Two-point Spatial Correlation Function Research Articles

Flickering of a radio-signal due to an atmospheric turbulence

Background. Turbulent fluctuations of the refractive index in the atmosphere lead to distortions during the passage of the radio signal. This can lead to distortion of the transmitted information due to the resulting fluctuations of the amplitude, phase and intensity of the electromagnetic wave that transmits the radio signal. Fluctuations in the intensity of the radio signal lead to flickering of the radio signal on the receiving antenna due to turbulent phenomena in the atmosphere, which are a complex multifunctional physical phenomenon. Aim. The problem of fluctuation of the intensity of the radio signal at the receiving antenna due to atmospheric turbulence is considered the flicker of the radio signal. This problem is currently extremely actual, because there is a tendency of active, negative interference in the process of high-quality transmission of the radio signal on the background of naturally caused turbulent fluctuations. Methods. A theoretical analysis of the passage of a radio signal through a turbulent atmosphere is carried out. The spatial correlation function of fluctuations in the intensity of the received radio signal due to atmospheric turbulence is investigated. Results. The concept of the radio signal flicker characteristic is introduced as the average value of a random variable over the cross section of the receiving antenna the dispersion of the logarithm of the radio signal power. A model of the occurrence of fluctuations in the case of two regions in the cross section of the receiving antenna with different levels of radio signal intensity is calculated. The correlation function for this model is found. Conclusion. Based on the Fourier-spectrum expansion of the two-point spatial correlation function of turbulent fluctuations of the refractive index, the dependence of the flicker characteristic of the radio signal on the wave number of turbulent fluctuations of the atmosphere is found. It is shown that the turbulence of the atmosphere has the greatest effect on the radio signal when the length of the electromagnetic wave is comparable to the scale of turbulent fluctuations.

The spatial correlation of high-mass X-ray binaries and young star clusters in nearby star-forming galaxies

ABSTRACT We present an analysis of the two-point spatial correlation functions of high-mass X-ray binary (HMXB) and young star cluster (YSC) populations in M31 and M33. We find evidence that HMXBs are spatially correlated with YSCs to a higher degree than would be expected from random chance in both galaxies. When supplemented with similar studies in the Milky Way, Small Magellanic Cloud, and NGC 4449, we find that the peak value of the spatial correlation function correlates strongly with the specific star formation rate of the host galaxy. We additionally perform an X-ray stacking analysis of 211 non-X-ray detected YSCs in M31 and 463 YSCs in M33. We do not detect excess X-ray emission at the stacked cluster locations down to 3σ upper limits of ∼1033 erg s−1 (0.35–8 keV) in both galaxies, which strongly suggests that dynamical formation within YSCs is not a major HMXB formation channel. We interpret our results in the context of (1) the recent star formation histories of the galaxies, which may produce differences in the demographics of compact objects powering the HMXBs, and (2) the differences in natal kicks experienced by compact objects during formation, which can eject newly formed HMXBs from their birth clusters.

Many-Body Correlations Are Non-negligible in Both Fragile and Strong Glassformers.

It is widely believed that the emergence of slow glassy dynamics is encoded in a material's microstructure. First-principles theory [mode-coupling theory (MCT)] is able to predict the dramatic slowdown of the dynamics from only static two-point correlations as input, yet it cannot capture all of the observed dynamical behavior. Here we go beyond two-point spatial correlation functions by extending MCT systematically to include higher-order static and dynamic correlations. We demonstrate that only adding the static triplet direct correlations already qualitatively changes the predicted glass-transition diagram of binary hard spheres and silica. Moreover, we find a nontrivial competition between static triplet correlations that work to stabilize the glass state and dynamic higher-order correlations that destabilize it for both materials. We conclude that the conventionally neglected static triplet direct correlations as well as higher-order dynamic correlations are, in fact, non-negligible in both fragile and strong glassformers.

