Power Spectrum Of Fluctuations Research Articles

The cosmological collider in R 2 inflation

Starobinsky's R 2 inflation manifests a best-fit scenario for the power spectrum of primordial density fluctuations. Observables derived from the slow-roll picture of the R 2 model in the Einstein frame relies on the conformal transformation of the metric, which inevitably induces a unique exponential-type couplings of the rolling scalaron with all matter fields during inflation. The “large-field” nature of the R 2 model further invokes non-negligible time and scale dependence to the matter sector through such an exponential coupling, modifying not only the dynamics of matter perturbations on superhorizon scales but also their decay rates. In this work, we identify the simplest observable of the cosmological collider physics built in the background of R 2 inflation, focusing on the so-called “quantum primordial clock” signals created by the non-local propagation of massive scalar perturbations. Our numerical formalism based on the unique conformal coupling can have extended applications to (quasi-)single-field inflationary models with non-trivial couplings to gravity or models that originated from the f(R) modification of gravity.

Surface Brightness Fluctuations in Two SPT Clusters: A Pilot Study

Studies of surface brightness fluctuations in the intracluster medium present an indirect probe of turbulent properties such as the turbulent velocities, injection scales, and the slope of the power spectrum of fluctuations toward smaller scales. With the advancement of Sunyaev–Zel’dovich (SZ) studies and surveys relative to X-ray observations, we seek to investigate surface brightness fluctuations in a sample of South Pole Telescope (SPT)-SZ clusters which also have archival XMM-Newton data. Here we present a pilot study of two typical clusters in that sample: SPT-CLJ0232-4421 and SPT-CLJ0638-5358. We infer injection scales larger than 500 kpc in both clusters and Mach numbers ≈ 0.5 in SPT-CLJ0232-4421 and Mach numbers ≈ 0.6–1.6 in SPT-CLJ0638-5358, which has a known shock. We find hydrostatic bias values for M 500 less than 0.2 for SPT-CLJ0232-4421 and less than 0.1 for SPT-CLJ0638-5358. These results show the importance to assess quantitative values via a detailed multiwavelength approach and suggest that the drivers of turbulence may occur at quite large scales.

Cosmological perturbations from five-dimensional inflation

It was recently proposed that five-dimensional inflation can relate the causal size of the observable universe to the present weakness of gravitational interactions by blowing up an extra compact dimension from the microscopic fundamental length of gravity to a large size in the micron range, as required in the Dark Dimension proposal. Here, we compute the power spectrum of all primordial fluctuations emerging from a 5-dimensional inflaton in a slow-roll region of its potential, showing an interesting change of behaviour at large scales corresponding to angles larger than about 10 degrees in the sky.

Phase transition in the noise power spectrum of interacting-spin fluctuations at infinite temperature

Phase transition in the noise power spectrum of interacting-spin fluctuations at infinite temperature

Transient RFI environment of LOFAR-LBA at 72–75 MHz

Context. Measurement of the highly redshifted and faint 21-cm signal of neutral hydrogen from the Cosmic Dawn and Epoch of Reionisation promises to unveil a wealth of information about the astrophysical processes that governed the structure formation and evolution of the universe during the first billion years of its evolution. Aims. The AARTFAAC Cosmic Explorer (ACE) program utilises the AARTFAAC wide-field imager of LOFAR to measure the power spectrum of the intensity fluctuations of the redshifted 21-cm signal from the Cosmic Dawn at z ∼ 18 corresponding to the global 21-cm absorption feature reported by the EDGES experiment. Radio frequency interference (RFI) from various sources, such as aeroplane communication, contaminates the observed data and it is crucial to exclude the RFI-affected data in the analysis for any reliable detection. In this work, we solely focus on investigating the impact of non-ground-based transient RFI on the analysis of ACE observations. Methods. We use cross-power spectra and cross-coherence metrics to assess the correlation of RFI over time and investigate the level of impact of transient RFI on the 21-cm signal power spectrum estimation. Results. We detected moving sky-based transient RFI sources that cross the field of view within a few minutes and appear to be mainly from aeroplane communication beacons at the location of the LOFAR core in the 72−75 MHz band (a part of the EDGES absorption trough), by inspecting filtered images. We find that this transient RFI is mostly uncorrelated over time and is only expected to dominate over the thermal noise for an extremely deep integration time of 3000 h or more with a hypothetical instrument that is sky temperature dominated at 75 MHz. We find no visible correlation over different k-modes in Fourier space in the presence of noise for realistic thermal noise scenarios. Conclusions. We conclude that the sky-based transient RFI from aeroplanes, satellites and meteorites at present does not pose a significant concern for the ACE analyses at the current level of sensitivity and after integrating over the available ∼500 h of observed data. However, it is crucial to mitigate or filter such transient RFI for more sensitive experiments aiming for significantly deeper integration.

