Two-point Correlation Research Articles

Where Do CABs Exist? Verification of a specific region containing concave Actin Bundles (CABs) in a 3-Dimensional confocal image.

CABs (Concave Actin Bundles) are oriented against the scaffold transversally in a manner different from traditional longitudinal F-actin bundles. CABs are present in a specific area, and do not exist in random areas. Biologically, CABs are developed to attach cells to fibers firmly so that CABs are found near cells. Based on this knowledge, we closely examined 3D confocal microcopy images containing fiber scaffolds, actin, and cells. Then, we assumed that the areas containing high values of compactness of fiber, compactness of actin, and density of cells would have many numbers of CABs.In this research, we wanted to prove this assumption. We first incorporated a two-point correlation function to define a measure of compactness. Then, we used the Bayes' theorem to prove the above assumption. As the assumption, our results verified that CABs exist in an area of high compactness of a fiber network, high compactness of actin distribution, and high density of cells. Thus, we concluded that CABs are developed to attach cells to a fibrillar scaffold firmly. This finding may be further verified mathematically in future studies.

Extraordinary-log Universality of Critical Phenomena in Plane Defects.

The recent discovery of the extraordinary-log (E-Log) criticality is a celebrated achievement in modern critical theory and calls for generalization. Using large-scale MonteCarlo simulations, we study the critical phenomena of plane defects in three- and four-dimensional O(n) critical systems. In three dimensions, we provide the first numerical proof for the E-Log criticality of plane defects. In particular, for n=2, the critical exponent q[over ^] of two-point correlation and the renormalization-group parameter α of helicity modulus conform to the scaling relation q[over ^]=(n-1)/(2πα), whereas the results for n≥3 violate this scaling relation. In four dimensions, it is strikingly found that the E-Log criticality also emerges in the plane defect. These findings have numerous potential realizations and would boost the ongoing advancement of conformal field theory.

Turbulent flow modification in the atmospheric surface layer over a dense city

Winds in the atmospheric surface layer (ASL) over distinctive urban morphology are investigated by building-resolved large-eddy simulation (LES). The exponential law is applied to urban canopy layers (UCLs) unprecedentedly to parameterize vertical profiles of mean-wind-speed u¯z and examine the influence of morphological factors. The skewness of streamwise velocity Su is peaked at the zero-plane displacement d (drag center) where flows decelerate mostly. The dynamics and intermittency in roughness sublayers (RSLs) are further contrasted. It helps determine the critical strength of the organized structures (ejection, Q2 and sweep Q4) in their contributions to the average momentum transport (i.e., 3<u”w”> to 5<u”w”>). Two key factors of the local-scale dynamics are revealed - building heterogeneity and upstream giant wakes that could amplify turbulence kinetic energy (TKE) and energetic intermittent Q4 by different mechanisms. The former is conductive for large-eddy generation that promotes vertical fluctuating velocity w”, stimulating intermittent, energetic Q2 and Q4. The latter, whose footprints are identified by the two-point correlation of streamwise velocity Ruu with specific size and inclination, facilitates intermittent, fast streamwise fluctuating velocity u”, forming vigorous Q4. Nevertheless, excessive planar density λp (≈ 0.7) is detrimental to both transport processes. These findings contribute to the theoretical and empirical wall models of large-scale roughness that help urban planners and policymakers to improve air quality.

The universe is worth 643 pixels: convolution neural network and vision transformers for cosmology

We present a novel approach for estimating cosmological parameters, Ω m , σ8 , w 0, and one derived parameter, S 8, from 3D lightcone data of dark matter halos in redshift space covering a sky area of 40° × 40° and redshift range of 0.3 < z < 0.8, binned to 643 voxels. Using two deep learning algorithms — Convolutional Neural Network (CNN) and Vision Transformer (ViT) — we compare their performance with the standard two-point correlation (2pcf) function. Our results indicate that CNN yields the best performance, while ViT also demonstrates significant potential in predicting cosmological parameters. By combining the outcomes of Vision Transformer, Convolution Neural Network, and 2pcf, we achieved a substantial reduction in error compared to the 2pcf alone. To better understand the inner workings of the machine learning algorithms, we employed the Grad-CAM method to investigate the sources of essential information in heatmaps of the CNN and ViT.Our findings suggest that the algorithms focus on different parts of the density field and redshift depending on which parameter they are predicting. This proof-of-concept work paves the way for incorporating deep learning methods to estimate cosmological parameters from large-scale structures, potentially leading to tighter constraints and improved understanding of the Universe.

