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## Primordial Black Holes in non-linear perturbation theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/10/2009
Português

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This thesis begins with a study of the origin of cosmological fluctuations
with special attention to those cases in which the non-Gaussian correlation
functions are large. The analysis shows that perturbations from an almost
massless auxiliary field generically produce large values of the non-linear
parameter f_NL. The effects of including non-Gaussian correlation functions in
the statistics of cosmological structure are explored by constructing a
non-Gaussian probability distribution function (PDF). Such PDF is derived for
the comoving curvature perturbation from first principles in the context of
quantum field theory, with n-point correlation functions as the only input. The
non-Gaussian PDF is then used to explore two important problems in the physics
of primordial black holes (PBHs): First, to compute non-Gaussian corrections to
the number of PBHs generated from the primordial curvature fluctuations. The
second application concerns new cosmological observables. The formation of PBHs
is known to depend on two main physical characteristics: the strength of the
gravitational field produced by the initial curvature inhomogeneity and the
pressure gradient at the edge of the curvature configuration. We account for
the probability of finding these configurations by using two parameters: The
amplitude of the inhomogeneity and its second radial derivative...

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## Particle drift in turbulent flows: the influence of local structure and inhomogeneity

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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The way particles interact with turbulent structures, particularly in regions
of high vorticity and strain rate, has been investigated in simulations of
homogeneous turbulence and in simple flows which have a periodic or persistent
structure e.g. separating flows and mixing layers. The influence on both
settling under gravity and diffusion has been reported and the divergence
(compressibility) of the underlying particle velocity field along a particle
trajectory has been recognized as an important quantity in quantifying these
features. This paper shows how these features can be incorporated in a formal
way into a two-fluid model of the dispersed particle phase. In particular the
PDF equation for the particle velocity and position is formerly derived on the
basis of a stochastic process that involves the statistics of both the particle
velocity and local compressibility along particle trajectories. The PDF
equation gives rise to contributions to both the drift and particle diffusion
coefficient that depend upon the correlation of these quantities with the local
carrier flow velocity. Key Words: turbulent structures, particle dispersion,
drift, PDF approach; Comment: 14 pages, 2 figures,4th Int. Conf. on Multiphase Flow, N. Orleans USA
May 27-June 1...

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## Non-Gaussian Statistics of Multiple Filamentation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/05/2010
Português

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#Nonlinear Sciences - Chaotic Dynamics#Nonlinear Sciences - Pattern Formation and Solitons#Physics - Optics

We consider the statistics of light amplitude fluctuations for the
propagation of a laser beam subjected to multiple filamentation in an amplified
Kerr media, with both linear and nonlinear dissipation. Dissipation arrests the
catastrophic collapse of filaments, causing their disintegration into almost
linear waves. These waves form a nearly-Gaussian random field which seeds new
filaments. For small amplitudes the probability density function (PDF) of light
amplitude is close to Gaussian, while for large amplitudes the PDF has a long
power-like tail which corresponds to strong non-Gaussian fluctuations, i.e.
intermittency of strong optical turbulence. This tail is determined by the
universal form of near singular filaments and the PDF for the maximum
amplitudes of the filaments.

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## Scaled unscented transform Gaussian sum filter: theory and application

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/05/2010
Português

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In this work we consider the state estimation problem in
nonlinear/non-Gaussian systems. We introduce a framework, called the scaled
unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas:
the scaled unscented Kalman filter (SUKF) based on the concept of scaled
unscented transform (SUT), and the Gaussian mixture model (GMM). The SUT is
used to approximate the mean and covariance of a Gaussian random variable which
is transformed by a nonlinear function, while the GMM is adopted to approximate
the probability density function (pdf) of a random variable through a set of
Gaussian distributions. With these two tools, a framework can be set up to
assimilate nonlinear systems in a recursive way. Within this framework, one can
treat a nonlinear stochastic system as a mixture model of a set of sub-systems,
each of which takes the form of a nonlinear system driven by a known Gaussian
random process. Then, for each sub-system, one applies the SUKF to estimate the
mean and covariance of the underlying Gaussian random variable transformed by
the nonlinear governing equations of the sub-system. Incorporating the
estimations of the sub-systems into the GMM gives an explicit (approximate)
form of the pdf, which can be regarded as a "complete" solution to the state
estimation problem...