OLIMPO: A balloon-borne SZE imager to probe ICM dynamics and the WHIM

OLIMPO is a proposed Antarctic balloon-borne Sunyaev-Zel’dovich effect (SZE) imager to study gas dynamics associated with structure formation along with the properties of the warm-hot intergalactic medium (WHIM) residing in the connective filaments. During a 25 day flight OLIMPO will image a total of 10 z∼0.05 galaxy clusters and 8 bridges at 145, 250, 365, and 460 GHz at an angular resolution of 1.0′–3.3′. The maps will be significantly deeper than those planned from CMB-S4 and CCAT-P, and will have excellent fidelity to the large angular scales of our low-z targets, which are difficult to probe from the ground. In combination with X-ray data from eROSITA and XRISM we will transform our current static view of galaxy clusters into a full dynamic picture by measuring the internal intra-cluster medium (ICM) velocity structure with the kinematic SZE, X-ray spectroscopy, and the power spectrum of ICM fluctuations. Radio observations from ASKAP and MeerKAT will be used to better understand the connection between ICM turbulence and shocks with the relativistic plasma. Beyond the cluster boundary, we will combine thermal SZE maps from OLIMPO with X-ray imaging from eROSITA to measure the thermodynamics of the WHIM residing in filaments, providing a better understanding of its properties and its contribution to the total baryon budget.

Physical consistency and invariance in machine learning of turbulent signals

This paper concerns an investigation of the invariance and consistency of deep learning of turbulent pressure fluctuations. The long-short-memory model is employed to predict wall pressure fluctuations across physical regimes featuring turbulence, shock–boundary layer interaction, and separation. The model's sensitivity to the data inputs is examined using different input data sets. Training the deep learning model based on the raw signals from different flow regions leads to large inaccuracies. It is shown that the data must be appropriately pre-processed before training for the deep learning model predictions to become consistent. Removing the mean and using the normalized fluctuating component of the signal, the deep learning predictions not only greatly improved in accuracy but, most importantly, converged and became consistent, provided that the signal sparsity remains within the inertial sub-range of the turbulence energy spectrum cascade. The power spectra of the surface pressure fluctuations reveal that the model provides high accuracy up to a certain frequency for the fully turbulent flow. The deep learning model's consistency is evidenced by being transferable across the various probe positions on the wall despite the significant differences in the turbulent flow properties in the training data set, i.e., signals obtained before, after, and inside the shock–boundary layer interaction regions. The model's prediction consistency and invariance to the turbulent signal training location(s) are promising for applying deep learning models to various turbulent flows.

