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## On the universality of supersonic turbulence

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Astrophysics - Solar and Stellar Astrophysics#Physics - Computational Physics#Physics - Fluid Dynamics

Compressible turbulence shapes the structure of the interstellar medium of
our Galaxy and likely plays an important role also during structure formation
in the early Universe. The density PDF and the power spectrum of such
compressible, supersonic turbulence are the key ingredients for theories of
star formation. However, both the PDF and the spectrum are still a matter of
debate, because theoretical predictions are limited and simulations of
supersonic turbulence require enormous resolutions to capture the
inertial-range scaling. To advance our limited knowledge of compressible
turbulence, we here present and analyse the world's largest simulations of
supersonic turbulence. We compare hydrodynamic models with numerical
resolutions of 256^3-4096^3 mesh points and with two distinct driving
mechanisms, solenoidal (divergence-free) driving and compressive (curl-free)
driving. We find convergence of the density PDF, with compressive driving
exhibiting a much wider and more intermittent density distribution than
solenoidal driving. Analysing the power spectrum of the turbulence, we find a
pure velocity scaling close to Burgers turbulence with P(v) k^(-2) for both
driving modes in our hydrodynamical simulations with Mach = 17. The spectrum of
the density-weighted velocity rho^(1/3)v...

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## Tuning the trip to KPZ asymptopia

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/04/2000
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Because of a close blood relationship between directed percolation & directed
polymers in random media, the latter's journey to asymptotic scaling can be
greatly retarded by an uninformed choice of departure point; i.e., the
bare-bond PDF employed in the transfer matrix study. Bisecting a gaussian noise
distribution, examining DPRM scaling for left & right halves separately, and
comparing results against the full PDF, reveals in the simplest possible manner
the essence of this dilemma. Paradoxically, when the bare-bond PDF possesses a
relative shortage [left demi-gaussian], rather than abundance [right
demi-gaussian] of low energy bonds, much better scaling is achieved. This
finding is somewhat counterintuitive since a zero-temperature DPRM seeks the
globally minimal path through a random energy landscape. Nevertheless, the
behavior is easily traced to the strong influence of the neighboring DP fixed
point function.
This note communicates, in part, unpublished work referenced in Phys. Rev.
E58, R4096 (1998). We discovered, as well, that the RG road to asymptopia can
be highly refined by bootstrapping the presumed universal distribution from the
getgo...; Comment: PRL Comment, 1 LaTeX page, w/ raw data included as supplementary
figure; subsequent...

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## On the Generalized Ratio of Uniforms as a Combination of Transformed Rejection and Extended Inverse of Density Sampling

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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In this work we investigate the relationship among three classical sampling
techniques: the inverse of density (Khintchine's theorem), the transformed
rejection (TR) and the generalized ratio of uniforms (GRoU). Given a monotonic
probability density function (PDF), we show that the transformed area obtained
using the generalized ratio of uniforms method can be found equivalently by
applying the transformed rejection sampling approach to the inverse function of
the target density. Then we provide an extension of the classical inverse of
density idea, showing that it is completely equivalent to the GRoU method for
monotonic densities. Although we concentrate on monotonic probability density
functions (PDFs), we also discuss how the results presented here can be
extended to any non-monotonic PDF that can be decomposed into a collection of
intervals where it is monotonically increasing or decreasing. In this general
case, we show the connections with transformations of certain random variables
and the generalized inverse PDF with the GRoU technique. Finally, we also
introduce a GRoU technique to handle unbounded target densities.

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## Diffusion of two particles with a finite interaction potential in one dimension

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/10/2008
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We investigate the dynamics of two interacting diffusing particles in an
infinite effectively one dimensional system; the particles interact through a
step-like potential of width b and height phi_0 and are allowed to pass one
another. By solving the corresponding 2+1-variate Fokker-Planck equation an
exact result for the two particle conditional probability density function
(PDF) is obtained for arbitrary initial particle positions. From the
two-particle PDF we obtain the overtake probability, i.e. the probability that
the two particles has exchanged positions at time t compared to the initial
configuration. In addition, we calculate the trapping probability, i.e. the
probability that the two particles are trapped close to each other (within the
barrier width b) at time t, which is mainly of interest for an attractive
potential, phi_0<0. We also investigate the tagged particle PDF, relevant for
describing the dynamics of one particle which is fluorescently labeled. Our
analytic results are in excellent agreement with the results of stochastic
simulations, which are performed using the Gillespie algorithm.; Comment: 10 pages, 5 figures. Journal of Chemical Physics (in press)

