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Digital rock physics (DRP) has been widely used as an effective approach for estimating the permeability of porous media. However, conventional implementation of DRP requires the reconstruction of three-dimensional (3D) pore networks, which suffer from intensive memory and underlying uncertainties. Therefore, it is highly significant to develop an approach only based on two-dimensional (2D) cross-sections of parent samples without 3D reconstruction. In this study, we present a novel approach that combines the Kozeny–Carman equation with fractal theory to derive a bridge function that links 2D cross-sectional images and 3D pore structures of parent samples in flow equivalence. Using this bridge function, we predicted the physical properties of the parent samples, including the permeability, bulk porosity, tortuosity, and pore fractal dimension. To validate our model, we performed Lattice Boltzmann (LB) simulations on nine carbonate samples and compared the LB simulation results with our model's predictions. We also compared our predicted results with available data on various porous materials, such as sandstone, glass beads, and carbonate, in the literature. Our findings demonstrate that without reconstructing 3D pore networks, our method provides a reliable estimation of sample permeability using 2D cross-sectional images. This approach not only simplifies the determination of sample permeability in heterogeneous porous media but also sheds new light on the inherent correlations between 2D cross-sectional information and 3D pore structures of parent samples. Moreover, the derived model may be conducible to a better understanding of flow in reservoirs during the extraction of unconventional onshore and offshore oil/gas. [ABSTRACT FROM AUTHOR]

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Digital rock physics (DRP) has been widely used as an effective approach for estimating the permeability of porous media. However, conventional implementation of DRP requires the reconstruction of three-dimensional (3D) pore networks, which suffer from intensive memory and underlying uncertainties. Therefore, it is highly significant to develop an approach only based on two-dimensional (2D) cross-sections of parent samples without 3D reconstruction. In this study, we present a novel approach that combines the Kozeny–Carman equation with fractal theory to derive a bridge function that links 2D cross-sectional images and 3D pore structures of parent samples in flow equivalence. Using this bridge function, we predicted the physical properties of the parent samples, including the permeability, bulk porosity, tortuosity, and pore fractal dimension. To validate our model, we performed Lattice Boltzmann (LB) simulations on nine carbonate samples and compared the LB simulation results with our model’s predictions. We also compared our predicted results with available data on various porous materials, such as sandstone, glass beads, and carbonate, in the literature. Our findings demonstrate that without reconstructing 3D pore networks, our method provides a reliable estimation of sample permeability using 2D cross-sectional images. This approach not only simplifies the determination of sample permeability in heterogeneous porous media but also sheds new light on the inherent correlations between 2D cross-sectional information and 3D pore structures of parent samples. Moreover, the derived model may be conducible to a better understanding of flow in reservoirs during the extraction of unconventional onshore and offshore oil/gas.

Latent Gaussian copula models provide a powerful means to perform multi-view data integration since these models can seamlessly express dependencies between mixed variable types (binary, continuous, zero-inflated) via latent Gaussian correlations. The estimation of these latent correlations, however, comes at considerable computational cost, having prevented the routine use of these models on high-dimensional data. Here, we propose a new computational approach for estimating latent correlations via a hybrid multilinear interpolation and optimization scheme. Our approach speeds up the current state of the art computation by several orders of magnitude, thus allowing fast computation of latent Gaussian copula models even when the number of variables p is large. We provide theoretical guarantees for the approximation error of our numerical scheme and support its excellent performance on simulated and real-world data. We illustrate the practical advantages of our method on high-dimensional sparse quantitative and relative abundance microbiome data as well as multi-view data from The Cancer Genome Atlas Project. Our method is implemented in the R package mixedCCA, available at . [ABSTRACT FROM AUTHOR]

Different advanced bridge function closures are utilized to investigate the structural and thermodynamic properties of dense Yukawa one‐component plasma liquids within the framework of integral equation theory. The isomorph‐based empirically modified hypernetted‐chain, the variational modified hypernetted‐chain, the Rogers–Young, and the Ballone–Pastore–Galli–Gazzillo approaches are compared at the level of thermodynamic properties, radial distribution functions, and bridge functions. The comparison, based on accuracy and computational speed, concludes that the two modified hypernetted‐chain approaches are superior and singles out the isomorph‐based variant as the most promising alternative to computer simulations of structural properties of dense Yukawa liquids. The possibility of further improvement through artificial crossover to exact asymptotic limits is studied. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the definition of Neutrosophic sets and present a method for extending crisp functions on Neutrosophic sets and study some properties of such extended functions.

