Density Power Spectrum Research Articles

Induced gravitational waves: the effect of first order tensor perturbations

Scalar induced gravitational waves contribute to the cosmological gravitational wave background. They can be related to the primordial density power spectrum produced towards the end of inflation and therefore are a convenient new tool to constrain models of inflation. These waves are sourced by terms quadratic in perturbations and hence appear at second order in cosmological perturbation theory. While the focus of research so far was on purely scalar source terms we also study the effect of including first order tensor perturbations as an additional source. This gives rise to two additional source terms: a term quadratic in the tensor perturbations and a cross term involving mixed scalar and tensor perturbations. We present full analytical expressions for the spectral density of these new source terms and discuss their general behaviour. To illustrate the generation mechanism we study two toy models containing a peak on small scales. For these models we show that the scalar-tensor contribution becomes non-negligible compared to the scalar-scalar contribution on smaller scales. We also consider implications for future gravitational wave surveys.

Periodically activated physics-informed neural networks for assimilation tasks for three-dimensional Rayleigh–Bénard convection

We apply physics-informed neural networks to three-dimensional Rayleigh–Bénard convection in a cubic cell with a Rayleigh number of Ra=106 and a Prandtl number of Pr=0.7 to assimilate the velocity vector field from given temperature fields and vice versa. With the respective ground truth data provided by a direct numerical simulation, we are able to evaluate the performance of the different activation functions applied (sine, hyperbolic tangent and exponential linear unit) and different numbers of neurons (32, 64, 128, 256) for each of the five hidden layers of the multi-layer perceptron. The main result is that the use of a periodic activation function (sine) typically benefits the assimilation performance in terms of the analyzed metrics, correlation with the ground truth and mean average error. The higher quality of results from sine-activated physics-informed neural networks is also manifested in the probability density function and power spectra of the inferred velocity or temperature fields. Regarding the two assimilation directions, the assimilation of temperature fields based on velocities appears to be more challenging in the sense that it exhibits a sharper limit on the number of neurons below which viable assimilation results cannot be achieved.

Planck Dust Polarization Power Spectra Are Consistent with Strongly Supersonic Turbulence

The polarization of the cosmic microwave background is rich in information but obscured by foreground emission from the Milky Way’s interstellar medium (ISM). To uncover relationships between the underlying turbulent ISM and the foreground power spectra, we simulated a suite of driven, magnetized, turbulent models of the ISM, varying the fluid properties via the sonic Mach number, MS , and magnetic (Alfvén) Mach number, MA . We measure the power spectra of density (ρ), velocity (v), magnetic field (H), total projected intensity (T), parity-even polarization (E), and parity-odd polarization (B). We find that the slopes of all six quantities increase with MS . Most increase with MA , while the magnetic field spectrum steepens with MA . By comparing spectral slopes of E and B to those measured by Planck, we infer typical values of MS and MA for the ISM. As the fluid velocity increases, MS>4 , the ratio of BB power to EE power increases to approach a constant value near the Planck-observed value of ∼0.5, regardless of the magnetic field strength. We also examine correlation coefficients between projected quantities, and find that r TE ≈ 0.3, in agreement with Planck, for appropriate combinations of MS and MA . Finally, we consider parity-violating correlations r TB and r EB.

Measurement of air-water counter-current flow rates in vertical annulus using multiple differential pressure signals and machine learning

Abstract Gas–liquid counter-current flow in vertical annulus is involved in several industrial fields such as petroleum engineering. For example, in coalbed methane wells with liquid pump drainage, obtaining the real-time flow rate of gas–liquid two-phase in the annulus is crucial for the development management of coalbed methane wells. However, due to complex flow conditions, this demand is difficult to achieve through traditional flow metering means. Therefore, this paper proposes a flow prediction method based on multi-group differential pressure signals and machine learning technology. Air-water two-phase flow experiments were carried out on a vertical annulus pipeline with inner and outer diameters of 75 mm/125 mm and adjustable eccentricity. The probability density function and power spectrum density of 3 groups of differential pressure signals collected at different height intervals in the annulus were used as model inputs. A gas–liquid two-phase flow prediction model was constructed based on the artificial neural network model, and the model hyper-parameters were optimized using Bayesian optimization. The results show that on the 440-group test dataset under the combined conditions of air superficial velocity of 0.06–5.04 m s−1, water superficial velocity of 0.03–0.25 m s−1, and pipeline eccentricity of 0, 0.25, 0.5, 0.75, 1, etc. This model can achieve average prediction errors of 9.12% and 29.34% for gas and water flow rates respectively. This method can be applied to the non-throttling, non-invasive measurement of phase flow rate under the condition of annulus air-liquid counter-current flow.

