Two-point Function Research Articles

On the acoustic wedge absorber design in underwater and its interior pressure computation in a chamber

This study presents a design of wedged shape absorber used in underwater in range of high frequency. The analysis of a set of periodical wedges, where each wedge is oriented 90 deg with other wedges. The set of periodical wedges is analyzed using finite element methods as a 3-D virtual impedance tube. The incident wave is on the normal direction of the tube. This 3-D model is able to simplify to a simple 2-D model and a two-point transfer function method is employed to compute reflection coefficient. The ation of frequencies higher than the cut-off plane wave frequency is addressed of that higher duct acoustic modes are excited by the wedge. These higher modes are recognized as stationary non-propagating waves, not contributing reflected waves away from the wedge. An impedance value associated with the reflection coefficient is identified based on plane wave condition. The impedance value is applied to surfaces of a closed space to computed interior pressures.

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.

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.

Protected and uniformly transcendental

We show that the two-point function of protected bi-scalar operators in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM evaluated in dimensional regularization exhibits a uniform transcendental weight up to three-loop order. We conjecture that this property holds for the whole perturbative series and leverage the explicit results to postulate a prediction for the leading, order ϵ, correction to all loop orders. We also consider the soft limit of three-point functions of such operators in momentum space and point out a simple and surprising perturbative relation to two-point functions, which we also extrapolate to all loop orders.

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.

Foliated asymptotically safe gravity in the fluctuation approach

The gravitational asymptotic safety program envisions a high-energy completion of gravity based on a non-Gaussian renormalization group fixed point. A key step in this program is the transition from Euclidean to Lorentzian signature spacetimes. One way to address this challenge is to formulate the quantum theory based on the Arnowitt-Deser-Misner decomposition of the metric field. This equips the Euclidean spacetime with a preferred direction which may serve as the time-direction in the Lorentzian setting. In this work we use the Wetterich equation in order to compute the renormalization group flow of the graviton two-point function. The resulting beta functions possess a non-Gaussian renormalization group fixed point suitable for rendering the theory asymptotically safe. The phase diagram underlying the flow of the two-point function is governed by the interplay between this non-Gaussian fixed point, the Gaussian fixed point, and an infrared fixed point. The latter ensures that the renormalized squared graviton mass cannot take negative values. These results are in qualitative agreement with fluctuation computations carried out in the covariant setting. We take this as non-trivial evidence that the asymptotic safety mechanism remains intact when considering quantum gravity on spacetimes carrying a foliation structure. Technically, our work constitutes the first fluctuation computation carried out within the ADM-framework. Therefore, we also provide a detailed discussion of the conceptual framework, highlighting the elements which differ from fluctuation computations in the covariant setting.

Microstructure quantification of oblique angle sputtered porous a-Si thin films as a basis for structure-property relations of solid phase microextraction coatings

Understanding processing-structure-property (PSP) linkages of solid-phase microextraction (SPME) coating materials is crucial for the rational design and advancement of these new materials. As SPME is a diffusion-based extraction technique, analyzing the morphology of its coating materials is important for optimizing its performance. In this study, we assess the morphological evolution of micro/mesoporous amorphous silicon (a-Si) thin films sputtered at an oblique angle onto silicon, which serve as models for support materials in SPME devices. The contrast of scanning transmission electron microscopy (STEM) images is enhanced via ZnO infiltration by atomic layer deposition (ALD). Various metrics, including physical descriptors and two-point statistics methods, are employed to follow the films' evolution. Analysis of the two-point correlation function reveals a simple ellipse/spherical local pore geometry in contrast to the long-range irregular arrangement of pores identified by a range of traditional and novel metrics. Additionally, analyzing the internal structure of the pores through homology metrics aligns well with the theoretical understanding of morphological evolution in oblique sputtered films. These analyses show that the “average ratio of principal moment of inertia”, “Betti numbers”, and “two-point statistics” based metrics can capture valuable information during film growth.The morphological analysis approach proposed in this study can be applied to analyze any nanoporous medium as a first step towards developing structure-property relationships that tie back to a given preparation method. Ultimately, a more extensive experimental and/or simulation-based study should confirm the correlations between these metrics and actual diffusion properties as the basis for process-structure-properties relations for improved design and optimization of this film.

