Spatial Correlation Function Research Articles

Physics-based scintillations for outdoor sound auralization.

The sound propagating in a turbulent atmosphere fluctuates in amplitude and phase. This phenomenon, known as acoustic scintillation, is caused by random fluctuations in the acoustic refractive index of the air induced by atmospheric turbulence. Auralization techniques should consider this phenomenon to increase the realism of the synthetic sound. This paper proposes a physics-based formulation to model sequences of log-amplitude and phase fluctuations of a sound propagating in a turbulent atmosphere. This method applies to slanted and vertical propagation of the sound, which is useful for simulating elevated noise sources such as aircraft, drones, and wind turbines. The theoretical framework is based on the spatial correlation functions for the log-amplitude and phase fluctuations for spherical waves, the von Kármán spectrum, and similarity theories to model atmospheric turbulence. Two applications with audio files are presented to demonstrate the applicability of this method to tonal and broadband noise.

Spatial intensity correlations of transmitted intensity patterns emerging from large particles.

Propagation of a coherent light beam through a random medium generates speckle patterns, in which some information of media and object is hidden. Speckles produced by particles smaller than wavelength are studied thoroughly, yet it is also essential to investigate speckles produced by larger particles. In this paper, the spatial intensity correlations of transmitted speckle patterns generated by large particles are studied theoretically and experimentally. A semi-empirical expression of spatial intensity correlation function of speckle patterns is derived based on Bethe-Salpeter equation, taking particle size and concentration into account. After performing experiments with various particle sizes and concentrations, we fit the theoretical expression to experimental results and determine the introduced parameters. We analyze the variation of spatial intensity correlation function with particle size and concentration. Theoretical analyses and experimental results given in this paper have potential applications in coherent imaging through random and disordered media.

3D geometry‐based UAV to vehicle multiple‐input multiple‐output channel model incorporating Unmanned aerial vehicle heaving motion

AbstractUnmanned aerial vehicles (UAVs) play a vital role in the beyond fifth‐generation (B5G) and sixth‐generation (6G) wireless communication scenarios. This paper proposes a non‐stationary three‐dimensional (3D) geometry‐based multiple‐input multiple‐output channel model for UAV to vehicle (U2V) communications considering UAV heaving motion. The proposed model incorporates the effects of UAV heaving along with the rotation, acceleration, and 3D velocity variation for matching the realistic U2V communication scenarios. The computation methods for time variant channel parameters such as Doppler frequencies, angle of arrival, and angle of departure are given and analysed. The theoretical and statistical properties, including spatial temporal correlation function, TCF, level crossing rate, average fade duration, and Doppler power spectral density are derived and analysed aiming to evaluate the proposed model. Simulation results show that the output statistical characteristics agree with the hypothetical and simulated outcomes, which shows the validity of both the channel model and theoretical derivations.The cover image is based on the Research Article 3D geometry‐based UAV to vehicle multiple‐input multiple‐output channel model incorporating Unmanned aerial vehicle heaving motion by Naeem Ahmed et al., https://doi.org/10.1049/mia2.12393

State-space prior distribution for parameter of nonhomogeneous Poisson spatiotemporal models.

This article proposes a new class of nonhomogeneous Poisson spatiotemporal model. In this approach, we use a state-space model-based prior distribution to handle the scale and shape parameters of the Weibull intensity function. The proposed prior distribution enables the inclusion of changes in the behavior of the intensity function over time. In defining the spatial correlation function of the model, we include anisotropy via spatial deformation. We estimate the model parameters from a Bayesian perspective, employ the Markov chain Monte Carlo approach, and validate this estimation procedure through a simulation exercise. Finally, the extreme rainfall in the southern semiarid region in northeastern Brazil is analyzed using the R10mm index. The proposed model showed better fit and prediction ability than did other nonhomogeneous Poisson spatiotemporal models available in the literature. This improvement in performance is mainly due to the flexibility of the intensity function that is achieved by allowing the incorporation, in time, of the climatic characteristics of thisregion.

Korrelyatsii zavikhrennosti vnutri kogerentnogo vikhrya

We investigate fluctuations of vorticity inside a coherent vortex generated by the inverse energy cascade in two-dimensional turbulence. Temporal and spatial correlations can be characterized by the pair correlation function. The interaction of fluctuations leads to a nonzero third moment of vorticity. We analyze the pair correlation function and the third moment using a model in which the pumping is short-correlated in time and derive explicit expressions for the Gaussian spatial correlation function for the pumping force.

