Power Spectrum Of Fluctuations Research Articles

Characterizing elastic turbulence in the three-dimensional von Kármán swirling flow using the Oldroyd-B model

We present a comprehensive three-dimensional numerical investigation of the von Kármán swirling flow between two parallel plates using the Oldroyd-B model and characterize the onset and development of elastic turbulence. We quantify the flow state with the secondary-flow strength, a measure of the average strength of the velocity fluctuations, and then define an order parameter as the time average of the secondary-flow strength. The order parameter displays a subcritical transition from the laminar to a bistable flow that switches between weakly chaotic flow and elastic turbulence. The transition to the bistable flow occurs at the critical Weissenberg number Wic=12. In the elastic turbulent state, we observe a strong increase in velocity fluctuations and flow resistance which we define as the total work performed on the fluid. Upon starting simulations in the turbulent state and subsequently lowering Wi below its critical value, we observe hysteretic behavior in the order parameter and the flow resistance, which is a common feature of a subcritical transition. Hysteresis has also been found in experiments. Additionally, we find power-law scaling in the spatial and temporal power spectra of the velocity fluctuations, a characteristic for elastic turbulence. The maximum values of the power-law exponents in our simulations are αt=3.69 for the temporal exponent and αs=3.18 for the spatial exponent, which are remarkably close to the values obtained in experiments.

Spatial Power Spectral Analysis of the Suzaku X-Ray Background

Power spectra of spatial fluctuations of X-ray emission may impose constraints on the origins of the emission independent of that from the energy spectra. We generated spatial power spectrum densities (PSDs) of blank X-ray skies observed with the Suzaku X-ray observatory utilizing the modified Δ-variance method. Using the total measured count rate as the diagnostic tool, we found that a model consisting of the sum of two components, one for the unresolved faint point sources and one for the uniform flat-field emission, can represent well the observed PSD in three different energy bands (0.2–0.5, 0.5–2, and 2–10 keV); only an upper limit is obtained for the latter component in 2–10 keV. X-ray counting rates corresponding to the best-fit PSD model functions and diffuse emission fractions were estimated, and we confirmed that the sum of the counting rates of two model components is consistent with those actually observed with the detector for all energy bands. The ratio of the flat-field counting rate to the total in 0.5–2 keV, however, is significantly larger than the diffuse emission fraction estimated from the model fits of energy spectra. We discussed that this discrepancy can be reconciled by systematic effects in the PSD and energy spectrum analyses. The present study demonstrates that the spatial power spectrum analysis is powerful in constraining the origins of the X-ray emission.

Power spectrum for perturbations in an inflationary model for a closed universe

We derive the power spectrum of primordial quantum fluctuations in an inflationary universe for curvature parameter {mathcal {K}}=1. This is achieved through a Born–Oppenheimer type of approximation scheme from the Wheeler–DeWitt equation of canonical quantum gravity using gauge-invariant variables. Compared to the flat model, the closed model exhibits a deficit of power at large scales.

Power Spectrum Sensitivity Analysis of the Global Mean Surface Temperature Fluctuations Simulated in a Two-Box Stochastic Energy Balance Model

Climate models used in theoretical studies and the long-term projections of climate change should be able to reproduce essential features of the Earth’s climate system including natural global scale variability on timescales from years to decades. It is notable then, that models simulate a very wide range in unforced “natural” variability, for example showing a 2 ½ fold range in standard deviation of decadal surface temperature. The global mean surface temperature (GMST) temporal fluctuations used as one of the main indicators of climate variability are usefully characterized by their power spectral density, which represents the distribution of temperature variance in the frequency domain. We applied a randomly-forced two-box energy balance model (EBM) with parameters that correspond to the Coupled Model Intercomparison Project Phase 5 (CMIP5) models to estimate the influence of such crucial aspects of the climate system as feedbacks, thermal inertia and deep ocean heat uptake on the power spectra of the GMST fluctuations (climate variability). These sensitivities can provide clues to allow us to better understand the reasons for the very wide range of climate variability derived from CMIP5 models. It is found that the influence of variations (uncertainties) in the EBM parameters on power spectra of the GMST fluctuations strongly depends on periods (frequencies) of these fluctuations. In particular, it was identified that the effect of variations in the feedback parameter significantly increases with increasing periods of GMST oscillations, while the influence of uncertainties in the climate thermal inertia parameter (effective heat capacity of the “atmosphere-mixed ocean layer” system) demonstrates the opposite behaviour. Variations in the deep-ocean heat uptake parameter tangibly affect GMST fluctuations on decadal and inter-decadal time scales. Meanwhile the uncertainty in the deep-ocean heat capacity parameter is minor for GMST fluctuations over all time scales.

