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two-point correlation function of ring polymers: Experiments and numerical simulations for the case of circular DNA in 2 dimensions

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REACTIVE & functionAL POLYMERS 2018年 133卷 66-70页

作者： Ropelewski, Sophia Uehara, Erica Lehmann, Caroline Deguchi, Tetsuo Dietler, Giovanni Ecole Polytech Fed Lausanne Inst Phys Lab Phys Matiere Vivante CH-1015 Lausanne Switzerland Ochanomizu Univ Dept Phys Bunkyo Ku 2-1-1 Ohtsuka Tokyo 1128610 Japan

The statistical properties of polymers have been actively investigated since the breakthrough results of relating their properties to the theory of second order phase transitions. It was also very soon realized that the polymer's topology would play an important role in the behavior of polymers, In fact, polymers can come in a multitude of topologies, from the most common linear topology to circular, branched, brushed and finally knotted topology. Here, Ropelewski et al examine the statistical properties of polymers using the two-point correlation function.

关键词： two-point correlation function Ring polymers Circular DNA AFM Critical exponents

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Hierarchical modeling of microstructural images for porosity prediction in metal additive manufacturing via two-point correlation function

A I I E Transactions

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A I I E Transactions 2023年第9期55卷

作者： Yuanyuan Gao Xinming Wang Junbo Son Xiaowei Yue Jianguo Wu a Industrial Engineering and Management Peking University Beijing China b Alfred Lerner College of Business & Economics University of Delaware Newark DE USA c Industrial and Systems Engineering Virginia Tech Blacksburg VA USA

Porosity is one of the most critical quality issues in Additive Manufacturing (AM). As process parameters are closely related to porosity formation, it is vitally important to study their relationship for better process optimization. In this article, motivated by the emerging application of metal AM, a three-level hierarchical mixed-effects modeling approach is proposed to characterize the relationship between microstructural images and process parameters for porosity prediction and microstructure reconstruction. Specifically, a two-point correlation function (TPCF) is used to capture the morphology of the pores quantitatively. Then, the relationship between the TPCF profile and process parameters is established. A blocked Gibbs sampling approach is developed for parameter inference. Our modeling framework can reconstruct the microstructure based on the predicted TPCF through a simulated annealing optimization algorithm. The effectiveness and advantageous features of our method are demonstrated by both the simulation study and the case study with real-world data from metal AM applications.

关键词： Additive manufacturing two-point correlation function Bayesian hierarchical model blocked Gibbs sampling porosity prediction

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correlcalc: A 'generic' recipe for calculation of two-point correlation function

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ASTRONOMY AND COMPUTING 2018年 25卷 149-158页

作者： Rohin, Y. Univ Delhi Dept Phys & Astrophys Delhi India

This article presents a recipe for computation of galaxy two-point correlation function (2pCF) from redshift surveys using python. One of the salient features of this approach is that it can be used for calculating galaxy clustering for any arbitrary geometry (or Cosmology) model. Being efficient enough to run on a low-spec desktop computer for small datasets, this 'recipe' can be used for quick validation of alternative models and for pedagogical purposes. (C) 2018 Elsevier B.V. All rights reserved.

关键词： two-point correlation function BallTree Galaxy clustering Redshift surveys 2pCF for alternative models

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two-point correlation function and Feynman-Kac Formula for the Stochastic Heat Equation

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POTENTIAL ANALYSIS 2017年第4期46卷 779-797页

作者： Chen, Le Hu, Yaozhong Nualart, David Univ Kansas Dept Math Lawrence KS 66045 USA

In this paper, we obtain an explicit formula for the two-point correlation function for the solutions to the stochastic heat equation on . The bounds for p-th moments proved in Chen and Dalang (Ann. Probab. 2015) are simplified. We validate the Feynman-Kac formula for the p-point correlation function of the solutions to this equation with measure-valued initial data.

关键词： Stochastic heat equation two-point correlation function Feynman-Kac formula Brownian local time Malliavin calculus

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Gravitational clustering of galaxies: Derivation of two-point galaxy correlation function using statistical mechanics of cosmological many-body problem

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ASTROPHYSICS AND SPACE SCIENCE 2016年第7期361卷 1-8页

作者： Ahmad, Farooq Malik, Manzoor A. Bhat, M. Maqbool Univ Kashmir Dept Phys Srinagar 190006 Kashmir India InterUniv Ctr Astron & Astrophys Pune 411007 Maharashtra India

We derive the spatial pair correlation function in gravitational clustering for extended structure of galaxies (e.g. galaxies with halos) by using statistical mechanics of cosmological many-body problem. Our results indicate that in the limit of point masses (epsilon = 0) the two-point correlation function varies as inverse square of relative separation of two galaxies. The effect of softening parameter 'epsilon' on the pair correlation function is also studied and results indicate that two-point correlation function is affected by the softening parameter when the distance between galaxies is small. However, for larger distance between galaxies, the two-point correlation function is not affected at all. The correlation length r(0) derived by our method depends on the random dispersion velocities < v(2)>(1/2) and mean number density (n) over bar, which is in agreement with N-body simulations and observations. Further, our results are applicable to the clusters of galaxies for their correlation functions and we apply our results to obtain the correlation length r(0) for such systems which again agrees with the data of N-body simulations and observations.