Particle acceleration by sub-proton cyclotron frequency spectrum of dispersive Alfven waves in inhomogeneous solar coronal plasmas

ABSTRACT The problem of explaining observed soft X-ray fluxes during solar flares, which invokes acceleration of large fraction of electrons, if the acceleration takes places at the solar coronal loop-top, can potentially be solved by postulating that flare at loop-top creates dispersive Alfven waves (DAWs) which propagate towards the foot-points. As DAWs move in progressively denser parts of the loop (due to gravitational stratification) the large fraction of electrons is no longer needed. Here, we extend our previous results by considering f−1 frequency spectrum of DAWs and add He++ ions using fully kinetic particle-in-cell (PIC) simulations. We consider cases when transverse density gradient is in the range 4–40c/ωpe and DAW driving frequency is 0.3–0.6ωcp. We find that (i) The frequency spectrum case does not affect electron acceleration fraction in the like-to-like cases, but few times larger percentage of He++ heating is seen due to ion cyclotron resonance; (ii) In cases when counter propagating DAWs collide multiple-times, much larger electron and ion acceleration fractions are found, but the process is intermittent in time. This is because intensive heating (temperature increase) makes the-above-thermal-fraction smaller; Also more isotropic velocity distributions are seen; (iii) Development of kink oscillations occurs when DAWs collide; (iv) Scaling of the magnetic fluctuations power spectrum steepening in the higher-density regions is seen, due to wave refraction. Our PIC runs produce much steeper slopes than the orginal spectrum, indicating that the electron-scale physics has a notable effect on DAW spectrum evolution.

Gravity Wave Characterization of Multiple Convections in the Beijing–Tianjin–Hebei Region

Using high-precision microbarograph data and radar data to analyze the gravity fluctuation characteristics of four convective processes of different intensities that occurred in the Beijing–Tianjin–Hebei region in June 2018, the results show that convective cases are accompanied by gravity fluctuations of different time scales and can be separated from the background field through the wavelet transform. The stronger the convective process, the larger the fluctuation amplitude. As the convection gradually approaches the station, the fluctuation frequency broadens, and smaller period fluctuations are excited. Through Fourier analysis, the longer period of fluctuation is concentrated at about 190 min, and the power spectrum of the short-period fluctuation is weak, with a peak frequency of about 2.04 × 10−4 Hz. The results obtained by wavelet transform are similar to them, but they reflect the characteristics of fluctuation evolution over time: (1) convection-related gravity wave periods are mainly concentrated in three bands: 15–40 min, 40–120 min, and 120–250 min; (2) there may be precursor activity before the occurrence of the convective flow, and the long-period fluctuation occurs about 1–4 h ahead of time; (3) there is a short-period fluctuation in the process of convective system development, and the period range is mainly concentrated at about 40–120 min; strong convective clouds may inspire shorter-period fluctuations. The geometrical relationship between the microbarograph stations shows that the short-period fluctuations of the four convective cases propagate at a speed of 14–37 m/s, and the azimuthal angle is consistent with the convective orientation, which indicates that there is a close relationship between gravity waves and convection.

Turbulence Properties of Interplanetary Coronal Mass Ejections in the Inner Heliosphere: Dependence on Proton Beta and Flux Rope Structure

Interplanetary coronal mass ejections (ICMEs) have low proton beta across a broad range of heliocentric distances and a magnetic flux rope structure at large scales, making them a unique environment for studying solar wind fluctuations. Power spectra of magnetic field fluctuations in 28 ICMEs observed between 0.25 and 0.95 au by Solar Orbiter and Parker Solar Probe have been examined. At large scales, the spectra were dominated by power contained in the flux ropes. Subtraction of the background flux rope fields increased the mean spectral index from −5/3 to −3/2 at kd i ≤ 10−3. Rope subtraction also revealed shorter correlation lengths in the magnetic field. The spectral index was typically near −5/3 in the inertial range at all radial distances regardless of rope subtraction and steepened to values consistently below −3 with transition to kinetic scales. The high-frequency break point terminating the inertial range evolved approximately linearly with radial distance and was closer in scale to the proton inertial length than the proton gyroscale, as expected for plasma at low proton beta. Magnetic compressibility at inertial scales did not show any significant correlation with radial distance, in contrast to the solar wind generally. In ICMEs, the distinctive spectral properties at injection scales appear mostly determined by the global flux rope structure while transition-kinetic properties are more influenced by the low proton beta; the intervening inertial range appears independent of both ICME features, indicative of a system-independent scaling of the turbulence.