The Blume–Emery–Griffiths Model on the FAD Point and on the AD Line

We analyse the Blume–Emery–Griffiths (BEG) model on the lattice Zd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Z}}^d$$\\end{document} on the ferromagnetic-antiquadrupolar-disordered (FAD) point and on the antiquadrupolar-disordered (AD) line. In our analysis on the FAD point, we introduce a Gibbs sampler of the ground states at zero temperature, and we exploit it in two different ways: first, we perform via perfect sampling an empirical evaluation of the spontaneous magnetization at zero temperature, finding a non-zero value in d=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=3$$\\end{document} and a vanishing value in d=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=2$$\\end{document}. Second, using a careful coupling with the Bernoulli site percolation model in d=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=2$$\\end{document}, we prove rigorously that under imposing +\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$+$$\\end{document} boundary conditions, the magnetization in the center of a square box tends to zero in the thermodynamical limit and the two-point correlations decay exponentially. Also, using again a coupling argument, we show that there exists a unique zero-temperature infinite-volume Gibbs measure for the BEG. In our analysis of the AD line we restrict ourselves to d=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=2$$\\end{document} and, by comparing the BEG model with a Bernoulli site percolation in a matching graph of Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Z}}^2$$\\end{document}, we get a condition for the vanishing of the infinite-volume limit magnetization improving, for low temperatures, earlier results obtained via expansion techniques.

Modulation instability of incoherent beams revisited.

We examine the spatial modulation instability (MI) of a partially incoherent laser beam. We show that the P < (a/rc)2P0 criterion of beam stability, with a laser peak power P, beam radius a, correlation radius rc, and critical power of self-focusing P0, is applicable only to a limited class of MIs, viz., MIs that can be described as instabilities of a pertinent transverse correlation function found as a solution to the evolution equation, where the expectation of the four-field-product nonlinear source term is factorized as a product of the field intensity and a two-point transverse correlation function. When extended to a more general class of MIs, field evolution analysis of partially coherent beams suggests that MIs can be attenuated, but never completely suppressed. We show that spatial incoherence can lower the MI-buildup rate, thus helping avoid MI-induced beam breakup in physical settings where the MI-buildup length lMI can be kept longer than the length of the nonlinear medium L. Because the lMI > L condition sets a limitation on the field intensity rather than the laser peak power, MI-induced beam breakup can be avoided, even at laser peak powers well above the critical power of self-focusing P0.

The Galaxy Number Density Profile of Halos

More precise measurements of galaxy clustering will be provided by the next generation of galaxy surveys, such as DESI, WALLABY, and the Square Kilometre Array. To utilize this information to improve our understanding of the Universe, we need to accurately model the distribution of galaxies in their host dark matter halos. In this work, we present a new galaxy number density profile of halos, which makes predictions for the positions of galaxies in the host halo, different to the widely adopted Navarro–Frenk–White (NFW) profile, since galaxies tend to be found more in the outskirts of halos (nearer the virial radius) than an NFW profile. The parameterized galaxy number density profile model of halos is fit and tested using the Dark Sage semi-analytic model of galaxy formation. We find that our galaxy number density profile model of halos can accurately reproduce the halo occupation distribution and galaxy two-point correlation function of the Dark Sage simulation. We also derive the analytic expressions for the circular velocity and gravitational potential energy for this profile model. We use the SDSS Data Release 10 galaxy group catalog to validate this galaxy number density profile model of halos. Compared to the NFW profile, we find that our model more accurately predicts the positions of galaxies in their host halo and the galaxy two-point correlation function.

Entanglement entropy in conformal quantum mechanics

We consider sets of states in conformal quantum mechanics associated to generators of time evolution whose orbits cover different regions of the time domain. States labelled by a continuous global time variable define the two-point correlation functions of the theory seen as a one-dimensional conformal field theory. Such states exhibit the structure of a thermofield double built on bipartite eigenstates of generators of non-global time evolution. In terms of the correspondence between radial conformal symmetries in Minkowski space-time and time evolution in conformal quantum mechanics proposed in [1, 2] these generators coincide with conformal Killing vectors tangent to worldlines of Milne and diamond observers at constant radius. The temperature of the thermofield double states in conformal quantum mechanics reproduces the temperatures perceived by such diamond and Milne observers. We calculate the entanglement entropy associated to the thermofield double states and obtain a UV divergent logarithmic behaviour analogous to known results in two-dimensional conformal field theory in which the entangling boundary is point-like.

