Density Power Spectrum Research Articles

Large-scale structure in brane-induced gravity. II. Numerical simulations

We use N-body simulations to study the nonlinear structure formation in brane-induced gravity, developing a new method that requires alternate use of Fast Fourier Transforms and relaxation. This enables us to compute the nonlinear matter power spectrum and bispectrum, the halo mass function, and the halo bias. From the simulation results, we confirm the expectations based on analytic arguments that the Vainshtein mechanism does operate as anticipated, with the density power spectrum approaching that of standard gravity within a modified background evolution in the nonlinear regime. The transition is very broad and there is no well defined Vainshtein scale, but roughly this corresponds to k_*~ 2 at redshift z=1 and k_*~ 1 at z=0. We checked that while extrinsic curvature fluctuations go nonlinear, and the dynamics of the brane-bending mode C receives important nonlinear corrections, this mode does get suppressed compared to density perturbations, effectively decoupling from the standard gravity sector. At the same time, there is no violation of the weak field limit for metric perturbations associated with C. We find good agreement between our measurements and the predictions for the nonlinear power spectrum presented in paper I, that rely on a renormalization of the linear spectrum due to nonlinearities in the modified gravity sector. A similar prediction for the mass function shows the right trends. Our simulations also confirm the induced change in the bispectrum configuration dependence predicted in paper I.

Some Statistical Properties of the Burgers Equation with White-Noise Initial Velocity

We revisit the one-dimensional Burgers equation in the inviscid limit for white-noise initial velocity. We derive the probability distributions of velocity and Lagrangian increments, measured on intervals of any length x. This also gives the velocity structure functions. Next, for the case where the initial density is uniform, we obtain the distribution of the density, over any scale x, and we derive the density two-point correlation and power spectrum. Finally, we consider the Lagrangian displacement field and we derive the distribution of increments of the Lagrangian map. We check that this gives back the well-known mass function of shocks. For all distributions we describe the limiting scaling functions that are obtained in the large-scale and small-scale limits. We also discuss how these results generalize to other initial conditions, or to higher dimensions, and make the connection with a heuristic multifractal formalism. We note that the formation of point-like masses generically leads to a universal small-scale scaling for the density distribution, which is known as the “stable-clustering ansatz” in the cosmological context (where the Burgers dynamics is also known as the “adhesion model”).

Light scattering in a phonon gas

Light-scattering spectrum in dielectric crystals is studied with extended thermodynamics (ET) for a phonon gas, covering from hydrodynamic to ballistic (collisionless) regimes. The ET equation is solved to obtain the power spectrum of the energy density in a phonon-gas mixture, which consists of interacting phonon gases of longitudinal and transverse acoustic (LA and TA) phonon modes. In the hydrodynamic regime, where phonon collisions take place frequently, it is found that the light-scattering spectrum consists of two components, which can be interpreted as the two normal modes formed by the two second-sound modes defined in each of the LA and TA phonon gases. Out of the two normal-mode spectra, the low-frequency component arises from thermal fluctuations and gives rise to a narrow quasielastic spectrum, which corresponds to the well-known thermal Rayleigh scattering due to thermal diffusion, i.e., due to overdamped second sound. With sufficient momentum-conserving phonon collisions (normal phonon scattering), the narrow quasielastic component is demonstrated to develop, from the diffusive central peak, into a pair of shifted inelastic peaks due to propagation of underdamped second sound. The other spectrum component gives rise to a much broader quasielastic scattering, whose wing extends out to the Brillouin-scattering lines of the LA and TA phonons (first sounds). The broader quasielastic spectrum has a linewidth equal to the phonon-collision rate, which suggests that this component originates from a nonequilibrium process in the phonon gas. As the ballistic regime is approached, the line shapes and linewidths of the two normal-mode spectra approach each other, and the two components finally coincide in the limit of the ballistic regime, which is in good agreement with the reported behavior for these spectra that were experimentally observed in many crystals. In the ballistic limit, the light-scattering mechanism in the present model is found to become formally equivalent to the previously proposed microscopic framework, i.e., the second-order difference Raman scattering (two-phonon difference light scattering) on a same phonon dispersion. The derived spectral formula is fitted to the spectra previously observed in the experiments for rutile $({\text{TiO}}_{2})$ and strontium titanate $({\text{SrTiO}}_{3})$. The fits are quite successful in wide ranges of frequency and temperature, i.e., regardless of degree of nonequilibrium, owing to the ET analysis. The relaxation times for the normal and resistive phonon collisions (${\ensuremath{\tau}}_{\text{N}}$ and ${\ensuremath{\tau}}_{\text{R}}$) are determined through the analysis. The temperature dependences of ${\ensuremath{\tau}}_{\text{N}}$ and ${\ensuremath{\tau}}_{\text{R}}$ indicate that the origin of the broad shifted peaks (the ``broad doublet''), which were observed in ${\text{SrTiO}}_{3}$ at around 30 K, is likely due to underdamped second sound at least in a narrow temperature range around 30 K.

