Measurement of Plasma Properties from the Cross Spectrum of Thermal Density Fluctuations

1972 ◽  
Vol 15 (1) ◽  
pp. 96 ◽  
Author(s):  
K. H. Geissler
Keyword(s):  
Density Fluctuations ◽  
Plasma Properties ◽  
Cross Spectrum ◽  
The Cross

scholarly journals Turbulent enhancement of radar reflectivity factor for polydisperse cloud droplets

2019 ◽  
Vol 19 (3) ◽  
pp. 1785-1799 ◽  
Author(s):  
Keigo Matsuda ◽  
Ryo Onishi
Keyword(s):  
Isotropic Turbulence ◽  
Density Fluctuations ◽  
Radar Reflectivity ◽  
Wave Number ◽  
Critical Wave Number ◽  
Cross Spectrum ◽  
Proposed Model ◽  
Droplet Sizes ◽  
The Cross ◽  
Reflectivity Factor

Abstract. The radar reflectivity factor is important for estimating cloud microphysical properties; thus, in this study, we determine the quantitative influence of microscale turbulent clustering of polydisperse droplets on the radar reflectivity factor. The theoretical solution for particulate Bragg scattering is obtained without assuming monodisperse droplet sizes. The scattering intensity is given by an integral function including the cross spectrum of number density fluctuations for two different droplet sizes. We calculate the cross spectrum based on turbulent clustering data, which are obtained by the direct numerical simulation (DNS) of particle-laden homogeneous isotropic turbulence. The results show that the coherence of the cross spectrum is close to unity for small wave numbers and decreases almost exponentially with increasing wave number. This decreasing trend is dependent on the combination of Stokes numbers. A critical wave number is introduced to characterize the exponential decrease of the coherence and parameterized using the Stokes number difference. Comparison with DNS results confirms that the proposed model can reproduce the rp3-weighted power spectrum, which is proportional to the clustering influence on the radar reflectivity factor to a sufficiently high accuracy. Furthermore, the proposed model is extended to incorporate the gravitational settling influence by modifying the critical wave number based on the analytical equation derived for the bidisperse radial distribution function. The estimate of the modified model also shows good agreement with the DNS results for the case with gravitational droplet settling. The model is then applied to high-resolution cloud-simulation data obtained from a spectral-bin cloud simulation. The result shows that the influence of turbulent clustering can be significant inside turbulent clouds. The large influence is observed at the near-top of the clouds, where the liquid water content and the energy dissipation rate are sufficiently large.

scholarly journals Turbulent enhancement of radar reflectivity factor for polydisperse cloud droplets

2018 ◽  
Author(s):  
Keigo Matsuda ◽  
Ryo Onishi
Keyword(s):  
Isotropic Turbulence ◽  
Stokes Number ◽  
Integral Function ◽  
Density Fluctuations ◽  
Radar Reflectivity ◽  
Cross Spectrum ◽  
Microphysical Properties ◽  
Droplet Sizes ◽  
The Cross ◽  
Reflectivity Factor

Abstract. The radar reflectivity factor is important for estimating cloud microphysical properties; thus, in this study, we determine the quantitative influence of microscale turbulent clustering of polydisperse droplets on the radar reflectivity factor. The theoretical solution for particulate Bragg scattering is obtained without assuming monodisperse droplet sizes. The scattering intensity is given by an integral function including the cross spectrum of number density fluctuations for two different droplet sizes. We calculate the cross spectrum based on turbulent clustering data, which are obtained by the direct numerical simulation (DNS) of particle-laden homogeneous isotropic turbulence. The results show that the coherence of the cross spectrum is close to unity for small wavenumbers and decreases almost exponentially with increasing wavenumber. This decreasing trend is dependent on the combination of Stokes numbers. A critical wavenumber is introduced to characterize the exponential decrease of the coherence and parametrized using the Stokes number difference. Comparison with DNS results confirms that the proposed model can reproduce the rp3-weighted power spectrum, which is proportional to the clustering influence on the radar reflectivity factor, to a sufficiently high accuracy. The model is then applied to high-resolution cloud-simulation data obtained from a spectral-bin cloud simulation. The result shows that the influence of turbulent clustering can be significant for the near-top of turbulent clouds.

