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A method of space ensemble (SE) and time ensemble (TEs) correlation function technique applied on ground penetration radar (GPR) B-scan raw data proves to result in detailed information for tracking buried objects. These computations help in site allocations by time ensemble correlation functions (TESCs) and time stamps of objects scattering by space ensemble correlation functions (SECFs) which are precisely consistent with the simulation results. While these results are applied for given data stack, randomness in physical parameters of tested ground always occurs. An introduction of randomness to the physical parameters of tested models by creating stochastic collocation (SC) ensembles incorporating randomness to B-scan via successive A-scans, SC-SE, and SC-TE ensembles enables sensitivity analysis (SA) study of GPR raw data which gives a tool to change the physical properties of the ground in search for better ground matching. This method can be added to GPR machines or simulation software to enhance raw data analysis. A field experiment of small non-metallic objects' allocation was carried out as a platform for assessing the realistic performance of the method.

Two techniques are presented for characterisation of cloud-feeding coherent boundary-layer structures through analysis of large-eddy simulations of shallow cumulus clouds, contrasting conditions with and without ambient shear. The first technique is a generalisation of the two-point correlation function, where the correlation length-scale as well as the orientation can be extracted. The second technique identifies individual coherent structures and decomposes their vertical transport by the shape, size, and orientation of these objects. The bulk-correlation technique is shown to capture the elongation and orientation of coherence by ambient wind, but is unable to characterise individual coherent structures. Using the object-based approach, it is found that the individual structures dominating the vertical flux are plume-like in character (extending from the surface into cloud) rather than thermal-like, show small width/thickness asymmetry, and rise near-vertically in the absence of ambient wind. The planar stretching and tilting of boundary-layer structures caused by the introduction of ambient shear is also quantified, demonstrating the general applicability of the techniques for future study of other boundary-layer patterns.

In this paper, a novel space-time non-stationary three-dimensional (3D) wideband massive multiple-input multiple-output (MIMO) channel model is proposed. We then propose a ray-level process to model the spatial-temporal evolution of individual multipath components (MPCs), including near-field effects and (dis)appearance, and cluster-level large-scale fading. The proposed evolution process can flexibly control rays’ lifespans and smoothness of (dis)appearance in both space and time domains. In addition, we propose an improved Rayleigh-distance criterion to determine the most adequate wavefront for each cluster and ray. Existing models can easily implement the proposed criterion and make a more efficient use of computation resources. Also, a Gamma-Poisson mixture distribution is introduced to model the distribution of the number of clusters when multiple locations of the mobile station are considered. Key statistical properties of the channel, including the autocorrelation function (ACF), Doppler power spectral density (PSD), spatial cross-correlation function (S-CCF), and frequency correlation function (FCF), are derived and the impact of the ray-level evolution process on them is analyzed. We demonstrate the correctness of the derived statistical properties through numerical and simulation results.

This article presents a numerical study of the wave scattering from a modulated rough surface characterized by a modulated correlation function that shows zero crossings along the lag distance. The zero crossings imply the presence of multiscale roughness. In such a way, we treat the rough surface to include a baseband correlation length and a modulation length. The modulation ratio, the ratio of baseband correlation length, and the modulated length determine the degree of multiscale roughness. We then examine the dependence of bistatic scattering, both in level and angular trends, on the modulation length. The results indicate that as the modulation ratio increases, the scattering coefficients reduce in the incident plane. Comparing the model predictions with two independent sets of measurement data demonstrates a good agreement of the scattering coefficients between the experimental data and the model predictions with modulation effects. The proposed modulated rough surface concept offers higher flexibility to model the radar scattering of multiscale rough surface.

This is a pre-copyedited, author-produced PDF of an article accepted for publication in Monthly Notices of the Royal Astronomical Society following peer review. The version of record Monthly Notices of the Royal Astronomical Society 510.1 (2022): 292-308 is available online at: https://academic.oup.com/mnras/article-abstract/510/1/292/6442269?redirectedFrom=fulltext#no-access-message, We study the clustering of H i intensity maps (IM) produced from simulations with a focus on baryonic acoustic oscillations (BAOs) and the effects induced by telescope beam smoothing and foreground cleaning. We start by creating an H i catalogue at z = 1.321 based on the Semi-Analytic Galaxy Evolution (SAGE) model applied to the UNIT simulations. With this catalogue, we investigate the relation between model H i and the dark matter haloes and we also study the abundance of H i, Omega rm{H small {rm I}}, predicted by this model. We then create synthetic H i IM with a nearest-grid-point approach. In order to simulate the telescope beam effect, a Gaussian smoothing is applied on the plane perpendicular to the line of sight. The effect of foreground removal methods is simulated by exponentially damping the largest wavelength Fourier modes on the radial direction. We study the anisotropic 2-point correlation function (2PCF) ζ(rpdbl, rpdbl) and how it is affected by the aforementioned observational effects. In order to better isolate the BAO signal, we study several 2PCF μ-wedges (with a restricted range of orientations μ) tailored to address the systematics effects and we compare them with different definitions of radial 2PCFs. Finally, we discuss our findings in the context of an SKA-like survey, finding a clear BAO signal in most of the estimators here proposed

The packing length p figures prominently in scaling predictions of the entanglement length and bulk modulus for polymer melts and solutions. p has been argued to scale as the ratio of chain displaced volume V and mean square end-to-end distance R2. This scaling works for several cases; however, it is not obvious how to apply it to chains with side groups, and the scaling must fail for sufficiently thin, stiff chains. In this work, we measure the packing length in simulations, without making any scaling assumptions, as the typical distance of closest approach of two polymer strands in a simulated bead-spring melt. We use the intermolecular correlation function to measure the distance up to which a given polymer strand dominates the local volume fraction. Using our measured packing length, we find good agreement of entanglement properties with Lin–Noolandi scaling for flexible polymers of different architectures.