Deterministic vortices evolving from partially coherent fields

Optical vortices—lines of zero intensity around which the field phase has a circulating or helical structure—have become important tools for many applications such as imaging, trapping, and communications. It has long been assumed, however, that there is an intrinsic conflict between optical vortices and partial coherence, in that a vortex is a deterministic phase structure, and a partially coherent field has a randomly fluctuating phase. In most cases, a vortex imposed on a partially coherent field evolves into a singularity of the two-point correlation function. We demonstrate, however, that it is possible to construct a beam that has no deterministic vortices in the source plane yet evolves such a deterministic vortex at a specified propagation distance.

Information loss, mixing and emergent type III1 factors

A manifestation of the black hole information loss problem is that the two-point function of probe operators in a large Anti-de Sitter black hole decays in time, whereas, on the boundary CFT, it is expected to be an almost periodic function of time. We point out that the decay of the two-point function (clustering in time) holds important clues to the nature of observable algebras, states, and dynamics in quantum gravity.We call operators that cluster in time “mixing” and explore the necessary and sufficient conditions for mixing. The information loss problem is a special case of the statement that in type I algebras, there exists no mixing operators. We prove that, in a thermofield double state (KMS state), if mixing operators form an algebra (close under multiplication), the resulting algebra must be a von Neumann type III1 factor. In other words, the physically intuitive requirement that all nonconserved operators should exponentially mix is so strong that it fixes the observable algebra to be an exotic algebra called a type III1 factor. More generally, for an arbitrary out-of-equilibrium state of a general quantum system (von Neumann algebra), we show that if the set of operators that mix under modular flow forms an algebra, it is a type III1 von Neumann factor.In a theory of Generalized Free Fields (GFF), we show that if the two-point function clusters in time, all operators are mixing, and the algebra is a type III1 factor. For example, in \U0001d4a9 = 4 SYM, above the Hawking-Page phase transition, clustering of the single trace operators implies that the algebra is a type III1 factor, settling a recent conjecture of Leutheusser and Liu. We explicitly construct the C∗-algebra and von Neumann subalgebras of GFF associated with time bands and, more generally, open sets of the bulk spacetime using the HKLL reconstruction map.

A novel machine learning approach for surface roughness quantification and optimization of cast-on-strap lead-antimony alloy via two-point correlation function

Surface roughness has a negative impact on the materials’ lifetime. It accelerates pitting corrosion, increases effective heat transfer, and increases the rate of effective charge loss. However, controlled surface roughness is desirable in many applications. The automotive lead-acid battery is very sensitive to such effects. In our case study, the cast-on-strap machine has the largest effect on the surface roughness of the lead-antimony alloy. In this regard, statistical correlation functions are commonly used as statistical morphological descriptors for heterogeneous correlation functions. Two-point correlation functions are fruitful tools to quantify the microstructure of two-phase material structures. Herein, we demonstrate the use of the two-point correlation function to quantify surface roughness and optimize lead-antimony poles and straps used in the lead-acid battery as a solution to reduce their electrochemical corrosion when used in highly corrosive media. However, we infer that this method can be used in surface roughness mapping in a wide range of applications, such as pipes submerged in seawater as well as laser cutting. The possibility of using information obtained from the two-point correlation function and applying the simulated annealing procedure to optimize the surface micro-irregularities is investigated. The results showed successful surface representation and optimization that agree with the initially proposed hypothesis.