Earthquake site response estimation: A weak-motion case study

1992 ◽  
Vol 82 (6) ◽  
pp. 2283-2307
Author(s):  
E. H. Field ◽  
K. H. Jacob ◽  
S. E. Hough
Keyword(s):  
Site Response ◽  
Spectral Ratio ◽  
Large Degree ◽  
One Dimensional ◽  
Loma Prieta Earthquake ◽  
Cross Spectrum ◽  
Downward Bias ◽  
Dimensional Models ◽  
The Cross ◽  
Input Motion

Abstract Using weak-motion recordings of aftershocks of the 1989 Loma Prieta earthquake recorded in Oakland, California, near the failed Nimitz Freeway, two methods have been applied to estimate the site response of an alluvium site and three mud-over-alluvium sites. The first estimate is the traditional spectral ratio, and the second utilizes the cross spectrum. Recordings obtained at a nearby bedrock site are used as estimates of the sediment site input motions. While the two site response estimates produce similar peaks and troughs, there is an approximate factor of 2 difference in amplitudes. This discrepancy is evidence that there is a much greater level of noise than would be expected from the pre-event ambient noise. We interpret this as signal-generated noise produced by scattering from heterogeneities, which causes the true sediment site input to differ significantly from the bedrock site recording. Given this level of noise, the cross-spectrum estimate suffers a severe downward bias (by a factor of 2 in this study) and should probably not be used when the input motion is estimated from a bedrock site recording. The spectral-ratio estimates are relatively unbiased, but the level of noise introduces a large degree of uncertainty. Therefore, inferences about site response from individual spectral ratios should probably be avoided. On the other hand, ensemble averages of the estimates significantly reduce the scatter to reveal resonances that agree quite well in frequency and overall shape with those of one-dimensional models whose parameters were determined independently. A discrepancy of higher observed amplitudes than predicted by theory remains unexplained but most likely results from the effects of boundary layer topography, which are not accounted for by the simple one-dimensional models.

scholarly journals Testing general relativity with the Doppler magnification effect

2019 ◽  
Vol 488 (3) ◽  
pp. 3759-3771 ◽  
Author(s):  
Sambatra Andrianomena ◽  
Camille Bonvin ◽  
David Bacon ◽  
Philip Bull ◽  
Chris Clarkson ◽  
...  
Keyword(s):  
General Relativity ◽  
Cross Correlation ◽  
Signal To Noise Ratio ◽  
Density Fluctuations ◽  
Signal To Noise ◽  
Tests Of General Relativity ◽  
Velocity Statistics ◽  
The Cross ◽  
Noise Ratio ◽  
Magnification Effect

ABSTRACT The apparent sizes and brightnesses of galaxies are correlated in a dipolar pattern around matter overdensities in redshift space, appearing larger on their near side and smaller on their far side. The opposite effect occurs for galaxies around an underdense region. These patterns of apparent magnification induce dipole and higher multipole terms in the cross-correlation of galaxy number density fluctuations with galaxy size/brightness (which is sensitive to the convergence field). This provides a means of directly measuring peculiar velocity statistics at low and intermediate redshift, with several advantages for performing cosmological tests of general relativity (GR). In particular, it does not depend on empirically calibrated scaling relations like the Tully–Fisher and Fundamental Plane methods. We show that the next generation of spectroscopic galaxy redshift surveys will be able to measure the Doppler magnification effect with sufficient signal-to-noise ratio to test GR on large scales. We illustrate this with forecasts for the constraints that can be achieved on parametrized deviations from GR for forthcoming low-redshift galaxy surveys with DESI and SKA2. Although the cross-correlation statistic considered has a lower signal-to-noise ratio than RSD, it will be a useful probe of GR since it is sensitive to different systematics.

scholarly journals Phase and Image Reconstruction from Pupil-Plane Observations in the Near Infrared: Integration of the Phasors

1994 ◽  
Vol 158 ◽  
pp. 197-200
Author(s):  
J.-L. Monin ◽  
N. Ageorges ◽  
L. Desbat ◽  
C. Perrier
Keyword(s):  
Image Reconstruction ◽  
Near Infrared ◽  
New Method ◽  
Data Set ◽  
Preliminary Results ◽  
Cross Spectrum ◽  
The Cross ◽  
Simulated Images ◽  
Pupil Plane

A new method to reconstruct the phase of bidimensional interferograms, obtained through pupil-plane interferometry is presented. We compute the average complex phasor components of the cross-spectrum on a data set to reconstruct the original unperturbed phase. We present preliminary results on simulated images which visibility phases are distorted using a model of atmospheric perturbed wavefronts.