The problem of modeling signals of various spatial coherence in radio engineering systems is considered. First, a mathematical model for spatially coherent signals in the form of stochastic differential equations is constructed, followed by its study in the Simulink environment. The following is a method for constructing a mathematical model for a more general case – partially coherent signals, and its accuracy is also evaluated. Based on the developed models, an algorithm for estimating the parameters of partially coherent signals is synthesized. Based on the obtained dependence of the sensitivity of the model to deviation from a priori data, conclusions are drawn about a sufficiently high accuracy of estimation using synthesized algorithms.

In order to realize the damage identification of the bridge, a method based on the correlation of vehicle-induced response of the bridge is proposed. Firstly, using the measured vibration responses of the bridge under vehicle load, damage indexes based on Pearson correlation coefficient, Spearman correlation coefficient and Kendall correlation coefficient are defined, respectively. Then, the proposed method is verified by numerical simulation and compared with the method based on Correlation function amplitude Vector (CorV). The effectiveness of the method for single damage and multiple damage of the bridge is examined. Numerical results demonstrate that the proposed method can effectively identify and locate the damage, and the effectiveness of the index based on Pearson correlation coefficient is the best. Finally, the proposed damage identification method is verified by experiments, and the results manifests that the comprehensive decision-making based on different damage indexes is helpful to improve the accuracy of damage location. Besides, the influence of road-surface roughness on damage identification is discussed. Results indicate that the damage indexes are affected by road-surface roughness, and the statistical mean value is beneficial to identify and locate the damage.

We present a methodical study of the thermoelectric properties of SrTi(1 − x)Zr(x)O3 (0 ≤ x ≤ 1), noting that STZO alloy using a computational quantum mechanical modelling method used in physics, density-functional theory (DFT), with full potential-linearised augmented plane wave (FP-LAPW) as used in Wien2K code with the Perdew Burke Ernzerhof (PBE) exchange correlation function under GGA was used for calculations. The thermoelectric properties including Seebeck coefficient, electrical conductivity, and thermal conductivity of SrTi(1 − x)Zr(x)O3 with x = 0.0, 0.25, 0.50, 0.75, and 1 are calculated by BoltzTrap code which uses Boltzmann transport phenomenon that is used for estimating transport properties of thermoelectric materials. The average values of electrical conductivity, thermal conductivity, and Seebeck coefficient with chemical potential are presented. We expect the STZO alloys to be good for thermoelectric applications. We also analysed the electrical conductivity, thermal conductivity, Seebeck coefficient, power factor, and the resistivity versus variable temperature, in which the maximum power factors are evaluated, suggesting that the compounds have good thermoelectric properties.

Point sources in spatially referenced data can impact outcomes in surrounding locations (e.g., a factory that emits air pollution). Previous statistical methods have sought to describe the non-stationary correlation induced by the presence of a point source, with fewer attempting to quantify its overall impact. We introduce directionally varying change points (DVCP), a model that aims to estimate the magnitude of the impact of a point source as well as its range of influence across the spatial domain. DVCP allows for a unique change point parameter, describing the range of influence of a point source, at every angle extending from the source and uses a Gaussian process with directionally defined correlation function to facilitate estimation of the parameters. The Gaussian predictive process approximation is used for fitting the model to large datasets. Through simulation, we show that DVCP can easily accommodate a wide range of shapes defining the range of influence. We apply DVCP to better understand spatial patterns of ambient PM $$_{2.5}$$ concentrations and issues related to environmental inequity in California and Colorado. The method is available in the R package DVCP. Supplementary materials accompanying this paper appear online.

The properties of uranium hexafluoride (UF6) are of importance to the nuclear industry as a precursor for the enrichment. Therefore it is of importance to obtain the most accurate properties for such a strategic compound. In this paper, some thermophysical properties of uranium hexafluoride (UF6) at low pressure and bellow the critical temperature are predicted and modeled using its correlation function of second virial coefficient and virial equation of state (VEOS). Studied properties consist of Joule-Thomson coefficient, enthalpy, deviation function, fugacity coefficient, thermal expansion and isothermal compressibility. So far, several researchers have studied virial coefficients of UF6 and some of them have presented its correlation function of second virial coefficient. In this work, The studied correlation functions are the ones suggested by Dymond and Zarkova. The obtained results show that the correlation equations presented have a good ability to predict and model the thermophysical properties of uranium hexafluoride and its deviation from the ideal state especially in the temperature range from 360 K up to critical temperature.

Electromagnetic scattering model from 3-D snowpack with arbitrary thickness is considered. A fully coherent model is presented through the usage of the Statistical S-Matrix Wave Propagation in Spectral Domain approach (SSWaP-SD). The computer-generated snow media is constructed using 3-D spatial exponential correlation function along with Lineal-Path function to preserve the connectivity of the snow particles as well. The SSWaP-SD in conjunction with a Method of Moments (MoM) code based on the discrete-dipole approximation (DDA) is chosen to leverage both the time-efficient computations of the DDA and the full-coherency of the SSWaP-SD method simultaneously. The SSWaP-SD depends on the discretization of the medium into thin slabs. Several realizations of a thin snow slab are solved numerically to form the statistics of the scattering matrix representing such a thin snow layer. For an arbitrarily thick snow layer, thin slabs of a snowpack are analyzed and a corresponding polarimetric N-port (representing different directions of scattering) S-matrix is generated. These S-matrices are cascaded using SSWaP-SD method to calculate the total forward and backward bistatic scattered fields in a fully coherent way. The simulation results of the backscattering from an arbitrary thick snow layer are presented and validated with measurements.