A designer approach to f(Q) gravity and cosmological implications

We investigate the evolution of linear perturbations in the Symmetric Teleparallel Gravity, namely $f(Q)$ gravity, for which we design the $f(Q)$ function to match specific expansion histories. We consider different evolutions of the effective dark energy equation of state, $w_Q(a)$, which includes $w_Q=-1$, a constant $w_Q \neq -1$ and a fast varying equation of state. We identify clear patterns in the effective gravitational coupling, which accordingly modifies the linear growth of large scale structures. We provide theoretical predictions for the product of the growth rate $\tilde{f}$ and the root mean square of matter fluctuations $\sigma_8$, namely $\tilde{f}\sigma_8$ and for the sign of the cross-correlation power spectrum of the galaxy fluctuations and the cosmic microwave background radiation anisotropies. These properties can be used to distinguish the $f(Q)$ gravity from the standard cosmological model using accurate cosmological observations.

Non-perturbative gauge invariant scalar fluctuations of the metric in Higgs inflation from complex geometrical scalar–tensor theory of gravity

In this letter we investigate gauge invariant scalar fluctuations of the metric in a non-perturbative formalism for a Higgs inflationary model recently introduced in the framework of a geometrical scalar–tensor theory of gravity. In this scenario the Higgs inflaton field has its origin in the Weyl scalar field of the background geometry. We found a nearly scale invariance of the power spectrum for linear scalar fluctuations of the metric. For certain parameters of the model we obtain values for the scalar spectral index n s and the scalar to tensor ratio r that fit well with the Planck 2018 results. Besides we show that in this model the trans-planckian problem can be avoided.

Two Fourier methods in membrane fluctation analysis: grid-based and least-squares

The energetics of lipid membrane deformations can be described by continuum theories for idealized fields representing lipid positions and orientations. We investigate systematic errors that arise while analyzing power spectra of these fields' thermal fluctuations. This requires an expansion in Fourier modes, which is typically done by interpolating the continuum fields on a grid and performing a finite Fourier transform. Unfortunately this discretization creates artifacts, such as spectral damping and aliasing.

Precision tests of CO and [CII] power spectra models against simulated intensity maps

Line intensity mapping (LIM) is an emerging technique with a unique potential to probe a wide range of scales and redshifts. Realizing the full potential of LIM, however, relies on accurate modeling of the signal. We introduce an extended halo model for the power spectrum of intensity fluctuations of CO rotational lines and [CII] fine transition line in real space, modeling nonlinearities in matter fluctuations and biasing relation between the line intensity fluctuations and the underlying dark matter distribution. We also compute the stochastic contributions beyond the Poisson approximation using the halo model framework. To establish the accuracy of the model, we create the first cosmological-scale simulations of CO and [CII] intensity maps, MithraLIMSims, at redshifts 0.5 ≤ z≤6, using halo catalogs from Hidden-Valley simulations, and painting halos according to mass-redshift-luminosity relations for each line. We show that at z=1 on scales kmax≲ 0.8 Mpc-11h, the model predictions of clustering power (with only two free parameters) are in agreement with the measured power spectrum at better than 5%. At higher redshift of z=4.5, this remarkable agreement extends to smaller scale of kmax≲ 2 Mpc-11h. Furthermore, we show that on large scales, the stochastic contributions to CO and CII power spectra are non-Poissonian, with amplitudes reproduced reasonably well by the halo model prescription. Lastly, we assess the performance of the theoretical model of the baryon acoustic oscillations (BAO) and show that hypothetical LIM surveys probing CO lines at z=1, that can be deployed within this decade, will be able to make a high significance measurement of the BAO. On a longer time scale, a space-based mission probing [CII] line can uniquely measure the BAO on a wide range of redshifts at an unprecedented precision.

