Theoretical calculation of the power spectra of the rolling and yawing moments on a wing in random turbulence
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Scale breaks (spatial scales at which power-law exponent changes occur) observed in Landsat radiances have proven to be useful indicators of radiative interactions, and have aided the development of improved techniques in the remote sensing of clouds. This work extends previous theoretical studies to absorbing wavelengths by using both Landsat Thematic Mapper (TM) observations and Monte Carlo (MC) simulations to infer the systematic dependencies of power spectral shape on cloud characteristics, illumination conditions, and wavelength. We show that MC simulations operating on a simple fractal model of horizontally inhomogeneous clouds produce power spectra that qualitatively resemble observed spectra. We also show that the decrease in the spectra power-law exponent seen at intermediate scales (referred to as "roughening") as the Sun becomes more oblique is more pronounced at absorbing wavelengths. An automated procedure designed to detect the small scale break location is unable to find systematic differences between TM Band 4 and Band 7, despite the fact that MC simulations point to systematic differences in horizontal fluxes. The effect of these qualitative characteristics of the spatial spectra on the retrieval of cloud optical properties is examined by comparing power spectra of nadir radiances with power spectra of optical properties retrieved using either traditional Independent Pixel Approximation approaches or modifications based on normalized radiance indices and the inverse Non-local Independent Pixel Approximation. Assuming that the actual cloud properties follow perfect scaling behavior at all scales, we show the improvement of the proposed retrieval modifications.
Using a single-scattering approximation, equations for the scattering attenuation coefficients of P-body and S-body waves are derived. The results are discussed in the light of the energy-renormalization approaches of Wu (1980, 1982) and Sato (1982) to seismic wave scattering. Practical methods for calculating the scattering attenuation coefficients for various earth models are emphasized. The conversions of P-waves to S-waves and S-waves to P-waves are included in the theory. The earth models are assumed to be randomly inhomogeneous, with their properties known only through their average-wavenumber power spectra. The power spectra are approximated with piecewise constant functions, each segment of which contributes to the net frequency-dependent scattering attenuation coefficient. The smallest and largest wavenumbers of a segment can be plotted along with the wavevectors of the incident and scattered waves on a wavenumber diagram. This diagram gives a geometric interpretation for the frequency behavior associated with each spectral segment, including a transition peak that is due entirely to the wavenumber limits of the segment. For regions of the earth where the inhomogeneity spectra are concentrated in a band of wavenumbers, it should be possible to observe such a peak in the apparent attenuation of seismic waves. Both the frequency and distance limits on the accuracy of the theoretical results are given.
A simple power law model consisting of a single spectral index, sigma(sub 2), is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index sigma(sub 2) greater than sigma(sub 1) above E(sub k). The maximum likelihood (ML) procedure was developed for estimating the single parameter sigma(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (Pl) consistency (asymptotically unbiased), (P2) efficiency (asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only be ascertained by calculating the CRB for an assumed energy spectrum- detector response function combination, which can be quite formidable in practice. However, the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are stained in practice are investigated.
A simple power law model consisting of a single spectral index, a is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index alpha(sub 2) greater than alpha(sub 1) above E(sub k). The Maximum likelihood (ML) procedure was developed for estimating the single parameter alpha(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (P1) consistency (asymptotically unbiased). (P2) efficiency asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only he ascertained by calculating the CRB for an assumed energy spectrum-detector response function combination, which can be quite formidable in practice. However. the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are attained in practice are investigated. The ML technique is then extended to estimate spectra information from an arbitrary number of astrophysics data sets produced by vastly different science instruments. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral parameter estimates based on the combination of data sets.