Pore structure is a crucial attribute in characterizing fluid flow through porous media. However, direct experimental measurements or numerical reconstructions are commonly expensive and not environmentally friendly, with great uncertainty caused by the complex nature of porous media. In this study, we demonstrate that one special bridge function, which is a function of the apparent length and tortuosity fractal dimension, can characterize the relationship of pore structures between two dimensions (2‐D) and three dimensions (3‐D), and it can serve as a conversion bridge of the radius to determine the capillary pressure curve (CPC). We compare estimations by the proposed method with experimental results obtained by mercury intrusion porosimetry in six typical natural sandstones with varying porosities and permeabilities. The result shows that cross sections of the global pore structure, such as thin section, electronic probe, and microcomputed tomography slices, give a reliable estimation of the CPC using the bridge function in porous media with a medium porosity. However, in unconventional porous media with a relatively low porosity (~10%) or extra high porosity (~30%), due to the empirical nature of the equation widely used to calculate the tortuosity fractal dimension, the necessary modification is necessary to obtain the CPC when applying the bridge function in such porous media. This insight can significantly simplify the procedure for obtaining the petrophysical properties of a porous medium, which may shed light on the inherent differences and correlations between the 2‐D and 3‐D pore structures of porous media. Key Points: One special bridge function can characterize the relationship of pore structures between 2‐D and 3‐D, serving as a bridge of 2‐D ‐to‐3‐DThe calculated capillary pressure curve by 2‐D cross section shows a good correspondence with experimental data for natural porous mediaThis study can be an important stepping stone for simplifying 2‐D‐to‐3‐D process for estimating petrophysical properties in porous media [ABSTRACT FROM AUTHOR]

Because shrub cover is related to many forest ecosystem functions, it is one of the most relevant variables for describing these communities. Nevertheless, a harmonized indicator of shrub cover for large-scale reporting is lacking. The aims of the study were threefold: to define a shrub indicator that can be used by European countries for harmonized shrub cover estimation using data from their respective national forest inventories (NFIs); to quantify the effects of using different NFI field cover scales; and to establish bridges to facilitate harmonized estimation. Data for shrub species cover from the Third Spanish NFI together with scales for cover assessment from 16 European NFIs were used. The indicator, mean species cover (MSC), was defined for each species and each European forest category. Estimates of MSC calculated using species covers recorded for field plots, with 1% interval widths (MSCobs), were compared with the MSC values that would be obtained for the same data with the different European cover scales (MSCpred). Residuals calculated as differences between MSCobs and MSCpred were analyzed, and a linear mixed model was used as bridging function to adjust predictions and thus further harmonize estimates. Scales with only two or three intervals produced the greatest residuals, while all the other analyzed scales had residuals less than 5%. Most scales, except those most similar to Braun-Blanquet, displayed a tendency to be unreliable for larger covers. The proposed mean species cover indicator provides comparable estimates for shrub communities at large scales. The linear models improved the harmonization of MSC for the scales having two and three intervals. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the definition of Neutrosophic sets and present a method for extending crisp functions on Neutrosophic sets and study some properties of such extended functions. [ABSTRACT FROM AUTHOR]