It is shown that modelling the first oxygen-oxygen peak in the neutron correlation function of a glass enables structural information about other correlations to be obtained, and the method is illustrated by application to a sodium silicate glass. The first O-O coordination number can be calculated from network theory, and sodium silicate crystal structures show that the mean O-O distance can be calculated from the Si-O distance, despite the distortion of the SiO4 tetrahedra. Modelling the O-O peak for a sodium silicate glass allows the Na-O bond length distribution to be determined. For a binary glass with 42.5 mol% Na2O, it is found that the Na-O coordination number is 4.8(2) with an average bond length of 2.45 Å, and the Na-O bond lengths are more widely distributed than in sodium silicate crystal structures. Sodium ions are bonded mostly to non-bridging oxygens (NBOs), and the Na-NBO coordination number may be four as in crystals. Sodium ions are also bonded to a smaller number of bridging oxygens (BOs). Contrary to previous reports, it is not concluded that Na-NBO bonds are shorter than Na-BO bonds, but instead that the Na-BO distribution is relatively narrow, whilst the Na-NBO distribution extends to both shorter and longer distance. The broad distribution of Na-O bond lengths arises from a relatively broad distribution of Na-NBO bond valences, subject to the overall requirement of charge balance.

We present a comparative study of the accuracy and precision of correlation function methods and full-field inference in cosmological data analysis. To do so, we examine a Bayesian hierarchical model that predicts log-normal fields and their two-point correlation function. Although a simplified analytic model, the log-normal model produces fields that share many of the essential characteristics of the present-day non-Gaussian cosmological density fields. We use three different statistical techniques: (i) a standard likelihood-based analysis of the two-point correlation function; (ii) a likelihood-free (simulation-based) analysis of the two-point correlation function; (iii) a field-level analysis, made possible by the more sophisticated data assimilation technique. We find that (a) standard assumptions made to write down a likelihood for correlation functions can cause significant biases, a problem that is alleviated with simulation-based inference; and (b) analysing the entire field offers considerable advantages over correlation functions, through higher accuracy, higher precision, or both. The gains depend on the degree of non-Gaussianity, but in all cases, including for weak non-Gaussianity, the advantage of analysing the full field is substantial., Comment: 6+8 pages, 4+5 figures. Matches MNRAS Letters published version. Appendices provide supplementary information, including calculations of Fisher matrices. Our code and data are publicly available at https://github.com/florent-leclercq/correlations_vs_field

Based on the basic-element expression method and correlation function theory in Extenics, combined with the knowledge of slope engineering, a method for evaluating the stability of complex slope is proposed. The evaluation process includes the selection of suitable evaluation indexes of slope stability, identificationof the classification standard for the slope stability, identificationof the weights of evaluation indexes by using the improved analytic hierarchy process,identificationof the classical domain, node domain and matter-element under evaluation,the calculation of the correlation of each stability class for each evaluation index, normalization of correlation,and so on. The selection rule of the slop stability evaluation indexes and selection of correlation function and optimal points are also discussed, which can provide reference for slope engineering designin construction industry.

Imaging problems are becoming increasingly important due to the development of systems for aerospace monitoring of the Earth, radio and sonar location, medical devices for early diagnosis of diseases, etc. However, most of the work on image processing is related to images defined on rectangular two-dimensional grids or grids of higher dimensions. In some practical situations, images are defined on a cylinder (for example, images of pipelines, blood vessels, rotation details) or on a circle (for example, images of a facies (thin film) of dried biological fluid, an eye, a cut of a tree trunk). The specifics of the field of assignment of such images must be taken into account in their models and processing algorithms. In this paper, autoregressive models of cylindrical and circular images are considered and expressions of the correlation function are given depending on the autoregressive parameters. Spiral scanning of a cylindrical image can be viewed as a quasi-periodic process due to the correlation of image lines. To represent heterogeneous images with random heterogeneity, “double stochastic” models are used, in which one or several control images set the parameters of the resulting image. The available image can be used to estimate the parameters of the model of its control images. However, this is not sufficient to fully identify the hidden control images. It is also necessary to evaluate their covariance functions and find out whether they correspond to the hypothetical ones. The paper proposes a test for testing the hypotheses about the covariance functions of cylindrical and circular images with a study of its power relative to the parameters of the image model.

Seismic demand and performance of bridges are highly dependent upon the level of irregularity. Although previous studies have proposed methodologies so as to quantify the irregularity of the bridges in terms of global regularity index, it still remains unclear how to determine the distribution of irregularity along a bridge, as well as to discover the irregularity sources. This research project is intended to develop a quantitative vector regularity criterion for single- and multiframe bridges based on the modified correlation function for spatial locations of scaled mode shapes of deck-alone and whole bridge. The proposed criterion calculates two types of regularity indices, namely, local (LRI) and global regularity indices (GRI). The GRI is a scalar value representing the overall regularity of the entire bridge, whereas the LRI highlights vector irregularity distribution along the bridge. Since the deck discontinuity due to the in-span hinges is one of the leading causes for irregularity, the proposed index has been employed in case of multiframe bridges as well. Furthermore, the current study aims to investigate the correlation between the proposed irregularity indicators and the nonlinear to linear demand ratio. Therefore, the appropriate analysis method can be chosen based on irregularity extent of bridges. Obtained results of the proposed indices reveal that in-span hinge is one of the main parameters affecting the distribution of local irregularity along a bridge. Therefore, multiframe bridges need to be investigated in detail so as to validate the special design requirements recommended by design codes.