Wander of a Gaussian-Beam Wave Propagating through Kolmogorov and Non-Kolmogorov Turbulence along Laser-Satellite Communication Uplink

It is accepted that there exists two kinds of atmospheric turbulence in the Earth’s aerosphere—Kolmogorov and non-Kolmogorov turbulence; therefore, it is important to research their combined impacts on laser-satellite communications. In this paper, the exponential power spectra of refractive-index fluctuations for non-Kolmogorov turbulence in the free troposphere and stratosphere are proposed, respectively. Based on these two spectra, using the Markov approximation, beam wander displacement variances of a Gaussian-beam wave are derived, respectively, which are valid under weak turbulent fluctuations condition. On this basis, using a three-layer altitude-dependent turbulent spectrum model for vertical/slant path, the combined influence of a three-layer atmospheric turbulence on wander of a Gaussian-beam wave as the carrier wave in laser-satellite communication is studied. This three-layer spectrum is more accurate than a two-layer model. Moreover, the variations of beam wander displacement with beam radius, zenith angles, and nominal value of the refractive-index structure parameter on the ground are estimated. The theory of optical wave propagation through non-Kolmogorov atmospheric turbulence is further enriched and a theoretical model of a three-layer atmospheric turbulence beam wander for a satellite-ground laser communication uplink is established.

Relation between turbulence characteristics and position/attitude control of a quad-rotor drone hovering in active grid turbulence

Drones are used in various situations, and they should be operated with a high level of safety. Drones should be stable under disturbances such as sudden strong winds and turbulence. Although the effect of aerodynamic disturbance is usually considered as a simplified wind model, it is desirable to take the characteristics of turbulence into account. For this purpose, we will clarify the effect of wind disturbance generated by active grid turbulence on the position and attitude of the hovering quad-rotor drone. The power spectrum of the velocity fluctuation generated by the active grid exhibits its slope of -5/3. With the present flight system consisting of an external depth camera and a quad-rotor drone with Blackbox functionality, the drone can hover at a target position in the wind tunnel and the time-series flight data can be obtained. It is found that the roll control signal is negatively correlated with the acceleration during hovering in the wind.

Turbulence Measurement of Two Velocity Components in a Boundary Layer by a Two Parallel Hot-Wire Anemometer

A novel hot-wire technique consisting of two parallel hot-wires is proposed. The gap between the two parallel wires is filled with an adhesive, which can be expected to improve the sensitivity to the flow angle at high velocity regions. In the present study, measurement accuracy of the two component velocity fluctuations is appraised experimentally in a flat-plate turbulent boundary layer. As a result, it was verified that the present probe can reproduce not only the DNS database but also the measurements obtained by the standard I- and X-type hot-wire probes. In addition, the proposed probe can be brought closer to the wall than the X-type one. However, it is observed that the turbulent intensity measurements in the streamwise direction are slightly reduced, and the power spectrum of the streamwise velocity fluctuations is attenuated accordingly in a high-frequency range. Thus, fluid-dynamical and thermal effects of the adhesive need to be investigated in more detail in the future.