First-order integral equation theories are much more computationally efficient than second-order theories, but the latter are usually much more accurate for computing correlation functions of fluids. We here test the accuracy of the Duh–Haymet–Henderson (DHH) integral equation theory by comparing radial distribution, cavity correlation and bridge functions computed from DHH, first-order and second-order Percus–Yevick theories, with molecular dynamics calculations for the Lennard–Jones fluid. We find that the DHH theory is almost as accurate as the second-order Percus–Yevick theory at liquid-like densities for both sub- and super-critical temperatures. However, the accuracy of the DHH theory decreases with decreasing density. The correlation functions computed from DHH theory are very similar to those computed from first-order Percus–Yevick theory at low densities. The cavity correlation and bridge functions at low densities computed from these two theories are qualitatively different from results computed from molecular simulations. However, the radial distribution functions computed from all three methods are essentially identical at low densities, indicating that errors in the cavity correlation and bridge functions at low densities cancel out to give high accuracy in the radial distribution function. [ABSTRACT FROM PUBLISHER]

Cavity correlation functions, pair correlation functions, and bridge functions for the Lennard-Jones fluid are calculated from first Percus–Yevick (PY) theory and second-order Percus– Yevick (PY2) theory, molecular dynamics, and grand canonical Monte Carlo techniques. We find that the PY2 theory is significantly more accurate than the PY theory, especially at high density and near the critical point. The pair correlation function near the critical point has the expected slowly decaying long-range behaviour. However, we do not observe any long-range behaviour in the bridge function for the state points near the critical point we have simulated. However, we do note that the bridge function, which is usually negative nearr= 0, becomes positive asr→ 0. This behaviour is seen for the bridge functions computed from both PY2 and molecular dynamics, but not from PY. [ABSTRACT FROM AUTHOR]

This paper proposes a new interleaving rule, with which a new IBF (IBF, intertwined bridge function) is generated. Not only does the new intertwined bridge function have a zero correlation zone, but also its cross-correlation performance is ideal. An ultra-wideband system is introduced, which uses the intertwined bridge functions as the spreading code. The sequence of interleaved bridge function with zero autocorrelation bridge area and zero cross-correlation zones can better reduce multiple access interference and multipath interference. It is shown by the simulation results that the ultra-wideband systems using the interleaved bridge function as the spreading sequence have better error rate performance. [ABSTRACT FROM AUTHOR]

In this report the radial distribution functions (RDFs) of liquid water are calculated on the basis of the classical density functional theory combined with the reference interaction site model for molecular liquids. The bridge functions, which are neglected in the hypernetted-chain (HNC) approximation, are taken into account through the density expansion for the Helmholtz free energy functional up to the third order. A factorization approximation to the ternary direct correlation functions in terms of the site-site pair correlation functions is then employed in the expression of the bridge functions, thus leading to a closed set of integral equations for the determination of the RDFs. It is confirmed through numerical calculations that incorporation of the oxygen-oxygen bridge function substantially improves the poor descriptions by the HNC approximation at room temperature, e.g., for the second peak of the oxygen-oxygen RDF. [ABSTRACT FROM AUTHOR]

We develop a method to extract site–site bridge functions from simulations of molecular liquids with the use of dielectric consistent reference interaction site model (DRISM). We reduce the problem to evaluations of short-range parts of direct correlation functions, providing consistent corrections to the DRISM integral equations. We reconstruct site–site bridge functions with the use of the corrected DRISM equations and Fourier transforms of simulated radial distribution functions. The performance of the algorithm has been tested for the SPC/E water model. The obtained bridge functions are quite close to those obtained with the use of the RISM approach. We evaluate structural properties of ambient water within the DRISM framework, using the bridge functions. All the calculated structural properties are in a good agreement with available experimental data. [ABSTRACT FROM AUTHOR]

We construct a closure theory for the bridge functional based on the third-order Ornstein–Zernike (OZ3) equation. The new closure is tested on the adsorption of the hard-core Yukawa fluid on a planar hard wall and its results are compared with Monte Carlo computer simulation. We show that in the particularly challenging cases of depletive adsorption, the density profiles near the wall obtained from the OZ3 theory improve considerably over conventional liquid-state theories, such as the hypernetted-chain and the Percus–Yevick equations. Some technical details of the implementation of the procedure of re-normalisation of the non-uniform indirect correlation function are also provided. [ABSTRACT FROM PUBLISHER]

Highlights: [•] Classical density functional theory for liquid water is formulated. [•] Triplet correlations and bridge functions are taken into account. [•] Factorization approximation for ternary direct correlation functions is employed. [•] Radial distribution functions for liquid water are calculated and compared with simulation results. [ABSTRACT FROM AUTHOR]