We present constraints on cosmological and astrophysical parameters from highresolution microwave background maps at 148 GHz and 218 GHz made by the Atacama Cosmology Telescope (ACT) in three seasons of observations from 2008 to 2010. A model of primary cosmological and secondary foreground parameters is fit to the map power spectra and lensing deflection power spectrum, including contributions from both the thermal Sunyaev-Zeldovich (tSZ) effect and the kinematic Sunyaev-Zeldovich (kSZ) effect, Poisson and correlated anisotropy from unresolved infrared sources, radio sources, and the correlation between the tSZ effect and infrared sources. The power l(sup 2)C(sub l)/2pi of the thermal SZ power spectrum at 148 GHz is measured to be 3.4 +/- 1.4 micro-K(sup 2) at l = 3000, while the corresponding amplitude of the kinematic SZ power spectrum has a 95% confidence level upper limit of 8.6 micro-K(sup 2). Combining ACT power spectra with the WMAP 7-year temperature and polarization power spectra, we find excellent consistency with the LCDM model. We constrain the number of effective relativistic degrees of freedom in the early universe to be N(sub eff) = 2.79 +/- 0.56, in agreement with the canonical value of N(sub eff) = 3.046 for three massless neutrinos. We constrain the sum of the neutrino masses to be sigma(mν) is less than 0.39 eV at 95% confidence when combining ACT and WMAP 7-year data with BAO and Hubble constant measurements. We constrain the amount of primordial helium to be Y(sub p) = 0.225 +/- 0.034, and measure no variation in the fine structure constant alpha since recombination, with alpha/alpha(sub 0) = 1.004 +/- 0.005. We also find no evidence for any running of the scalar spectral index, derivative(n(sub s))/derivative(ln k) = −0.004 +/- 0.012.
ABSTRACT Future large-scale structure surveys will measure the locations and shapes of billions of galaxies. The precision of such catalogues will require meticulous treatment of systematic contamination of the observed fields. We compare several existing methods for removing such systematics from galaxy clustering measurements. We show how all the methods, including the popular pseudo-Cℓ Mode Projection and Template Subtraction methods, can be interpreted under a common regression framework and use this to suggest improved estimators. We show how methods designed to mitigate systematics in the power spectrum can be used to produce clean maps, which are necessary for cosmological analyses beyond the power spectrum, and we extend current methods to treat the next-order multiplicative contamination in observed maps and power spectra, which reduced power spectrum errors from $\Delta \chi ^2_{\rm C_\ell }\simeq 10$ to ≃ 1 in simulated analyses. Two new mitigation methods are proposed, which incorporate desirable features of current state-of-the-art methods while being simpler to implement. Investigating the performance of all the methods on a common set of simulated measurements from Year 5 of the Dark Energy Survey, we test their robustness to various analysis cases. Our proposed methods produce improved maps and power spectra when compared to current methods, while requiring almost no user tuning. We end with recommendations for systematics mitigation in future surveys, and note that the methods presented are generally applicable beyond the galaxy distribution to any field with spatial systematics.
The feasibility of designing a prediction and warning system for severe weather conditions on the basis of time series analysis and pattern recognition is examined. Data accumulated by Taylor (1972) on the rate of atmospherics produced by severe, tornado-producing storms that struck Oklahoma City during April 1970 are analyzed by time series analysis and pattern recognition. Power spectra, cross-power spectra, coherence functions, and time-varying patterns are analyzed.
The presence of mode-mode coupling in turbulent fluctuations in the positive column of a glow discharge in argon is studied experimentally and analytically. The auto-power spectra, the cross power spectra, the phase spectra, the cross correlation functions and the bispectrum are determined. The results are relevant to the theoretical speculations of Grabec and Mikac (1974) and it is shown that ionization instability is the primary cause of the turbulence. The phase spectra indicate that the system is nearly linear at low frequency and the bispectrum plots show that nonlinear wave-wave interactions play a role in the development of the fluctuation components in the turbulent spectrum. Distinctions are made between the azimuthal and axial behaviors of the fluctuations and the results imply a trend toward longer azimuthal scales and shorter axial scales for characterizing fluctuation wave-packets as the density of the turbulent environment increases.