Evolution of matter and galaxy clustering in cosmological hydrodynamical simulations

ABSTRACT We quantify the evolution of matter and galaxy clustering in cosmological hydrodynamical simulations via correlation and bias functions of matter and galaxies. We use simulations TNG100 and TNG300 with epochs from z = 5 to z = 0. We calculate spatial correlation functions (CFs) of galaxies, ξ(r), for simulated galaxies and dark matter (DM) particles to characterize the evolving cosmic web. We find that bias parameters decrease during the evolution, confirming earlier results. Bias parameters of the lowest luminosity galaxies, b0, estimated from CFs are lower relative to CFs of particle density-limited clustered samples of DM. At low and medium luminosities, bias parameters of galaxies are equal, suggesting that dwarf galaxies reside in the same filamentary web as brighter galaxies. We find that bias parameters b0, estimated from CFs of clustered DM, agree with the expected values from the fraction of particles in the clustered population, b = 1/Fc. The cosmic web contains filamentary structures of various densities, and fractions of matter in the clustered and the unclustered populations are both less than unity. Thus, the CF amplitude of the clustered matter is always higher than that for all matter, i.e. bias parameter must be b > 1. Differences between CFs of galaxies and clustered DM suggest that these functions describe different properties of the cosmic web.

Solid State Neuroscience: Spiking Neural Networks as Time Matter

We aim at building a bridge between to a priori disconnected fields: Neuroscience and Material Science. We construct an analogy based on identifying spikes events in time with the positions of particles of matter. We show that one may think of the dynamical states of spiking neurons and spiking neural networks as time-matter. Namely, a structure of spike-events in time having analogue properties to that of ordinary matter. We can define for neural systems notions equivalent to the equations of state, phase diagrams and their phase transitions. For instance, the familiar Ideal Gas Law relation (Pυ = constant) emerges as analogue of the Ideal Integrate and Fire neuron model relation (Iin ISI = constant). We define the neural analogue of the spatial structure correlation function, that can characterize spiking states with temporal long-range order, such as regular tonic spiking. We also define the “neuro-compressibility” response function in analogy to the lattice compressibility. We show that similarly to the case of ordinary matter, the anomalous behavior of the neuro-compressibility is a precursor effect that signals the onset of changes in spiking states. We propose that the notion of neuro-compressibility may open the way to develop novel medical tools for the early diagnose of diseases. It may allow to predict impending anomalous neural states, such as Parkinson’s tremors, epileptic seizures, electric cardiopathies, and perhaps may even serve as a predictor of the likelihood of regaining consciousness.

Full view on the dynamics of an impurity coupled to two one-dimensional baths

We consider a model for the motion of an impurity interacting with two parallel, one-dimensional baths, described as two Tomonaga-Luttinger liquid systems. The impurity is able to move along the baths, and to jump from one to the other. We provide a perturbative expression for the evolution of the system when the impurity is injected in one of the baths, with a given wave packet. We obtain an approximation formally of infinite order in the impurity-bath coupling, which allows us to reproduce the orthogonality catastrophe. We monitor and discuss the dynamics of the impurity and its effect on the baths, in particular for a Gaussian wave packet. Besides the motion of the impurity, we also analyze the dynamics of the bath density and momentum density (i.e., the particle current), and show that it fits an intuitive semiclassical interpretation. We also quantify the correlation that is established between the baths by calculating the interbath, equal-time spatial correlation functions of both bath density and momentum, finding a complex pattern. We show that this pattern contains information on both the impurity motion and on the baths, and that these can be unveiled by taking appropriate ``slices'' of the time evolution.

Local and global measures of the shear moduli of jammed disk packings.