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## The advection-condensation model and water vapour PDFs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/05/2011
Português

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#Physics - Fluid Dynamics#Physics - Atmospheric and Oceanic Physics#Physics - Data Analysis, Statistics and Probability

The statistically steady humidity distribution resulting from an interaction
of advection, modeled as an uncorrelated random walk of moist parcels on an
isentropic surface, and a vapour sink, modeled as immediate condensation
whenever the specific humidity exceeds a specified saturation humidity, is
explored with theory and simulation. A source supplies moisture at the
deep-tropical southern boundary of the domain, and the saturation humidity is
specified as a monotonically decreasing function of distance from the boundary.
The boundary source balances the interior condensation sink, so that a
stationary spatially inhomogeneous humidity distribution emerges. An exact
solution of the Fokker-Planck equation delivers a simple expression for the
resulting probability density function (PDF) of the water vapour field and also
of the relative humidity. This solution agrees completely with a numerical
simulation of the process, and the humidity PDF exhibits several features of
interest, such as bimodality close to the source and unimodality further from
the source. The PDFs of specific and relative humidity are broad and
non-Gaussian. The domain averaged relative humidity PDF is bimodal with
distinct moist and dry peaks, a feature which we show agrees with middleworld
isentropic PDFs derived from the ERA interim dataset.; Comment: 13 pages...

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## Primordial Non-Gaussianity and Extreme-Value Statistics of Galaxy Clusters

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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What is the size of the most massive object one expects to find in a survey
of a given volume? In this paper, we present a solution to this problem using
Extreme-Value Statistics, taking into account primordial non-Gaussianity and
its effects on the abundance and the clustering of rare objects. We calculate
the probability density function (pdf) of extreme-mass clusters in a survey
volume, and show how primordial non-Gaussianity shifts the peak of this pdf. We
also study the sensitivity of the extreme-value pdfs to changes in the mass
functions, survey volume, redshift coverage and the normalization of the matter
power spectrum, {\sigma}_8. For 'local' non-Gaussianity parametrized by f_NL,
our correction for the extreme-value pdf due to the bias is important when f_NL
> O(100), and becomes more significant for wider and deeper surveys. Applying
our formalism to the massive high-redshift cluster XMMUJ0044.0-2-33, we find
that its existence is consistent with f_NL = 0, although the conclusion is
sensitive to the assumed values of the survey area and {\sigma}_8. We also
discuss the convergence of the extreme-value distribution to one of the three
possible asymptotic forms, and argue that the convergence is insensitive to the
presence of non-Gaussianity.; Comment: Revised version...

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## A QCD analysis of ZEUS data including DIS inclusive cross sections with longitudinally polarised leptons and data run at lower proton beam energies

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/07/2009
Português

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New ZEUS data are added into the NLO QCD analysis of the ZEUS-JETS PDF fit.
The addition of high-$Q^2$ NC and CC $e^-p$ inclusive cross-section data
improves the determination of the $u$-valence quark at high $x$. The addition
of high-$Q^2$ CC $e^+p$ inclusive cross-section data improves the determination
of the $d$-valence quark at high $x$. The addition of lower-$Q^2$ NC $e^+p$
inclusive cross-section data, run at three different proton beam energies,
improves the determination of the sea and gluon PDFs at small $x$. The new PDF
fit is called the ZEUS09 PDF fit.; Comment: Invited talk on behalf of the ZEUS Collaboration at DIS 2009, The
17th International Workshop on Deep Inelastic Scattering, Madrid, April 2009.
% pages, 6 figures

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## Recovering the topology of the IGM at z~2

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 28/01/2008
Português

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We investigate how well the 3D density field of neutral hydrogen in the
Intergalactic Medium (IGM) can be reconstructed using the Lyman-alpha
absorptions observed along lines of sight to quasars separated by arcmin
distances in projection on the sky. We use cosmological hydrodynamical
simulations to compare the topologies of different fields: dark matter, gas and
neutral hydrogen optical depth and to investigate how well the topology of the
IGM can be recovered from the Wiener interpolation method implemented by Pichon
et al. (2001). The global statistical and topological properties of the
recovered field are analyzed quantitatively through the power-spectrum, the
probability distribution function (PDF), the Euler characteristics, its
associated critical point counts and the filling factor of underdense regions.
The local geometrical properties of the field are analysed using the local
skeleton by defining the concept of inter-skeleton distance. At scales larger
than ~1.4 , where is the mean separation between lines of sight,
the reconstruction accurately recovers the topological features of the large
scale density distribution of the gas, in particular the filamentary
structures. At scales larger than the intrinsic smoothing length of the
inversion procedure...