The Spatial Distribution of Gamma-Ray Bursts with Measured Redshifts from 24 Years of Observation

Gamma-ray bursts (GRBs) are the most luminous objects known: they outshine their host galaxies, making them ideal candidates for probing large-scale structure. Our aim is to determine the Spatial Two-Point Correlation Function of the GRBs with spectroscopic redshifts. We used all observations till 4 June 2021, and we also split the data according to the origin of the redshift (afterglow or host galaxy). We analyzed the possible correlation between the GRB redshift and sky position. There is only one region, called the Faraway GRB Patch, where nine distant GRBs shows deviation from the randomness with an ≈1% significance, showing that the sky and the radial component of the GRB distribution could be factorized and both can be determined independently. The GRBs’ cumulative monthly distribution was used to show that it is impossible to synthesize the Sky Exposure Function, even from the perfect observational logs. We estimated the Sky Exposure Function using the Gaussian kernel, and with the radial distribution, it was used for the estimation of the Spatial Two-Point Correlation Function. Monte Carlo simulations were used to determine the Poissonian errors. Our result shows that the current Spatial Two-Point Correlation Function estimations are consistent with zero for the full and the afterglow/host galaxy datasets.

Emerging spatiotemporal patterns in cyclic predator-prey systems with habitats.

Three-species cyclic predator-prey systems are known to establish spiral waves that allow species to coexist. In this study, we analyze a structured heterogeneous system which gives one species an advantage to escape predation in an area that we refer to as a habitat and study the effect on species coexistence and emerging spatiotemporal patterns. Counterintuitively, the predator of the advantaged species emerges as dominant species with the highest average density inside the habitat. The species given the advantage in the form of an escape rate has the lowest average density until some threshold value for the escape rate is exceeded, after which the density of the species with the advantage overtakes that of its prey. Numerical analysis of the spatial density of each species as well as of the spatial two-point correlation function for both inside and outside the habitats allow a detailed quantitative discussion. Our analysis is extended to a six-species game that exhibits spontaneous spiral waves, which displays similar but more complicated results.

Spatial and Kinematic Clustering of Stars in the Galactic Disk

Abstract The Galactic disk is expected to be spatially and kinematically clustered on many scales due to both star formation and the Galactic potential. In this work we calculate the spatial and kinematic two-point correlation functions (TPCF) using a sample of 1.7 × 106 stars with radial velocities from Gaia DR2. Clustering is detected on spatial scales of 1–300 pc and a velocity scale of 15 km s−1. After removing bound structures, the data have a power-law index of γ ≈ −1 for 1 pc < Δr < 100 pc and γ ≲ −1.5 for Δr > 100 pc. We interpret these results with the aid of a star-by-star simulation of the Galaxy, in which stars are born in clusters orbiting in a realistic potential that includes spiral arms, a bar, and giant molecular clouds. We find that the simulation largely agrees with the observations at most spatial and kinematic scales. In detail, the TPCF in the simulation is shallower than the data at ≲20 pc scales, and steeper than the data at ≳30 pc. We also find a persistent clustering signal in the kinematic TPCF for the data at large Δv (>5 km s−1) that is not present in the simulations. We speculate that this mismatch between observations and simulations may be due to two processes: hierarchical star formation and transient spiral arms. We also predict that the addition of ages and metallicities measured with a precision of 50% and 0.05 dex, respectively, will enhance the clustering signal beyond current measurements.

Surface acoustic wave attenuation in polycrystals: Numerical modeling using a statistical digital twin of an actual sample

Grain boundary scattering-induced attenuation and phase-velocity dispersion of Rayleigh-type surface acoustic waves are studied with a time-domain finite-element method (FEM). The FEM simulation incorporates a realistic material model based on matching the spatial two-point correlation function of a Laguerre tessellation with that obtained from optical micrographs of a previously studied aluminum sample. Plane surface acoustic waves are excited in a multitude of statistically equivalent virtual polycrystals, and their surface displacement fields are averaged for subsequent extraction of the coherent-wave attenuation coefficient and phase velocity. Comparisons to previous laser-ultrasonic experiments, an analytical mean-field model, and the FEM results show good agreement in a broad frequency range from about 10 to 130MHz. Observed discrepancies between models and measurement reveal the importance of spatial averaging in the context of mean-field approaches and suggest improvement strategies for future experimental studies and advanced analytical models. A different attenuation power law for Rayleigh waves is found in the stochastic scattering regime compared to bulk acoustic waves.