This work presents an efficient methodology for the optimum design of functionally graded structures using a Kriging-based approach. The method combines an adaptive Kriging framework with a hybrid particle swarm optimization (PSO) algorithm to improve the computational efficiency of the optimization process. In this approach, the surrogate model is used to replace the high-fidelity structural responses obtained by a NURBS-based isogeometric analysis. In addition, the impact of key factors on surrogate modelling, as the correlation function, the infill criterion used to update the surrogate model, and the constraint handling is assessed for accuracy, efficiency, and robustness. The design variables are related to the volume fraction distribution and the thickness. Displacement, fundamental frequency, buckling load, mass, and ceramic volume fraction are used as objective functions or constraints. The effectiveness and accuracy of the proposed algorithm are illustrated through a set of numerical examples. Results show a significant reduction in the computational effort over the conventional approach.

In this work, we investigate thermodynamic properties of the one-dimensional (1D) spin-crossover molecular chain being a subject of a constant external pressure. Effective compressible degenerate Ising model is used as a theoretical framework. Using transfer matrix formalism analytic results for the low spin -- high spin crossover were obtained. We derive the exact expressions for the fraction of molecules in the high spin state, correlation function and heat capacity. We provide analysis of parameters region where the spin crossover takes place and demonstrate how pressure changes location of the crossover., 9 pages, 5 figures, submitted to Low Temperature Physics

The paper contributes by developing computational and reviewing theoretical methods to propagate electromagnetic fields in free space, while taking account of the fact that the sources are typicall...

Consider a particle whose drift velocity fluctuates due to transitions among discrete states or due to diffusion in a confined moving fluid. At long times, the dynamics of the particle in the direction of transport can be described in terms of the average drift velocity and an effective diffusivity. For both types of fluctuations, we show that the effective diffusivity is the sum of the average intrinsic diffusivity and the time integral of the velocity correlation function of the deviation of the fluctuating velocity from its mean value. For nearest-neighbor interstate transitions and for one-dimensional diffusion in a perpendicular direction, the time integral can be found in closed form. Our analytical expressions for the effective diffusivity recover the classic results for Taylor dispersion in the laminar flow of viscous fluid and for cargo transport along microtubules by molecular motors.

In this paper, we calculate Joule–Thomson, the enthalpy changes relative to the pressure and deviation functions at low pressure for refrigerant fluids in order to evaluate the performance of their correlation function. The studied refrigerants are R11, R123, R124, R134a, R143a, R152a, R141b, R142b, R227ea, and R236ea. The studied corresponding state principle is the one suggested by Meng et al. In addition, to compare with the data obtained by others, Boyle temperature, Boyle volume, and maximum inversion temperature were also calculated using the correlation. The obtained results show that the correlation equation presented has a good ability to predict the thermophysical properties of materials and their deviation from the ideal state over a wide range of temperatures.

This work develops a second-order approximation (SOA) model and a three-dimensional (3D) finite element (FE) model to calculate scattering-induced attenuation for elastic wave propagation in polycrystals with elongated grains of arbitrary crystal symmetry. The SOA model accounts for some degree of multiple scattering, whereas the 3D FE model includes all scattering possibilities. The SOA model incorporates the accurate geometric two-point correlation function obtained from the FE material systems to enable comparative studies between the two models. Also, the analytical Rayleigh and stochastic asymptotes are presented to provide explicit insights into propagation behaviors. Quantitative agreement is found between the FE and analytical models for all evaluated cases. In particular, the FE simulations support the SOA model prediction that grain shape does not exert influence on attenuation in the Rayleigh regime and its effect emerges as frequency increases to the stochastic regime showing anisotropy in attenuation. This attenuation anisotropy intensifies with the increase in frequency, but it exhibits a complicated behavior as frequency transits into the geometric regime. Wavefield fluctuations captured from the FE simulations are provided to help observe these complex scattering behaviors. The proportionality of attenuation to elastic scattering factors is also quantitatively evaluated.

SUMMARY We propose a new correlation function called the similarity coefficient (SC) based on the normal time–frequency transform (NTFT) to evaluate the similarity between two non-stationary seismic signals as a function of the delay time. The SC is defined in the time–frequency spectrum of the NTFT, and the instantaneous phase and amplitude of each frequency component in a signal are used to calculate the SC. Our simulation experiments demonstrate that the SC method can effectively recognize similar signals compared to the conventional normalized cross-correlation coefficient (NCC) under high background noise conditions. The SC presents good robustness in identifying similar signals and performs well in the case of an extremely low signal-to-noise ratio (SNR), which makes it suitable for detecting weak seismic signals concealed by noise. As a real application case, we use the SC method to detect quasi-Love (QL) surface waves. QL waves are scattered Love waves and are important indicators for lateral anisotropic gradients in the upper mantle. We detect the QL waves at 21 stations deployed across Japan after the 23 December 2004 Mw 8.1 Macquarie earthquake by using the SC method. Obvious QL waves are observed at 19 stations, and we locate the Love-to-Rayleigh scatterers by applying the delay times between the QL and main Love waves. Our results show that the QL wave scatterers were mostly generated in two areas: Mariana subduction and Papua New Guinea. The observations of QL waves suggest the presence of lateral gradients in anisotropy beneath those two areas. The spatial distribution of the 13 scatterers in the Mariana subduction zone agrees well with the Mariana Island Arc, and we infer that the Mariana slab may have melted and coupled with the surrounding mantle at depth.