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## Scaling in Gravitational Clustering, 2D and 3D Dynamics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/07/1997
Português

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Perturbation Theory (PT) applied to a cosmological density field with
Gaussian initial fluctuations suggests a specific hierarchy for the correlation
functions when the variance is small. In particular quantitative predictions
have been made for the moments and the shape of the one-point probability
distribution function (PDF) of the top-hat smoothed density. In this paper we
perform a series of systematic checks of these predictions against N-body
computations both in 2D and 3D with a wide range of featureless power spectra.
In agreement with previous studies, we found that the reconstructed PDF-s work
remarkably well down to very low probabilities, even when the variance
approaches unity. Our results for 2D reproduce the features for the 3D
dynamics. In particular we found that the PT predictions are more accurate for
spectra with less power on small scales. The nonlinear regime has been explored
with various tools, PDF-s, moments and Void Probability Function (VPF). These
studies have been done with unprecedented dynamical range, especially for the
2D case, allowing in particular more robust determinations of the asymptotic
behaviour of the VPF. We have also introduced a new method to determine the
moments based on the factorial moments. Results using this method and taking
into account the finite volume effects are presented.; Comment: 13 pages...

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## Stochastic Approach to Plasticity and Yield in Amorphous Solids

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/09/2015
Português

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We focus on the probability distribution function (pdf) $P(\Delta \gamma;
\gamma)$ where $\Delta \gamma$ are the {\em measured} strain intervals between
plastic events in an athermal strained amorphous solids, and $\gamma$ measures
the accumulated strain. The tail of this distribution as $\Delta \gamma\to 0$
(in the thermodynamic limit) scales like $\Delta \gamma^\eta$. The exponent
$\eta$ is related via scaling relations to the tail of the pdf of the
eigenvalues of the {\em plastic modes} of the Hessian matrix $P(\lambda)$ which
scales like $\lambda^\theta$, $\eta=(\theta-1)/2$. The numerical values of
$\eta$ or $\theta$ can be determined easily in the unstrained material and in
the yielded state of plastic flow. Special care is called for in the
determination of these exponents between these states as $\gamma$ increases.
Determining the $\gamma$ dependence of the pdf $P(\Delta \gamma; \gamma)$ can
shed important light on plasticity and yield. We conclude that the pdf's of
both $\Delta \gamma$ and $\lambda$ are not continuous functions of $\gamma$. In
slowly quenched amorphous solids they undergo two discontinuous transitions,
first at $\gamma=0^+$ and then at the yield point $\gamma=\gamma_{_{\rm Y}}$ to
plastic flow. In quickly quenched amorphous solids the second transition is
smeared out due to the non existing stress peak before yield. The nature of
these transitions and scaling relations with the system size dependence of
$\langle \Delta \gamma\rangle$ are discussed.; Comment: 8 pages...

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## Quantitative size-dependent structure and strain determination of CdSe nanoparticles using atomic pair distribution function analysis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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The size-dependent structure of CdSe nanoparticles, with diameters ranging
from 2 to 4 nm, has been studied using the atomic pair distribution function
(PDF) method. The core structure of the measured CdSe nanoparticles can be
described in terms of the wurtzite atomic structure with extensive stacking
faults. The density of faults in the nanoparticles ~50% . The diameter of the
core region was extracted directly from the PDF data and is in good agreement
with the diameter obtained from standard characterization methods suggesting
that there is little surface amorphous region. A compressive strain was
measured in the Cd-Se bond length that increases with decreasing particle size
being 0.5% with respect to bulk CdSe for the 2 nm diameter particles. This
study demonstrates the size-dependent quantitative structural information that
can be obtained even from very small nanoparticles using the PDF approach.; Comment: 10 pages, 7 figures and 3 tables. Phys. Rev. B, submitted (2007)

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## Review of AdS/CFT Integrability: An Overview