3D-porous-GAN: a high-performance 3D GAN for digital core reconstruction from a single 3D image

The 3D digital rock technology is extensively utilized in analyzing rock physical properties, reservoir modeling, and other related fields. This technology enables the visualization, quantification, and analysis of microstructures in rock cores, leading to precise predictions and optimized designs of reservoir properties. Although the accuracy of 3D digital rock reconstruction algorithms based on physical experiments is high, the associated acquisition costs and reconstruction processes are expensive and complex, respectively. On the other hand, the 3D digital rock random reconstruction method based on 2D slices is advantageous in terms of its low cost and easy implementation, but its reconstruction effect still requires significant improvement. This article draws inspiration from the Concurrent single-image generative adversarial network and proposes an innovative algorithm to reconstruct 3D digital rock by improving the generator, discriminator, and noise vector in the network structure. Compared to traditional numerical reconstruction methods and generative adversarial network algorithms, the method proposed in this paper is shown to achieve good agreement with real samples in terms of Dykstra-Parson coefficient, porosity, two-point correlation function, Minkowski functionals, and visual display.

Two-point functions and constant mean curvature surfaces in ℝ3

Two-point functions and constant mean curvature surfaces in ℝ3

Correlation functions in textrm{T}overline{textrm{T}} -deformed Conformal Field Theories

We study the correlation functions of local operators in unitary textrm{T}overline{textrm{T}} -deformed field theories, using their formulation in terms of Jackiw-Teitelboim gravity. The position of the operators is defined using the dynamical coordinates of this formalism. We focus on the two-point correlation function in momentum space, when the undeformed theory is a conformal field theory. In particular, we compute the large momentum behavior of the correlation functions, which manifests the non-locality of the textrm{T}overline{textrm{T}} -deformed theory. The correlation function has UV-divergences, which are regulated by a point-splitting regulator. Renormalizing the operators requires multiplicative factors depending on the momentum, unlike the behavior in local QFTs. The large momentum limit of the correlator, which is the main result of this paper, is proportional to {left|qright|}^{-frac{q^2}{pi left|Lambda right|}} , where q is the momentum and 1/|Λ| is the deformation parameter. Interestingly, the exponent here has a different sign from earlier results obtained by resummation of small q computations. The decay at large momentum implies that the operators behave non-locally at the scale set by the deformation parameter.

Conformal dispersion relations for defects and boundaries

We derive a dispersion relation for two-point correlation functions in defect conformal field theories. The correlator is expressed as an integral over a (single) discontinuity that is controlled by the bulk channel operator product expansion (OPE). This very simple relation is particularly useful in perturbative settings where the discontinuity is determined by a subset of bulk operators. In particular, we apply it to holographic correlators of two chiral primary operators in \mathcal{N}=4𝒩=4 Super Yang-Mills theory in the presence of a supersymmetric Wilson line. With a very simple computation, we are able to reproduce and extend existing results. We also propose a second relation, which reconstructs the correlator from a double discontinuity, and is controlled by the defect channel OPE. Finally, for the case of codimension-one defects (boundaries and interfaces) we derive a dispersion relation which receives contributions from both OPE channels and we apply it to the boundary correlator in the O(N) critical model. We reproduce the order \epsilon^2ϵ2 result in the \epsilonϵ-expansion using as input a finite number of boundary CFT data.

The formation of supermassive black holes from Population III.1 seeds. II. Evolution to the local universe

ABSTRACT We present predictions for cosmic evolution of populations of supermassive black holes (SMBHs) forming from Population III.1 seeds, i.e. early, metal-free dark matter minihaloes forming far from other sources, parametrized by isolation distance, diso. Extending previous work that explored this scenario to z = 10, we follow evolution of a $(60\, {\rm {Mpc}})^3$ volume to z = 0. We focus on evolution of SMBH comoving number densities, halo occupation fractions, angular clustering, and 3D clustering, exploring a range of diso constrained by observed local number densities of SMBHs. We also compute synthetic projected observational fields, in particular, a case comparable to the Hubble Ultra Deep Field. We compare Pop III.1 seeding to a simple halo mass threshold model, commonly adopted in cosmological simulations of galaxy formation. Major predictions of the Pop III.1 model include that all SMBHs form by z ∼ 25, after which their comoving number densities are near-constant, with low merger rates. Occupation fractions evolve to concentrate SMBHs in the most massive haloes by z = 0, but with rare cases of SMBHs in haloes down to $\sim 10^8\, M_\odot$. The diso scale at epoch of formation, e.g. $100\,$kpc-proper at z ∼ 30, i.e. $\sim 3\,$Mpc-comoving, is imprinted in the SMBH two-point angular correlation function, remaining discernible as a low-amplitude feature to z ∼ 1. The SMBH 3D two-point correlation function at z = 0 also shows lower amplitude compared to equivalently massive haloes. We discuss prospects for testing these predictions with observational surveys of SMBH populations.