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## On the Origin of the Global Schmidt Law of Star Formation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/03/2003
Português

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One of the most puzzling properties of observed galaxies is the universality
of the empirical correlation between the star formation rate and average gas
surface density on kiloparsec scales (the Schmidt law). In this study I present
results of self-consistent cosmological simulations of high-redshift galaxy
formation that reproduce the Schmidt law naturally, without assuming it, and
provide some clues to this puzzle. The simulations incorporate the main
physical processes critical to various aspects of galaxy formation and have a
dynamic range high enough to identify individual star forming regions. The
results indicate that the global Schmidt law is a manifestation of the overall
density distribution of the interstellar medium (ISM). In particular, the
density probability distribution function (PDF) in the simulated disks is
similar to that observed in recent state-of-the-art modeling of the turbulent
ISM and has a well-defined generic shape. The shape of the PDF in a given
region of the disk depends on the local average surface density Sigma_g. The
dependence is such that the fraction of gas mass in the high-density tail of
the distribution scales as Sigma_g^{n-1} with n~1.4, which gives rise to the
Schmidt-like correlation. The high-density tail of the PDF is remarkably
insensitive to the inclusion of feedback and details of the cooling and heating
processes. This indicates that the global star formation rate is determined by
the supersonic turbulence driven by gravitational instabilities on large
scales...

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## PDFgetX3: A rapid and highly automatable program for processing powder diffraction data into total scattering pair distribution functions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/11/2012
Português

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PDFgetX3 is a new software application for converting X-ray powder
diffraction data to atomic pair distribution function (PDF). PDFgetX3 has been
designed for ease of use, speed and automated operation. The software can
readily process hundreds of X-ray patterns within few seconds and is thus
useful for high-throughput PDF studies, that measure numerous datasets as a
function of time, temperature or other environment parameters. In comparison to
the preceding programs, PDFgetX3 requires fewer inputs, less user experience
and can be readily adopted by novice users. The live-plotting interactive
feature allows to assess the effects of calculation parameters and select their
optimum values. PDFgetX3 uses an ad-hoc data correction method, where the
slowly-changing structure independent signal is filtered out to obtain coherent
X-ray intensities that contain structure information. The outputs from PDFgetX3
have been verified by processing experimental PDFs from inorganic, organic and
nanosized samples and comparing them to their counterparts from previous
established software. In spite of different algorithm, the obtained PDFs were
nearly identical and yielded highly similar results when used in structure
refinement. PDFgetX3 is written in Python language and features well
documented...

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## Is turbulent mixing a self convolution process ?

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 28/03/2008
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Experimental results for the evolution of the probability distribution
function (PDF) of a scalar mixed by a turbulence flow in a channel are
presented. The sequence of PDF from an initial skewed distribution to a sharp
Gaussian is found to be non universal. The route toward homogeneization depends
on the ratio between the cross sections of the dye injector and the channel. In
link with this observation, advantages, shortcomings and applicability of
models for the PDF evolution based on a self-convolution mechanisms are
discussed.; Comment: 4 pages

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## A General Formulation of the Source Confusion Statistics and Application to Infrared Galaxy Surveys

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/12/2003
Português

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Source confusion has been a long-standing problem in the astronomical
history. In the previous formulation, sources are assumed to be distributed
homogeneously on the sky. This fundamental assumption is not realistic in many
applications. In this work, by making use of the point field theory, we derive
general analytic formulae for the confusion problems with arbitrary
distribution and correlation functions. As a typical example, we apply these
new formulae to the source confusion of infrared galaxies. We first calculate
the confusion statistics for power-law galaxy number counts as a test case.
When the slope of differential number counts, \gamma, is steep, the confusion
limits becomes much brighter and the probability distribution function (PDF) of
the fluctuation field is strongly distorted. Then we estimate the PDF and
confusion limits based on the realistic number count model for infrared
galaxies. The gradual flattening of the slope of the source counts makes the
clustering effect rather mild. Clustering effects result in an increase of the
limiting flux density with \sim 10%. In this case, the peak probability of the
PDF decreases up to \sim 15% and its tail becomes heavier.; Comment: ApJ in press, 21 pages, 9 figures, using aastex.cls...