Hybrid model of condensate and particle dark matter: Linear perturbations in the hydrodynamic limit

We analyze perturbations of self-interacting, scalar field dark matter that contains modes in both a coherent condensate state and an incoherent particlelike state. Starting from the coupled equations for the condensate, the particles’ phase-space distribution, and their mutual gravitational potential, first derived from first principles in earlier work by the authors, we derive a hydrodynamic limit of two coupled fluids and study their linearized density perturbations in an expanding universe, also including particle pressure under an assumption for an equation of state consistent with the dynamical equations. We find that away from the condensate-only or particle-only limits, and for certain ranges of the parameters, such self-interacting mixtures can significantly enhance the density power spectrum above the standard linear ΛCDM value at localized wave numbers, even pushing structure formation into the nonlinear regime earlier than expected in ΛCDM for these scales. We also note that such mixtures can lead to degeneracies between models with different boson masses and self-coupling strengths, in particular, between self-coupled models and noncoupled fuzzy dark matter made up of heavier bosons. These findings open up the possibility of a richer phenomenology in scalar field dark matter models and could further inform efforts to place observational limits on their parameters. Published by the American Physical Society 2024

Direct measurements of sea spray particle fluxes using a high temporal resolution optical particle counter over the coastal ocean

ABSTRACT Sea spray particles play a key role in transferring momentum, heat, and gas across the atmosphere–ocean interface at high wind speeds and represent an important source of cloud condensation nuclei which affect the genesis, chemistry, and radiative properties of marine clouds. Here, we present direct measurements of sea spray particle fluxes obtained using an eddy covariance technique through the use of a newly developed high temporal resolution optical particle counter. With this instrumentation measurements were made over the coastal ocean during a 5-week field campaign conducted at an observation pier from November to December 2021. Our optical particle counter was capable of measuring size spectra at a rate of 10 Hz in 8 channels covering a range of mean radii between 0.3 and 15. The power spectra of particle number density followed the Kolmogorov −2/3 power law. The shape of the cospectrum of the particle number density flux was basically similar to that of the cospectra of the heat and gas fluxes. The measured sea spray particle fluxes at mean wind speeds of up to 21 m s−1 were dominated by an upward flux, which likely represents aerosol production caused by the bursting of bubbles at the ocean surface.

Fluctuation-dissipation relation in cosmic microwave background

We study the fluctuation-dissipation relation for sound waves in the cosmic microwave background (CMB), employing effective field theory (EFT) for fluctuating hydrodynamics.Treating sound waves as the linear response to thermal radiation, we establish the fluctuation-dissipation relation within a cosmological framework.While dissipation is elucidated in established linear cosmological perturbation theory, the standard Boltzmann theory overlooks the associated noise, possibly contributing to inconsistencies in Lambda Cold Dark Matter (ΛCDM) cosmology. This paper employs EFT for fluctuating hydrodynamics in cosmological perturbation theory, deriving sound wave noise.Notably, the long-time limit of the noise spectrum is independent of viscosity details, resembling a Brownian motion bounded in a harmonic potential.The net energy transfer between the sound wave system and the radiation environment reaches a balance within Hubble time, suggesting the thermal equilibrium of the sound waves themselves.The induced density power spectrum is characterized as white noise dependent on the inverse of the entropy density, which is negligibly small on the CMB scale. The energy density of the entire sound wave system scales as a -4, akin to radiation. While the numerical factor is not determined in the present calculation, the back reaction of the sound wave system to the background radiation may not be negligible, serving as a potential source for various fitting issues in ΛCDM cosmology.