Cosmology from LOFAR Two-metre Sky Survey Data Release 2: angular clustering of radio sources

ABSTRACT Covering $\sim 5600\, \deg ^2$ to rms sensitivities of ∼70−100 $\mu$Jy beam−1, the LOFAR Two-metre Sky Survey Data Release 2 (LoTSS-DR2) provides the largest low-frequency (∼150 MHz) radio catalogue to date, making it an excellent tool for large-area radio cosmology studies. In this work, we use LoTSS-DR2 sources to investigate the angular two-point correlation function of galaxies within the survey. We discuss systematics in the data and an improved methodology for generating random catalogues, compared to that used for LoTSS-DR1, before presenting the angular clustering for ∼900 000 sources ≥1.5 mJy and a peak signal-to-noise ≥ 7.5 across ∼80 per cent of the observed area. Using the clustering, we infer the bias assuming two evolutionary models. When fitting angular scales of $0.5 \le \theta \lt 5{^\circ }$, using a linear bias model, we find LoTSS-DR2 sources are biased tracers of the underlying matter, with a bias of $b_{\rm C}= 2.14^{+0.22}_{-0.20}$ (assuming constant bias) and $b_{\rm E}(z=0)= 1.79^{+0.15}_{-0.14}$ (for an evolving model, inversely proportional to the growth factor), corresponding to $b_{\rm E}= 2.81^{+0.24}_{-0.22}$ at the median redshift of our sample, assuming the LoTSS Deep Fields redshift distribution is representative of our data. This reduces to $b_{\rm C}= 2.02^{+0.17}_{-0.16}$ and $b_{\rm E}(z=0)= 1.67^{+0.12}_{-0.12}$ when allowing preferential redshift distributions from the Deep Fields to model our data. Whilst the clustering amplitude is slightly lower than LoTSS-DR1 (≥2 mJy), our study benefits from larger samples and improved redshift estimates.

Anisotropic strong lensing as a probe of dark matter self-interactions

ABSTRACT Galaxy-scale strongly lensed systems have been shown to provide a unique technique for exploring the underlying physics of dark matter at sub-galactic scales. In the past, much attention was given to detecting and studying individual haloes in a strong lens system. In addition to the subhaloes, line-of-sight haloes contribute significantly to the small perturbations in lensed images. In prior work, we demonstrated that these line-of-sight haloes imprint a distinctive anisotropic signature and hence give rise to a detectable non-zero parity-even quadrupole moment in the effective convergence field’s two-point correlation function. In this study, we show that these line-of-sight haloes also produce a non-zero curl component of the effective deflection field with a parity-odd quadrupole moment of the two-point function. These multipole moments have the ability to statistically separate line-of-sight haloes from dark matter substructure. In this paper, we examine how these multipole moments evolve in the presence of warm dark matter and self-interacting dark matter in terms of central density evolution and dark matter halo abundance. Importantly, we show that these different multipole moments display exquisite sensitivity to both the amplitude and the velocity dependence of the dark matter self-interaction cross-section. Our approach opens the door for strong lensing observations to probe dark matter self-interaction over a broad range of relative velocities.

Thermalization in quenched open quantum cosmology

In this article, we study the quantum field theoretic generalization of the Caldeira-Leggett model in general curved space-time considering interactions between two scalar fields in a classical gravitational background. The thermalization phenomena is then studied from the obtained de Sitter solution using quantum quench from one scalar field model obtained from path integrated effective action. We consider an instantaneous quench in the time-dependent mass protocol of the field of our interest. We find that the dynamics of the field post-quench can be described in terms of the state of the generalized Calabrese-Cardy (gCC) form and computed the different types of two-point correlation functions in this context. We explicitly found the conserved charges of W∞ algebra that represents the gCC state after a quench in de Sitter space and found it to be significantly different from the flat space-time results. We extend our study for the different two-point correlation functions not only considering the pre-quench state as the ground state, but also a squeezed state. We found that irrespective of the pre-quench state, the post quench state can be written in terms of the gCC state showing that the subsystem of our interest thermalizes in de Sitter space. Furthermore, we provide a general expression for the two-point correlators and explicitly show the thermalization process by considering a thermal Generalized Gibbs ensemble (GGE). Finally, from the equal time momentum dependent counterpart of the obtained results for the two-point correlators, we have studied the hidden features of the power spectra and studied its consequences for different choices of the quantum initial conditions.