Generation of vorticity and velocity dispersion by orbit crossing

We study the generation of vorticity and velocity dispersion by orbit crossing using cosmological numerical simulations, and calculate the backreaction of these effects on the evolution of large-scale density and velocity divergence power spectra. We use Delaunay tessellations to define the velocity field, showing that the power spectra of velocity divergence and vorticity measured in this way are unbiased and have better noise properties than for standard interpolation methods that deal with mass-weighted velocities. We show that high resolution simulations are required to recover the correct large-scale vorticity power spectrum, while poor resolution can spuriously amplify its amplitude by more than 1 order of magnitude. We measure the scalar and vector modes of the stress tensor induced by orbit crossing using an adaptive technique, showing that its vector modes lead, when input into the vorticity evolution equation, to the same vorticity power spectrum obtained from the Delaunay method. We incorporate orbit-crossing corrections to the evolution of large-scale density and velocity fields in perturbation theory by using the measured stress tensor modes. We find that at large scales ($k\ensuremath{\simeq}0.1h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$) vector modes have very little effect in the density power spectrum, while scalar modes (velocity dispersion) can induce percent-level corrections at $z=0$, particularly in the velocity divergence power spectrum. In addition, we show that the velocity power spectrum is smaller than predicted by linear theory until well into the nonlinear regime, with little contribution from virial velocities.

C/NOFS observations of intermediate and transitional scale‐size equatorial spread F irregularities

We present initial results of the analysis of high sampling rate (512 Hz) measurements made by the Planar Langmuir Probe (PLP) instrument and the Vector Electric Field Instrument (VEFI) onboard the Communication/Navigation Outage Forecasting System (C/NOFS) satellite. This letter focuses on the analysis of irregularities with scale‐sizes in the intermediate (0.1–10 km) and transitional (10–100 m) domains observed when the satellite was flying through a large equatorial spread F (ESF) depletion on the night of October 9–10, 2008 over South America. The results presented in this letter suggest the operation of a diffusive subrange in the density power spectra and the possibility of an inertial plasma regime being observed at relatively low altitudes as a result of the long‐lasting solar minimum conditions.

NONIDEAL MAGNETOHYDRODYNAMIC TURBULENT DECAY IN MOLECULAR CLOUDS

It is well known that non-ideal magnetohydrodynamic effects are important in the dynamics of molecular clouds: both ambipolar diffusion and possibly the Hall effect have been identified as significant. We present the results of a suite of simulations with a resolution of 512-cubed of turbulent decay in molecular clouds incorporating a simplified form of both ambipolar diffusion and the Hall effect simultaneously. The initial velocity field in the turbulence is varied from being super-Alfv\'enic and hypersonic, through to trans-Alfv\'enic but still supersonic. We find that ambipolar diffusion increases the rate of decay of the turbulence increasing the decay from $t^{-1.25}$ to $t^{-1.4}$. The Hall effect has virtually no impact in this regard. The power spectra of density, velocity and the magnetic field are all affected by the non-ideal terms, being steepened significantly when compared with ideal MHD turbulence with exponents. The density power spectra components change from about 1.4 to about 2.1 for the ideal and non-ideal simulations respectively, and power spectra of the other variables all show similar modifications when non-ideal effects are considered. Again, the dominant source of these changes is ambipolar diffusion rather than the Hall effect. There is also a decoupling between the velocity field and the magnetic field at short length scales. The Hall effect leads to enhanced magnetic reconnection, and hence less power, at short length scales. The dependence of the velocity dispersion on the characteristic length scale is studied and found not to be power-law in nature.