This work presents scattering functions of conjugates consisting of a colloid particle and a self-avoiding polymer chain as a model for protein–polymer conjugates and nanoparticle–polymer conjugates in solution. The model is directly derived from the two-point correlation function with the inclusion of excluded volume effects. The dependence of the calculated scattering function on the geometric shape of the colloid and polymer stiffness is investigated. The model is able to describe the experimental scattering signature of the solutions of suspending hard particle–polymer conjugates and provide additional conformational information. This model explicitly elucidates the link between the global conformation of a conjugate and the microstructure of its constituent components.

Discrete fracture network (DFN) is an effective means of describing the coupling of heat flow in an underground fractured rock mass. In this paper, an improved DFN is proposed by introducing the correlation function of fracture trace length and aperture, which is more consistent with the real fracture data. Next, based on the improved model, the influence of fracture roughness on the fluid flow and heat transmission was evaluated, and the relationship between the fracture aperture and the joint roughness coefficient (JRC) is established. Finally, based on the exponential function between confining pressure and aperture, the influence of confining pressure on the heat‐flow coupling process is considered in the improved model. Besides, the reliability of the model was verified by comparing with the analytical solution of the two‐dimensional single‐fracture heat‐flow coupling problem. The results show that under the same conditions, considering the correlation between the geometric parameters of the fracture, the seepage and heat transfer rates of the model increased, the outlet boundary flow reached the maximum value, and the average outlet temperature dropped rapidly. However, the fracture roughness reduces the outlet flow rate and the decline rate of average temperature. The confining pressure will lead to a decrease of about 3.5% in the outlet flow of the model, which is consistent with the seepage law in practical engineering. The model presented in this paper is an effective supplement to the two‐dimensional fracture network heat‐flow coupling model and can provide a theoretical basis and a numerical calculation tool for related underground rock mass engineering.

In the present work, Cu-doped indium sulfide thin films (In2S3:Cu) have been produced by chemical bath deposition (CBD) method on the glass substrates. The deposited films have been post-annealed at 300 °C temperature for about one hour. The morphological properties of produced thin films have been investigated analytically before and after the Cu doping process. To this end, the atomic force microscopy analysis has been used to study the height fluctuations of these rough thin films. By the monofractal analysis, the height distribution, and the higher-order moments (skewness and kurtosis) of the surface height have been studied. The deviation from the Gaussian distribution has been shown by the results. Also, the correlation function and therefore the correlation length of the produced surfaces have been investigated. The numerical calculations revealed that the morphology and the statistical properties of thin films depend on the growth method. The power spectral density has been evaluated, and the achieved results of higher-order moments of the surface height have been confirmed. The skewness values of thin films heights are nonzero; moreover, the obtained kurtosis values illustrate the mild peak respect to Gaussian distribution. The Hurst exponent and thus the fractal dimensions of surfaces have been estimated.

It has been a vital issue to ensure both the accuracy and efficiency of computational models for analyzing the ballistic impact response of fiber-reinforced composite plates (FRCP). In this paper, a machine learning (ML) model is established in an effort to bridge the ballistic impact protective performance and the characteristics of microstructure for unidirectional FRCP (UD-FRCP), where the microstructure of the UD-FRCP is characterized by the two-point correlation function. The results showed that the ML model, after trained by 175 cases, could reasonably predict the ballistic impact energy absorption of the UD-FRCP with a maximum error of 13%, indicating that the model can ensure both computational accuracy and efficiency. Besides, the model’s critical parameter sensitivities are investigated, and three typical ML algorithms are analyzed, showing that the gradient boosting regression algorithm has the highest accuracy among these algorithms for the ballistic impact problem of UD-FRCP. The study proposes an effective solution for the traditional difficulty of the ballistic impact simulation of composites with both high efficiency and accuracy.

Coarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of re-capturing these interactions by means of the dislocation-dislocation correlation functions. The framework depends on a coarse-graining length to define slip-system-specific dislocation densities. Following a statistical definition of this coarse-graining process, we define a spatial correlation function which will allow relative positions of dislocation pairs, and thus the strength of their interactions at short range, to be recaptured into a mean field description of dislocation dynamics. Through a statistical homogeneity argument, we present a method of evaluating this correlation function from discrete dislocation dynamics simulations. Finally, results of this evaluation are shown in the form of self-correlation of dislocation densities on the same slip-system. These correlation functions are seen to depend weakly on plastic strain (and, in turn, the total dislocation density), but are seen to depend strongly on the coarse-graining length. Implications of these correlation functions in regard to continuum dislocation dynamics as well as future directions of investigation are also discussed., Comment: 51 pages, 8 figures, submitted to Materials Theory

We present a new statistical analysis of the large-scale stellar mass distribution in the Sloan Digital Sky Survey (data release 7). A set of volume-limited samples shows that the stellar mass of galaxies is concentrated in a range of galaxy luminosities that is very different from the range selected by the usual analysis of galaxy positions. Nevertheless, the two-point correlation function is a power-law with the usual exponent $\gamma=1.71$--$1.82$, which varies with luminosity. The mass concentration property allows us to make a meaningful analysis of the angular distribution of the full flux-limited sample. With this analysis, after suppressing the shot noise, we extend further the scaling range and thus obtain $\gamma=1.83$ and a clustering length \redc{$r_0= 5.8$--$7.0\,h^{-1}$Mpc.} Fractional statistical moments of the coarse-grained stellar mass density exhibit multifractal scaling. Our results support a multifractal model with a transition to homogeneity at about $10\,h^{-1}$Mpc., Comment: 19 pages, 6 figures; new results: shot noise suppression, fractional moments, analysis of VL samples; to be published in Advances in Astronomy