Local turbulence generation using conditional generative adversarial networks toward Reynolds-averaged Navier–Stokes modeling

Data-driven turbulence modeling has been extensively studied in recent years. To date, only high-fidelity data from the mean flow field have been used for Reynolds-averaged Navier–Stokes (RANS) modeling, while the instantaneous turbulence fields from direct numerical simulation and large eddy simulation simulations have not been utilized. In this paper, a new framework is proposed to augment machine learning RANS modeling with features extracted from instantaneous turbulence flow data. A conditional generative model is trained to model the probability distribution of the local instantaneous turbulence field given local mean flow features. Then, the generative model is transferred to machine learning RANS modeling. The present work is mainly focused on generating a local instantaneous turbulence field using conditional generative adversarial networks (CGANs). Several GANs are trained first on the turbulence data from channel flow and periodic hill flow to generate complete one-dimensional and two-dimensional turbulence fields. Then, a CGAN is trained on the periodic hill flow data to generate local turbulence fields. Statistical analysis is performed on the generated samples from the GAN models. The first and second moments, the two-point correlation, and the energy spectra conform well to those of real turbulence. Finally, the information learned by the CGAN is used for machine learning RANS modeling by multitask learning, and the feasibility of the framework proposed in this paper is initially verified.

Influence of hemisphere disturbance on laminar boundary layer at low Reynolds numbers

We experimentally investigate the two-dimensional flow characteristics caused by hemisphere disturbance in the laminar boundary layer, with the aim of analyzing the periodic vortex structures generated by the hemisphere at different freestream velocities. For flow fields with Reynolds numbers of ReD= 1919, 2386, and 2819, instantaneous snapshots of the streamwise–wall-normal plane and streamwise–spanwise plane are acquired by time-resolved particle image velocimetry. The velocity distribution near the hemisphere model in the laminar flow state and the conditions for the generation of periodic structures are discussed. Strong shear occurs in the dense area of velocity contours, including a stable horizontal shear layer and inclined shear layer of shedding vortex structures, and the Reynolds shear stress attains a local maximum. The feasibility of three frequency extraction methods for hemisphere disturbance is also compared, and the periodic structures corresponding to each frequency are analyzed in detail. At higher values of ReD, the disordered flow field is formed by a multi-frequency superposition. Spatial two-point cross correlation analysis, which can be regarded as a flow visualization of frequency spectrum analysis, illustrates that the correlation and periodicity of the coherent structures are strongest in the inclined shear layer. Spectral proper orthogonal decomposition appears to be more effective in capturing periodic information about the streamwise–spanwise plane of the hemisphere disturbance. The three frequency extraction methods show that with an increase in ReD gradually transforms the periodic vortex structures from a single frequency state to a multi-frequency superposition state.

Large-eddy simulation of turbulent channel flows with antifouling-featured bionic microstructures

The large-eddy simulation of a shark skin surface at Reynolds numbers of Reτ=1200, 2400, and 4500 is carried out in a fully turbulent flow channel to investigate the antifouling mechanism of shark skin from the perspective of hydrodynamics. The antifouling properties are validated through the confocal laser scanning microscopy of microorganism settlement and a measurement of the reduction in pollutant mass. A large-eddy simulation database is then analyzed, focusing on mean and turbulent statistics, to explain the flow characteristics of time-varying fields of the flow that surrounds and skims over the shark skin. A phenomenological scenario based on instantaneous visualizations of vortical events using the Q-criterion is put forward to identify the spatiotemporal evolution of turbulent coherent structures in the outer region. Subsequently, the proposed scenario is accessed by analyzing two-point correlation coefficients, the conditional averaging of vortical events, the wall friction coefficient distribution, and the spatiotemporal evolution of vortices. The flow patterns are predominantly driven by the periodic emission of hairpin-type vortices, which form a strong shear layer and exacerbate shear stress and momentum exchange. Furthermore, these vortices are associated with the generation of a bicyclical system involving an unsteady propagation of turbulent fluids, which develops separately near the front and back of each shark scale. These modes elaborate the antifouling mechanism of shark skin. Analysis of the probability density function and the spatiotemporal map reveals that these strong events have high levels of intermittency in time and space, which vitally contributes to the antifouling properties manifested in the evolution of periodic shear friction over different surfaces.

Multi-GPU lattice Boltzmann simulations of turbulent square duct flow at high Reynolds numbers

Based on the multi-GPU lattice Boltzmann method with the half-way bounce-back scheme, fully developed turbulent duct flows at the friction Reynolds numbers Reτ of 300, 600, 1,200, 1,500, 1,800, and 2,000 were simulated. The parallel performance of multi-GPU lattice Boltzmann simulations is up to 300.162 GLUPS using 1.57 billion grids with 384 GPUs. The simulated friction factor f was consistent with other DNS and experiment results, as well as the Karman–Prandtl theoretical friction law, which verified a sufficient grid resolution Δ+≤3.3, and the LBGK model is stable for Δ+≤5 at high Reynolds numbers. The secondary flows were successfully captured, and turbulence statistics of root-mean-square (r.m.s.) velocity and Reynolds stress were analyzed. The two-point velocity correlation functions and turbulent energy spectra at different positions showed that secondary flows in the near-corner region changed spatial turbulence distribution. Multi-GPU lattice Boltzmann simulations with large grid scales can deal with turbulent square duct flows at high Reynolds numbers and show promise for high-fidelity and scale-resolving fluid dynamics.

