispersion $\sigma_s^2$ which scales like the square turbulent Mach
number $\tilde M^2$, where $s\equiv \ln \rho$ and $\rho$ is the fluid density.
This leads to much higher fluctuations than those due to shock jump relations.
Extrapolating the model to the case $\gamma \not =1$, we find that, as the
Mach number becomes large, the density PDF is expected to asymptotically
approach a power-law regime, at high densities when $\gamma<1$, and at low
densities when $\gamma>1$. This effect can be traced back to the fact that the
pressure term in the momentum equation varies exponentially with $s$, thus
opposing the growth of fluctuations on one side of the PDF...

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## The PDF4LHC Working Group Interim Recommendations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/01/2011
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This note provides an interim summary of the current recommendations of the
PDF4LHC working group for the use of parton distribution functions (PDFs) and
of PDF uncertainties at the LHC, for cross section and cross section
uncertainty calculations. It also contains a succinct user guide to the
computation of PDF uncertainties and correlations using available PDF sets.
A companion note (the PDF4LHC Working Group Interim Report) summarizes
predictions for benchmark cross sections at the LHC (7 TeV) at NLO using modern
PDFs currently available from 6 PDF fitting groups.; Comment: 12 pages

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## The Probability Distribution Function of Column Density in Molecular Clouds

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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(Abridged) We discuss the probability distribution function (PDF) of column
density resulting from density fields with lognormal PDFs, applicable to
isothermal gas (e.g., probably molecular clouds). We suggest that a
``decorrelation length'' can be defined as the distance over which the density
auto-correlation function has decayed to, for example, 10% of its zero-lag
value, so that the density ``events'' along a line of sight can be assumed to
be independent over distances larger than this, and the Central Limit Theorem
should be applicable. However, using random realizations of lognormal fields,
we show that the convergence to a Gaussian is extremely slow in the high-
density tail. Thus, the column density PDF is not expected to exhibit a unique
functional shape, but to transit instead from a lognormal to a Gaussian form as
the ratio $\eta$ of the column length to the decorrelation length increases.
Simultaneously, the PDF's variance decreases. For intermediate values of
$\eta$, the column density PDF assumes a nearly exponential decay. We then
discuss the density power spectrum and the expected value of $\eta$ in actual
molecular clouds. Observationally, our results suggest that $\eta$ may be
inferred from the shape and width of the column density PDF in
optically-thin-line or extinction studies. Our results should also hold for gas
with finite-extent power-law underlying density PDFs...

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