Capturing Statistical Isotropy Violation with Generalized Isotropic Angular Correlation Functions of Cosmic Microwave Background Anisotropy

The exquisitely measured maps of fluctuations in the cosmic microwave background (CMB) present the possibility of systematically testing the principle of statistical isotropy of the Universe. A systematic approach based on strong mathematical formulation allows any nonstatistical isotropic (nSI) feature to be traced to the nature of physical effects or observational artifacts. Bipolar spherical harmonics (BipoSH) representation has emerged as an overarching general formalism for quantifying the departures from statistical isotropy for a field on a 2D sphere. We adopt a little-known reduction of the BipoSH functions, dubbed minimal harmonics in the original paper by Manakov et al. We demonstrate that this reduction technique of BipoSH leads to a new generalized set of isotropic angular correlation functions referred to here as minimal BipoSH functions that are observable quantifications of nSI features in a sky map. This paper presents a novel observable quantification of deviation from statistical isotropy in terms of generalized angular correlation functions that are compact and complementary to the BipoSH spectra that generalize the angular power spectrum of CMB fluctuations.

Excitation of a Separated Flow by a Series of Protuberances Near the Leading Edge of a Model Aerofoil

Abstract This article documents the manifestation of a shear layer under the excitation of a series of hemispherical protuberances near the leading edge of a constant-thickness airfoil. The experiments are performed at a Reynolds number of 1.6 × 105 based on the chord length and inlet velocity, where freestream turbulence is 1.2%. The hotwire and particle image velocimetry data are analyzed to appreciate the flow feature, illustrating the growth of perturbations, vortex dynamics, intermittency, and spectral response. A laminar separation bubble (LSB) appears near the leading edge for a smooth surface, and the shear layer is inviscidly unstable. The evolution of the shear layer significantly changes with a series of protuberances. The breakdown of the shear layer occurs almost immediately, triggering local turbulence resulting in a considerable reduction of the bubble length. However, a separation bubble of varying spanwise lengths is formed in this case. Although the power spectra of velocity fluctuations reveal the selective amplification of frequencies even with protuberances, the immediate augmentation of turbulence followed by faster decay suggests the transient growth of turbulence. The study has documented insight into features of a separation bubble subjected to leading-edge perturbations and might influence future studies on separation control over an airfoil.

Estimates of the wavenumber wavelet power spectrum of magnetic fluctuations during magnetic reconnection

Fluctuation analyses of experimental observations generally lack high temporal resolution and are in frequency-space f, contrary to theoretical efforts in wavenumber-space k. This is due to the inherent limits of the Fourier transform, though it is prominent due to the ease of diagnostic implementation. Advances in wavelet-based analysis have provided relief due to its temporal resolution, but in its common use, is still hard to compare to theoretical models. By using the two-point correlation technique in conjunction with large data sets, a wavelet power spectrum in wavenumber-space can be created. Dubbed the wavenumber wavelet power spectrum, this spectrum relates wavenumber to power in time. This analysis technique more closely connects characterizations of experimentally observed fluctuations with other system parameters and theoretical predictions. In this article, we develop the wavenumber wavelet power spectrum using magnetic fluctuations caused by tearing instability driven magnetic reconnection in reproducible, high temperature laboratory plasmas. These dynamic magnetic fluctuations generated in reversed field pinch plasmas are broadband, ranging from the low frequency, 10's of kHz, up to the ion gyroradii frequencies, 100's of kHz. The dominant fluctuations have poloidal and toroidal mode numbers (m,n)=(1,6−10) and can grow to 2%–3% of the mean magnetic field. During these reconnection events, ions, and electrons are energized, magnetic fluctuation amplitudes increase, plasma flow is halted, and the toroidal magnetic flux increases, all on a semi-periodic basis. The newly developed spectrum provides better temporal resolution of spectrum characteristics to correlate with these particle energization phenomena.

