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Alyssa A Goodman - One of the best experts on this subject based on the ideXlab platform.
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the Spectral Correlation function of molecular clouds a statistical test for theoretical models
The Astrophysical Journal, 2003Co-Authors: Paolo Padoan, Alyssa A Goodman, M JuvelaAbstract:We compute the Spectral Correlation function (SCF) of 13CO J = 1-0 maps of molecular cloud complexes. The SCF is a power law over approximately an order of magnitude in spatial separation in every map. The power-law slope of the SCF, α, its normalization, S0(1 pc), and the Spectral line width averaged over the whole map, σv, are computed for all the observational maps. The values of α, S0(1 pc), and σv are combined to obtain empirical Correlations to be used as tests for theoretical models of molecular clouds. Synthetic Spectral maps are computed from different theoretical models, including solutions of the magnetohydrodynamic (MHD) equations with different values of the rms Mach number of the flow and stochastic models with different power spectra of the velocity field. In order to compute the radiative transfer from the MHD models, it is necessary to assign the models a physical scale and a physical density. When these assignments are made according to Larson-type relations, the best fit to the observational Correlations is obtained. Unphysical stochastic models are instead ruled out by the empirical Correlations. MHD models with equipartition of magnetic and kinetic energy of turbulence do not reproduce the observational data when their average magnetic field is oriented approximately parallel to the line of sight.
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the effects of noise and sampling on the Spectral Correlation function
The Astrophysical Journal, 2001Co-Authors: Paolo Padoan, Erik Rosolowsky, Alyssa A GoodmanAbstract:The effects of noise and sampling on the Spectral Correlation function (SCF) introduced by Rosolowsky and coworkers are studied using observational data, numerical simulations of magnetohydrodynamic turbulence, and simple models of Gaussian Spectral line profiles. The most significant innovations of this paper are (1) the normalization of the SCF based on an analytic model for the effect of noise and (2) the computation of the SCF as a function of the spatial lag between spectra within a map. A new definition of the "quality" of a spectrum, Q, is introduced, which is correlated with the usual definition of signal-to-noise ratio. The prenormalization value of the SCF is a function of Q. We derive analytically the effect of noise on the SCF, and then normalize the SCF to its analytic approximation. By computing the dependence of the SCF on the spatial lag, S0(Δr), we have been able to conclude the following: (1) S0(Δr) is a power law, with slope α, in the range of scales li < l < lo. (2) The Correlation outer scale, lo, is determined by the size of the map, and no evidence for a true departure from self-similarity on large scales has been found. (3) The Correlation inner scale, li, is a true estimate of the smallest self-similar scale in a map. (4) The Spectral slope, α, in a given region, is independent of velocity resolution (above a minimum resolution threshold), spatial resolution, and average spectrum quality. (5) Molecular transitions that trace higher gas density yield larger values of α (steeper slopes) than transitions tracing lower gas density. (6) Nyquist sampling, bad pixels in detector arrays, and reference-sharing data acquisition need to be taken into account for a correct determination of the SCF at Δr = 1. The value of α, however, can be computed correctly without a detailed knowledge of observational procedures.
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the Spectral Correlation function a new tool for analyzing Spectral line maps
The Astrophysical Journal, 1999Co-Authors: Erik Rosolowsky, Alyssa A Goodman, David J Wilner, Jonathan P WilliamsAbstract:The "Spectral Correlation function" analysis we introduce in this paper is a new tool for analyzing Spectral line data cubes. Our initial tests, carried out on a suite of observed and simulated data cubes, indicate that the Spectral Correlation function (SCF) is likely to be a more discriminating statistic than other statistical methods normally applied. The SCF is a measure of similarity between neighboring spectra in the data cube. When the SCF is used to compare a data cube consisting of Spectral line observations of the interstellar medium (ISM) with a data cube derived from MHD simulations of molecular clouds, it can find differences that are not found by other analyses. The initial results presented here suggest that the inclusion of self-gravity in numerical simulations is critical for reproducing the Correlation behavior of spectra in star-forming molecular clouds.
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the Spectral Correlation function a new tool for analyzing Spectral line maps
arXiv: Astrophysics, 1999Co-Authors: Erik Rosolowsky, Alyssa A Goodman, David J Wilner, Jonathan P WilliamsAbstract:The "Spectral Correlation function" analysis we introduce in this paper is a new tool for analyzing Spectral-line data cubes. Our initial tests, carried out on a suite of observed and simulated data cubes, indicate that the Spectral Correlation function [SCF] is likely to be a more discriminating statistic than other statistical methods normally applied. The SCF is a measure of similarity between neighboring spectra in the data cube. When the SCF is used to compare a data cube consisting of Spectral-line observations of the ISM with a data cube derived from MHD simulations of molecular clouds, it can find differences that are not found by other analyses. The initial results presented here suggest that the inclusion of self-gravity in numerical simulations is critical for reproducing the Correlation behavior of spectra in star-forming molecular clouds.
P H Damgaard - One of the best experts on this subject based on the ideXlab platform.