Statistical anisotropy in galaxy ellipticity correlations

As well as the galaxy number density and peculiar velocity, the galaxy intrinsic alignment can be used to test the cosmic isotropy. We study distinctive impacts of the isotropy breaking on the configuration-space two-point correlation functions (2PCFs) composed of the spin-2 galaxy ellipticity field. For this purpose, we build a formalism for general types of the isotropy-violating 2PCFs and a methodology to efficiently compute them by generalizing the polypolar spherical harmonic decomposition approach to the spin-weighted version. As a demonstration, we analyze the 2PCFs when the matter power spectrum has a well-known g *-type isotropy-breaking term (induced by, e.g., dark vector fields). We then confirm that some anisotropic distortions indeed appear in the 2PCFs and their shapes rely on a preferred direction causing the isotropy violation, d̂. Such a feature can be a distinctive indicator for testing the cosmic isotropy. Comparing the isotropy-violating 2PCFs computed with and without the plane parallel (PP) approximation, we find that, depending on d̂, the PP approximation is no longer valid when an opening angle between the directions towards target galaxies is 𝒪(1°) for the density-ellipticity and velocity-ellipticity cross correlations and around 10° for the ellipticity auto correlation. This suggests that an accurate test for the cosmic isotropy requires the formulation of the 2PCF without relying on the PP approximation.

Tomographic Alcock–Paczyński Test with Redshift-space Correlation Function: Evidence for the Dark Energy Equation-of-state Parameter w > −1

The apparent shape of galaxy clustering depends on the adopted cosmology used to convert observed redshift to comoving distance, the r(z) relation, as it changes the line elements along and across the line of sight differently. The Alcock–Paczyński (AP) test exploits this property to constrain the expansion history of the universe. We present an extensive review of past studies on the AP test. We adopt an extended AP test method introduced by Park et al., which uses the full shape of redshift-space two-point correlation function (CF) as the standard shape, and apply it to the Sloan Digital Sky Survey DR7, BOSS, and eBOSS LRG samples covering the redshift range up to z = 0.8. We calibrate the test against the nonlinear cosmology-dependent systematic evolution of the CF shape using Multiverse simulations. We focus on examining whether or not the flat Lambda cold dark matter (ΛCDM) concordance model is consistent with observation. We constrain the flat wCDM model to have and from our AP test alone, which is significantly tighter than the constraints from the BAO or SNe Ia methods by a factor of 3–6. When the AP test result is combined with the recent BAO and SNe Ia results, we obtain and . This puts a strong tension with the flat ΛCDM model with w = −1 at the 4.2σ level. Consistency with w = −1 is obtained only when the Planck cosmic microwave background (CMB) observation is combined. It remains to be seen whether this tension between observations of galaxy distribution at low redshifts and CMB anisotropy at the decoupling epoch becomes greater in future studies and leads us to a new paradigm of cosmology.

Factorization of density matrices in the critical RSOS models

We study reduced density matrices of the integrable critical restricted solid-on-solid (RSOS) model in a particular topological sector containing the ground state. Similar as in the spin- Heisenberg model it has been observed that correlation functions of this model on short segments can be ‘factorized’: they are completely determined by a single nearest-neighbour two-point function ω and a set of structure functions. While ω captures the dependence on the system size and the state of the system the structure functions can be expressed in terms of the possible operators on the segment, in the present case representations of the Temperley–Lieb algebra , and are independent of the model parameters. We present explicit results for the function ω in the infinite system ground state of the model and compute multi-point local height probabilities for up to four adjacent sites for the RSOS model and the related three-point correlation functions of non-Abelian anyons.