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Turbulent Velocity Structure in Molecular Clouds

Ossenkopf, Volker; Mac Low, Mordecai-Mark
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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We compare velocity structure in the Polaris Flare molecular cloud at scales ranging from 0.015 pc to 20 pc to simulations of supersonic hydrodynamic and MHD turbulence computed with the ZEUS MHD code. We use several different statistical methods to compare models and observations. The Delta-variance wavelet transform is most sensitive to characteristic scales and scaling laws, but is limited by a lack of intensity weighting. The scanning-beam size-linewidth relation is more robust with respect to noisy data. Obtaining the global velocity scaling behaviour requires that large-scale trends in the maps not be removed but treated as part of the turbulent cascade. We compare the true velocity PDF in our models to velocity centroids and average line profiles in optically thin lines, and find that the line profiles reflect the true PDF better unless the map size is comparable to the total line-of-sight thickness of the cloud. Comparison of line profiles to velocity centroid PDFs can thus be used to measure the line-of-sight depth of a cloud. The observed density and velocity structure is consistent with supersonic turbulence with a driving scale at or above the size of the molecular cloud and dissipative processes below 0.05 pc. Ambipolar diffusion could explain the dissipation. The velocity PDFs exclude small-scale driving such as that from stellar outflows as a dominant process in the observed region. In the models...

Closure testing NNPDF3.0 with LHC observables

Deans, Christopher S.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 24/06/2015 Português
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A thorough understanding of PDFs and their uncertainties is important for the LHC and for future collider experiments. The recently released NNPDF3.0 set was presented alongside results from closure tests, where PDF fits were performed on pseudo-data generated from a chosen input PDF set. The results there demonstrate the validity of the NNPDF methodology and also provide some information about different contributions to the PDF uncertainties. Here I present a number of additional closure test results, specifically an investigation into the effect of using cross-validation in the fits, and an assessment of the successful reproduction of LHC cross-sections in closure tests. The results are consistent with those previously shown in the NNPDF3.0 paper.; Comment: 6 pages, 4 figures, to appear in the proceedings of the XXIII International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2015), Dallas, Texas, 27 April - 1 May 2015

Nonequilibrium Green's function approach to the pair distribution function of quantum many-body systems out of equilibrium

Bonitz, M.; Hermanns, S.; Kobusch, K.; Balzer, K.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 01/11/2012 Português
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The pair distribution function (PDF) is a key quantity for the analysis of correlation effects of a quantum system both in equilibrium and far from equilibrium. We derive an expression for the PDF in terms of the single-particle Green's functions---the solutions of the Keldysh/Kadanoff-Baym equations in the two-time plane---for a one- or two-component system. The result includes initial correlations and generalizes previous density matrix expressions from single-time quantum kinetic theory. Explicit expressions for the PDF are obtained in second Born approximation.

Interpretations of some parameter dependent generalizations of classical matrix ensembles

Forrester, Peter J.; Rains, Eric M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 18/11/2002 Português
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Two types of parameter dependent generalizations of classical matrix ensembles are defined by their probability density functions (PDFs). As the parameter is varied, one interpolates between the eigenvalue PDF for the superposition of two classical ensembles with orthogonal symmetry and the eigenvalue PDF for a single classical ensemble with unitary symmetry, while the other interpolates between a classical ensemble with orthogonal symmetry and a classical ensemble with symplectic symmetry. We give interpretations of these PDFs in terms of probabilities associated to the continuous Robinson-Schensted-Knuth correspondence between matrices, with entries chosen from certain exponential distributions, and non-intersecting lattice paths, and in the course of this probability measures on partitions and pairs of partitions are identified. The latter are generalized by using Macdonald polynomial theory, and a particular continuum limit -- the Jacobi limit -- of the resulting measures is shown to give PDFs related to those appearing in the work of Anderson on the Selberg integral. By interpreting Anderson's work as giving the PDF for the zeros of a certain rational function, it is then possible to identify random matrices whose eigenvalue PDFs realize the original parameter dependent PDFs. This line of theory allows sampling of the original parameter dependent PDFs...

