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## On the probability distribution of power fluctuations in turbulence

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We study local power fluctuations in numerical simulations of stationary,
homogeneous, isotropic turbulence in two and three dimensions with Gaussian
forcing. Due to the near-Gaussianity of the one-point velocity distribution,
the probability distribution function (pdf) of the local power is well modelled
by the pdf of the product of two joint normally distributed variables. In
appropriate units, this distribution is parameterised only by the mean
dissipation rate, $\epsilon$. The large deviation function for this
distribution is calculated exactly and shown to satisfy a Fluctuation Relation
(FR) with a coefficient which depends on $\epsilon$. This FR is entirely
statistical in origin. The deviation from the model pdf are most pronounced for
positive fluctuations of the power and can be traced to a slightly faster than
Gaussian decay of the tails of the one-point velocity pdf. The resulting
deviations from the FR are consistent with several recent experimental studies.; Comment: 5 Pages, 5 Figures

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## The break up of heavy electrons at a quantum critical point

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 31/07/2003
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The point at absolute zero where matter becomes unstable to new forms of
order is called a quantum critical point (QCP). The quantum fluctuations
between order and disorder that develop at this point induce profound
transformations in the finite temperature electronic properties of the
material. Magnetic fields are ideal for tuning a material as close as possible
to a QCP, where the most intense effects of criticality can be studied. A
previous study on theheavy-electron material $YbRh_2Si_2$ found that near a
field-induced quantum critical point electrons move ever more slowly and
scatter off one-another with ever increasing probability, as indicated by a
divergence to infinity of the electron effective mass and cross-section. These
studies could not shed light on whether these properties were an artifact of
the applied field, or a more general feature of field-free QCPs. Here we report
that when Germanium-doped $YbRh_2Si_2$ is tuned away from a chemically induced
quantum critical point by magnetic fields there is a universal behavior in the
temperature dependence of the specific heat and resistivity: the characteristic
kinetic energy of electrons is directly proportional to the strength of the
applied field. We infer that all ballistic motion of electrons vanishes at a
QCP...

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## Parton Distribution Benchmarking with LHC Data

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#High Energy Physics - Phenomenology#High Energy Physics - Experiment#Nuclear Experiment#Nuclear Theory

We present a detailed comparison of the most recent sets of NNLO PDFs from
the ABM, CT, HERAPDF, MSTW and NNPDF collaborations. We compare parton
distributions at low and high scales and parton luminosities relevant for LHC
phenomenology. We study the PDF dependence of LHC benchmark inclusive cross
sections and differential distributions for electroweak boson and jet
production in the cases in which the experimental covariance matrix is
available. We quantify the agreement between data and theory by computing the
chi2 for each data set with all the various PDFs. PDF comparisons are performed
consistently for common values of the strong coupling. We also present a
benchmark comparison of jet production at the LHC, comparing the results from
various available codes and scale settings. Finally, we discuss the
implications of the updated NNLO PDF sets for the combined PDF+alphaS
uncertainty in the gluon fusion Higgs production cross section.; Comment: 52 pages, 22 figures, accepted for publication in JHEP

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## Rate-Distortion Bounds for High-Resolution Vector Quantization via Gibbs's Inequality

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/07/2015
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Gibbs's inequality states that the differential entropy of a random variable
with probability density function (pdf) $f$ is less than or equal to its cross
entropy with any other pdf $g$ defined on the same alphabet, i.e., $h(X)\leq
-\mathsf{E}[\log g(X)]$. Using this inequality with a cleverly chosen $g$, we
derive a lower bound on the smallest output entropy that can be achieved by
quantizing a $d$-dimensional source with given expected $r$th-power distortion.
Specialized to the one-dimensional case, and in the limit of vanishing
distortion, this lower bound converges to the output entropy achieved by a
uniform quantizer, thereby recovering the result by Gish and Pierce that
uniform quantizers are asymptotically optimal as the allowed distortion tends
to zero. Our lower bound holds for any $d$-dimensional memoryless source that
has a pdf and whose differential entropy and R\'enyi information dimension are
finite. In contrast to Gish and Pierce, we do not require any additional
constraints on the continuity or decay of the source pdf.; Comment: 15 pages, 2 figures