Measurement of the Dark Matter Velocity Dispersion with Galaxy Stellar Masses, UV Luminosities, and Reionization

The root-mean-square of non-relativistic warm dark matter particle velocities scales as vhrms(a)=vhrms(1)/a , where a is the expansion parameter of the universe. This velocity dispersion results in a cut-off of the power spectrum of density fluctuations due to dark matter free-streaming. Let kfs (teq) be the free-streaming comoving cut-off wavenumber at the time of equal densities of radiation and matter. We obtain , and , at 68% confidence, from the observed distributions of galaxy stellar masses and rest frame ultra-violet luminosities. This result is consistent with reionization. From the velocity dispersion cut-off mass we obtain the limits vhrms(1)kfs (teq) >1.5 Mpc-1. These results are in agreement with previous measurements based on spiral galaxy rotation curves, and on the formation of first galaxies and reionization. These measured parameters determine the temperature-to-mass ratio of warm dark matter. This ratio happens to be in agreement with the no freeze-in and no freeze-out warm dark matter scenario of spin 0 dark matter particles decoupling early on from the standard model sector. Spin 1/2 and spin 1 dark matter are disfavored if nature has chosen the no freeze-in and no freeze-out scenario. An extension of the standard model of quarks and leptons, with scalar dark matter that couples to the Higgs boson that is in agreement with all current measurements, is briefly reviewed. Discrepancies with limits on dark matter particle mass that can be found in the literature are addressed.

Properties of Hall-MHD Turbulence at Sub-Ion Scales: Spectral Transfer Analysis

We present results of a multiscale study of Hall-magnetohydrodynamic (MHD) turbulence, carried out on a dataset of compressible nonlinear 2D Hall-MHD numerical simulations of decaying Alfvénic turbulence. For the first time, we identify two distinct regimes of fully developed turbulence. In the first one, the power spectrum of the turbulent magnetic fluctuations at sub-ion scales exhibits a power law with a slope of ∼−2.9, typically observed both in solar wind and in magnetosheath turbulence. The second regime, instead, shows a slope of −7/3, in agreement with classical theoretical models of Hall-MHD turbulence. A spectral-transfer analysis reveals that the latter regime occurs when the energy transfer rate at sub-ion scales is dominated by the Hall term, whereas in the former regime, the governing process is the dissipation (and the system exhibits large intermittency). Results of this work are relevant to the space plasma community, as they may potentially reconcile predictions from theoretical models with results from numerical simulations and spacecraft observations.

An In Situ Study of Turbulence near Stellar Bow Shocks

Abstract Stellar bow shocks are observed in a variety of interstellar environments and shaped by the conditions of gas in the interstellar medium (ISM). In situ measurements of turbulent density fluctuations near stellar bow shocks are only achievable with a few observational probes, including Hα-emitting bow shocks and the Voyager Interstellar Mission (VIM). In this paper, we examine density variations around the Guitar Nebula, an Hα bow shock associated with PSR B2224+65, in tandem with density variations probed by VIM near the boundary of the solar wind and ISM. High-resolution Hubble Space Telescope observations of the Guitar Nebula taken between 1994 and 2006 trace density variations over scales from hundreds to thousands of au, while VIM density measurements made with the Voyager 1 Plasma Wave System constrain variations from thousands of meters to tens of au. The power spectrum of density fluctuations constrains the amplitude of the turbulence wavenumber spectrum near the Guitar Nebula to log 10 C n 2 = − 0.8 ± 0.2 m−20/3 and for the very local ISM probed by Voyager to log 10 C n 2 = − 1.57 ± 0.02 m−20/3. Spectral amplitudes obtained from multiepoch observations of four other Hα bow shocks also show significant enhancements from values that are considered typical for the diffuse, warm ionized medium, suggesting that density fluctuations near these bow shocks may be amplified by shock interactions with the surrounding medium or selection effects that favor Hα emission from bow shocks embedded in denser media.