Strain-controlled isotropic compression gives rise to jammed packings of repulsive, frictionless disks with either positive or negative global shear moduli. We carry out computational studies to understand the contributions of the negative shear moduli to the mechanical response of jammed disk packings. We first decompose the ensemble-averaged, global shear modulus as 〈G〉=(1-F_{-})〈G_{+}〉+F_{-}〈G_{-}〉, where F_{-} is the fraction of jammed packings with negative shear moduli and 〈G_{+}〉 and 〈G_{-}〉 are the average values from packings with positive and negative moduli, respectively. We show that 〈G_{+}〉 and 〈|G_{-}|〉 obey different power-law scaling relations above and below pN^{2}∼1. For pN^{2}>1, both 〈G_{+}〉N and 〈|G_{-}|〉N∼(pN^{2})^{β}, where β∼0.5 for repulsive linear spring interactions. Despite this, 〈G〉N∼(pN^{2})^{β^{'}} with β^{'}≳0.5 due to the contributions from packings with negative shear moduli. We show further that the probability distribution of global shear moduli P(G) collapses at fixed pN^{2} and different values of p and N. We calculate analytically that P(G) is a Γ distribution in the pN^{2}≪1 limit. As pN^{2} increases, the skewness of P(G) decreases and P(G) becomes a skew-normal distribution with negative skewness in the pN^{2}≫1 limit. We also partition jammed disk packings into subsystems using Delaunay triangulation of the disk centers to calculate local shear moduli. We show that the local shear moduli defined from groups of adjacent triangles can be negative even when G>0. The spatial correlation function of local shear moduli C(r[over ⃗]) displays weak correlations for pn_{sub}^{2}<10^{-2}, where n_{sub} is the number of particles within each subsystem. However, C(r[over ⃗]) begins to develop long-ranged spatial correlations with fourfold angular symmetry for pn_{sub}^{2}≳10^{-2}.

High-Order Sinc-Correlated Model Vortex Beams

We propose a new partially coherent vortex source model in which the spatial correlation function is a sinc function on the difference from the q-th power of the coordinates of two points of the source field. The beam radiated by such source is termed the high-order sinc-correlated model vortex (SCMV) beam. We derived the propagating formula of the cross-spectral density (CSD) function for SCMV beams in atmospheric disturbances. On the basis of the derived analytical expression, the behavior of the spectral density of the SCMV beams propagating in free space and atmosphere turbulence was investigated under comparative analysis. The results show that the spectral densities of such beams exhibited interesting novel features, which were significantly different from those of the trivial vortex beams.

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.

Intensity correlation scan (IC-scan) technique to characterize the optical nonlinearities of scattering media

Light scattering, whether caused by desired or spurious elements, is considered one of the main phenomena that present great challenges for the nonlinear (NL) optical characterization of turbid media. The most relevant disturbing factor is the random deformation suffered by the spatial intensity distribution of the laser beam due to multiple scattering. In this work, we report the intensity correlation scan (IC-scan) technique as a new tool to characterize the NL optical response of scattering media, by taking advantage of light scattering to generate speckle patterns sensitive to wavefront changes induced by the self-focusing and self-defocusing effects. Peak-to-valley transmittance curves, with a higher signal-to-noise ratio, are obtained by analyzing the spatial intensity correlation functions of the different speckle patterns, even in very turbid media where conventional NL spectroscopy techniques fail. To demonstrate the potential of the IC-scan technique, the NL characterization of colloids that contain a high concentration of silica nanospheres as scatterers, as well as gold nanorods, which act as NL particles and light scatterers, was performed. The results show that the IC-scan technique is more accurate, precise and robust to measure NL refractive indices in turbid media, overcoming limitations imposed by well-established Z-scan and D4σ techniques.

Statistical Modeling of Extreme Precipitation in Summer in the Baikal Region with the Use of the Correlation Theory of Random Fields

A probabilistic model of the sums of extreme precipitation was developed for heavy showers covering large areas in the Baikal region. The spatial correlation functions of precipitation fields over one day and the entire rain period were studied. Data on the Iya River basin were used to evaluate the errors in estimating the mean values over a specified contour of extreme precipitation. Errors in the interpolation of precipitation estimates for the Baikal region were evaluated in the absence of observation data with estimation of the errors of the obtained values by Drozdov–Shepelevskii formulas. These errors amounted to about 10–15% and more. The specific features of precipitation field structures were studied with the use of their expansion in series in natural orthogonal functions for one day and over a rain period for different samples: for the entire combination of cases and for samples containing 10 and 30 maximal precipitation totals for each weather station, i.e., for extreme events. It was found that, if the observation data are limited to a range of maximal values, the structure of precipitation fields is simplified and the first 4–5 decomposition components are enough for its description. The obtained results are of importance for forecast problems and for the construction of simulation models of precipitation fields for further use in deterministic runoff simulation.