Abstract: Increased attention has been paid to the transportation and removal efficiencies of nanoparticles during water treatment. Here, C60 was selected as nano-pollutant to investigate its removal efficiency in the process of coagulation by Al3+ in regard to different ions. Negatively charged C60 tends to adsorb hydrated Al3+ to form positively charged C60-Al(OH)n (m-δ)+ particles, leading to the restabilization of C60. Multivalent anions, i.e., CO3 2−, SO4 2−, HPO4 2−,and humic acid (HA), were shown to bridge the C60-Al (OH)n (m-δ)+ particles together and induce the formation of flocs, resulting in enhanced C60 removal (>80%). Monovalent anions, such as OH−, NO3 − and the surfactant SDS, were not able to bridge the C60-Al (OH)n (m-δ)+ particles together; hence, they had no effect on the C60 removal. The addition of Na+ and Ca2+ increased the ionic strength of the aqueous solution, which compressed the electric double layer and induced the C60-Al(OH)n (m-δ)+ particles to aggregate. However, they are not the essential factors for flocs formation. This is the first study to report the bridging phenomena between multivalent anions and C60-Al(OH)n (m-δ)+ in water treatments, and it highlights that the presence of multivalent anions and cations in raw water are important for the effective removal of C60. [Copyright &y& Elsevier]

The bridge function of hard spheres is accurately calculated from computer simulation data on the pair distribution function via the inverted Ornstein-Zernike equation at reduced densities ρ*  Nσ3/V ranging from 0.2 to 1.02, i.e. from low densities through densities in a vicinity of the phase transition to crystal to densities of metastable fluid region. The data are used to propose an analytical representation of the bridge function as a function of the interparticle distance and density. They are further used to construct the so-called Duh- Haymet plot. It is demonstrated that a "general closure" to the Ornstein-Zernike equation in the form B(r) = f[γ(γ)], where γ is the indirect (or series) correlation function, does not match the data. Nor does an extended closure B(r) = f[γ(r),ρ*] even in the simplest case of the one component hard sphere fluid. A relative success of literature closures to the Ornstein-Zernike equation is discussed. [ABSTRACT FROM AUTHOR]

This paper is an extension of our previous experimental results to the numerical prediction of the dissociation process relative to cellulase enzymes with increasing temperatures. We have computed the quantities of interest, that is, the pair correlation and bridge functions, using integral equation theory with an appropriate closure relation. The central result of our work is the existence of the cut-off distance; above it the attractive tail of the Lennard-Jones potential becomes negligible and the enzymes reach their globular conformation. The effects of temperature, number density, and potential parameters on the pair correlation and bridge functions are also discussed. [ABSTRACT FROM AUTHOR]

Abstract: The goal of this paper is to show that the wetting behavior of simple fluids on a repulsive solid surface – especially the “drying” phenomenon – is closely related to the proximity of the supercritical state of the bulk fluids to their vapor–liquid coexistence region. We propose here a new DFT (the star-function based density functional theory, s-DFT) that is based on the functional Taylor expansion of the intrinsic free energy F[ρ] and the singlet direct correlation to arrive at closed-form expressions for both quantities without truncations or approximations. The two formulas are mutually consistent because of the introduction of a star function that has been shown to be the functional primitive of the bridge function , i.e. (L.L. Lee, J. Chem. Phys. 97 (1992) 8606 ). The new formulation is applied to the Lennard-Jones molecules adsorbed on a planar hard wall (LJ/HW). We carried out new Monte Carlo simulations for this system. Since the s-DFT uses a bridge function , we demonstrate (i) the existence of a set of data (inverted from the MC information) that can perform as the bridge function and reproduce accurately the density profiles ; (ii) this set of data can be “fitted” by a function-form with acronym ZSEP; finally (iii) ZSEP expresses the bridge function in terms of a new renormalized basis function γ H , i.e. . The existence of a bridge function dispels some of the misconceptions that the bridge-function based formulations did not describe the “drying” behavior. We also show that for the high density case ZSEP equation can qualify as a “closure relation”, but seems to deteriorate for the two low-density supercritical states that are close to the bulk saturated liquid phase boundaries. [ABSTRACT FROM AUTHOR]