Time evolution of probability density function of gamma ray burst (GRB) - a possible indication of turbulence origin of GRB

Bhatt, Nilay; Bhattacharyya, Subir
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 11/11/2011 Português
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Gamma ray burst (GRB) time series is a non-stationary time series with all its statistical properties varying with time. Considering that each GRB is a different manifestation of the same stochastic process we studied the time dependent as well as time averaged probability density function (\emph{pdf}) characterizing the underlying stochastic process. The \emph{pdf}s are fitted with Gaussian distribution function and it has been argued that the Gaussian \emph{pdf}s possibly indicate the turbulence origin of GRB. The spectral and temporal evolution of GRBs are also studied through the evolution of spectral forms, color-color diagrams and hysteresis loops. The results do not contradict the turbulence interpretation of GRB.; Comment: Accepted for publication in MNRAS

Spatial Extent of Branching Brownian Motion

Ramola, Kabir; Majumdar, Satya N.; Schehr, Gregory
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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We study the one dimensional branching Brownian motion starting at the origin and investigate the correlation between the rightmost ($X_{\max}\geq 0$) and leftmost ($X_{\min} \leq 0$) visited sites up to time $t$. At each time step the existing particles in the system either diffuse (with diffusion constant $D$), die (with rate $a$) or split into two particles (with rate $b$). We focus on the regime $b \leq a$ where these two extreme values $X_{\max}$ and $X_{\min}$ are strongly correlated. We show that at large time $t$, the joint probability distribution function (PDF) of the two extreme points becomes stationary $P(X,Y,t \to \infty) \to p(X,Y)$. Our exact results for $p(X,Y)$ demonstrate that the correlation between $X_{\max}$ and $X_{\min}$ is nonzero, even in the stationary state. From this joint PDF, we compute exactly the stationary PDF $p(\zeta)$ of the (dimensionless) span $\zeta = {(X_{\max} - X_{\min})}/{\sqrt{D/b}}$, which is the distance between the rightmost and leftmost visited sites. This span distribution is characterized by a linear behavior ${p}(\zeta) \sim \frac{1}{2} \left(1 + \Delta \right) \zeta$ for small spans, with $\Delta = \left(\frac{a}{b} -1\right)$. In the critical case ($\Delta = 0$) this distribution has a non-trivial power law tail ${p}(\zeta) \sim 8 \pi \sqrt{3} /\zeta^3$ for large spans. On the other hand...

Non-Gaussianity in Cosmic Microwave Background Temperature Fluctuations from Cosmic (Super-)Strings

Takahashi, Keitaro; Naruko, Atsushi; Sendouda, Yuuiti; Yamauchi, Daisuke; Yoo, Chul-Moon; Sasaki, Misao
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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We compute analytically the small-scale temperature fluctuations of the cosmic microwave background from cosmic (super-)strings and study the dependence on the string intercommuting probability $P$. We develop an analytical model which describes the evolution of a string network and calculate the numbers of string segments and kinks in a horizon volume. Then we derive the probability distribution function (pdf) which takes account of finite angular resolution of observation. The resultant pdf consists of a Gaussian part due to frequent scatterings by long string segments and a non-Gaussian tail due to close encounters with kinks. The dispersion of the Gaussian part is reasonably consistent with that obtained by numerical simulations by Fraisse et al.. On the other hand, the non-Gaussian tail contains two phenomenological parameters which are determined by comparison with the numerical results for P=1. Extrapolating the pdf to the cases with $P<1$, we predict that the non-Gaussian feature is suppressed for small $P$.; Comment: 6 pages, 2 figure, version accepted by JCAP

Single-file dynamics with different diffusion constants

Ambjornsson, Tobias; Lizana, Ludvig; Lomholt, Michael A.; Silbey, Robert J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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We investigate the single-file dynamics of a tagged particle in a system consisting of N hardcore interacting particles (the particles cannot pass each other) which are diffusing in a one-dimensional system where the particles have different diffusion constants. For the two particle case an exact result for the conditional probability density function (PDF) is obtained for arbitrary initial particle positions and all times. The two-particle PDF is used to obtain the tagged particle PDF. For the general N-particle case (N large) we perform stochastic simulations using our new computationally efficient stochastic simulation technique based on the Gillespie algorithm. We find that the mean square displacement for a tagged particle scales as the square root of time (as for identical particles) for long times, with a prefactor which depends on the diffusion constants for the particles; these results are in excellent agreement with very recent analytic predictions in the mathematics literature.; Comment: 9 pages, 5 figures. Journal of Chemical Physics (in press)

Crystal structure solution from experimentally determined atomic pair distribution functions