We have monitored the pulse frequencies of the two soft gamma repeaters SGR 1806-20 and SGR 1900+14 through the beginning of year 2001 using primarily Rossi X-ray Timing Explorer Proportional Counter Array observations. In both sources, we observe large changes in the spin-down torque up to a factor of approximately 4, which persist for several months. Using long baseline phase-connected timing solutions as well as the overall frequency histories, we construct torque noise power spectra for each SGR. The power spectrum of each source is very red (power-law slope approximately -3.5). These power spectra are consistent in normalization with some accreting systems, yet much steeper in slope than any known accreting source. To the best of our knowledge, torque noise power spectra with a comparably steep frequency dependence have only been seen in young, glitching radio pulsars (e.g. Vela). The observed changes in spin-down rate do not correlate with burst activity, therefore, the physical mechanisms behind each phenomenon are also likely unrelated. Within the context of the magnetar model, seismic activity cannot account for both the bursts and the long-term torque changes unless the seismically active regions are decoupled from one another.
The purpose of this grant was to develop and to start to apply new precision methods for measuring the power spectrum and redshift distortions from the anticipated new generation of large redshift surveys. A highlight of work completed during the award period was the application of the new methods developed by the PI to measure the real space power spectrum and redshift distortions of the IRAS PSCz survey, published in January 2000. New features of the measurement include: (1) measurement of power over an unprecedentedly broad range of scales, 4.5 decades in wavenumber, from 0.01 to 300 h/Mpc; (2) at linear scales, not one but three power spectra are measured, the galaxy-galaxy, galaxy-velocity, and velocity-velocity power spectra; (3) at linear scales each of the three power spectra is decorrelated within itself, and disentangled from the other two power spectra (the situation is analogous to disentangling scalar and tensor modes in the Cosmic Microwave Background); and (4) at nonlinear scales the measurement extracts not only the real space power spectrum, but also the full line-of-sight pairwise velocity distribution in redshift space.
Throughout this work, we construct nonlinear inflaton potential-energy densities that describe not necessarily very slowly rolling closed and open inflation models, and compute tilted primordial spatial inhomogeneity power spectra that follow from quantum-mechanical fluctuations during inflation in these models. Earlier nonflat inflation model power spectra computations assumed an inflaton potential-energy density with a linear slope that resulted in very slow roll during inflation and untilted power spectra. These new tilted power spectra differ from those that have previously been used to study cosmological data in nonflat cosmological models.
Direct observations of the solar wind between 1965 and 1972 indicate the existence of significant large scale (L is greater than 10 to the 6th km) turbulence in the solar system at heliocentric distances from 1 to 3 AU. These results are based on power spectra of the solar wind proton data obtained by plasma spectrometers on Pioneer 6 and Pioneer 10. The power spectra indicate that there is a power-law frequency dependence between 10 to the -4 Hz and 10 to the -3 Hz of the power spectra of the solar wind proton number density and streaming speed between 1 and 3 AU. The slopes and the amplitudes of the power spectra provide qualitative information concerning the cosmic ray diffusion tensor between 1965 and 1972 and at heliocentric distances between 1 AU and 3 AU.
I compare the power spectra of the radiation fields from two recent sets of fully-coupled simulations that model cosmic reionization: “Cosmic Reionization On Computers” (CROC) and “Thesan”. While both simulations have similar power spectra of the radiation sources, the power spectra of the photoionization rate are significantly different at the same values of cosmic time or the same values of the mean neutral hydrogen fraction. However, the power spectra of the photoionization rate can be matched at large scales for the two simulations when the matching snapshots are allowed to vary independently. I.e., on large scales, the clustering of the radiation field in two simulations evolves similarly, but the exact timing of this evolution is different in different simulations and is not parameterized by an easily interpretable physical quantity like the mean neutral fraction or the mean free path. On small scales, large differences are present and remain partially unexplained. Both CROC and Thesan use the Variable Eddington Tensor approximation for modeling radiative transfer, but adopt different closure relations (optically thin OTVET versus M1). The role of this key difference is tested by using smaller simulations with a new cosmological simulation code that implements both closure relations in a controlled environment (the same hydro, cooling, and gravity solvers and the star formation recipe). In these controlled tests, both the M1 closure and the OTVET ansatz follow the expected behavior from a simple analytical approximation, demonstrating that the differences in the 2-point function of the radiation field induced by the choice of the Eddington tensor are not dominant.