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## Connected graphs cospectral with a Friendship graph

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/01/2014
Português

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Let $n$ be any positive integer, the friendship graph $F_n$ consist of $n$
edge-disjoint triangles that all of them meeting in one vertex. A graph $G$ is
called cospectral with a graph $H$ if their adjacency matrices have the same
eigenvalues. Recently in [http://arxiv.org/pdf/1310.6529v1.pdf] it is proved
that if $G$ is any graph cospectral with $F_n$ $(n\neq 16)$, then $G\cong F_n$.
In this note, we give a proof of special case of the latter: Any connected
graph cospectral with $F_n$ is isomorphic to $F_n$. Our proof is independent of
ones given in [http://arxiv.org/pdf/1310.6529v1.pdf] and the proofs are based
on our recent results given in [Trans. Com., 2 no. 4 (2013) 37-52.] Using an
upper bound for the largest eigenvalue of a connected graph given in [J.
Combinatorial Theory, Ser. B, 81 (2001) 177-183.].; Comment: 3 pages, 2 figures

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## On the use of fractional calculus for the probabilistic characterization of random variables

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/01/2013
Português

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#Mathematical Physics#Mathematics - Statistics Theory#Physics - Data Analysis, Statistics and Probability

In this paper, the classical problem of the probabilistic characterization of
a random variable is re-examined. A random variable is usually described by the
probability density function (PDF) or by its Fourier transform, namely the
characteristic function (CF). The CF can be further expressed by a Taylor
series involving the moments of the random variable. However, in some
circumstances, the moments do not exist and the Taylor expansion of the CF is
useless. This happens for example in the case of $\alpha$--stable random
variables. Here, the problem of representing the CF or the PDF of random
variables (r.vs) is examined by introducing fractional calculus. Two very
remarkable results are obtained. Firstly, it is shown that the fractional
derivatives of the CF in zero coincide with fractional moments. This is true
also in case of CF not derivable in zero (like the CF of $\alpha$--stable
r.vs). Moreover, it is shown that the CF may be represented by a generalized
Taylor expansion involving fractional moments. The generalized Taylor series
proposed is also able to represent the PDF in a perfect dual representation to
that in terms of CF. The PDF representation in terms of fractional moments is
especially accurate in the tails and this is very important in engineering
problems...

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## Generalized Gibbs ensemble and work statistics of a quenched Luttinger liquid

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We analyze the probability distribution function (PDF) of work done on a
Luttinger liquid for an arbitrary finite duration interaction quench and show
that it can be described in terms a generalized Gibbs ensemble. We construct
the corresponding density matrix with explicit intermode correlations, and
determine the duration and interaction dependence of the probability of an
adiabatic transition and the PDF of non-adiabatic processes. In the
thermodynamic limit, the PDF of work exhibits a non-Gaussian maximum around the
excess heat, carrying almost all spectral weight. In contrast, in the small
system limit most spectral weight is carried by a delta peak at the energy of
the adiabatic process, and an oscillating PDF with dips at energies
commensurate to the quench duration and with an exponential envelope develops.
Relevance to cold atom experiments is also discussed.; Comment: 5+3 pages, 1+2 figures, new results on the generalized Gibbs ensemble
and on the details of the calculations are added

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## The VIMOS VLT Deep Survey: Evolution of the non-linear galaxy bias up to z=1.5

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We present the first measurements of the Probability Distribution Function
(PDF) of galaxy fluctuations in the VIMOS-VLT Deep Survey (VVDS) cone, covering
0.4x0.4 deg between 0.40.8; ii) the formation of bright galaxies is inhibited below a
characteristic mass-overdensity threshold whose amplitude increases with
redshift and luminosity; iii) the biasing function is non linear in all the
redshift bins investigated with non-linear effects of the order of a few to 10%
on scales >5Mpc.; Comment: 30 pages...