Juhas, Pavol; Granlund, Luke; Gujarathi, Saurabh R.; Duxbury, Phillip M.; Billinge, Simon J. L.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 04/03/2010 Português
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The paper describes an extension of the Liga algorithm for structure solution from atomic pair distribution function (PDF), to handle periodic crystal structures with multiple elements in the unit cell. The procedure is performed in 2 separate steps - at first the Liga algorithm is used to find unit cell sites consistent with pair distances extracted from the experimental PDF. In the second step the assignment of atom species over cell sites is solved by minimizing the overlap of their empirical atomic radii. The procedure has been demonstrated on synchrotron x-ray PDF data from 16 test samples. The structure solution was successful for 14 samples including cases with enlarged super cells. The algorithm success rate and the reasons for failed cases are discussed together with enhancements that should improve its convergence and usability.; Comment: 16 pages, 1 figure, submitted to Journal of Applied Crystallography

Notes on the sum and maximum of independent exponentially distributed random variables with different scale parameters

Bibinger, Markus
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 15/07/2013 Português
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We consider the distribution of the sum and the maximum of a collection of independent exponentially distributed random variables. The focus is laid on the explicit form of the density functions (pdf) of non-i.i.d. sequences. Those are recovered in a simple and direct way based on conditioning. A connection between the pdf and a representation of the convolution characteristic function as a linear combination of the single characteristic functions is drawn. It is demonstrated how the results on the pdf of order statistics and the convolution merge.

The stellar population histories of early-type galaxies. III. The Coma Cluster

Trager, S. C.; Faber, S. M.; Dressler, Alan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 04/03/2008 Português
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We present stellar population parameters of twelve early-type galaxies (ETGs) in the Coma Cluster based on spectra obtained using the Low Resolution Imaging Spectrograph on the Keck II Telescope. Our data allow us to examine in detail the zero-point and scatter in their stellar population properties. Our ETGs have SSP-equivalent ages of on average 5-8 Gyr with the models used here, with the oldest galaxies having ages of ~10 Gyr old. This average age is identical to the mean age of field ETGs. Our ETGs span a large range in velocity dispersion but are consistent with being drawn from a population with a single age. Specifically, ten of the twelve ETGs are consistent within their formal errors of having the same age, 5.2+/-0.2 Gyr, over a factor of more than 750 in mass. We therefore find no evidence for downsizing of the stellar populations of ETGs in the core of the Coma Cluster. We suggest that Coma Cluster ETGs may have formed the majority of their mass at high redshifts but suffered small but detectable star formation events at z~0.1-0.3. Previous detections of 'downsizing' from stellar populations of local ETGs may not reflect the same downsizing seen in lookback studies of RSGs, as the young ages of the local ETGs represent only a small fraction of their total masses. (abridged); Comment: 49 pages...

On the Initial Conditions for Star Formation and the IMF

Elmegreen, Bruce G.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 25/02/2011 Português
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Density probability distribution functions (PDFs) for turbulent self-gravitating clouds should be convolutions of the local log-normal PDF, which depends on the local average density rho-ave and Mach number M, and the probability distribution functions for rho-ave and M, which depend on the overall cloud structure. When self-gravity drives a cloud to increased central density, the total PDF develops an extended tail. If there is a critical density or column density for star formation, then the fraction of the local mass exceeding this threshold becomes higher near the cloud center. These elements of cloud structure should be in place before significant star formation begins. Then the efficiency is high so that bound clusters form rapidly, and the stellar initial mass function (IMF) has an imprint in the gas before destructive radiation from young stars can erase it. The IMF could arise from a power-law distribution of mass for cloud structure. These structures should form stars down to the thermal Jeans mass MJ at each density in excess of a threshold. The high-density tail of the PDF, combined with additional fragmentation in each star-forming core, extends the IMF into the Brown Dwarf regime. The core fragmentation process is distinct from the cloud structuring process and introduces an independen core fragmentation mass function (CFMF). The CFMF would show up primarily below the IMF peak.; Comment: 16 pages...