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microscopic eigenvalue Correlations in qcd with imaginary isospin chemical potential
Physical Review D, 2006Co-Authors: P H Damgaard, U M Heller, K Splittorff, Benjamin Svetitsky, D ToublanAbstract:We consider the chiral limit of QCD subjected to an imaginary isospin chemical potential. In the {epsilon}-regime of the theory we can perform precise analytical calculations based on the zero-momentum Goldstone modes in the low-energy effective theory. We present results for the Spectral Correlation functions of the associated Dirac operators.
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consistency conditions for finite volume partition functions
Physics Letters B, 1998Co-Authors: Gernot Akemann, P H DamgaardAbstract:Abstract Using relations from random matrix theory, we derive exact expressions for all n -point Spectral Correlation functions of Dirac operator eigenvalues in terms of finite-volume partition functions. This is done for both chiral symplectic and chiral unitary random matrix ensembles, which correspond to SU ( N c ≥3) gauge theories with N f fermions in the adjoint and fundamental representations, respectively. In the latter case we infer from this an infinite sequence of consistency conditions that must be satisfied by the corresponding finite-volume partition functions.
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consistency conditions for finite volume partition functions
arXiv: High Energy Physics - Theory, 1998Co-Authors: Gernot Akemann, P H DamgaardAbstract:Using relations from random matrix theory, we derive exact expressions for all $n$-point Spectral Correlation functions of Dirac operator eigenvalues in terms of finite-volume partition functions. This is done for both chiral symplectic and chiral unitary random matrix ensembles, which correspond to $SU(N_c \geq 3)$ gauge theories with $N_f$ fermions in the adjoint and fundamental representations, respectively. In the latter case we infer from this an infinite sequence of consistency conditions that must be satisfied by the corresponding finite-volume partition functions.
Erik Rosolowsky - One of the best experts on this subject based on the ideXlab platform.
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the effects of noise and sampling on the Spectral Correlation function
The Astrophysical Journal, 2001Co-Authors: Paolo Padoan, Erik Rosolowsky, Alyssa A GoodmanAbstract:The effects of noise and sampling on the Spectral Correlation function (SCF) introduced by Rosolowsky and coworkers are studied using observational data, numerical simulations of magnetohydrodynamic turbulence, and simple models of Gaussian Spectral line profiles. The most significant innovations of this paper are (1) the normalization of the SCF based on an analytic model for the effect of noise and (2) the computation of the SCF as a function of the spatial lag between spectra within a map. A new definition of the "quality" of a spectrum, Q, is introduced, which is correlated with the usual definition of signal-to-noise ratio. The prenormalization value of the SCF is a function of Q. We derive analytically the effect of noise on the SCF, and then normalize the SCF to its analytic approximation. By computing the dependence of the SCF on the spatial lag, S0(Δr), we have been able to conclude the following: (1) S0(Δr) is a power law, with slope α, in the range of scales li < l < lo. (2) The Correlation outer scale, lo, is determined by the size of the map, and no evidence for a true departure from self-similarity on large scales has been found. (3) The Correlation inner scale, li, is a true estimate of the smallest self-similar scale in a map. (4) The Spectral slope, α, in a given region, is independent of velocity resolution (above a minimum resolution threshold), spatial resolution, and average spectrum quality. (5) Molecular transitions that trace higher gas density yield larger values of α (steeper slopes) than transitions tracing lower gas density. (6) Nyquist sampling, bad pixels in detector arrays, and reference-sharing data acquisition need to be taken into account for a correct determination of the SCF at Δr = 1. The value of α, however, can be computed correctly without a detailed knowledge of observational procedures.
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the Spectral Correlation function a new tool for analyzing Spectral line maps
The Astrophysical Journal, 1999Co-Authors: Erik Rosolowsky, Alyssa A Goodman, David J Wilner, Jonathan P WilliamsAbstract:The "Spectral Correlation function" analysis we introduce in this paper is a new tool for analyzing Spectral line data cubes. Our initial tests, carried out on a suite of observed and simulated data cubes, indicate that the Spectral Correlation function (SCF) is likely to be a more discriminating statistic than other statistical methods normally applied. The SCF is a measure of similarity between neighboring spectra in the data cube. When the SCF is used to compare a data cube consisting of Spectral line observations of the interstellar medium (ISM) with a data cube derived from MHD simulations of molecular clouds, it can find differences that are not found by other analyses. The initial results presented here suggest that the inclusion of self-gravity in numerical simulations is critical for reproducing the Correlation behavior of spectra in star-forming molecular clouds.
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the Spectral Correlation function a new tool for analyzing Spectral line maps
arXiv: Astrophysics, 1999Co-Authors: Erik Rosolowsky, Alyssa A Goodman, David J Wilner, Jonathan P WilliamsAbstract:The "Spectral Correlation function" analysis we introduce in this paper is a new tool for analyzing Spectral-line data cubes. Our initial tests, carried out on a suite of observed and simulated data cubes, indicate that the Spectral Correlation function [SCF] is likely to be a more discriminating statistic than other statistical methods normally applied. The SCF is a measure of similarity between neighboring spectra in the data cube. When the SCF is used to compare a data cube consisting of Spectral-line observations of the ISM with a data cube derived from MHD simulations of molecular clouds, it can find differences that are not found by other analyses. The initial results presented here suggest that the inclusion of self-gravity in numerical simulations is critical for reproducing the Correlation behavior of spectra in star-forming molecular clouds.