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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This is the introductory chapter of a review collection on integrability in
the context of the AdS/CFT correspondence. In the collection we present an
overview of the achievements and the status of this subject as of the year
2010.; Comment: 31 pages, v2: reference added, references to other chapters updated,
v3: footnote 1 on location of references added, v4: minor changes, references
added, accepted for publication in Lett. Math. Phys, v5: minor corrections,
links to chapters updated, attached IntAdS.pdf with all chapters in one file,
see http://arxiv.org/src/1012.3982/anc/IntAdS.pdf or
http://www.phys.ethz.ch/~nbeisert/IntAdS.pdf

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## The Nyquist-Shannon sampling theorem and the atomic pair distribution function

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/04/2011
Português

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We have systematically studied the optimal real-space sampling of atomic pair
distribution data by comparing refinement results from oversampled and
resampled data. Based on nickel and a complex perovskite system, we demonstrate
that the optimal sampling is bounded by the Nyquist interval described by the
Nyquist-Shannon sampling theorem. Near this sampling interval, the data points
in the PDF are minimally correlated, which results in more reliable uncertainty
prediction. Furthermore, refinements using sparsely sampled data may run many
times faster than using oversampled data. This investigation establishes a
theoretically sound limit on the amount of information contained in the PDF,
which has ramifications towards how PDF data are modeled.; Comment: 10 pages, 4 figures

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## The rule for a subdiffusive particle in an extremely diverse environment

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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The dynamics of a subdiffusive continuous time random walker in an
inhomogeneous environment is analyzed. In each microscopic jump, a random time
is drawn from a waiting time probability density function (WT-PDF) that decays
as a power law: phi(t;k)~k/(1+kt)^(1+beta), 0 beta;, mu=beta, but when 1-gamma

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## Dissecting the spin distribution of Dark Matter halos

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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(Abridged) We apply a very general statistical theorem introduced by Cramer
(1936) to study the origin of the deviations of the halo spin PDF from the
reference lognormal shape. We find that these deviations originate from
correlations between two quantities entering the definition of spin, namely the
ratio $J/M^{5/2}$ (which depends only on mass) and the total gravitational
binding energy $E$. To reach this conclusion, we have made usage of the results
deduced from two high spatial- and mass resolution simulations. Our simulations
cover a relatively small volume and produce a sample of more than 16.000
gravitationally bound halos, each traced by at least 300 particles. We verify
that our results are stable to different systematics, by comparing our results
with those derived by the GIF2 and by a more recent simulation performed by
Maccio' et al. We find that the spin probability distribution function shows
systematic deviations from a lognormal, at all redshifts z <= 1. These
deviations depend on mass and redshift: at small masses they change little with
redshift, and also the best lognormal fits are more stable. The J-M
relationship is well described by a power law of exponent $\alpha$ very near to
the linear theory prediction (alpha=5/3)...

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## Lyman Break Galaxies and the Lyman-alpha Forest

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We use hydrodynamic simulations to predict correlations between Lya forest
absorption and galaxies at redshift z~3. The probability distribution function
(PDF) of Lya flux decrements shifts systematically towards higher values in the
vicinity of galaxies, reflecting the overdense environments in which these
galaxies reside. The predicted signal remains strong in spectra smoothed over
50-200 km/s, allowing tests with moderate resolution quasar spectra. The strong
bias of high redshift galaxies towards high density regions imprints a clear
signature on the flux PDF, but the predictions are not sensitive to galaxy
baryon mass or star formation rate, and they are similar for galaxies and for
dark matter halos. The dependence of the flux PDF on galaxy proximity is
sensitive to redshift determination errors, with rms errors of 150-300 km/s
substantially weakening the predicted trends. On larger scales, the mean galaxy
overdensity in a cube of 5 or 10 Mpc/h (comoving) is strongly correlated with
the mean Lya flux decrement on a line of sight through the cube center. The
slope of the correlation is ~3 times steeper for galaxies than for dark matter
as a result of galaxy bias. The predicted large scale correlation is in
qualitative agreement with recently reported observational results. However...