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## Singularities and the distribution of density in the Burgers/adhesion model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We are interested in the tail behavior of the pdf of mass density within the
one and $d$-dimensional Burgers/adhesion model used, e.g., to model the
formation of large-scale structures in the Universe after baryon-photon
decoupling. We show that large densities are localized near ``kurtoparabolic''
singularities residing on space-time manifolds of codimension two ($d \le 2$)
or higher ($d \ge 3$). For smooth initial conditions, such singularities are
obtained from the convex hull of the Lagrangian potential (the initial velocity
potential minus a parabolic term). The singularities contribute {\em
\hbox{universal} power-law tails} to the density pdf when the initial
conditions are random. In one dimension the singularities are preshocks
(nascent shocks), whereas in two and three dimensions they persist in time and
correspond to boundaries of shocks; in all cases the corresponding density pdf
has the exponent -7/2, originally proposed by E, Khanin, Mazel and Sinai (1997
Phys. Rev. Lett. 78, 1904) for the pdf of velocity gradients in one-dimensional
forced Burgers turbulence. We also briefly consider models permitting particle
crossings and thus multi-stream solutions, such as the Zel'dovich approximation
and the (Jeans)--Vlasov--Poisson equation with single-stream initial data: they
have singularities of codimension one...

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## Pion Valence-quark Parton Distribution Function

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/10/2014
Português

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Within the Dyson-Schwinger equation formulation of QCD, a rainbow ladder
truncation is used to calculate the pion valence-quark distribution
function(PDF). The gap equation is renormalized at a typical hadronic scale, of
order 0.5GeV, which is also set as the default initial scale for the pion PDF.
We implement a corrected leading-order expression for the PDF which ensures
that the valence-quarks carry all of the pion's light-front momentum at the
initial scale. The scaling behavior of the pion PDF at a typical partonic scale
of order 5.2GeV is found to be $(1-x)^{\nu}$, with $\nu\simeq 1.6$, as $x$
approaches one.; Comment: 5 pages, 2 figures

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## The Effects of Radiative Transfer on the PDFs of Molecular MHD Turbulence

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/04/2013
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We study the effects of radiative transfer on the Probability Distribution
Functions (PDFs) of simulations of magnetohydrodynamic turbulence in the widely
studied $^{13}$CO 2-1 transition. We find that the integrated intensity maps
generally follow a log-normal distribution, with the cases that have $\tau
\approx 1$ best matching the PDF of the column density. We fit a 2D
variance-sonic Mach number relationship to our logarithmic PDFs of the form
$\sigma_{ln(\Sigma/\Sigma_0)}^2=A\times ln(1+b^2{\cal M}_s^2)$ and find that,
for parameter $b=1/3$, parameter $A$ depends on the radiative transfer
environment. We also explore the variance, skewness, and kurtosis of the linear
PDFs finding that higher moments reflect both higher sonic Mach number and
lower optical depth. Finally, we apply the Tsallis incremental PDF function and
find that the fit parameters depend on both Mach numbers, but also are
sensitive to the radiative transfer parameter space, with the $\tau \approx 1$
case best fitting the incremental PDF of the true column density. We conclude
that, for PDFs of low optical depth cases, part of the gas is always
sub-thermally excited so that the spread of the line intensities exceeds the
spread of the underlying column densities and hence the PDFs do not reflect the
true column density. Similarly...

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## Information-theoretic significance of the Wigner distribution

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/09/2006
Português

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A coarse grained Wigner distribution p_{W}(x,u) obeying positivity derives
out of information-theoretic considerations. Let p(x,u) be the unknown joint
PDF (probability density function) on position- and momentum fluctuations x,u
for a pure state particle. Suppose that the phase part Psi(x,z) of its Fourier
transform F.T.[p(x,u)]=|Z(x,z)|exp[iPsi(x,z)] is constructed as a hologram.
(Such a hologram is often used in heterodyne interferometry.) Consider a
particle randomly illuminating this phase hologram. Let its two position
coordinates be measured. Require that the measurements contain an extreme
amount of Fisher information about true position, through variation of the
phase function Psi(x,z). The extremum solution gives an output PDF p(x,u) that
is the convolution of the Wigner p_{W}(x,u) with an instrument function
defining uncertainty in either position x or momentum u. The convolution arises
naturally out of the approach, and is one-dimensional, in comparison with the
two-dimensional convolutions usually proposed for coarse graining purposes. The
output obeys positivity, as required of a PDF, if the one-dimensional
instrument function is sufficiently wide. The result holds for a large class of
systems: those whose amplitudes a(x) are the same at their boundaries
(Examples: states a(x) with positive parity; with periodic boundary conditions;
free particle trapped in a box).; Comment: pdf version has 16 pages. No figures. Accepted for publ. in PRA