Spatial modeling of concrete strength based on data

Structural verification of concrete structures relies on an underlying probabilistic model of the concrete strength. This concrete strength exhibits a spatial variability, which is of particular relevance in existing concrete structures, for which the strength is assessed based on samples. To accurately account for the spatial variability of the concrete material, a random field modeling approach can be adopted, which includes a spatial correlation function. Unfortunately, the available literature on spatial variability of concrete strength is not sufficient to make an educated choice of this correlation function. In this paper, we propose a hierarchical Bayesian random field model, that enables learning the parameters of a selected correlation function with in-situ spatially distributed measurements of the concrete strength. We propose a correlation function that accounts for the composite nature of the material through distinguishing micro-scale and meso-scale variability. The predictive spatial distribution of the proposed random field model given the spatial data is then obtained through an analytical random field update, resulting in a non-homogeneous random field model with log-Student’s t-marginal distribution. The proposed approach provides an effective means to employ in-situ measurements for updating verification predictions of concrete structures. We apply our approach to two case studies on chamber walls of ship locks, where measurements of the concrete strength are available from core samples.

Correcting Deviations of Emulated Spatial Correlation for Prefaded Signal Synthesis Method With Limited Number of Random Drops in MIMO OTA Testing

The prefaded signals synthesis (PFS) is a well-established over-the-air (OTA) testing solution, which can reconstruct the desired spatial profiles of the target channel by adjusting the power weights of the multiple probes. However, practical channel emulation campaigns tend to use a limited number of random drops due to limited time budget and hardware capacity constraint, which may cause the emulated spatial correlation to be deviated from the expected one due to the loss of ergodicity. In this article, the properties of the emulated channel under the PFS method are reexamined for a given set of initial subpath phases that are randomly configured at different probes. The analytical expressions of the spatial–temporal correlation function (STCF) are thus derived by averaging over time, compared with the general manipulations of ensemble averaging in the literature. Our derivations indicate that the spatial correlation function (SCF) of the emulated channel may deviate from the expected form for a given set of initial subpath phases in the classic PFS method. An improved configuration method for initial subpath phases is proposed. Simulation results show that the proposed method can reproduce the exact SCF in any random drop while unaffecting other important channel properties, for example, the temporal correlation function (TCF).

Molecular dynamics simulation of polymorphic transformation between ε-CL-20 and β-CL-20 by short range order and orientational order parameter

Phase transition simulation of molecular crystals is a challenge. In order to clarify the polymorphic transformation mechanism of molecular crystal, a molecular dynamics (MD) simulation of the transformation between ε-CL-20 and β-CL-20 was carried out by the short range order g(r) and local orientational order parameter (OPs) P2(cosθ) as well as the spatial orientation correlation function. The effects of the temperature on them were performed. The results indicate that the g(r), orientational OPs and spatial orientation correlation function, composed of the structural parameters from three CL-20 molecules in three different single crystal, could be used to simulate the process of the polymorphic transformation between ε-CL-20 and β-CL-20. Only at a high temperature, could two kinds of the CL-20 supercells realize the transformation of crystal form. Furthermore, there were local and global minimum energy points, indicating that there could be the metastable or stable crystal forms in the process of the transformation from β-CL-20 to ε-CL-20. The values of P2(cosθ) were well related to results of the surface electrostatic potentials (ESPs), suggesting that the ESPs have an influence on polymorphic transformation.