The bridge function required to yield a singlet integral equation (IE) up to the second order in density expansion for the hard sphere fluid confined in a slit-pore is evaluated. The slit-fluid bridge function can be divided into wall-particle bridge diagrams with hb-bond, which were evaluated by recently proposed Transition Matrix Monte Carlo (TMMC) Mayer-sampling method. The bulk-fluid total correlation function hb(r) used in cluster integrals is determined by solution of the bulk-fluid Ornstein-Zernike (OZ) equation with a hypernetted chain closure (HNC). The calculation is performed for the reduced density of bulk fluid in equilibrium with the fluid in slit-pores from 0.3 to 0.7 with narrow slit width of 3.0σ and 4.0σ. The quantity of the slit-fluid bridge function is assessed by comparison of the density profile obtained from the singlet IE theory and the grand canonical Monte Carlo (GCMC) simulation. Good agreement between the proposed approach and the GCMC data is observed. The reduced normal pressure is also calculated, and agrees well with the simulation data at low to medium densities but becomes a little larger at high density. It is expected that the result can be improved by adding higher order bridge coefficients. The direct evaluation of the slit-fluid bridge function seems to be practical since a great improvement of the quality of the singlet IE theory has been achieved for predicting the structural and thermodynamic properties of fluids confined in narrow slit pores. [ABSTRACT FROM AUTHOR]

This paper is a research on the variation character of stagnation point heat flux for hypersonic pointed bodies from continuum to rarefied flow states by using theoretical analysis and numerical simulation methods. The newly developed near space hypersonic cruise vehicles have sharp noses and wingtips, which desires exact and relatively simple methods to estimate the stagnation point heat flux. With the decrease of the curvature radius of the leading edge, the flow becomes rarefied gradually, and viscous interaction effects and rarefied gas effects come forth successively, which results in that the classical Fay-Riddell equation under continuum hypothesis will become invalid and the variation of stagnation point heat flux is characterized by a new trend. The heat flux approaches the free molecular flow limit instead of an infinite value when the curvature radius of the leading edge tends to 0. The physical mechanism behind this phenomenon remains in need of theoretical study. Firstly, due to the fact that the whole flow regime can be described by Boltzmann equation, the continuum and rarefied flow are analyzed under a uniform framework. A relationship is established between the molecular collision insufficiency in rarefied flow and the failure of Fourier’s heat conduction law along with the increasing significance of the nonlinear heat flux. Then based on an inspiration drew from Burnett approximation, control factors are grasped and a specific heat flux expression containing the nonlinear term is designed in the stagnation region of hypersonic leading edge. Together with flow pattern analysis, the ratio of nonlinear to linear heat flux W r is theoretically obtained as a parameter which reflects the influence of nonlinear factors, i.e. a criterion to classify the hypersonic rarefied flows. Ultimately, based on the characteristic parameter W r, a bridge function with physical background is constructed, which predicts comparative reasonable results in coincidence well with DSMC and experimental data in the whole flow regime. [ABSTRACT FROM AUTHOR]

The first bridge diagrams of the classical theory of liquids are discussed for two fluids of Lennard-Jones spheres and for a fluid of a two-centre Lennard-Jones model of liquid bromine. The bridge diagram of liquid bromine is calculated using a biased Monte-Carlo method. We investigate the first bridge diagrams, the bonds of which are either Mayer functions f or total correlation functions h. The Mayer f-bond representation leads to very high values of the first bridge diagram, which can not be used alone in a truncated expansion of the diagrammatic series of the bridge function. We analyse the origin of these high values. In the case of the h-function representation, the bridge function series truncated to the sole first bridge diagram is introduced into the closure of the Ornstein-Zernike equation and leads to some improvement of the pair distribution function upon the HNC result, as compared to the exact simulated values. [ABSTRACT FROM AUTHOR]