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## MSTW PDFs and impact of PDFs on cross sections at Tevatron and LHC

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/01/2012
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We briefly summarise the "MSTW 2008" determination of parton distribution
functions (PDFs), and subsequent follow-up studies, before reviewing some
topical issues concerning the PDF dependence of cross sections at the Tevatron
and LHC. We update a recently published study of benchmark Standard Model total
cross sections (W, Z, gg->H and t-tbar production) at the 7 TeV LHC, where we
account for all publicly available PDF sets and we compare to LHC data for W,
Z, and t-tbar production. We show the sensitivity of the Higgs cross sections
to the gluon distribution, then we demonstrate the ability of the Tevatron jet
data, and also the LHC t-tbar data, to discriminate between PDF sets with
different high-x gluon distributions. We discuss the related problem of
attempts to extract the strong coupling alpha_S from only deep-inelastic
scattering data, and we conclude that a direct data constraint on the high-x
gluon distribution is required to obtain a meaningful result. We therefore
discourage the use of PDF sets obtained from "non-global" fits where the high-x
gluon distribution is not directly constrained by data.; Comment: 20 pages, 16 figures. To appear in the proceedings of the Ringberg
Workshop on "New Trends in HERA Physics 2011"...

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## Parton distributions: HERA-Tevatron-LHC

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/01/2010
Português

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The parton distribution functions (PDFs) are a non-negotiable input to almost
all theory predictions at hadron colliders. In this talk, I introduce PDF
determination by global analysis and discuss selected topics concerning recent
relevant data from HERA and the Tevatron, before giving some prospects for the
LHC. The combination of H1 and ZEUS cross sections reduces uncertainties and
will be an important input to future global PDF analyses. The theoretical
description of the heavy-quark contribution to structure functions at HERA has
a significant influence on predictions at the LHC. New W and Z data from the
Tevatron Run II provide important PDF constraints, but there are currently
problems describing the latest data on the lepton charge asymmetry from W -> l
nu decays. The Tevatron Run II jet production data prefer a smaller high-x
gluon than the previous Run I data, which impacts on predictions for Higgs
cross sections at the Tevatron. It is now possible to consistently calculate a
combined "PDF+alpha_S" uncertainty on hadronic cross sections, which is around
2-3% for the W and Z total cross sections at the LHC, reflecting their
potential as a "standard candle" to measure machine luminosity. Parton
luminosity functions are useful quantities for studying properties of hadronic
cross sections. Precision measurements at the LHC will provide further
constraints on PDFs as data accumulates in the early running period.; Comment: 6 pages. Invited talk at the XXth Hadron Collider Physics Symposium
(HCP 2009)...

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## On the behavior of homogeneous, isotropic and stationary turbulence

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/03/2010
Português

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The recent development of a statistical model for incompressible
Navier-Stokes (NS) fluids based on inverse kinetic theory (IKT, 2004-2008)
poses the problem of searching for particular realizations of the theory which
may be relevant for \textit{the statistical description of turbulence} and in
particular for the so-called \textit{homogeneous, isotropic}and
\textit{stationary} turbulence (HIST). Here the problem is set in terms of the
$1-$point velocity probability density function (PDF) which determines a
complete IKT-statistical model for NS fluids. This raises the interesting
question of identifying the statistical assumptions under which a Gaussian PDF
can be achieved in such a context. In this paper it is proven that for the IKT
statistical model, HIST requires necessarily that $f_{1}$ must be SIED (namely
\textit{stationary}, \textit{isotropic} and \textit{% everywhere-defined}).
This implies, in turn, that the functional form of the PDF is uniquely
prescribed at all times. In particular, it is found that necessarily the PDF
must coincide with an isotropic Gaussian distribution. The conclusion is
relevant for the investigation of the so-called homogenous, isotropic and
stationary turbulence.