Bayesian deep learning for cosmic volumes with modified gravity

Context. The new generation of galaxy surveys will provide unprecedented data that will allow us to test gravity deviations at cosmological scales at a much higher precision than could be achieved previously. A robust cosmological analysis of the large-scale structure demands exploiting the nonlinear information encoded in the cosmic web. Machine-learning techniques provide these tools, but no a priori assessment of the uncertainties. Aims. We extract cosmological parameters from modified gravity (MG) simulations through deep neural networks that include uncertainty estimations. Methods. We implemented Bayesian neural networks (BNNs) with an enriched approximate posterior distribution considering two cases: the first case with a single Bayesian last layer (BLL), and the other case with Bayesian layers at all levels (FullB). We trained both BNNs with real-space density fields and power spectra from a suite of 2000 dark matter-only particle-mesh N-body simulations including MG models relying on MG-PICOLA, covering 256 h−1 Mpc side cubical volumes with 1283 particles. Results. BNNs excel in accurately predicting parameters for Ωm and σ8 and their respective correlation with the MG parameter. Furthermore, we find that BNNs yield well-calibrated uncertainty estimates that overcome the over- and under-estimation issues in traditional neural networks. The MG parameter leads to a significant degeneracy, and σ8 might be one possible explanation of the poor MG predictions. Ignoring MG, we obtain a deviation of the relative errors in Ωm and σ8 by 30% at least. Moreover, we report consistent results from the density field and power spectrum analysis and comparable results between BLL and FullB experiments. This halved the computing time. This work contributes to preparing the path for extracting cosmological parameters from complete small cosmic volumes towards the highly nonlinear regime.

An analytical description of substructure-induced gravitational perturbations in stellar systems

ABSTRACT Perturbations to stellar systems can reflect the gravitational influence of dark matter substructures. On scales much smaller than the size of a stellar system, we point out analytical connections between the stellar and dark matter distributions. In particular, the density and velocity power spectra of the stars are proportional to the density power spectrum of the perturbing dark matter, scaled by k−4. This relationship allows easy evaluation of the suitability of a stellar system for detecting dark substructure. As examples, we show that the Galactic stellar halo is expected to be sensitive to cold dark matter substructure at wavenumbers k ≲ 0.3 kpc−1, and the Galactic disc might be sensitive to substructure at wavenumbers k ∼ 4 kpc−1. The perturbations considered in this work are short-lived, being rapidly erased by the stellar velocity dispersion, so it may be possible to attribute a detection to dark matter substructure without ambiguity.

Mass density vs. energy density at cosmological scales

In the presence of the gravitational field, the energy density of matter no longer coincides with its mass density. A discrepancy exists, of course, also between the associated power spectra. Within the Λ CDM model, we derive a formula that relates the power spectrum of the energy density to that of the mass density and test it with the help of N-body simulations run in comoving boxes of 2.816 Gpc/h. The results confirm the validity of the derived formula and simultaneously show that the power spectra diverge significantly from one another at large cosmological scales.

Detection of Pairwise Kinetic Sunyaev–Zel’dovich Effect with DESI Galaxy Groups and Planck in Fourier Space

We report a ∼5.2σ detection of the kinetic Sunyaev–Zel’dovich (kSZ) effect in Fourier space, by combining the DESI galaxy groups and the Planck data. We use the density-weighted pairwise kSZ power spectrum as the summary statistic, and the detailed procedure of its measurement is presented in this paper. Meanwhile, we analyze the redshift space group density power spectrum to constrain its bias parameters and photo-z uncertainties. These best-fitted parameters are substituted to a nonlinear kSZ model, and we fit the measured kSZ power spectrum with this model to constrain the group optical depth τ¯ . Selected by a varying lower mass threshold M th, the galaxy group catalogs with different median masses ( M˜ ) are constructed from the Data Release 9 data of the DESI Legacy Imaging Surveys. M˜ spans a wide range of ∼1013–1014 M ⊙/h and the heaviest M˜∼1014 M⊙/h is larger than those of most other kSZ detections. When the aperture photometric filter radius θ AP is set to be 4.′2, the M˜=1.75×1013 M⊙/h group sample at the median redshift z˜=0.64 has the highest kSZ detection signal-to-noise ratio = 5.2. By fitting τ¯s from various samples against their M˜ s, we obtain a linear logτ¯−logM˜ relation: logτ¯=γ(logM˜−14)+logβ , in which γ = 0.55 ± 0.1. We also vary the aperture photometric filter radius and measure the τ¯ profiles of group samples, whose constraints on the baryon distribution within and around dark matter halos will be discussed in a companion paper.