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## Structural properties of disk galaxies I. The intrinsic ellipticity of bulges

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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(Abridged) A variety of formation scenarios was proposed to explain the
diversity of properties observed in bulges. Studying their intrinsic shape can
help in constraining the dominant mechanism at the epochs of their assembly.
The structural parameters of a magnitude-limited sample of 148 unbarred S0--Sb
galaxies were derived in order to study the correlations between bulges and
disks as well as the probability distribution function (PDF) of the intrinsic
equatorial ellipticity of bulges. It is presented a new fitting algorithm
(GASP2D) to perform the two-dimensional photometric decomposition of galaxy
surface-brightness distribution. This was assumed to be the sum of the
contribution of a bulge and disk component characterized by elliptical and
concentric isophotes with constant (but possibly different) ellipticity and
position angles. Bulge and disk parameters of the sample galaxies were derived
from the J-band images which were available in the Two Micron All Sky Survey.
The PDF of the equatorial ellipticity of the bulges was derived from the
distribution of the observed ellipticities of bulges and misalignments between
bulges and disks. Strong correlations between the bulge and disk parameters
were found. About 80% of bulges in unbarred lenticular and
early-to-intermediate spiral galaxies are not oblate but triaxial ellipsoids.
Their mean axial ratio in the equatorial plane is

**= 0.85. There is not significant dependence of their PDF on morphology...**

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## Distinguishing Dark Matter from Unresolved Point Sources in the Inner Galaxy with Photon Statistics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Astrophysics - Cosmology and Nongalactic Astrophysics#Astrophysics - High Energy Astrophysical Phenomena#High Energy Physics - Phenomenology

Data from the Fermi Large Area Telescope suggests that there is an extended
excess of GeV gamma-ray photons in the Inner Galaxy. Identifying potential
astrophysical sources that contribute to this excess is an important step in
verifying whether the signal originates from annihilating dark matter. In this
paper, we focus on the potential contribution of unresolved point sources, such
as millisecond pulsars (MSPs). We propose that the statistics of the
photons---in particular, the flux probability density function (PDF) of the
photon counts below the point-source detection threshold---can potentially
distinguish between the dark-matter and point-source interpretations. We
calculate the flux PDF via the method of generating functions for these two
models of the excess. Working in the framework of Bayesian model comparison, we
then demonstrate that the flux PDF can potentially provide evidence for an
unresolved MSP-like point-source population.; Comment: 27 pages, 8 figures; v2, reference added and other minor changes

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## Lognormal Property of Weak Lensing Fields

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/02/2002
Português

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The statistical property of the weak lensing fields is studied quantitatively
using the ray-tracing simulations. Motivated by the empirical lognormal model
that characterizes the probability distribution function(PDF) of the
three-dimensional mass distribution excellently, we critically investigate the
validity of lognormal model in the weak lensing statistics. Assuming that the
convergence field, $\kappa$, is approximately described by the lognormal
distribution, we present analytic formulae of convergence for the one-point PDF
and the Minkowski functionals. Comparing those predictions with ray-tracing
simulations in various cold dark matter models, we find that the one-point
lognormal PDF can describe the non-Gaussian tails of convergence fields
accurately up to $\nu\sim10$, where $\nu$ is the level threshold given by
$\nu\equiv\kappa/\var^{1/2}$, although the systematic deviation from lognormal
prediction becomes manifest at higher source redshift and larger smoothing
scales. The lognormal formulae for Minkowski functionals also fit to the
simulation results when the source redshift is low. Accuracy of the
lognormal-fit remains good even at the small angular scales, where the
perturbation formulae by Edgeworth expansion break down. On the other hand...

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## Modelling the term structure of interest rates \'{a} la Heath-Jarrow-Morton but with non Gaussian fluctuations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We consider a generalization of the Heath Jarrow Morton model for the term
structure of interest rates where the forward rate is driven by Paretian
fluctuations. We derive a generalization of It\^{o}'s lemma for the calculation
of a differential of a Paretian stochastic variable and use it to derive a
Stochastic Differential Equation for the discounted bond price. We show that it
is not possible to choose the parameters of the model to ensure absence of
drift of the discounted bond price. Then we consider a Continuous Time Random
Walk with jumps driven by Paretian random variables and we derive the large
time scaling limit of the jump probability distribution function (pdf). We show
that under certain conditions defined in text the large time scaling limit of
the jump pdf in the Fourier domain is \tilde{omega}_t(k,t) \sim \exp{-K/(\ln(k
t))^2} and is different from the case of a random walk with Gaussian
fluctuations. We also derive the master equation for the jump pdf and discuss
the relation of the master equation to Distributed Order Fractional Diffusion
Equations.; Comment: Elsevier style file, 22 pages, one postscript figure, revised on
07/09/2004