A New Non-Invasive Statistical Method to Assess the Spontaneous Cardiac Baroreflex in Humans

1995 ◽  
Vol 88 (6) ◽  
pp. 651-655 ◽  
Author(s):  
Michel Ducher ◽  
Jean Pierre Fauvel ◽  
Marie Paule Gustin ◽  
Catherine Cerutti ◽  
Robert Najem ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Heart Rate ◽  
Systolic Blood Pressure ◽  
Spectrum Analysis ◽  
Baroreflex Sensitivity ◽  
Correlation Coefficients ◽  
Statistical Dependence ◽  
High Systolic Blood Pressure ◽  
Cross Spectrum ◽  
The Cross

1. A new method was developed to evaluate cardiac baroreflex sensitivity. The association of a high systolic blood pressure with a low heart rate or the converse is considered to be under the influence of cardiac baroreflex activity. This method is based on the determination of the statistical dependence between systolic blood pressure and heart rate values obtained non-invasively by a Finapres device. Our computerized analysis selects the associations with the highest statistical dependence. A ‘Z-coefficient’ quantifies the strength of the statistical dependence. The slope of the linear regression, computed on these selected associations, is used to estimate baroreflex sensitivity. 2. The present study was carried out in 11 healthy resting male subjects. The results obtained by the ‘Z-coefficient’ method were compared with those obtained by cross-spectrum analysis, which has already been validated in humans. Furthermore, the reproducibility of both methods was checked after 1 week. 3. The results obtained by the two methods were significantly correlated (r = 0.78 for the first and r = 0.76 for the second experiment, P < 0.01). When repeated after 1 week, the average results were not significantly different. Considering individual results, test—retest correlation coefficients were higher with the Z-analysis (r = 0.79, P < 0.01) than with the cross-spectrum analysis (r = 0.61, P < 0.05). 4. In conclusion, as the Z-method gives results similar to but more reproducible than the cross-spectrum method, it might be a powerful and reliable tool to assess baroreflex sensitivity in humans.

scholarly journals Spectral Analysis of Multidimensional Stochastic Geophysical Models with an Application to Decadal ENSO Variability

2011 ◽  
Vol 68 (1) ◽  
pp. 13-25 ◽  
Author(s):  
Richard Kleeman
Keyword(s):  
Normal Mode ◽  
Linear Models ◽  
Decadal Variability ◽  
Normal Modes ◽  
Spectral Character ◽  
Stochastic Forcing ◽  
Spectral Matrix ◽  
Enso Variability ◽  
Cross Spectrum ◽  
The Cross

Abstract Simple linear models with additive stochastic forcing have been rather successful in explaining the observed spectrum of important climate variables. Motivated by this, the authors analyze the spectral character of such a general stochastic system of finite dimension. The spectral matrix is derived in the case that the spectrum is a linear combination of dynamical variables and their stochastic forcings. It is found that the most convenient basis for analysis is provided by the normal modes. In general the spectrum consists of two pieces. The first “diagonal” piece is a symmetric Lorentzian curve centered on the normal mode frequencies with breadth and strength determined by the normal mode dissipation. The second cross-spectrum piece derives usually from the coherency of the stochastic forcing of two different normal modes. The cross-spectrum is smaller in magnitude than the corresponding two diagonal pieces. This relative magnitude is controlled by the Wiener coherency, which is equal to the magnitude of the correlation of the stochastic forcings of different normal modes. This new analysis framework is studied in detail for the ENSO case for which a two-dimensional stochastically forced oscillator has been previously suggested as a minimal model. It is found that the observed spectrum is rather easily reproduced given appropriate dissipation. Further, it is found that the cross-spectrum results in a phase-dependent enhancement or suppression of frequencies smaller than the dominant ENSO frequency. This therefore provides a new mechanism for decadal ENSO variability. Since the cross-spectrum is phase dependent, the decadal variability generated has a distinctive spatial character. The significance of the cross-spectrum depends on the Wiener coherency, which in turn depends on the statistics of the stochastic forcing.

scholarly journals Implementation of a Cross-Spectrum FFT Analyzer for a Phase-Noise Test System in a Low-Cost FPGA

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Patrick Fleischmann ◽  
Heinz Mathis ◽  
Jakub Kucera ◽  
Stefan Dahinden
Keyword(s):  
Phase Noise ◽  
Cross Correlation ◽  
Dynamic Range ◽  
Low Cost ◽  
Test System ◽  
Low Noise ◽  
Noise Levels ◽  
High Quality ◽  
Cross Spectrum ◽  
The Cross

The cross-correlation method allows phase-noise measurements of high-quality devices with very low noise levels, using reference sources with higher noise levels than the device under test. To implement this method, a phase-noise analyzer needs to compute the cross-spectral density, that is, the Fourier transform of the cross-correlation, of two time series over a wide frequency range, from fractions of Hz to tens of MHz. Furthermore, the analyzer requires a high dynamic range to accommodate the phase noise of high-quality oscillators that may fall off by more than 100 dB from close-in noise to the noise floor at large frequency offsets. This paper describes the efficient implementation of a cross-spectrum analyzer in a low-cost FPGA, as part of a modern phase-noise analyzer with very fast measurement time.

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