Infrared Divergence of Pure Einstein Gravity Contributions to the Cosmological Density Power Spectrum

We probe the pure Einstein gravity contributions to the second-order density power spectrum. On the small scale, we discover that Einstein's gravity contribution is negligibly small. This guarantees that Newton's gravity is currently sufficient to handle the baryon acoustic oscillation scale. On the large scale, however, we discover that Einstein's gavity contribution to the second-order power spectrum dominates the linear-order power spectrum. Thus, the pure Einstein gravity contribution appearing in the third-order perturbation leads to an infrared divergence in the power spectrum.

Studies of the Interaction of Ionic Liquid and Gas in a Small-Diameter Bubble Column

Gas bubbling through a column of ionic liquid has been investigated using high-speed video and a conductivity method to measure a cross-sectionally averaged void fraction. For comparison, other liquids with similar physical properties, e.g., a glycerol/water mixture and glycerol/water with dissolved potassium chloride, were also employed. Air was used for the gas phase. The similarities and differences of flow characteristics were observed from the images. The differences in flow patterns were revealed by analysis of the time series of conductance signals in the form of the probability density function, autocorrelation, and power spectrum density. Furthermore, the velocities and frequencies of flow structures were deduced. The flow characteristics of ionic liquid were found to be similar to those of the other liquids studied.

Multiple phase screen calculation of wide bandwidth propagation

This paper presents results from a two‐dimensional multiple phase screen (MPS) calculation that computes numerical realizations or sample functions of the electric field after propagation through the ionosphere. The MPS code solves the parabolic wave equation and allows for direct computation of realizations of the received signal. The ionization is represented by a series of random phase screens that characterize the severity and spectrum of the electron density fluctuations. For wide bandwidth signals, the MPS code is exercised for many frequencies over the bandwidth of the propagating signal; Fourier transform techniques are used to obtain the propagating signal in the time domain. The MPS simulation is quite general and may be applied to problems involving numerous, separated, layers of ionization characterized by spatially varying electron density power spectra. MPS techniques can handle all levels of ionospheric disturbances from the least severe, where only small phase fluctuations occur, to the most severe case of frequency selective scintillation. Several examples of propagating signals are presented that simultaneously show the development of the ionospheric transfer function and the impulse response function. The calculations are repeated, and the realizations are averaged to obtain the two‐frequency, two‐position mutual coherence function (MCF), Γ(x, f) and its Fourier transform S(q,τ), the generalized power spectrum. The wide bandwidth MPS results closely match results obtained from strong scatter theory as utilized in the phase screen diffraction method.

Local turbulence simulations for the multiphase ISM

In this paper we show results of numerical simulations for the turbulence in the interstellar medium. These results were obtained using a Riemann solver-free numerical scheme for high-Mach number hyperbolic equations. Here we especially concentrate on the physical properties of the ISM. That is, we do not present turbulence simulations trimmed to be applicable to the interstellar medium. The simulations are rather based on physical estimates for the relevant parameters of the interstellar gas. Applying our code to simulate the turbulent plasma motion within a typical interstellar molecular cloud, we investigate the influence of different equations of state (isothermal and adiabatic) on the statistical properties of the resulting turbulent structures. We find slightly different density power spectra and dispersion maps, while both cases yield qualitatively similar dissipative structures, and exhibit a departure from the classical Kolmogorov case towards a scaling described by the She-Leveque model. Solving the full energy equation with realistic heating/cooling terms appropriate for the diffuse interstellar gas, we are able to reproduce a realistic two-phase distribution of cold and warm plasma. When extracting maps of polarised intensity from our simulation data, we find encouraging similarity to actual observations. Finally, we compare the actual magnetic field strength of our simulations to its value inferred from the rotation measure. We find these to be systematically different by a factor of about 1.5, thus highlighting the often underestimated influence of varying line-of-sight particle densities on the magnetic field strength derived from observed rotation measures.