Dong Wang - One of the best experts on this subject based on the ideXlab platform.
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a simple and fast guideline for generating enhanced squared envelope spectra from Spectral coherence for bearing fault diagnosis
Mechanical Systems and Signal Processing, 2019Co-Authors: Dong Wang, Xuejun Zhao, Linlin Kou, Yong Qin, Yang Zhao, Kwokleung TsuiAbstract:Abstract Rolling element bearings are widely used in machines to support rotating shafts and their health conditions degrade over time due to harsh working conditions. Once a fault occurs on the surface of either an inner race or an outer race, impacts caused by rollers striking the fault surface excite resonant frequencies of a machine and then repetitive transients are observed in vibration signals collected from the casing of the machine. Spectral Correlation and its normalized version, Spectral coherence, are a function of Spectral frequency and cyclic frequency, and they are able to simultaneously display resonant frequency bands and bearing fault frequencies. Moreover, it has been proved that integrating Spectral Correlation over an informative Spectral frequency band is related to a squared envelope spectrum which is more conveniently used to detect bearing fault frequencies than the direct inspection of the bi-spectra map of Spectral Correlation/Spectral coherence. Therefore, generating enhanced/squared envelope spectra from Spectral Correlation/Spectral coherence is an important step for the use of Spectral Correlation/Spectral coherence for bearing fault diagnosis. However, in the past years, determining informative Spectral frequency bands for generating enhanced/squared envelope spectra from Spectral Correlation/Spectral coherence mainly depends on expertise and careful observations from Spectral Correlation/Spectral coherence. In the case of weak bearing fault frequencies and strong interruptions from other cyclic frequencies, it is not easy for users to determine an informative Spectral frequency band for generating an enhanced/squared envelope spectrum from Spectral Correlation/Spectral coherence for bearing fault diagnosis. To solve this problem, a simple and fast guideline is proposed in this paper. Laboratorial bearing fault data and industrial railway axle bearing fault data are used to illustrate how the proposed guideline works. Results showed that the proposed guideline is effective in determining informative Spectral frequency bands for generating enhanced/squared envelope spectra from Spectral coherence for bearing fault diagnosis. Comparisons with the fast Kurtogram and an enhanced squared envelope spectrum generated from integrating Spectral coherence over the whole Spectral frequency band are conducted to highlight the superiority of the proposed guideline.
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an equivalent cyclic energy indicator for bearing performance degradation assessment
Journal of Vibration and Control, 2016Co-Authors: Dong Wang, Changqing ShenAbstract:Bearing performance degradation assessment has attracted much attention in recent years because it is a key step to estimating the remaining useful life of bearings. Because cyclic Spectral analysis has superior ability to characterize some kinds of non-stationary signals, such as non-stationary bearing fault signals, many efforts have been made to use cyclic Spectral analysis for bearing fault diagnosis. However, the application of cyclic Spectral analysis to bearing prognosis, especially bearing performance degradation assessment, is rarely reported. Recently, based on the integration of Spectral Correlation over Spectral frequency, a novel bearing heath indicator, the cyclic energy indicator (CEI), was proposed by some scholars. In this paper, an equivalent cyclic energy indicator (ECEI) is introduced. It is mathematically proofed that the ECEI is equal to the CEI. Additionally, because the calculations of the ECEI do not involve Spectral Correlation, which is a two-dimensional power density function a...
Gernot Akemann - One of the best experts on this subject based on the ideXlab platform.
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consistency conditions for finite volume partition functions
Physics Letters B, 1998Co-Authors: Gernot Akemann, P H DamgaardAbstract:Abstract Using relations from random matrix theory, we derive exact expressions for all n -point Spectral Correlation functions of Dirac operator eigenvalues in terms of finite-volume partition functions. This is done for both chiral symplectic and chiral unitary random matrix ensembles, which correspond to SU ( N c ≥3) gauge theories with N f fermions in the adjoint and fundamental representations, respectively. In the latter case we infer from this an infinite sequence of consistency conditions that must be satisfied by the corresponding finite-volume partition functions.
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consistency conditions for finite volume partition functions
arXiv: High Energy Physics - Theory, 1998Co-Authors: Gernot Akemann, P H DamgaardAbstract:Using relations from random matrix theory, we derive exact expressions for all $n$-point Spectral Correlation functions of Dirac operator eigenvalues in terms of finite-volume partition functions. This is done for both chiral symplectic and chiral unitary random matrix ensembles, which correspond to $SU(N_c \geq 3)$ gauge theories with $N_f$ fermions in the adjoint and fundamental representations, respectively. In the latter case we infer from this an infinite sequence of consistency conditions that must be satisfied by the corresponding finite-volume partition functions.