Finite N corrections to the limiting distribution of the smallest eigenvalue of Wishart complex matrices

Perret, Anthony; Schehr, Gregory
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 08/06/2015 Português
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We study the probability distribution function (PDF) of the smallest eigenvalue of Laguerre-Wishart matrices $W = X^\dagger X$ where $X$ is a random $M \times N$ ($M \geq N$) matrix, with complex Gaussian independent entries. We compute this PDF in terms of semi-classical orthogonal polynomials, which are deformations of Laguerre polynomials. By analyzing these polynomials, and their associated recurrence relations, in the limit of large $N$, large $M$ with $M/N \to 1$ -- i.e. for quasi-square large matrices $X$ -- we show that this PDF, in the hard edge limit, can be expressed in terms of the solution of a Painlev\'e III equation, as found by Tracy and Widom, using Fredholm operators techniques. Furthermore, our method allows us to compute explicitly the first $1/N$ corrections to this limiting distribution at the hard edge. Our computations confirm a recent conjecture by Edelman, Guionnet and P\'ech\'e. We also study the soft edge limit, when $M-N \sim {\cal O}(N)$, for which we conjecture the form of the first correction to the limiting distribution of the smallest eigenvalue.; Comment: 28 pages, 2 Figures

Universal features and tail analysis of the order-parameter distribution of the two-dimensional Ising model: An entropic sampling Monte Carlo study

Malakis, Anastasios; Fytas, Nikolaos G.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 15/09/2008 Português
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We present a numerical study of the order-parameter probability density function (PDF) of the square Ising model for lattices with linear sizes $L=80-140$. A recent efficient entropic sampling scheme, combining the Wang-Landau and broad histogram methods and based on the high-levels of the Wang-Landau process in dominant energy subspaces is employed. We find that for large lattices there exists a stable window of the scaled order-parameter in which the full ansatz including the pre-exponential factor for the tail regime of the universal PDF is well obeyed. This window is used to estimate the equation of state exponent and to observe the behavior of the universal constants implicit in the functional form of the universal PDF. The probability densities are used to estimate the universal Privman-Fisher coefficient and to investigate whether one could obtain reliable estimates of the universal constants controlling the asymptotic behavior of the tail regime.; Comment: 24 pages, 5 figures

Statistics of surface gravity wave turbulence in the space and time domains

Nazarenko, S.; Lukaschuk, S.; McLelland, S.; Denissenko, P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/11/2008 Português
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We present experimental results on simultaneous space-time measurements for the gravity wave turbulence in a large laboratory flume. We compare these results with predictions of the weak turbulence theory (WTT) based on random waves, as well as with predictions based on the coherent singular wave crests. We see that both wavenumber and the frequency spectra are not universal and dependent on the wave strength, with some evidence in favor of WTT at larger wave intensities when the finite flume effects are minimal. We present further theoretical analysis of the role of the random and coherent waves in the wave probability density function (PDF) and the structure functions (SFs). Analyzing our experimental data we found that the random waves and the coherent structures/breaks coexist: the former show themselves in a quasi-gaussian PDF core and in the low-order SFs, and the latter - in the PDF tails and the high-order SF's. It appears that the x-space signal is more intermittent than the t-space signal, and the x-space SFs capture more singular coherent structures than do the t-space SFs. We outline an approach treating the interactions of these random and coherent components as a turbulence cycle characterized by the turbulence fluxes in both the wavenumber and the amplitude spaces.; Comment: 29 pages...

Uncertainties of the Inclusive Higgs Production Cross Section at the Tevatron and the LHC

Belyaev, Alexander; Pumplin, Jon; Tung, Wu-Ki; Yuan, C. --P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/08/2005 Português
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We study uncertainties of the predicted inclusive Higgs production cross section due to the uncertainties of parton distribution functions (PDF). Particular attention is given to bbH Yukawa coupling enhanced production mechanisms in beyond SM scenarios, such as MSSM. The PDF uncertainties are determined by the robust Lagrange Multiplier method within the CTEQ global analysis framework. We show that PDF uncertainties dominate over theoretical uncertainties of the perturbative calculation (usually estimated by the scale dependence of the calculated cross sections), except for low Higgs masses at LHC. Thus for the proper interpretation of any Higgs signal, and for better understanding of the underlying electroweak symmetry breaking mechanism, it is important to gain better control of the uncertainties of the PDFs.; Comment: LaTeX, JHEP, 19 pages, 14 figures

Evaluation of Symmetric Mutual Information of the Simplified TDMR Channel Model

Wadayama, Tadashi
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 31/03/2015 Português
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In the present paper, a simplified two-dimensional magnetic recording (TDMR) channel model is proposed in order to capture the qualitative features of writing and read-back processes of TDMR systems.The proposed channel model incorporates the effects of both linear interference from adjacent bit-cells and signal-dependent noise due to irregular grain boundaries between adjacent bit-cells. The simplicity of the proposed model enables us to derive the closed form of the conditional PDF representing the probabilistic nature of the channel. The conditional PDF is Gaussian distributed and is parameterized by a signal-dependent covariance matrix. Based on this conditional PDF, a Monte Carlo method for approximating the symmetric mutual information of this channel is developed. The symmetric mutual information is closely related to the areal density limit for TDMR systems. The numerical results suggest that we may need low-rate coding, e.g., 2/3 or 1/2, when the jitter-like noise becomes dominant.