Turbulence and wave transmission at an ICME-driven shock observed by the Solar Orbiter and Wind

Aims.An interplanetary coronal mass ejection (ICME) event was observed by the Solar Orbiter at 0.8 AU on 2020 April 19 and by Wind at 1 AU on 2020 April 20. Futhermore, an interplanetary shock wave was driven in front of the ICME. Here, we focus on the transmission of the magnetic fluctuations across the shock and we analyze the characteristic wave modes of solar wind turbulence in the vicinity of the shock observed by both spacecraft.Methods.The observed ICME event is characterized by a magnetic helicity-based technique. The ICME-driven shock normal was determined by magnetic coplanarity method for the Solar Orbiter and using a mixed plasma and field approach for Wind. The power spectra of magnetic field fluctuations were generated by applying both a fast Fourier transform and Morlet wavelet analysis. To understand the nature of waves observed near the shock, we used the normalized magnetic helicity as a diagnostic parameter. The wavelet-reconstructed magnetic field fluctuation hodograms were used to further study the polarization properties of waves.Results.We find that the ICME-driven shock observed by Solar Orbiter and Wind is a fast, forward oblique shock with a more perpendicular shock angle at the Wind position. After the shock crossing, the magnetic field fluctuation power increases. Most of the magnetic field fluctuation power resides in the transverse fluctuations. In the vicinity of the shock, both spacecraft observe right-hand polarized waves in the spacecraft frame. The upstream wave signatures fall within a relatively broad and low frequency band, which might be attributed to low frequency MHD waves excited by the streaming particles. For the downstream magnetic wave activity, we find oblique kinetic Alfvén waves with frequencies near the proton cyclotron frequency in the spacecraft frame. The frequency of the downstream waves increases by a factor of ∼7–10 due to the shock compression and the Doppler effect.

Mathematical Modelling of Climate Change and Variability in the Context of Outdoor Ergonomics

The current climate change, unlike previous ones, is caused by human activity and is characterized by an unprecedented rate of increase in the near-surface temperature and an increase in the frequency and intensity of hazardous weather and climate events. To survive, society must be prepared to implement adaptation strategies and measures to mitigate the negative effects of climate change. This requires, first of all, knowledge of how the climate will change in the future. To date, mathematical modelling remains the only method and effective tool that is used to predict the climate system’s evolution under the influence of natural and anthropogenic perturbations. It is important that mathematics and its methods and approaches have played a vital role in climate research for several decades. In this study, we examined some mathematical methods and approaches, primarily, mathematical modelling and sensitivity analysis, for studying the Earth’s climate system, taking into account the dependence of human health on environmental conditions. The essential features of stochastic climate models and their application for the exploration of climate variability are examined in detail. As an illustrative example, we looked at the application of a low-order energy balance model to study climate variability. The effects of variations in feedbacks and the climate system’s inertia on the power spectrum of global mean surface temperature fluctuations that characterized the distribution of temperature variance over frequencies were estimated using a sensitivity analysis approach. Our confidence in the obtained results was based on the satisfactory agreement between the theoretical power spectrum that was derived from the energy balance model and the power spectrum that was obtained from observations and coupled climate models, including historical runs of the CMIP5 models.

Probability density function of fiber-coupling efficiency and temporal power spectrum of irradiance fluctuations in the anisotropic non-Kolmogorov satellite-to-ground downlink

As many related experimental and theoretical results are identified, scholars have found that the anisotropy of turbulence cells is indispensable in the atmospheric turbulence. In this paper, based on a new anisotropic non-Kolmogorov turbulence spectrum for the satellite links that is applicable to both vertical and slant links, the probability density function of fiber-coupling efficiency and the temporal power spectrum of irradiance fluctuations for a plane wave propagating through the weak anisotropic non-Kolmogorov satellite-to-ground downlink are developed. The results show that when the zenith angle is greater than a certain angle, the probability density function of fiber-coupling efficiency shifts to the side with smaller coupling efficiency with the rising of anisotropic factor, and the temporal power spectrum of irradiance fluctuations and the absolute value of power exponent at high frequencies increase with the growing of anisotropic factor and power law, but while the zenith angle is less than the certain angle, the opposite trend will appear. It is anticipated that this work will benefit the understanding of laser beam transmission in anisotropic non-Kolmogorov satellite links and provide the theoretical basis for the design and parameter optimization of satellite optical communication systems based on fiber-coupling.