Coherent Eddies Transporting Passive Scalars Through the Plant Canopy Revealed by Large-Eddy Simulations Using the Lattice Boltzmann Method

A double-distribution-function lattice Boltzmann model for large-eddy simulations of a passive scalar field in a neutrally stratified turbulent flow is described. In simulations of the scalar turbulence within and above a homogeneous plant canopy, the model’s performance is found to be comparable with that of a conventional large-eddy simulation model based on the Navier–Stokes equations and a scalar advection–diffusion equation in terms of the mean turbulence statistics, budgets of the second moments, power spectra, and spatial two-point correlation functions. For a top-down scalar, for which the plant canopy serves as a distributed sink, the variance and flux of the scalar near the canopy top are predominantly determined by sweep motions originating far above the canopy. These sweep motions, which have spatial scales much larger than the canopy height, penetrate deep inside the canopy and cause scalar sweep events near the canopy floor. By contrast, scalar ejection events near the canopy floor are induced by coherent eddies generated near the canopy top. The generation of such eddies is triggered by the downward approach of massive sweep motions to existing wide regions of weak ejective motions from inside to above the canopy. The non-local transport of scalars from above the canopy to the canopy floor, and vice versa, is driven by these eddies of different origins. Such non-local transport has significant implications for the scalar variance and flux budgets within and above the canopy, as well as the transport of scalars emitted from the underlying soils to the atmosphere.

Experimental investigation on drag reduction in a turbulent boundary layer with a submerged synthetic jet

This work investigates the active control of a fully developed turbulent boundary layer by a submerged synthetic jet actuator. The impacts of the control are explored by measuring the streamwise velocities using particle image velocimetry, and reduction of the skin-friction drag is observed in a certain range downstream of the orifice. The coherent structure is defined and extracted using a spatial two-point correlation function, and it is found that the synthetic jet can efficiently reduce the streamwise scale of the coherent structure. Proper orthogonal decomposition analysis reveals that large-scale turbulent kinetic energy is significantly attenuated with the introduction of a synthetic jet. The conditional averaging results show that the induction effect of the prograde vortex on the low-speed fluid in a large-scale fluctuation velocity field is deadened, thereby suppressing the bursting process near the wall.

Large-Eddy Simulation of Neutrally-Stratified Turbulent Flow Within and Above Plant Canopy Using the Central-Moments-Based Lattice Boltzmann Method

A central-moments-based lattice Boltzmann model for large-eddy simulation of neutrally-stratified turbulent flows is described. Through comparative simulations of the airflow within and above a homogeneous plant canopy, the performance of the model is evaluated with respect to a conventional large-eddy-simulation model based on the incompressible Navier–Stokes equations. Simulated turbulence statistics, such as the mean velocity, velocity variances, velocity skewness, and power spectra, are shown to be almost identical between the two models. The spatial structure of coherent eddies and their maintenance processes are also confirmed to be properly represented by the lattice Boltzmann method through analysis of the turbulence kinetic energy budget and spatial two-point correlation functions. Using the simulated results, the energetics of the streamwise-elongated streaky structures commonly observed over vegetation and urban canopies are examined. While the short-wavelength components of the shear-generated streamwise kinetic energy are redirected rapidly by pressure to the lateral and vertical velocity components, long-wavelength energy tends to remain in the streamwise velocity component, which is dissipated in relatively slower processes. Consequently, the streaky structures persist in the streamwise velocity component.

High throughput rapid detection for SLM manufactured elements using ultrasonic measurement

Both pore parameters and elastic properties are important for the elements manufactured by the Selective Laser Melting (SLM) technology; however, their measurements are usually destructive and time-consuming. Thus, the ultrasonic longitudinal and transverse wave velocities (dual-mode velocities) method is extended here; then it is combined with the longitudinal wave attenuation to develop an ultrasonic high throughput rapid detection for SLM manufactured elements. As the focal transducer is used, a multi-Gaussian beam model is introduced to correct the diffraction attenuation. Twenty-eight parameters can be obtained by a single ultrasonic experiment, including the pore parameters and their distributions, the two-point spatial correlation function, and the Young’s modulus. Ti-6Al-4V samples with different porosities manufactured by SLM technology are used to conduct the ultrasonic experiment. The experimental results agree well with the results of metallographic, tensile experiment and micro-CT results. This method provides a useful tool for nondestructively, rapidly and accurately evaluating the pore parameters and elastic properties of SLM manufactured elements.