HERAFitter, Open Source QCD Fit Project

Alekhin, S.; Behnke, O.; Belov, P.; Borroni, S.; Botje, M.; Britzger, D.; Camarda, S.; Cooper-Sarkar, A. M.; Daum, K.; Diaconu, C.; Feltesse, J.; Gizhko, A.; Glazov, A.; Guffanti, A.; Guzzi, M.; Hautmann, F.; Jung, A.; Jung, H.; Kolesnikov, V.; Kowalski,
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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HERAFitter is an open-source package that provides a framework for the determination of the parton distribution functions (PDFs) of the proton and for many different kinds of analyses in Quantum Chromodynamics (QCD). It encodes results from a wide range of experimental measurements in lepton-proton deep inelastic scattering and proton-proton (proton-antiproton) collisions at hadron colliders. These are complemented with a variety of theoretical options for calculating PDF-dependent cross section predictions corresponding to the measurements. The framework covers a large number of the existing methods and schemes used for PDF determination. The data and theoretical predictions are brought together through numerous methodological options for carrying out PDF fits and plotting tools to help visualise the results. While primarily based on the approach of collinear factorisation, HERAFitter also provides facilities for fits of dipole models and transverse-momentum dependent PDFs. The package can be used to study the impact of new precise measurements from hadron colliders. This paper describes the general structure of HERAFitter and its wide choice of options.; Comment: 18 pages, 7 figures

The Decay of Passive Scalars Under the Action of Single Scale Smooth Velocity Fields in Bounded 2D Domains : From non self similar pdf's to self similar eigenmodes

Sukhatme, Jai; Pierrehumbert, Raymond T.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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We examine the decay of passive scalars with small, but non zero, diffusivity in bounded 2D domains. The velocity fields responsible for advection are smooth (i.e., they have bounded gradients) and of a single large scale. Moreover, the scale of the velocity field is taken to be similar to the size of the entire domain. The importance of the initial scale of variation of the scalar field with respect to that of the velocity field is strongly emphasized. If these scales are comparable and the velocity field is time periodic, we see the formation of a periodic scalar eigenmode. The eigenmode is numerically realized by means of a deterministic 2D map on a lattice. Analytical justification for the eigenmode is available from theorems in the dynamo literature. Weakening the notion of an eigenmode to mean statistical stationarity, we provide numerical evidence that the eigenmode solution also holds for aperiodic flows (represented by random maps). Turning to the evolution of an initially small scale scalar field, we demonstrate the transition from an evolving (i.e., {\it non} self similar) pdf to a stationary (self similar) pdf as the scale of variation of the scalar field progresses from being small to being comparable to that of the velocity field (and of the domain). Furthermore...

The 1-Point Cluster Distribution Function and its Moments

Plionis, M.; Valdarnini, R.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 02/09/1994 Português
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We derive the 1-point probability density function of the smoothed 3-D Abell-ACO cluster density field and we compare it with that of artificial cluster samples, generated as high peaks of a Gaussian field in such a way that they reproduce the low-order (2- and 3-point) correlation functions and the observed cluster selection functions. We find that both real and simulated {\em pdf}'s are well approximated by a log-normal distribution even when the Gaussian smoothing radius is as large as 40 $h^{-1}$ Mpc. Furthermore the low-order moments of the {\em pdf} are found to obey a relation $\gamma = S_{3} \sigma^4$, with $\gamma$ being the skewness and $S_{3}\approx 1.8$. These results are consistent with clusters being high-peaks of an underlying initial Gaussian density field. A by-product of our analysis is that when we rescale the {\em pdf} cluster moments to those of the QDOT-IRAS galaxies, using linear biasing with $b_{cI}\sim 4.5$ and for the common smoothing radius of 20 $h^{-1}$ Mpc, we find them to be significantly smaller than those directly estimated from the QDOT data by Saunders et al. (1991).; Comment: LaTex file. Submitted in MNRAS June 1994. Figures upon request