Quasielastic neutron scattering (QENS) allows measurement of the molecular displacements in time and space, from pico- to tens of nanoseconds and from Ångstroms to nanometers, respectively. The method probes dynamics from fast vibrational modes down to slow diffusive motion. Every scattering experiment leads to a dynamic structure factor $$S\left( {\vec Q,\omega } \right)$$ S Q → , ω or its spatial and temporal Fourier transform (van Hove correlation function $$G\left( {\vec r,t} \right)$$ G r → , t ). This shows exactly where the atoms are and how they move. In this manuscript the basics of the QENS method are presented and a few examples highlighting the potentials of QENS are given: (i) diffusion of liquids and gases in nano- and mesoporous materials; (ii) hydrogen dynamics in a high temperature polymer electrolyte fuel cell (HT-PEFC) and (iii) influence of the surface interactions on polymer dynamics in nanopores.

Understanding the nature of active sites is a non-trivial task, especially when the catalyst is sensitively affected by chemical reactions and environmental conditions. The challenge lies on capturing explicitly the dynamics of catalyst evolution during reactions. Despite the complexity of catalyst reconstruction, we can untangle them into several elementary processes, of which surface diffusion is of prime importance. By applying density functional theory–kinetic Monte Carlo (DFT–KMC) simulation employed with cluster expansion (CE), we investigated the microscopic mechanism of surface diffusion of Cu with defects such as steps and kinks. Based on the result, the energetics obtained from CE have shown good agreement with DFT calculations. Various diffusion events during the step fluctuations are discussed as well. Aside from the adatom attachment, the diffusion along the step edge is found to be the dominant mass transport mechanism, indicated by the lowest activation energy. We also calculated time correlation functions at 300, 400, and 500 K. However, the time exponent in the correlation function does not strictly follow the power law behavior due to the limited step length, which inhibits variation in the kink density.

A synthetic inflow turbulence generator was implemented in the idealised Weather Research and Forecasting large eddy simulation (WRF-LES v3.6.1) model under neutral atmospheric conditions. This method is based on an exponential correlation function and generates a series of two-dimensional slices of data which are correlated both in space and in time. These data satisfy a spectrum with a near “-5/3” inertial subrange, suggesting its excellent capability for high Reynolds number atmospheric flows. It is more computationally efficient than other synthetic turbulence generation approaches, such as three-dimensional digital filter methods. A WRF-LES simulation with periodic boundary conditions was conducted to provide prior mean profiles of first and second moments of turbulence for the synthetic turbulence generation method, and the results of the periodic case were also used to evaluate the inflow case. The inflow case generated similar turbulence structures to those of the periodic case after a short adjustment distance. The inflow case yielded a mean velocity profile and second-moment profiles that agreed well with those generated using periodic boundary conditions, after a short adjustment distance. For the range of the integral length scales of the inflow turbulence (±40 %), its effect on the mean velocity profiles is negligible, whereas its influence on the second-moment profiles is more visible, in particular for the smallest integral length scales, e.g. those with the friction velocity of less than 4 % error of the reference data at x/H=7. This implementation enables a WRF-LES simulation of a horizontally inhomogeneous case with non-repeated surface land-use patterns and can be extended so as to conduct a multi-scale seamless nesting simulation from a meso-scale domain with a kilometre-scale resolution down to LES domains with metre-scale resolutions.

A problem related to the development of instability of a homogeneous state in an ensemble of screw dislocations under plastic deformation of metals is considered . The study of the development of instability and structure formation in the dislocation ensemble is carried out on the basis of the method developed for charged particles in plasma and associated with the correlation interaction of electrons and positively charged ions. Accordingly, the screw dislocation ensemble is represented as a system of dislocations with an opposite Burgers vector, i.e., as a plasma-like medium with opposite dislocation charges. The total dislocation charge of the dislocation ensemble is equal to zero due to the law of conservation of the Burgers vector. In this situation, the elastic field of dislocations is “cut off”. The stress field of a single dislocation is shielded by a uniformly distributed dislocation “background” and is characterized by a certain effective potential. It is found that at long distances it decreases exponentially. Therefore, the value in the argument of the falling potential can be considered as the radius of screening of the elastic field of dislocations. It is shown that the screening radius is equal to the correlation radius, which makes it possible to construct a two-particle correlation function and find the energy of the correlation interaction of dislocations. A system of kinetic equations for a dislocation ensemble is formulated, taking into account the elastic and correlation interaction of dislocations, as well as the processes of their generation and annihilation. The criterion of instability of the homogeneous distribution of dislocations for the formulated system of equations is established. The instability criterion is met under the condition that the dislocation density exceeds a certain critical value that depends on the square of the flow stress and material constants (such as the Burgers vector modulus and shear modulus, as well as indirectly, the packing defect energy). In the framework of linear analysis, it is shown that when one system of sliding screw dislocations is taken into account, a one – dimensional periodic dislocation dissipative structure is formed at the moment of instability occurrence, and when multiple sliding is taken into account, solutions appear in the form of various variants of polyhedral lattices (cellular structures). It is established that the characteristic size of the cellular structure coincides with the experimental dependence both qualitatively and quantitatively ( the cell size is proportional to the square root of the dislocation density, and the proportionality coefficient is about ten). It is shown that the origin of spatially inhomogeneous dislocation structures, based on correlation instability, depends mainly on the features of the elastic interaction of dislocations and is not critical to the choice of the mechanisms of their kinetics (i.e., the mechanisms of generation, annihilation, and runoff of dislocations).