Deep learning cosmic ray transport from density maps of simulated, turbulent gas

The coarse-grained propagation of galactic cosmic rays (CRs) is traditionally constrained by phenomenological models of Milky Way CR propagation fit to a variety of direct and indirect observables; however, constraining the fine-grained transport of CRs along individual magnetic field lines—for instance, diffusive vs streaming transport models—is an unsolved challenge. Leveraging a recent training set of magnetohydrodynamic turbulent box simulations, with CRs spanning a range of transport parameters, we use convolutional neural networks (CNNs) trained solely on gas density maps to classify CR transport regimes. We find that even relatively simple CNNs can quite effectively classify density slices to corresponding CR transport parameters, distinguishing between streaming and diffusive transport, as well as magnitude of diffusivity, with class accuracies between 92% and 99%. As we show, the transport-dependent imprints that CRs leave on the gas are not all tied to the resulting density power spectra: classification accuracies are still high even when image spectra are flattened (85%–98% accuracy), highlighting CR transport-dependent changes to turbulent phase information. We interpret our results with saliency maps and image modifications, and we discuss physical insights and future applications.

Prototyping of vibration testing machine that is generated non-gaussian random vibration which is determined by probability density function and power spectrum

Prototyping of vibration testing machine that is generated non-gaussian random vibration which is determined by probability density function and power spectrum

Prototyping of vibration testing machine that is generated non-gaussian random vibration which is determined by probability density function and power spectrum

Prototyping of vibration testing machine that is generated non-gaussian random vibration which is determined by probability density function and power spectrum

Visual and Pressure Signal Investigations on Bubble Produced by Ejector Bubble Generator

This study aims to investigate the pattern of bubble flow coming out of the ejector bubble generator (EBG). The flow pattern was captured using a high-speed camera. The pressure signal on the bubble generator outlet was also recorded using a differential pressure transducer, which was then processed to obtain a probability density function (PDF) and Power Spectrum Density (PSD). It indicates the flow pattern flowing at the bubble generator outlet. The results of this study occurred a time delay in the production of bubbles coming out of the EBG. The greater the air flow rate, the lower the time delay for bubble production. The bubble flow region produced by EBG was classified into the entrance, developed, and fully developed regions. In the fully developed region, large and small bubbles are separated. The greater the air flow rate, the higher the two-phase flow pressure at the EBG outlet and the PDF has one peak with a skewness value that tends to be positive (shift to the right side). The maximum value of the spectrum is at a low frequency (<100Hz) with a low magnitude as an indicator of the bubble flow pattern in the EBG outlet.

Cosmological Parameter Constraints from the SDSS Density and Momentum Power Spectra

We extract the galaxy density and momentum power spectra from a subset of early-type galaxies in the Sloan Digital Sky Survey (SDSS) DR7 main galaxy catalog. Using galaxy distance information inferred from the improved fundamental plane described in Yoon and Park, we reconstruct the peculiar velocities of the galaxies and generate number density and density-weighted velocity fields, from which we extract the galaxy density and momentum power spectra. We compare the measured values to the theoretical expectation of the same statistics, assuming an input Λ cold dark matter (CDM) model and using a third-order perturbative expansion. After validating our analysis pipeline with a series of mock data sets, we apply our methodology to the SDSS data and arrive at constraints and at a mean redshift . Our result is consistent with the Planck cosmological best-fit parameters for the ΛCDM model. The momentum power spectrum is found to be strongly contaminated by small-scale velocity dispersion, which suppresses power by on intermediate scales k ∼ 0.05 h Mpc−1.

Prediction of equivalent sand-grain size and identification of drag-relevant scales of roughness – a data-driven approach

Despite decades of research, a universal method for prediction of roughness-induced skin friction in a turbulent flow over an arbitrary rough surface is still elusive. The purpose of the present work is to examine two possibilities; first, predicting equivalent sand-grain roughness size $k_s$ based on the roughness height probability density function and power spectrum (PS) leveraging machine learning as a regression tool; and second, extracting information about relevance of different roughness scales to skin-friction drag by interpreting the output of the trained data-driven model. The model is an ensemble neural network (ENN) consisting of 50 deep neural networks. The data for the training of the model are obtained from direct numerical simulations (DNS) of turbulent flow in plane channels over 85 irregular multi-scale roughness samples at friction Reynolds number $Re_\tau =800$ . The 85 roughness samples are selected from a repository of 4200 samples, covering a wide parameter space, through an active learning (AL) framework. The selection is made in several iterations, based on the informativeness of samples in the repository, quantified by the variance of ENN predictions. This AL framework aims to maximize the generalizability of the predictions with a certain amount of data. This is examined using three different testing data sets with different types of roughness, including 21 surfaces from the literature. The model yields overall mean error 5 %–10 % on different testing data sets. Subsequently, a data interpretation technique, known as layer-wise relevance propagation, is applied to measure the contributions of different roughness wavelengths to the predicted $k_s$ . High-pass filtering is then applied to the roughness PS to exclude the wavenumbers identified as drag-irrelevant. The filtered rough surfaces are investigated using DNS, and it is demonstrated that despite significant impact of filtering on the roughness topographical appearance and statistics, the skin-friction coefficient of the original roughness is preserved successfully.