Experimental and numerical investigation of a disc-attached cylinder near a wall

An experimental and numerical study is carried out to investigate the flow up- and downstream of a disc-attached cylinder near a wall with a Reynolds number of Re=U0d/ν=5.4⋅104 (U0 is the mean upstream flow velocity, d is the diameter of the cylinder, and ν is the kinematic viscosity). Laser Doppler Velocimetry measurements were conducted to obtain statistical flow parameters such as the mean velocity and turbulent kinetic energy. The experimental results show that the mean flow can be characterized as two-dimensional at a transverse distance of more than d away from the disc. Furthermore, it is shown that the effect of the disc and the cylinder fades away downstream. Analysis of a power spectrum of the vertical velocity fluctuations shows that vortex shedding is disturbed downstream of the disc. The numerical simulation is performed using a Reynolds-Averaged Navier–Stokes model. The turbulent kinetic energy and mean velocities are well-predicted by the numerical model. An increase in the peak amplitudes of the power spectra obtained from the vertical velocity fluctuations is found at a transverse distance of 3.75d from the centerline of the disc for both the experimental and numerical study, caused by vortices being transported by a transverse flow related to the disc.

Voltage fluctuations and probe frequency jitter in electric force microscopy of a conductor.

Electric force microscopy probes the statistics of electric field fluctuations from a sample surface, both through measurement of the noncontact friction exerted on the oscillating charged probe and by determination of the power spectrum of stochastic probe frequency fluctuations, referred to as "jitter." Here we calculate the frequency jitter power spectrum determined over a conducting sample of finite thickness, whose response is characterized by a dielectric function that is wavevector-dependent. These calculations complement previous predictions of the coefficient of noncontact friction in an electric force microscopy measurement for the same model, and also previous predictions of the jitter power spectrum for a dielectric continuum. The inclusion both of a finite sample thickness and a wavevector-dependent dielectric response can significantly enhance the magnitude of the predicted jitter spectrum for a conductor, relative to a simpler model of an infinitely thick dielectric continuum. These calculations provide a baseline prediction of the jitter power spectrum generated by the dynamics of conduction electrons in a metal sample.

Development of a new power spectrum of refractive-index fluctuations for ocean turbulence

Development of a new power spectrum of refractive-index fluctuations for ocean turbulence

Kinetic field theory: generic effects of alternative gravity theories on non-linear cosmic density-fluctuations

Non-linear cosmic structures contain valuable information on the expansion history of the background space-time, the nature of dark matter, and the gravitational interaction. The recently developed kinetic field theory of cosmic structure formation (KFT) allows to accurately calculate the non-linear power spectrum of cosmic density fluctuations up to wave numbers of k ≲ 10 h Mpc-1 at redshift zero. Cosmology and gravity enter this calculation via two functions, viz. the background expansion function and possibly a time-dependent modification of the gravitational coupling strength.The success of the cosmological standard model based on general relativity suggests that cosmological models in generalized theories of gravity should have observable effects differing only weakly from those in standard cosmology. Based on this assumption, we derive the functional, first-order Taylor expansion of the non-linear power spectrum of cosmic density fluctuations obtained from the mean-field approximation in KFT in terms of the expansion function and the gravitational coupling strength. This allows us to study non-linear power spectra expected in large classes of generalized gravity theories. To give one example, we apply our formalism to generalized Proca theories.