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## The distribution of annihilation luminosities in dark matter substructure

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We calculate the probability distribution function (PDF) of the expected
annihilation luminosities of dark matter subhalos as a function of subhalo mass
and distance from the Galactic center using a semi-analytical model of halo
evolution. We find that the PDF of luminosities is relatively broad, exhibiting
a spread of as much as an order of magnitude at fixed subhalo mass and
halo-centric distance. The luminosity PDF allows for simple construction of
mock samples of gamma-ray luminous subhalos and assessment of the variance in
among predicted gamma-ray signals from dark matter annihilation. Other
applications include quantifying the variance among the expected luminosities
of dwarf spheroidal galaxies, assessing the level at which dark matter
annihilation can be a contaminant in the expected gamma-ray signal from other
astrophysical sources, as well as estimating the level at which nearby subhalos
can contribute to the antimatter flux.; Comment: 10 pages, 5 figures. Replaced with version accepted for publication
in Phys. Rev. D

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## Finite-Horizon Parameterizing Manifolds, and Applications to Suboptimal Control of Nonlinear Parabolic PDEs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Mathematics - Optimization and Control#Mathematics - Analysis of PDEs#35K10, 37L05, 37L25, 37L65, 49K15, 49K20

This article proposes a new approach based on finite-horizon parameterizing
manifolds (PMs) for the design of low-dimensional suboptimal controllers to
optimal control problems of nonlinear partial differential equations (PDEs) of
parabolic type. Given a finite horizon $[0,T]$ and a low-mode truncation of the
PDE, a PM provides an approximate parameterization of the uncontrolled high
modes by the controlled low ones so that the unexplained high-mode energy is
reduced, in an $L^2$-sense, when this parameterization is applied. Analytic
formulas of such PMs are derived by application of the method of pullback
approximation of the high-modes (Chekroun, Liu, and Wang, 2013,
http://arxiv.org/pdf/1310.3896v1.pdf). These formulas allow for an effective
derivation of reduced ODE systems, aimed to model the evolution of the low-mode
truncation of the controlled state variable, where the high-mode part is
approximated by the PM function applied to the low modes. A priori error
estimates between the resulting PM-based low-dimensional suboptimal controller
$u_R^\ast$ and the optimal controller $u^*$ are derived. These estimates
demonstrate that the closeness of $u_R^\ast$ to $u^*$ is mainly conditioned on
two factors: (i) the parameterization defect of a given PM...

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## Robust Distributed Maximum Likelihood Estimation with Dependent Quantized Data

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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In this paper, we consider distributed maximum likelihood estimation (MLE)
with dependent quantized data under the assumption that the structure of the
joint probability density function (pdf) is known, but it contains unknown
deterministic parameters. The parameters may include different vector
parameters corresponding to marginal pdfs and parameters that describe
dependence of observations across sensors. Since MLE with a single quantizer is
sensitive to the choice of thresholds due to the uncertainty of pdf, we
concentrate on MLE with multiple groups of quantizers (which can be determined
by the use of prior information or some heuristic approaches) to fend off
against the risk of a poor/outlier quantizer. The asymptotic efficiency of the
MLE scheme with multiple quantizers is proved under some regularity conditions
and the asymptotic variance is derived to be the inverse of a weighted linear
combination of Fisher information matrices based on multiple different
quantizers which can be used to show the robustness of our approach. As an
illustrative example, we consider an estimation problem with a bivariate
non-Gaussian pdf that has applications in distributed constant false alarm rate
(CFAR) detection systems. Simulations show the robustness of the proposed MLE
scheme especially when the number of quantized measurements is small.; Comment: submitted to journal

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## Trajectory statistics of confined L\'{e}vy flights and Boltzmann-type equilibria

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 27/03/2013
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We analyze a specific class of random systems that are driven by a symmetric
L\'{e}vy stable noise, where Langevin representation is absent. In view of the
L\'{e}vy noise sensitivity to environmental inhomogeneities, the pertinent
random motion asymptotically sets down at the Boltzmann-type equilibrium,
represented by a probability density function (pdf) $\rho_*(x) \sim \exp [-\Phi
(x)]$. Here, we infer pdf $\rho (x,t)$ based on numerical path-wise simulation
of the underlying jump-type process. A priori given data are jump transition
rates entering the master equation for $\rho (x,t)$ and its target pdf
$\rho_*(x)$. To simulate the above processes, we construct a suitable
modification of the Gillespie algorithm, originally invented in the chemical
kinetics context. We exemplified our algorithm simulating different jump-type
processes and discuss the dynamics of real physical systems where it can be
useful.; Comment: Presented at 25th Marian Smoluchowski Symposium on Statistical
Physics, Cracow, Sept. 10-13, 2012

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