The structure of the planar surface of colloidal solutions of amorphous 27-nm silica sol particles enriched with heavy K+, Rb+, and Cs+ alkali ions is studied by the methods of reflectometry and diffuse (nonspecular) scattering of synchrotron radiation. For liquid-phase systems, we have used a self-consistent approach that makes it possible to reconstruct from experimental data the electron density profiles perpendicular to the hydrosol surface, as well as the spectra of the height–height correlation function in the plane of the surface without using any a priori information about the near-surface structure. Analysis represented here shows that for high values of pH, alkali cations with a large radius and a surface concentration of (5 ± 1) × 1018 m–2 replace Na+ ions with a smaller radius. This result is in qualitative agreement with the dependence of the Kharkats–Ukstrup single-ion electrostatic free energy on the ion radius and in good quantitative agreement with the results obtained by other authors using the capillary-wave approach. The integrated value of the effective height of interface roughness (3.2 ± 0.5 A) coincides to within the measuring error with the prediction of the capillary-wave theory; however, the experimental spectra of the height-to-height correlation function basically differ from the theoretical spectra in the range of low spatial frequencies ν < 10–3 nm–1. The approximation of the spectra by the sum of two K-correlation distributions indicates a transition from the natural roughness of the compact layer of alkali metal ions to the capillary roughness of the liquid surface in the correlation length range of about 1 μm. In our opinion, the aggregate of available data indicates the dispersion of this layer into 2D clusters (Wigner islands).

The topology of density fluctuations on the surfaces of amorphous thin films prepared from solutions of some flexible-chain polymers has been studied based on electron microscopy data on submicron and micron scales. It is shown that the microphase-separation effects in the films become stronger with an increase in the initial solution concentrations due to self-organization of macromolecular aggregates (clusters): anisotropy, long-range order, and correlation length ξ of density fluctuations increase. The self-organization is completed with formation of an infinite cluster of particles with a periodically inhomogeneous density, which occupies ~30% of the film surface. The density–density correlation function of this cluster on the ~ξ scale is universal and independent of the polymer composition and molecular weight.

We prove a theorem describing the limiting fine-scale statistics of orbits of a point in hyperbolic space under the action of a discrete subgroup. Similar results have been proved only in the lattice case, with two recent infinite-volume exceptions by Zhang for Apollonian circle packings and certain Schottky groups. Our results hold for general Zariski dense, non-elementary, geometrically finite subgroups in any dimension. Unlike in the lattice case, orbits of geometrically finite subgroups do not necessarily equidistribute on the whole boundary of hyperbolic space. But rather, they may equidistribute on a fractal subset. Understanding the behaviour of these orbits near the boundary is central to Patterson-Sullivan theory and much further work. Our theorem characterizes the higher order spatial statistics and thus addresses a very natural question. As a motivating example our work applies to sphere packings (in any dimension) which are invariant under the action of such discrete subgroups. At the end of the paper we show how this statistical characterization can be used to prove convergence of moments and to write down the limiting formula for the two-point correlation function and nearest neighbor distribution. Moreover we establish an formula for the 2 dimensional limiting gap distribution (and cumulative gap distribution) which was not known previously even in the lattice case., 33 pages, 1 figure; Accepted for Publication in Mathematical Proceedings of the Cambridge Philosophical Society

We explain how the axioms of Conformal Field Theory are used to make predictions about critical exponents of continuous phase transitions in three dimensions, via a procedure called the conformal bootstrap. The method assumes conformal invariance of correlation functions, and imposes some relations between correlation functions of different orders. Numerical analysis shows that these conditions are incompatible unless the critical exponents take particular values, or more precisely that they must belong to a small island in the parameter space., Comment: 16 pages, 3 figures, accepted for publication by C.R.Physique

—The paper studies the features of the cross-correlation function of a chirp signal reflected from a rotating propeller with an emitted replica signal. In the obtained correlation function, in addition to the main peak corresponding to the propagation time of the signal to the scatterer and back, additional informative maxima are observed in the form of multiplets, the presence of which is determined by sound scattered by the rotating propeller. The parameters of the additional maxima depend on the diffuser characteristics (distance to the propeller, its rotation rate, number of blades, orientation relative to the direction of irradiation). The results of numerical simulation and experimental data processing are presented. The results point to the possibility of using additional correlation function peaks as an informative parameter to identify a rotating propeller.

Fluctuating hydrodynamics (FH) is one of the theories that describes the dynamics of the fluctuations for fluids at mesoscopic scales. However, it is only valid for Markovian processes. Here we extend this approach for a viscoelastic liquid by using a generalized Langevin equation (GLE). We obyain general analytic expressions for the density fluctuations correlation function, the dynamic structure factor and the light scattering spectrum. In particular, we calculate the intermediate scattering function when the time memory and the noise correlation function are power-laws. We find that the difference in values of this quantity as functions of the viscoelasticity may be ∼62% and might be measurable.