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## Thermalization of Levy flights: Path-wise picture in 2D

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/03/2013
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We analyze two-dimensional (2D) random systems driven by a symmetric L\'{e}vy
stable noise which, under the sole influence of external (force) potentials
$\Phi (x) $, asymptotically set down at Boltzmann-type thermal equilibria. Such
behavior is excluded within standard ramifications of the Langevin approach to
L\'{e}vy flights. In the present paper we address the response of L\'{e}vy
noise not to an external conservative force field, but directly to its
potential $\Phi (x)$. We prescribe a priori the target pdf $\rho_*$ in the
Boltzmann form $\sim \exp[- \Phi (x)]$ and next select the L\'evy noise of
interest. Given suitable initial data, this allows to infer a reliable
path-wise approximation to a true (albeit analytically beyond the reach)
solution of the pertinent master equation, with the property $\rho
(x,t)\rightarrow \rho_*(x)$ as time $t$ goes to infinity. We create a suitably
modified version of the time honored Gillespie's algorithm, originally invented
in the chemical kinetics context. A statistical analysis of generated sample
trajectories allows us to infer a surrogate pdf dynamics which consistently
sets down at a pre-defined target pdf. We pay special attention to the response
of the 2D Cauchy noise to an exemplary locally periodic "potential landscape"
$\Phi (x)...

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## Towards the NNPDF3.0 parton set for the second LHC run

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/07/2014
Português

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The full exploitation of the increasingly precise LHC measurements is
essential in order to reduce the uncertainty of theoretical predictions at
hadron colliders. The NNPDF2.3 fit was the first PDF determination including
the effect of the early LHC data. Here the new NNPDF3.0 PDF set is announced
and its main features are presented. The novel NNPDF analysis is based on an
improved fitting methodology, statistically validated by closure tests. Over a
thousand new data points are included, both the recent HERA II measurements and
a wide set of new LHC data. In this contribution details on the experimental
data are given and their impact on PDF uncertainties is displayed.; Comment: 5 pages, 3 figures

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## Wave Turbulence

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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In this paper we review recent developments in the statistical theory of
weakly nonlinear dispersive waves, the subject known as Wave Turbulence (WT).
We revise WT theory using a generalisation of the random phase approximation
(RPA). This generalisation takes into account that not only the phases but also
the amplitudes of the wave Fourier modes are random quantities and it is called
the ``Random Phase and Amplitude'' approach. This approach allows to
systematically derive the kinetic equation for the energy spectrum from the the
Peierls-Brout-Prigogine (PBP) equation for the multi-mode probability density
function (PDF). The PBP equation was originally derived for the three-wave
systems and in the present paper we derive a similar equation for the four-wave
case. Equation for the multi-mode PDF will be used to validate the statistical
assumptions about the phase and the amplitude randomness used for WT closures.
Further, the multi-mode PDF contains a detailed statistical information, beyond
spectra, and it finally allows to study non-Gaussianity and intermittency in
WT, as it will be described in the present paper. In particular, we will show
that intermittency of stochastic nonlinear waves is related to a flux of
probability in the space of wave amplitudes.; Comment: 25 pages...

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## Density probability distribution functions of diffuse gas in the Milky Way

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/06/2008
Português

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In a search for the signature of turbulence in the diffuse interstellar
medium in gas density distributions, we determined the probability distribution
functions (PDFs) of the average volume densities of the diffuse gas. The
densities were derived from dispersion measures and HI column densities towards
pulsars and stars at known distances. The PDFs of the average densities of the
diffuse ionized gas (DIG) and the diffuse atomic gas are close to lognormal,
especially when lines of sight at |b|<5 degrees and |b|>=5 degrees are
considered separately. The PDF of at high |b| is twice as wide as that
at low |b|. The width of the PDF of the DIG is about 30 per cent smaller than
that of the warm HI at the same latitudes. The results reported here provide
strong support for the existence of a lognormal density PDF in the diffuse ISM,
consistent with a turbulent origin of density structure in the diffuse gas.; Comment: 5 pages, 3 figures, accepted for publication in MNRAS Letters