关键词： Cosmological many-body problem two-point correlation function Large scale structure

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two-point Statistics without Bins: A Continuous-function Generalization of the correlation function Estimator for Large-scale Structure

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ASTROPHYSICAL JOURNAL 2021年第2期909卷

作者： Storey-Fisher, Kate Hogg, David W. NYU Ctr Cosmol & Particle Phys Dept Phys New York NY 10003 USA New York Univ Ctr Data Sci New York NY USA Max Planck Inst Astron Heidelberg Germany Simons Fdn Flatiron Inst New York NY USA

The two-point correlation function (2pcf) is the key statistic in structure formation;it measures the clustering of galaxies or other density field tracers. Estimators of the 2pcf, including the standard Landy-Szalay (LS) estimator, evaluate the 2pcf in hard-edged separation bins, which is scientifically inappropriate and results in a poor trade-off between bias and variance. We present a new 2pcf estimator, the Continuous-function Estimator, which generalizes LS to a continuous representation and obviates binning in separation or any other pair property. Our estimator, inspired by the mathematics of least-squares fitting, replaces binned pair counts with projections onto basis functions;it outputs the best linear combination of basis functions to describe the 2pcf. The choice of basis can take into account the expected form of the 2pcf, as well as its dependence on pair properties other than separation. We show that the Continuous-function Estimator with a cubic-spline basis better represents the shape of the 2pcf compared to LS. We also estimate directly the baryon acoustic scale, using a small number of physically motivated basis functions. Critically, this leads to a reduction in the number of mock catalogs required for covariance estimation, which is currently the limiting step in many 2pcf analyses. We discuss further applications of the Continuous-function Estimator, including determination of the dependence of clustering on galaxy properties and searches for potential inhomogeneities or anisotropies in large-scale structure.

关键词： two-point correlation function Large-scale structure of the universe Cosmology Astrostatistics techniques Baryon acoustic oscillations Redshift surveys Spatial point processes Clustering Cosmological parameters from large-scale structure

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The accurate prediction and further optimization of thermal conductivity for 3D fully ceramic microencapsulated fuel via graph convolutional neural network

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MATERIALS TODAY COMMUNICATIONS 2025年 42卷

作者： Hou, Jianhua Gong, Zhanpeng Ding, Xiangdong Sun, Jun Tang, Rui Xiao, Hongxing Deng, Junkai Xi An Jiao Tong Univ State Key Lab Mech Behav Mat Xian 710049 Peoples R China Nucl Power Inst China Natl Key Lab Nucl Reactor Technol Chengdu 610213 Peoples R China

Fully ceramic microencapsulated (FCM) is a new type of composite fuel in the nuclear energy field;it has emerged as a promising candidate for accident-tolerant fuel (ATF), owing to its good structural stability and retention capability of fission products. However, the inherently low thermal conductivity of FCM fuel poses a challenge and increases the risk of accidents in reactors. It is well-accepted that the microstructures of the fuel affect their physical properties. Thus, establishing the correlation between the 3D microstructures and corresponding properties of the fuel is crucial for improving their properties by optimizing the microstructure. In this study, we investigate the relationship between the 3D microstructures of FCM fuel and their corresponding effective thermal conductivity (ETC) by using the graph convolutional network (GCN) model. A dataset comprising 100,000 3D microstructures, generated through high-throughput finite element method simulations, was employed in the study. By transforming the 3D microstructure into graph data, the GCN model exhibited superior performance in predicting the ETC of 3D FCM fuel, with an error of 0.2 %. Furthermore, a microstructural feature influencing the ETC of the FCM fuel was identified using a two-point correlation function. This new microstructural feature contributes to the design of microstructures with enhanced ETC values and the improved performance of the GCN model in the present task, indicating its essential role in determining the ETC of FCM fuel. This work demonstrates the excellent performance of the GCN model in establishing microstructure-property correlations for 3D composites.