Measurement of coherent surface acoustic wave attenuation in polycrystalline aluminum

Attenuation of Rayleigh-type surface acoustic waves induced by grain-boundary scattering is studied experimentally and theoretically by an effective medium approach. A frequency domain opto-acoustic laboratory setup, capable of measuring a coherent Rayleigh wave response by emulating an ensemble average via spatial averaging, is presented. Measurements are conducted on polycrystalline aluminum at ultrasonic frequencies from 10 MHz to 130 MHz. A constant effective phase velocity of 2893 m s−1 is found below 80 MHz. The effective attenuation coefficient varies in the whole frequency range by nearly two orders of magnitude, and shows classical scattering behavior, comprising stochastic and geometric scattering regimes. A semi-analytical attenuation model is presented, valid below the geometric limit. The model incorporates the material’s spatial two-point correlation function obtained from metallurgical micrographs. Comparisons to experimentally obtained attenuation coefficients show good quantitative agreement, with differences in the frequency power-law dependence. This study attempts to elucidate microstructure induced surface acoustic wave attenuation experimentally by means of a statistical approach. The proposed method and the obtained findings contribute to the understanding of wave propagation in heterogeneous media, and promote the use of surface acoustic waves in non-destructive microstructure characterization.

Correlation of elastic wave attenuation and scattering with volumetric grain size distribution for polycrystals of statistically equiaxed grains

This study establishes an explicit relation between spatial two-point correlation function (TPCF) and volumetric (or three-dimensional) grain size distribution for aggregates of statistically equiaxed grains by extending a prior study (Sha, JASA, 2018). This relation is further validated by applying it to available TPCF and volumetric grain size distribution in the literature. Based on this relation, analytical attenuation coefficients for longitudinal and transverse waves, accounting for volumetric grain size distribution, are derived under Born approximation for macroscopically isotropic polycrystals of equiaxed triclinic grains. These attenuation models are applicable for whole frequency range except geometric region. Moreover, scattering coefficients for a polycrystal of equiaxed triclinic grains with a volumetric grain size distribution are obtained. Finally, the analytical attenuation model for the longitudinal wave is verified by comparison with existing 3D finite element simulation results in the literature. This theoretic study has practical applications to the inverse determination of volumetric grain size distribution from ultrasonic measurements.

Discovery of Kolmogorov-like magnetic energy spectrum in Tycho’s supernova remnant by two-point correlations of synchrotron intensity

The spectral slope of the magnetic energy in supernova remnants (SNRs) can be obtained by analysis of spatial two-point correlation functions of synchrotron intensities. This method has been originally developed for the analysis of magnetic field structure in diffuse interstellar medium and applied when the geometry of the emission region is simple and known. In this paper, applying this correlation analysis to Tycho's SNR, for which the synchrotron emission region is known to be a spherical shell, we find that the magnetic energy spectrum shows the Kolmogorov-like scaling. Our results can be explained by turbulence developed downstream of the shock front via Richtmyer-Meshkov instability or an amplification of upstream magnetic field induced by cosmic rays. They could be discriminated by future observations with a sub arcsecond resolution such as Square Kilometer Array.

The H0 and σ8 tensions and the scale invariant spectrum

In a previous communication [1] it was shown that a joint analysis of Cosmic Microwave Background (CMB) data and the current measurement of the local expansion rate favours a model with a scale invariant spectrum (HZP) over the minimal ΛCDM scenario provided that the effective number of relativistic degrees of freedom, Neff, is taken as a free parameter. Such a result is basically obtained due to the Hubble Space Telescope (HST) value of the Hubble constant, H0 = 73.24 ± 1.74 km . s−1.Mpc−1 (68% C.L.), as the CMB data alone discard the HZP+Neff model. Although such a model is not physically motivated by current scenarios of the early universe, observations pointing to a scale invariant spectrum may indicate that the origin of cosmic perturbations lies in an unknown physical process. Here, we extend the previous results performing a Bayesian analysis using joint CMB, HST, and Baryon Acoustic Oscillations (BAO) measurements. In order to take into account the well-known tension on the value of the fluctuation amplitude parameter, σ8, we also consider Cluster Number counts (CN) and Weak Lensing (WL) data. We use two different samples of BAO data, which are obtained using two-point spatial (BAO 2PCF) and angular (BAO 2PACF) correlation functions. Our results show that the joint CMB+HST+WL+NC dataset favor the extensions of the ΛCDM model over its minimal parameterization. Also, analysis with the BAO 2PCF always discard the HZP+Neff model with respect to standard scenario, whereas the combinations using BAO 2PACF favor the former model. We, therefore, find that all dataset disfavor the ΛCDM model with respect to the HZP+Neff extension, the only exception being the joint analysis with BAO (2PCF).