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## AGN Jet-induced Feedback in Galaxies. I. Suppression of Star Formation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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(Abridged) We study the interaction of relativistic jets from AGNs with the
ISM in their host galaxy, using a series of Adaptive Mesh Refinement
simulations of the evolution of the interaction between the cocoon produced by
the jet with a dense cloud, placed very near the cocoon's path. We vary only
the jet's input power between P_{jet} = 10^{41}-10^{47} {\rm erg/sec}. The
density Probability Distribution Function (PDF) within the cocoon can be
described in terms of two distinct components, which are also spatially
distinct: a low- and a high-density component. The PDF of the post-shocked
region is well approximated by a modified lognormal distribution, for all
values of $P_{jet}$. During the active phase, when the jet is fed by the AGN,
the cloud is subject both to compression and stripping, which tend to increase
its density and diminish its total mass. When the jet is switched off (i.e.
during the passive phase) the shocked cloud cools further and tends to become
more filamentary, under the action of a back-flow which develops within the
cocoon. We study the evolution of the star formation rate within the cloud,
assuming that is determined by a Schmidt-Kennicutt law, and we analyze the
different physical factors which have an impact on the star formation rate. We
show that...

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## Stationary States in Bistable System Driven by L\'evy Noise

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/10/2012
Português

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We study the properties of the probability density function (PDF) of a
bistable system driven by heavy tailed white symmetric L\'evy noise. The shape
of the stationary PDF is found analytically for the particular case of the
L\'evy index \alpha = 1 (Cauchy noise). For an arbitrary L\'evy index we employ
numerical methods based on the solution of the stochastic Langevin equation and
space fractional kinetic equation. In contrast with the bistable system driven
by Gaussian noise, in the L\'evy case the positions of maxima of the stationary
PDF do not coincide with the positions of minima of the bistable potential. We
provide a detailed study of the distance between the maxima and the minima as a
function of the potential's depth and L\'evy noise parameters.; Comment: Accepted to EPJST

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## Probing the Low-Energy Electronic Structure of Complex Systems by ARPES

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/07/2003
Português

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Angle-resolved photoemission spectroscopy (ARPES) is one of the most direct
methods of studying the electronic structure of solids. By measuring the
kinetic energy and angular distribution of the electrons photoemitted from a
sample illuminated with sufficiently high-energy radiation, one can gain
information on both the energy and momentum of the electrons propagating inside
a material. This is of vital importance in elucidating the connection between
electronic, magnetic, and chemical structure of solids, in particular for those
complex systems which cannot be appropriately described within the
independent-particle picture. The last decade witnessed significant progress in
this technique and its applications, thus ushering in a new era in
photoelectron spectroscopy; today, ARPES experiments with 2 meV energy
resolution and 0.2 degree angular resolution are a reality even for
photoemission on solids. In this paper we will review the fundamentals of the
technique and present some illustrative experimental results; we will show how
ARPES can probe the momentum-dependent electronic structure of solids providing
detailed information on band dispersion and Fermi surface, as well as on the
strength and nature of those many-body correlations which may profoundly affect
the one-electron excitation spectrum and...

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## IGM Constraints from the SDSS-III/BOSS DR9 Ly-alpha Forest Flux Probability Distribution Function

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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The Ly$\alpha$ forest transmission probability distribution function (PDF) is
an established probe of the intergalactic medium (IGM) astrophysics, especially
the temperature-density relationship of the IGM. We measure the transmission
PDF from 3393 Baryon Oscillations Spectroscopic Survey (BOSS) quasars from SDSS
Data Release 9, and compare with mock spectra that include careful modeling of
the noise, continuum, and astrophysical uncertainties. The BOSS transmission
PDFs, measured at $\langle z \rangle = [2.3,2.6,3.0]$, are compared with PDFs
created from mock spectra drawn from a suite of hydrodynamical simulations that
sample the IGM temperature-density relationship, $\gamma$, and temperature at
mean-density, $T_0$, where $T(\Delta) = T_0 \Delta^{\gamma-1}$. We find that a
significant population of partial Lyman-limit systems with a column-density
distribution slope of $\beta_\mathrm{pLLS} \sim -2$ are required to explain the
data at the low-transmission end of transmission PDF, while uncertainties in
the mean Ly$\alpha$ forest transmission affect the high-transmission end. After
modelling the LLSs and marginalizing over mean-transmission uncertainties, we
find that $\gamma=1.6$ best describes the data over our entire redshift range...

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