Inflationary gravitational-wave background and measurements of the scalar spectral index

Inflation predicts a stochastic background of gravitational waves over a broad range of frequencies, from those accessible with cosmic microwave background (CMB) measurements, to those accessible directly with gravitational-wave detectors, like NASA's Big-Bang Observer (BBO), currently under study. In a previous paper [Phys. Rev. D 73, 023504 (2006)] we connected CMB constraints to the amplitude and tensor spectral tilt of the inflationary gravitational-wave background (IGWB) at BBO frequencies for four classes of models of inflation by directly solving the inflationary equations of motion. Here we extend that analysis by including results obtained in the Wilkinson Microwave Anisotropy Probe third-year data release as well as by considering two additional classes of inflationary models. As often noted in the literature, the recent indication that the primordial density power spectrum has a red spectral index implies (with some caveats) that the amplitude of the IGWB may be large enough to be observable in the CMB polarization. Here we also explore the implications for the direct detection of the IGWB.

Information Content in the Galaxy Angular Power Spectrum from the Sloan Digital Sky Survey and Its Implication on Weak-Lensing Analysis

We analyze the photometric redshift catalog of the Sloan Digital Sky Survey Data Release 5 (SDSS DR5) to estimate the Fisher information in the galaxy angular power spectrum with the help of the Rimes-Hamilton technique. It is found that the amount of Fisher information contained in the galaxy angular power spectrum is saturated at lensing multipole scale 300<= l <= 2000 in the redshift range 0.1<= photo-z <0.5. At l=2000, the observed information is two orders of magnitude lower than the case of Gaussian fluctuations. This supports observationally that the translinear regime of the density power spectrum contains little independent information about the initial cosmological conditions, which is consistent with the numerical trend shown by Rimes-Hamilton. Our results also suggest that the Gaussian-noise description may not be valid in weak lensing measurements.

Nonlinear cosmological power spectrum in Einstein’s gravity

Is Newton's gravity sufficient to handle the weakly nonlinear evolution stages of the large-scale cosmic structures? Here we resolve the issue by analytically deriving the density and velocity power spectra to the second order in the context of Einstein's gravity. The recently found pure general relativistic corrections appearing in the third-order perturbation contribute to power spectra to the second order. In this work the complete density and velocity power spectra to the second order are derived. The power transfers among different scales in the density power spectrum are estimated in the context of Einstein's gravity. The relativistic corrections in the density power spectrum are estimated to be smaller than the Newtonian one to the second order, but these could be larger than higher-order nonlinear Newtonian terms.

Effects of a preinflation radiation-dominated epoch to CMB anisotropy

We consider that the preinflation era is radiation dominated, transiting smoothly to the inflationary era. We work out in detail the dynamics of inflaton fluctuations across the phase transition and the proper choices of initial vacuum states. It is found that this phase transition can suppress long-wavelength quantum fluctuations of inflaton. This may attribute to the large-scale CMB anisotropy a lower power than predicted in the standard $\ensuremath{\Lambda}\mathrm{CDM}$ model. In constraining this transitional effect by WMAP anisotropy data, we use the WMAP best-fit scale-invariant $\ensuremath{\Lambda}\mathrm{CDM}$ model with the density power spectrum replaced by the one found in this work. We find that the transition occurs at least about 10 e-folds before the comoving scales comparable to the size of our present horizon cross the Hubble radius during inflation.