One of the standard methods used to measure the hydrodynamic diameter of nanoparticles is photon correlation spectroscopy, especially dynamic light scattering (DLS). In principle, this technique is to analyze correlation function of the scattered light from the nanoparticles undergoing Brownian motion in solution and to calculate the diffusion coefficient from the correlation function which is converted into the hydrodynamic diameter. However, when using this technique, one needs to pay careful attention to interaction effects (i.e., particle-particle and particle-solvent interactions) on the diffusion coefficient of the particles in solution. If not, then incorrect information can be obtained on the self-diffusion coefficients of nanoparticles. In order to facilitate a strict procedure for obtaining real size of the nanoparticles in solution, we used 20 nm, 50 nm and 100 nm-nominal polystyrene latex (PSL) nanoparticle solutions for DLS measurement. We represented that a rigorous scrutinizing the concentration dependence of the diffusion coefficient of the PSL nanoparticles made it possible to separate the interaction effect from the diffusion phenomena of the PSL nanoparticles suspended in water and to give real size of the PSL nanoparticles.

Low embankment strategy is one of the effective methods to control time-dependent settlement of soft soils in infrastructure construction projects. Spatial variability of soil characteristics is a crucial factor, affecting the reliability of predictions of the long-term settlement in soft soils. In this paper, the time-dependent behaviour of soft soils is analysed incorporating spatial variability of elastic visco-plastic model parameters. Standard Gaussian random fields for correlated elastic-plastic model parameter ( λ / V ) and the initial creep coefficient ( ψ 0 / V ) are generated adopting Karhunen-Loeve expansion method based on the spectral decomposition of correlation function into eigenvalues and eigenfunctions. Then the generated random fields are incorporated in the proposed non-linear elastic visco-plastic (EVP) creep model. The impacts of spatially variable elastic visco-plastic model parameters (i.e. ψ 0 / V and λ / V ) on long-term settlement predictions are evaluated through random field analysis (RF) with different spatial correlation lengths, and results are then compared to a single random variable (SRV) analysis. The probability of failure (PF) is calculated adopting RF and SRV analysis to determine the critical spatial correlation length, resulted in a maximum probability of failure. This study can be employed by design engineers to determine the critical spatial correlation length for safe design in the absence of adequate data to determine the exact spatial correlation length. The results also confirm that SRV analysis is not always the most conservative analysis in predicting time-dependent settlement of soft soils; and it is essential to perform RF analysis considering the spatial correlation length to reduce the risk and increase the reliability of the design to be applied in construction.

We consider the extinction regime in the spatial stochastic logistic model in R d (a.k.a. Bolker–Pacala–Dieckmann–Law model of spatial populations) using the first-order perturbation beyond the mea...

Modeling a mineral microstructure accurately in three dimensions can render realistic mineralogical patterns which can be used for three-dimensional processing simulations and calculation of three-dimensional mineral quantities. The present study introduces a flexible approach to model the microstructure of mineral material composed of a large number of facies. The common plurigaussian method, a valuable approach in geostatistics, can account for correlations within each facies and in principle be extended to correlations between the facies. Assuming stationarity and isotropy, founded on a new description of this model, formulas for first- and second-order characteristics, such as volume fraction, correlation function and cross-correlation function can be given by a multivariate normal distribution. In this particular situation, based on first- and second-order statistics, a fitting procedure can be developed which requires only numerical inversion of several one-dimensional monotone functions. The paper describes the whole workflow. The covariance structure is quickly obtained from two-dimensional particle pixel images using Fourier transform. Followed by model fitting and sampling, where the resulting three-dimensional microstructure is then efficiently represented by tessellations. The applicability is demonstrated for the three-dimensional case by modeling the microstructure from a Mineral Liberation Analyzer image data set of an andesitic basalt breccia.

The prediction of spin-lattice dynamics is a challenging computational and theoretical problem due to the complex interplay among atomic motion and spin interactions. Here, we employ machine-learning paradigms to generate a first-principles-accurate and computationally inexpensive model that predicts both conformational energy and spin Hamiltonian parameters of an organic radical as function of its molecular distortions. This model is applied to the study of the g tensor correlation function during molecular dynamics in solution and it is shown that it is possible to access the time dependence of the spin Hamiltonian parameters without making assumptions on the type of molecular motion or spin-lattice dynamics’ time-scales involved. We further use these approach to disentangle inter- and intra-molecular contributions to the g tensor correlation function and provide new insights into the nature of vibronic-coupling in organic semiconductors.

We study a nonclassical thermal state by repeatedly operating the number operator on normal thermal state. Then, we investigate the nonclassical features of this state according to the P-function, photon-number distribution, Mandel’s Q-parameter, second-order correlation function and negative Wigner distribution as well as squeezing properties. Our results show that this state presents nonclassical properties, such as sub-Poissonian statistics, anti-bunching effects and negative Wigner distribution, at low temperature with small parameter m, which is the number of times for the number operator operates on normal thermal state. However, the squeezing effect of this state is not found.

Systematic expressions of the cluster expansion for one and two-body terms of elastic form factors and charge densities for 1g-2d shell nuclei with N≠Z (such as: 42 92 Mo , 46 104 Pd , 50 118 Sn , 60 142 Nd , 62 152 Sm and 64 154 Gd ) are derived. Using the harmonic oscillator size parameter b and the correlation parameter β which creates from the Jastrow correlation function. Here, the parameters b and β are determined via the fitting to the experimental elastic form factors. The inserting of short-range correlations imitates the measured elastic form factors at the high momentum transfers (q ≥ 2 fm−1). It is seen that embedding this effect is important for obtaining an adjustment in the calculated elastic form factors which leads to defining the data of electron scattering well through all range of considered momentum transfers.