关键词： Fully ceramic microencapsulated (FCM) fuel Thermal conductivity Graph convolution network two-point correlation function Structure-property correlation

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Reconstruction of granite microstructure model using simulated annealing method and Voronoi tessellation

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ENGINEERING COMPUTATIONS 2023年第6期40卷 1289-1304页

作者： Chen, Bin Wang, Yuan Cui, Shaoqing Xiang, Jiansheng Latham, John-Paul Fu, Jinlong Hohai Univ Coll Water Conservancy & Hydropower Engn Nanjing Peoples R China Hohai Univ Natl Key Lab Water Disaster Prevent Nanjing Peoples R China Swansea Univ Zienkiewicz Inst Modelling Data & AI Fac Sci & Engn Swansea Wales Imperial Coll London Fac Engn Dept Earth Sci & Engn London England

PurposeAccurate presentation of the rock microstructure is critical to the grain-scale analysis of rock deformation and failure in numerical modelling. 3D granite microstructure modelling has only been used in limited studies with the mineral pattern often remaining poorly constructed. In this study, the authors developed a new approach for generating 2D and 3D granite microstructure models from a 2D image by combining a heterogeneous material reconstruction method (simulated annealing method) with Voronoi ***/methodology/approachMore specifically, the stochastic information in the 2D image is first extracted using the two-point correlation function (TPCF). Then an initial 2D or 3D Voronoi diagram with a random distribution of the minerals is generated and optimised using a simulated annealing method until the corresponding TPCF is consistent with that in the 2D image. The generated microstructure model accurately inherits the stochastic information (e.g. volume fraction and mineral pattern) from the 2D image. Lastly, the authors compared the topological characteristics and mechanical properties of the 2D and 3D reconstructed microstructure models with the model obtained by direct mapping from the 2D image of a real rock *** good agreements between the mapped and reconstructed models indicate the accuracy of the reconstructed microstructure models on topological characteristics and mechanical ***/valueThe newly developed reconstruction method successfully transfers the mineral pattern from a granite sample into the 2D and 3D Voronoi-based microstructure models ready for use in grain-scale modelling.

关键词： Rock microstructure Voronoi tessellation Simulated annealing method two-point correlation function Granite

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An improved 3D microstructure reconstruction approach for porous media

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ACTA MATERIALIA 2023年 242卷

作者： Li, Kai-Qi Liu, Yong Yin, Zhen-Yu Wuhan Univ Inst Engn Risk & Disaster Prevent State Key Lab Water Resources & Hydropower Engn Sc 299 Bayi Rd Wuhan 430072 Peoples R China Hong Kong Polytech Univ Dept Civil & Environm Engn Hong Kong Peoples R China

Microstructure reconstruction of porous media is vital for the evaluation of material properties, which has been applied in many fields. Various approaches have been proposed for the reconstruction mod-eling of porous media. However, most of them considered the porous medium as an ideal two-phase material, and little attention is paid to the isolated solid clusters among pore domains. Porous media with solid isolations are inconsistent with actual structures and are likely to result in computational er-rors when determining the transport properties. Aiming to address this issue, an efficient approach to reconstruct the microstructure of porous media is proposed, which utilizes the watershed algorithm to identify and eliminate the isolated solid clusters. In addition, several morphological descriptors, including Minkowski functions, pore size distribution and permeability, are involved in measuring the discrepan-cies between target structures and reconstructions. Results demonstrated that the proposed method re-builds microstructures without isolations from two-dimension images or autocorrelation functions and preserves valuable morphological information within the microstructures. By means of a simple work-flow, the proposed method can be employed to reconstruct porous media without isolated solids and applied to investigate the transport mechanisms of porous media.(c) 2022 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

关键词： Porous media Microstructure reconstruction two-point correlation function Solid isolations Morphological descriptors

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A new framework for the reconstruction of porous media based on statistical characteristics: Multiscale erosion simulated annealing method

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2023年 616卷

作者： Chen, DongDong Wang, XiaoRui Nan, JiaoFen Zhengzhou Univ Light Ind Sch Comp & Commun Engn Zhengzhou 450000 Peoples R China

In this paper, a multiscale erosion simulated annealing method (MESA) is proposed, which can improve the computational efficiency of microstructure reconstruction by an order of magnitude. The reconstruction is performed on two-dimensional (2D) and three-dimensional (3D) microstructure based on simulated annealing (SA) and MESA, where the two-point correlation function is selected as the morphological information descriptor. The two-point cluster function containing significant high-order statistical information is used to verify the reconstruction results. From the analysis of 2D recon- struction, it can be found that although the proposed MESA technology can improve the reconstruction efficiency, the reconstruction is still not perfect. That is because the two - point correlation function contains insufficient information. In the 3D reconstruction, the two-point correlation function of the reconstructed 3D microstructure has a good consistency with the original 2D two-point correlation function, indicating that our proposed method is effective for the 3D microstructure reconstruction. By comparing the energy and computation time of SA and MESA, it is shown that our proposed method is one order of magnitude faster than SA method. This is because only a small part of pixels in the overall scales need to be sampled.(c) 2023 Elsevier B.V. All rights reserved.

关键词： Multiscale erosion simulated annealing method Microstructure reconstruction two-point correlation function two-point cluster function

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