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## Theory for the single-point velocity statistics of fully developed turbulence

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We investigate the single-point velocity probability density function (PDF)
in three-dimensional fully developed homogeneous isotropic turbulence within
the framework of PDF equations focussing on deviations from Gaussianity. A
joint analytical and numerical analysis shows that these deviations may be
quantified studying correlations of dynamical quantities like pressure
gradient, external forcing and energy dissipation with the velocity. A
stationary solution for the PDF equation in terms of these quantities is
presented, and the theory is validated with the help of direct numerical
simulations indicating sub-Gaussian tails of the PDF.; Comment: 6 pages, 4 figures, corrected typo in eq. (4)

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## Kolmogorov stochasticity parameter as a measure of quantum chaos

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 28/01/2011
Português

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We propose the Kolmogorov stochasticity parameter, $\lambda$ for energy level
spectra to classify quantum systems with corresponding classical dynamics
ranging from integrable to chaotic. We also study the probability distribution
function (PDF) of $\lambda$. Remarkably, the PDF of all the integrable systems
studied here is the same and is found to be completely different from the PDF
of chaotic systems. We also note that $\lambda_n$ for $n$ energy levels scales
as $\lambda_n \sim n^{-\alpha}$. Furthermore, with $\alpha$, the stochastic
probability (calculated from PDF) is seen to jump by about an order of
magnitude as the systems turn chaotic.

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## Relation between firing statistics of spiking neuron with instantaneous feedback and without feedback

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We consider a wide class of spiking neuron models, defined by rather general
set of conditions typical for basic models like leaky integrate and fire, or
binding neuron model. A neuron is fed with a point renewal process. A relation
between the three probability density functions (pdf): (i) pdf of input
interspike intervals, (ii) pdf of output interspike intervals of a neuron with
instantaneous feedback and (iii) pdf for that same neuron without feedback is
derived. This allows to calculate any of the three pdfs provided the another
two are given. Similar relation between corresponding means and variances is
derived. The relations are checked exactly for the binding neuron model.; Comment: 5 pages letter. In this version, section about moments and variances
is added, text style and language improved

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## Velocity Statistics of the Nagel-Schreckenberg Model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/11/2015
Português

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The statistics of velocities in the cellular automaton model of Nagel and
Schreckenberg for traffic are studied. From numerical simulations, we obtain
the probability distribution function (PDF) for vehicle velocities and the
velocity-velocity (vv) correlation function. We identify the probability to
find a standing vehicle as a potential order parameter that signals nicely the
transition between free congested flow for sufficiently large number of
velocity states. Our results for the vv correlation function resemble features
of a second order phase transition. We develop a 3-body approximation that
allows us to relate the PDFs for velocities and headways. Using this relation,
an approximation to the velocity PDF is obtained from the headway PDF observed
in simulations. We find a remarkable agreement between this approximation and
the velocity PDF obtained from simulations.; Comment: 8 pages, 8 figures

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## Understanding star formation in molecular clouds II. Signatures of gravitational collapse of IRDCs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We analyse column density and temperature maps derived from Herschel dust
continuum observations of a sample of massive infrared dark clouds
(G11.11-0.12, G18.82-0.28, G28.37+0.07, G28.53-0.25). We disentangle the
velocity structure of the clouds using 13CO 1-0 and 12CO 3-2 data, showing that
these IRDCs are the densest regions in massive giant molecular clouds and not
isolated features. The probability distribution function (PDF) of column
densities for all clouds have a power-law distribution over all (high) column
densities, regardless of the evolutionary stage of the cloud: G11.11-0.12,
G18.82-0.28, and G28.37+0.07 contain (proto)-stars, while G28.53-0.25 shows no
signs of star formation. This is in contrast to the purely log-normal PDFs
reported for near/mid-IR extinction maps. We only find a log-normal
distribution for lower column densities, if we perform PDFs of the column
density maps of the whole GMC in which the IRDCs are embedded. By comparing the
PDF slope and the radial column density profile, we attribute the power law to
the effect of large-scale gravitational collapse and to local free-fall
collapse of pre- and protostellar cores. Independent from the PDF analysis, we
find infall signatures in the spectral profiles of 12CO for G28.37+0.07 and
G11.11-0.12...

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