Low-Frequency Lyα Power Spectra Observed by UVCS in a Polar Coronal Hole

The occurrence of f−1 noise in interplanetary magnetic fields (in the 1 × 10−5 to 1 × 10−4 Hz band) and other plasma parameters has now been known for about 20 years and has been recently identified also in the photospheric magnetic fields. However, the relationship between interplanetary and solar fluctuation spectra and the identification of their sources at the Sun are problems that still need to be addressed. Moreover, interplanetary density and magnetic field power spectra show a f−2 interval at frequencies smaller that ~6 × 10−4 Hz whose source on the Sun is at present not fully understood. In this work we report on the first study of low-frequency density fluctuations in the solar corona at 2.1 R☉. In 2006 June the Ultraviolet Coronagraph Spectrometer (SOHO UVCS) observed over a period of about 9.2 days H Lyα intensity fluctuations at 2.1 R☉ over a polar coronal hole. The Lyα intensity power spectra S(f) (related mainly to density fluctuations) showed a S(f) ∝ f−2 frequency interval between 2.6 × 10−6 and 3.0 × 10−5 Hz and a S(f) ∝ f−1 frequency interval between 3.0 × 10−5 and 1.3 × 10−4 Hz. The detection of a f−2 interval, in agreement with interplanetary density and magnetic field power spectra, has been also predicted in solar wind models as a consequence of phase-mixing mechanisms of waves propagating in coronal holes. High-latitude power spectra show a f−1 band approximately in the same frequency interval where f−1 noise has been detected in interplanetary densities, and interplanetary and photospheric magnetic fields, providing a connection between photospheric, coronal, and interplanetary f−1 noises.

Experimental-stochastic investigation of the combustion cyclic variability in HSDI diesel engine using ethanol–diesel fuel blends

An experimental investigation is conducted to evaluate the combustion characteristics of a fully instrumented, high-speed, direct injection (HSDI), standard ‘Hydra’ diesel engine, at various loads when using ethanol–diesel fuel blends up to 15% by vol. ethanol. In each test, combustion chamber and fuel injection pressure diagrams of many consecutive cycles were obtained using a specially developed, high-speed, data acquisition and processing system. Following a performance and exhaust emissions investigation and a heat release analysis of the measured cylinder pressure diagrams reported by the authors, the present work focuses on the cycle-by-cycle combustion variation (cyclic variability) as reflected in the pressure indicator diagrams, by analyzing for the maximum pressure, maximum pressure rate, (gross) indicated mean effective pressure, and dynamic injection timing and ignition delay. These parameters were analyzed using stochastic analysis techniques for averages, standard deviations, coefficients of variation, probability density functions, auto-correlations, power spectra and cross-correlation coefficients. Thus, any cause and effect relationship between cyclic pressure variations and the injection system or the kind of fuel used can be revealed, given the concern for the low cetane number of ethanol blends promoting cyclic variability that can lead to degraded performance and emissions characteristics.

Reconstruction method of local density fluctuation for heavy ion beam probe measurements

Heavy ion beam probe (HIBP) is an excellent diagnostic to measure the density and potential fluctuations simultaneously in magnetically confined plasmas. However, it has been well known that the density fluctuation measured with the HIBP is not local but contains the fluctuations along the beam orbits. In this article, a method is proposed to evaluate local density fluctuation in the HIBP measurements by removing the well-known path integral effects. The reconstructed density fluctuation amplitude and power spectrum are shown, for example, by applying the proposed method on the density fluctuation measurement data obtained in a toroidal helical plasma, Compact Helical System.