Geometry versus growth

We carry out a multi-probe self-consistency test of the flat Lambda Cold Dark Matter (ΛCDM) model with the aim of exploring potential causes of the reported tensions between high- and low-redshift cosmological observations. We divide the model into two theory regimes determined by the smooth background (geometry) and the evolution of matter density fluctuations (growth), each governed by an independent set of ΛCDM cosmological parameters. This extended model is constrained by a combination of weak gravitational lensing measurements from the Kilo-Degree Survey, galaxy clustering signatures extracted from Sloan Digital Sky Survey campaigns and the Six-Degree Field Galaxy Survey, and the angular baryon acoustic scale and the primordial scalar fluctuation power spectrum measured in Planck cosmic microwave background (CMB) data. For both the weak lensing data set individually and the combined probes, we find strong consistency between the geometry and growth parameters, as well as with the posterior of standard ΛCDM analysis. In the non-split analysis, for which one single set of parameters was used, tension in the amplitude of matter density fluctuations as measured by the parameter S8 persists at around 3σ, with a 1.5% constraint of S8 = 0.776−0.008+0.016 for the combined probes. We also observe a less significant preference (at least 2σ) for higher values of the Hubble constant, H0 = 70.5−1.5+0.7 km s−1 Mpc−1, as well as for lower values of the total matter density parameter Ωm = 0.289−0.005+0.007 compared to the full Planck analysis. Including the subset of the CMB information in the probe combination enhances these differences rather than alleviate them, which we link to the discrepancy between low and high multipoles in Planck data. Our geometry versus growth analysis does not yet yield clear signs regarding whether the origin of the discrepancies lies in ΛCDM structure growth or expansion history but holds promise as an insightful test for forthcoming, more powerful data.

Critical current fluctuations in graphene Josephson junctions

We have studied 1/f noise in critical current I_c in h-BN encapsulated monolayer graphene contacted by NbTiN electrodes. The sample is close to diffusive limit and the switching supercurrent with hysteresis at Dirac point amounts to simeq 5 nA. The low frequency noise in the superconducting state is measured by tracking the variation in magnitude and phase of a reflection carrier signal v_{rf} at 600–650 MHz. We find 1/f critical current fluctuations on the order of delta I_c/I_c simeq 10^{-3} per unit band at 1 Hz. The noise power spectrum of critical current fluctuations S_{I_c} measured near the Dirac point at large, sub-critical rf-carrier amplitudes obeys the law S_{I_c}/{I{_c}}^2 = a/f^{beta } where asimeq 4times 10^{-6} and beta simeq 1 at f > 0.1 Hz. Our results point towards significant fluctuations in I_c originating from variation of the proximity induced gap in the graphene junction.

VLBI Data Processing on Coronal Radio-sounding Experiments of Mars Express

Abstract The ESA’s Mars Express solar corona experiments were performed at two solar conjunctions in the years 2015 and 2017 by a number of radio telescopes in the European VLBI Network. This paper presents the methods to measure the frequency and phase fluctuations of the spacecraft radio signal, and the applications to study the characteristics of the plasma turbulence effects on the signal at a single station and at multiple stations via cross correlation. The power spectra of the frequency fluctuations observed between 4.9 and 76.3 R s have a power-law shape close to a Kolmogorov spectrum over the frequency interval ν lo < ν < ν up, where the nominal value of ν lo is set to 3 mHz and ν up is in the range of 0.03–0.15 Hz. The rms of the frequency fluctuations is presented as a function of the heliocentric distance. Furthermore, we analyze the variations of the electron column density fluctuations at solar offsets 4.9 R s and 9.9 R s and the cross-correlation products between the VLBI stations. The power density of the differential fluctuations between different stations decreases at ν < 0.01 Hz. Finally, the fast flow speeds of solar wind >700 km s−1 are derived from the cross correlation of frequency fluctuations at ν < 0.01 Hz. The fast flow speeds of solar wind correspond to the high heliolatitude of the coronal region that the radio rays passed. The VLBI observations and analysis methods can be used to study the electron column density fluctuations and the turbulence at multiple spatial points in the inner solar wind by providing multiple lines of sight between the Earth and the spacecraft.