Characterization of microscopic deformation through two-point spatial correlation functions.

The molecular rearrangements of most fluids under flow and deformation do not directly follow the macroscopic strain field. In this work, we describe a phenomenological method for characterizing such nonaffine deformation via the anisotropic pair distribution function (PDF). We demonstrate how the microscopic strain can be calculated in both simple shear and uniaxial extension, by perturbation expansion of anisotropic PDF in terms of real spherical harmonics. Our results, given in the real as well as the reciprocal space, can be applied in spectrum analysis of small-angle scattering experiments and nonequilibrium molecular dynamics simulations of soft matter under flow.

Influence of grain morphology on ultrasonic wave attenuation in polycrystalline media with statistically equiaxed grains.

The influence of a polycrystals' grain structure on elastic wave scattering is studied with analytical and numerical methods in a broad frequency range. A semi-analytical attenuation model, based on an established scattering theory, is presented. This technique accurately accounts for the grain morphology without prior assumptions on grain statistics. This is achieved by incorporating a samples' exact spatial two-point correlation function into the theory. The approach is verified by using a finite element method (FEM) to simulate P-wave propagation in 3D Voronoi crystals with equal mean grain diameter, but different grain shape uniformity. Aluminum and Inconel serve as representatives for weak and strong scattering cubic class materials for simulations and analytical calculations. It was found that the shape of the grains has a strong influence on the attenuation curve progression in the Rayleigh-stochastic transition region, which was attributed to mode conversion scattering. Comparisons between simulations and theory show excellent agreement for both materials. This demonstrates the need for accurately taking the microstructure of heterogeneous materials into account, to get precise analytical predictions for their scattering behaviour. It also demonstrates the impressive accuracy and flexibility of the scattering theory which was used.

Computation of fluid flow and pore-space properties estimation on micro-CT images of rock samples

Accurate determination of the petrophysical properties of rocks, namely REV, mean pore and grain size and absolute permeability, is essential for a broad range of engineering applications. Here, the petrophysical properties of rocks are calculated using an integrated approach comprising image processing, statistical correlation and numerical simulations. The Stokes equations of creeping flow for incompressible fluids are solved using the Finite-Volume SIMPLE algorithm. Simulations are then carried out on three-dimensional digital images obtained from micro-CT scanning of two rock formations: one sandstone and one carbonate. Permeability is predicted from the computed flow field using Darcy's law. It is shown that REV, REA and mean pore and grain size are effectively estimated using the two-point spatial correlation function. Homogeneity and anisotropy are also evaluated using the same statistical tools. A comparison of different absolute permeability estimates is also presented, revealing a good agreement between the numerical value and the experimentally determined one for the carbonate sample, but a large discrepancy for the sandstone. Finally, a new convergence criterion for the SIMPLE algorithm, and more generally for the family of pressure-correction methods, is presented. This criterion is based on satisfaction of bulk momentum balance, which makes it particularly useful for pore-scale modelling of reservoir rocks.

Spatial correlations, additivity, and fluctuations in conserved-mass transport processes.

We exactly calculate two-point spatial correlation functions in steady state in a broad class of conserved-mass transport processes, which are governed by chipping, diffusion, and coalescence of masses. We find that the spatial correlations are in general short-ranged and, consequently, on a large scale, these transport processes possess a remarkable thermodynamic structure in the steady state. That is, the processes have an equilibrium-like additivity property and, consequently, a fluctuation-response relation, which help us to obtain subsystem mass distributions in the limit of subsystem size large.

Statistics of highly heterogeneous flow fields confined to three-dimensional random porous media

We present a strong relationship between the microstructural characteristics of, and the fluid velocity fields confined to, three-dimensional random porous materials. The relationship is revealed through simultaneously extracting correlation functions R_{uu}(r) of the spatial (Eulerian) velocity fields and microstructural two-point correlation functions S_{2}(r) of the random porous heterogeneous materials. This demonstrates that the effective physical transport properties depend on the characteristics of complex pore structure owing to the relationship between R_{uu}(r) and S_{2}(r) revealed in this study. Further, the mean excess plot was used to investigate the right tail of the streamwise velocity component that was found to obey light-tail distributions. Based on the mean excess plot, a generalized Pareto distribution can be used to approximate the positive streamwise velocity distribution.