A numerical study of two-point correlation functions of the two-periodic weighted Aztec diamond in mesoscopic limit

A numerical study of two-point correlation functions of the two-periodic weighted Aztec diamond in mesoscopic limit

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.

A deep adversarial approach for the generation of synthetic titanium alloy microstructures with limited training data

Microstructures play a central role in determining the mechanical and functional properties of a material. An important aspect in computational materials science is to reliably predict the key microstructural features, and to utilise them in bridging the processing and properties of new materials. The existing microstructure characterization and reconstruction (MCR) techniques have inherent limitations in terms of the lack of design variables and information loss due to various assumptions. In previous studies, Generative Adversarial Network (GAN) models were trained using more than 10,000 image datasets, however without performance analysis using quantitative morphometric and statistical measures. In this perspective, the present work demonstrates the capability of GAN architectures to learn the mapping between random latent vectors and synthetic microstructural images, even in a limited data regime (1225 images). Three different architectures Deep Convolutional GAN (DCGAN) ,Wasserstein GAN- Gradient Penalty (WGAN-GP), StyleGAN2- Adaptive Discriminator Augmentation (ADA) were explored, together with comprehensive statistical and morphological analysis, while training on a publicly accessible Ti-6Al-4V (Ti64) alloy microstructure dataset. The StyleGAN2-ADA outperforms the other two GAN models to generate realistic synthetic microstructures of higher resolution, with good qualitative similarity to original images. The analysis of performance metrics, like Frechet Inception Distance (FID), Kernel Inception Distance (KID), and Inception Score (IS) scores, reveal that the generated image distribution is statistically close to the original distribution of microstructural features. The morphometric parameters, including α/β phase fractions, local α/β boundary thickness, and orientation of lamellar morphology, were also used to compare original and synthetic images quantitatively. More importantly, two-point correlation and t-stochastic neighbour embedding (t-SNE) illustrate the statistical similarity between the original and synthetic microstructures. Taken together, the present work establishes the capability of generative models like GAN in generating representative microstructures of Titanium alloy in a statistically reliable manner. Such an approach, when adopted, will accelerate the field of microstructure fingerprinting.

Glass-like random catalogues for two-point estimates on the light-cone

ABSTRACT We introduce grlic, a publicly available Python tool for generating glass-like point distributions with a radial density profile n(r) as it is observed in large-scale surveys of galaxy distributions on the past light-cone. Utilizing these glass-like catalogues, we assess the bias and variance of the Landy–Szalay (LS) estimator of the first three two-point correlation function (2PCF) multipoles in halo and particle catalogues created with the cosmological N-body code gevolution. Our results demonstrate that the LS estimator calculated with the glass-like catalogues is biased by less than 10−4 with respect to the estimate derived from Poisson-sampled random catalogues, for all multipoles considered and on all but the smallest scales. Additionally, the estimates derived from glass-like catalogues exhibit significantly smaller standard deviation σ than estimates based on commonly used Poisson-sampled random catalogues of comparable size. The standard deviation of the estimate depends on a power of the number of objects NR in the random catalogue; we find a power law $\sigma \propto N_\mathit{R}^{-0.9}$ for glass-like catalogues as opposed to $\sigma \propto N_\mathit{R}^{-0.48}$ using Poisson-sampled random catalogues. Given a required precision, this allows for a much reduced number of objects in the glass-like catalogues used for the LS estimate of the 2PCF multipoles, significantly reducing the computational costs of each estimate.

Effective diffusivity of hardened cement paste from 3D microstructures: A critical comparison of real and virtual microstructures

This study compares experimentally obtained hardened cement paste microstructures from μCT and virtual microstructures generated by two hydration models, namely CEMHYD3D and HYMOSTRUC. Several microstructural features (phase volume fractions, connectivity, pore size distribution, and two-point correlation functions) were cross-validated among the microstructures on the basis of image analysis. In addition, the corresponding effective diffusivities in a fully saturated state were compared. The simulated effective diffusivities of the μCT and CEMHYD3D microstructures agree well with the experimental data, where HYMOSTRUC overestimates. However, none of the virtual microstructures can fully capture the actual microstructural features. HYMOSTRUC produces realistic pore size distributions but overly connected capillary pores, whereas CEMHYD3D generates excessive scattering of small pores with low connectivity. The impact of the differences in the pore structure on the output diffusivity is presented.