Cosmic ray fluctuations and MHD waves in the solar wind

During large-scale solar wind disturbances, variations in galactic cosmic rays with periods from several minutes to 2–3 hours, which are called cosmic ray fluctuations in the scientific literature, often occur. Such fluctuations are not observed in the absence of disturbances. Since cosmic rays are charged particles, their modulation in the heliosphere occurs mainly under the influence of the interplanetary magnetic field, or rather its turbulent part — MHD waves. In order to adequately describe the relationship between their fluctuation spectra, it is necessary to be able to isolate a certain type of MHD waves from direct measurements of the interplanetary medium parameters. In this paper, we consider some methods for determining the contribution of three solar wind MHD turbulence branches, namely, Alfvén, fast, and slow magnetosonic waves corresponding to the turbulence spectrum inertial region frequencies 10⁻⁴<ν<10⁻¹ Hz, at which cosmic ray fluctuations are observed, to the observed power spectra of interplanetary magnetic field modulus fluctuations. To do this, we apply the methods of spectral and polarization analysis. In the absence of measurement data on SW parameters, to identify the type of MHD turbulence we use the known wave polarization properties that Alfvén and magnetosonic waves are polarized in different planes relative to the plane containing the average IMF vector and wave vector.
 Our results show that with the correct determination of the spectra of three MHD wave types, their sum, within the limits of errors, agrees well with the observed spectra of the interplanetary magnetic field modulus, and a small difference can be attributed to static inhomogeneities and oscillations frozen into plasma, as well as to various discontinuities that are always inevitably present in the solar wind.

Флуктуации космических лучей и МГД-волны в солнечном ветре

During large-scale solar wind disturbances, variations in galactic cosmic rays with periods from several minutes to 2–3 hours, which are called cosmic ray fluctuations in the scientific literature, often occur. Such fluctuations are not observed in the absence of disturbances. Since cosmic rays are charged particles, their modulation in the heliosphere occurs mainly under the influence of the interplanetary magnetic field, or rather its turbulent part — MHD waves. In order to adequately describe the relationship between their fluctuation spectra, it is necessary to be able to isolate a certain type of MHD waves from direct measurements of the interplanetary medium parameters. In this paper, we consider some methods for determining the contribution of three solar wind MHD turbulence branches, namely, Alfvén, fast, and slow magnetosonic waves corresponding to the turbulence spectrum inertial region frequencies 10⁻⁴<ν<10⁻¹ Hz, at which cosmic ray fluctuations are observed, to the observed power spectra of interplanetary magnetic field modulus fluctuations. To do this, we apply the methods of spectral and polarization analysis. In the absence of measurement data on SW parameters, to identify the type of MHD turbulence we use the known wave polarization properties that Alfvén and magnetosonic waves are polarized in different planes relative to the plane containing the average IMF vector and wave vector. 
 Our results show that with the correct determination of the spectra of three MHD wave types, their sum, within the limits of errors, agrees well with the observed spectra of the interplanetary magnetic field modulus, and a small difference can be attributed to static inhomogeneities and oscillations frozen into plasma, as well as to various discontinuities that are always inevitably present in the solar wind.

The Evolution of the 1/f Range within a Single Fast-solar-wind Stream between 17.4 and 45.7 Solar Radii

The power spectrum of magnetic field fluctuations in the fast solar wind (V SW > 500 km s−1) at magnetohydrodynamic scales is characterized by two different power laws on either side of a break frequency f b. The low-frequency range at frequencies f smaller than f b is often viewed as the energy reservoir that feeds the turbulent cascade at f > f b. At heliocentric distances r exceeding 60 solar radii (R s), the power spectrum often has a 1/f scaling at f < f b, i.e., the spectral index is close to −1. In this study, measurements from the Parker Solar Probe's Encounter 10 with the Sun are used to investigate the evolution of the magnetic field power spectrum at f < f b at r < 60 R s during a fast radial scan of a single fast-solar-wind stream. We find that the spectral index in the low-frequency part of the spectrum decreases from approximately −0.61 to −0.94 as r increases from 17.4 to 45.7 R s. Our results suggest that the 1/f spectrum that is often seen at large r in the fast solar wind is not produced at the Sun, but instead develops dynamically as the wind expands outward from the corona into the interplanetary medium.