Statistical properties of dust far-infrared emission

Context. Far-infrared dust emission has a self-similar structure which reveals the complex dynamical processes that shape the interstellar medium. The description of the statistical properties of this emission gives important constraints on the physics of the interstellar medium but it is also a useful way to estimate the contamination of diffuse interstellar emission in the cases where it is considered a nuisance. Aims. The main goals of this analysis of the power spectrum and non-Gaussian properties of far-infrared dust emission are 1) to estimate the power spectrum of interstellar matter density in three dimensions; 2) to review and extend previous estimates of the cirrus noise due to dust emission; and 3) to produce simulated dust emission maps that reproduce the observed statistical properties. Methods. To estimate the statistical properties of dust emission we analyzed the power spectrum and wavelet decomposition of 100 μ m IRIS data (an improved version of the IRAS data) over 55% of the sky. The simulation of realistic infrared emission maps is based on modified Gaussian random fields. Results. The main results are the following. 1) The cirrus noise level as a function of brightness has been previously overestimated. It is found to be proportional to $\langle I\rangle $ instead of $\langle I\rangle^{1.5}$, where $\langle I\rangle $ is the local average brightness at 100 μ m. This scaling is in accordance with the fact that the brightness fluctuation level observed at a given angular scale on the sky is the sum of fluctuations of increasing amplitude with distance on the line of sight. 2) The spectral index of dust emission at scales between 5 arcmin and 12.5° is $\langle\gamma\rangle=-2.9$ on average but shows significant variations over the sky. Bright regions have systematically steeper power spectra than diffuse regions. 3) The skewness and kurtosis of brightness fluctuations are high, indicative of strong non-Gaussianity. Unlike the standard deviation of the fluctuations, the skewness and kurtosis do not depend significantly on brightness, except in bright regions (>10 MJy sr -1 ) where they are systematically higher, probably due to contrasted structures related to star formation activity. 4) Based on our characterization of the 100 μ m power spectrum we provide a prescription of the cirrus confusion noise as a function of wavelength and scale. 5) Finally we present a method based on a modification of Gaussian random fields to produce simulations of dust maps which reproduce the power spectrum and non-Gaussian properties of interstellar dust emission.

On the Perception of Crackle in High-Amplitude Jet Noise

DOI: 10.2514/1.26484 Crackle is a phenomenon sometimes found in supersonic jet noise and can comprise an annoying and dominant part of the overall perceived noise. In the past, crackle has been commonly quantified by the skewness of the time waveform. In this investigation, a simulated waveform with a virtually identical probability density function and power spectrum as an actual F/A-18E afterburner recording has been created by nonlinearly transforming a statistically Gaussian waveform. Although the afterburner waveform crackles noticeably, playback of the nonGaussian simulated waveform yields no perception of crackle at all, despite its relatively high skewness. Closer examinationofthetwowaveformsrevealsthatalthoughtheyhavevirtuallyidenticalstatistics,thereareconsiderable differences in their time rates of change in the intense compressive portions of the waveforms. The afterburner waveform is much more shocklike with its more rapid variations in pressure than the non-Gaussian simulated waveform. This results in a significant difference in the probability distributions of the time derivatives of the actual and simulated data and suggests that the perception of crackle in jet noise waveforms may be better quantified with statistics of the time derivative of the waveform, rather than by the skewness of the time waveform itself.

Higher Order Contributions to the 21 cm Power Spectrum

We consider the contribution of third- and fourth-order terms to the 21 cm power spectrum during the epoch of reionization, which arise because the 21 cm brightness temperature involves a product of the hydrogenic neutral fraction and the gas density. The third-order terms vanish for Gaussian random fields and have been previously neglected or ignored. We measure these terms from radiative transfer simulations and estimate them using cosmological perturbation theory. In our simulated models, the higher order terms are significant, and neglecting them leads to inaccurate 21 cm power spectrum estimates. On small scales the higher order terms are produced by gravitational mode coupling. Small-scale structure grows more readily in large-scale overdense regions, but the same regions tend to be ionized and hence do not contribute to the 21 cm signal. This modifies an earlier intuition that the 21 cm power spectrum simply traces the density power spectrum on scales smaller than that of a typical bubble and implies that small-scale measurements contain more information about the ionizing sources than previously believed. On large scales, higher order moments are not directly related to gravity. They are nonzero because overdense regions tend to ionize first and are important in magnitude at late times, due to large fluctuations in the neutral fraction. Finally, we show that second-order Lagrangian perturbation theory approximately reproduces the statistics of the density field from full numerical simulations for all redshifts and scales of interest, including the mode-coupling effects mentioned above. It can, therefore, be used in conjunction with semianalytic models to explore the broad regions of parameter space relevant for future 21 cm surveys.