Experimental characterisation and data-driven modelling of unsteady wall pressure fields induced by a supersonic jet over a tangential flat plate

This work deals with the investigation and modelling of wall pressure fluctuations induced by a supersonic jet over a tangential flat plate. The analysis is performed at several nozzle pressure ratios around the nozzle design Mach number, including slightly over-expanded and under-expanded conditions, and for different radial positions of the rigid plate. Pitot measurements and flow visualizations through the background oriented schlieren technique provided a general overview of the aerodynamic interactions between the jet flow and the plate at the different regimes and configurations. Wall pressure fluctuations were measured using a couple of piezoelectric pressure transducers flush mounted over the plate surface. The spectral analysis has been carried out to clarify the effect of the plate position on the single and multivariate wall pressure statistics, including the screech tone amplitude. The experimental dataset is used to assess and validate a surrogate model based on artificial neural networks. Sound pressure levels and coherence functions are modelled by means of a single fully connected network, built on the basis of a recently implemented fully deterministic topology optimization algorithm. The metamodel uncertainty is also quantified using the spatial correlation function. It is shown that the flow behaviour as well as the screech and broadband noise signatures are significantly influenced by the presence of the plate, and the effects on spectral quantities are correctly reproduced by the proposed data-driven model that provides predictions in agreement with the available data.

Quantum phase transitions in non-Hermitian [formula omitted]-symmetric transverse-field Ising spin chains

We present a theoretical study of quantum phases and quantum phase transitions occurring in non-Hermitian PT-symmetric superconducting qubits chains described by a transverse-field Ising spin model. A non-Hermitian part of the Hamiltonian is implemented via imaginary staggered longitudinal magnetic field, which corresponds to a local staggered gain and loss terms. By making use of a direct numerical diagonalization of the Hamiltonian for spin chains of a finite size N, we explore the dependencies of the energy spectrum, including the energy difference between the first excited and the ground states, the spatial correlation function of local polarization (z-component of local magnetization) on the adjacent spins interaction strength J and the local gain (loss) parameter γ. A scaling procedure for the correlation length ξ allows us to establish a complete quantum phase diagram of the system. We obtain two quantum phases for J<0, namely, PT-symmetry broken antiferromagnetic state and PT-symmetry preserved paramagnetic state, and the quantum phase transition line between them is the line of exception points. For J>0 the PT-symmetry of the ground state is retained in a whole region of parameter space of J and γ, and a system shows two intriguing quantum phase transitions between ferromagnetic and paramagnetic states for a fixed parameter γ>1. We also provide the qualitative quantum phase diagram γ−J derived in the framework of the Bethe–Peierls approximation that is in a good accord with numerically obtained results.

Turbulent Flame Propagation in Hydrogen-Air and Methane-Air Mixtures in the Field of Synthetic Turbulence: Direct Numerical Simulation

A technique alternative to the direct numerical simulation of turbulent combustion of gas mixtures is proposed. It is based on the solution of the three-dimensional transport equations for species concentrations and the energy conservation equation in the “synthetic” field of constant-pressure homogeneous, isotropic and statistically stationary (forced) turbulence using the detailed reaction mechanism. The synthetic turbulence with given spatial and temporal correlation functions is generated using the Monte Carlo method, assuming that the components of the vector of fluctuation velocity obey the normal Gaussian distribution. The technique is applied to the problem of turbulent combustion of fuel-lean and stoichiometric mixtures of hydrogen and methane with air at a turbulence intensity up to 10 m/s. The calculated turbulent flame propagation velocities agree satisfactorily with the values measured in the fan-stirred bomb. The predicted volume fractions of active reaction centers H, O, and OH in a turbulent flame are shown to be less than in a laminar flame up to an order of magnitude, which also agrees with the experiment. In general, calculations indicate that the “wrinkled flame” model is applicable to fuel-lean and stoichiometric mixtures of hydrogen and methane with air at turbulence intensities up to 10 m/s

Van der Waals Dispersion Potential between Excited Chiral Molecules via the Coupling of Induced Dipoles

The retarded van der Waals dispersion potential between two excited chiral molecules was calculated using an approach, in which electric and magnetic dipole moments are induced in each particle by fluctuations in the vacuum electromagnetic field. An expectation value of the coupling of the moments at different centres to the dipolar interaction tensors was taken over excited matter states and the ground state radiation field, the former yielding excited molecular polarisabilities and susceptibilities, and the latter field–field spatial correlation functions. The dispersion potential term proportional to the mixed dipolar polarisability is discriminatory, dependent upon molecular handedness, and contains additional terms due to transitions that de-excite each species as well as the usual u-integral term over imaginary frequency, which applies to both upward and downward transitions. Excited state dispersion potentials of a comparable order of magnitude involving paramagnetic and diamagnetic couplings were also computed. Pros and cons of the method adopted are compared to other commonly used approaches.