Can the low-redshift Lyman alpha forest constrain AGN feedback models?

ABSTRACT We investigate the potential of low-redshift Lyman alpha (Lyα) forest for constraining active galactic nuclei (AGNs) feedback models by analysing the Illustris and IllustrisTNG simulation at z = 0.1. These simulations are ideal for studying the impact of AGN feedback on the intergalactic medium (IGM) as they share initial conditions with significant differences in the feedback prescriptions. Both simulations reveal that the IGM is significantly impacted by AGN feedback. Specifically, feedback is stronger in Illustris and results in reducing cool baryon fraction to 23 per cent relative to 39 per cent in IllustrisTNG. However, when comparing various statistics of Lyα forest such as 2D and marginalized distributions of Doppler widths and H i column density, line density, and flux power spectrum with real data, we find that most of these statistics are largely insensitive to the differences in feedback models. This lack of sensitivity arises because of the fundamental degeneracy between the fraction of cool baryons and the H i photoionization rate (ΓHI) as their product determines the optical depth of the Lyα forest. Since the ΓHI cannot be precisely predicted from first principles, it needs to be treated as a nuisance parameter adjusted to match the observed Lyα line density. After adjusting ΓHI, the distinctions in the considered statistics essentially fade away. Only the Lyα flux power spectrum at small spatial scales exhibits potentially observable differences, although this may be specific to the relatively extreme feedback model employed in Illustris. Without independent constraints on either ΓHI or cool baryon fraction, constraining AGN feedback with low-redshift Lyα forest will be very challenging.

The WISDOM of power spectra: how the galactic gravitational potential impacts a galaxy’s central gas reservoir in simulations and observations

ABSTRACT Observations indicate that the central gas discs are smoother in early-type galaxies than their late-type counterparts, while recent simulations predict that the dynamical suppression of star formation in spheroid-dominated galaxies is preceded by the suppression of fragmentation of their interstellar media. The mass surface density power spectrum is a powerful tool to constrain the degree of structure within a gas reservoir. Specifically here, we focus on the power spectrum slope and aim to constrain whether the shear induced by a dominant spheroidal potential can induce sufficient turbulence to suppress fragmentation, resulting in the smooth central gas discs observed. We compute surface density power spectra for the nuclear gas reservoirs of fourteen simulated isolated galaxies and twelve galaxies observed as part of the mm-Wave Interferometric Survey of Dark Object Masses (WISDOM) project. Both simulated and observed galaxies range from disc-dominated galaxies to spheroids, with central stellar mass surface densities, a measure of bulge dominance, varying by more than an order of magnitude. For the simulations, the power spectra steepen with increasing central stellar mass surface density, thereby clearly linking the suppression of fragmentation to the shear-driven turbulence induced by the spheroid. The WISDOM observations show a different (but potentially consistent) picture: while there is no correlation between the power spectrum slopes and the central stellar mass surface densities, the slopes scatter around a value of 2.6. This is similar to the behaviour of the slopes of the simulated galaxies with high central stellar mass surface densities, and could indicate that high shear eventually drives incompressible turbulence.

A 3D Numerical Study of Anisotropies in Supernova Remnants

We develop a suite of 3D hydrodynamic models of supernova remnants (SNRs) expanding against the circumstellar medium (CSM). We study the Rayleigh–Taylor instability forming at the expansion interface by calculating an angular power spectrum for each of these models. The power spectra of young SNRs are seen to exhibit a dominant angular mode, which is a diagnostic of their ejecta density profile as found by previous studies. The steep scaling of power at smaller modes and the time evolution of the spectra are indicative of the absence of a turbulent cascade. Instead, as the time evolution of the spectra suggests, they may be governed by an angular mode-dependent net growth rate. We also study the impact of anisotropies in the ejecta and in the CSM on the power spectra of velocity and density. We confirm that perturbations in the density field (whether imposed on the ejecta or the CSM) do not influence the anisotropy of the remnant significantly unless they have a very large amplitude and form large-scale coherent structures. In any case, these clumps can only affect structures on large angular scales. The power spectrum on small angular scales is completely independent of the initial clumpiness and governed only by the growth and saturation of the Rayleigh–Taylor instability.