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arXiv 2024年

作者： Newby, Eli Shi, Wenlong Jiao, Yang Albert, Reka Torquato, Salvatore Department of Physics Pennsylvania State University University ParkPA16802 United States Materials Science and Engineering Arizona State University TempeAZ85287 United States Department of Physics Arizona State University TempeAZ85287 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Disordered hyperuniform many-particle systems are recently discovered exotic states of matter, characterized by a complete suppression of normalized infinite-wavelength density fluctuations, as in perfect crystals, and lack of conventional long-range order, as in liquids and glasses. In this work, we begin a program to quantify the structural properties of nonhyperuniform and hyperuniform networks. In particular, large two-dimensional (2D) Voronoi networks (graphs) containing approximately 10,000 nodes are created from a variety of different point configurations, including the antihyperuniform hyperplane intersection process (HIP), nonhyperuniform Poisson process, nonhyperuniform random sequential addition (RSA) saturated packing, and both non-stealthy and stealthy hyperuniform point processes. We carry out an extensive study of the Voronoi-cell area distribution of each of the networks through determining multiple metrics that characterize the distribution, including their higher-cumulants (i.e., skewness 1 and excess kurtosis 2). We show that the HIP distribution is far from Gaussian, as evidenced by a high skewness (γ1 = 3.16) and large positive excess kurtosis (γ2 = 16.2). The Poisson (with γ1 = 1.07 and γ2 = 1.79) and non-stealthy hyperuniform (with γ1 = 0.257 and γ2 = 0.0217) distributions are Gaussian-like distributions, since they exhibit a small but positive skewness and excess kurtosis. The RSA (with γ1 = 0.450 and γ2 = -0.0384) and the highest stealthy hyperuniform distributions (with γ1 = 0.0272 and γ2 = -0.0626) are also non-Gaussian because of their low skewness and negative excess kurtosis, which is diametrically opposite non-Gaussian behavior of the HIP. The fact that the cell-area distributions of large, finite-sized RSA and stealthy hyperuniform networks (e.g., with N ≈ 10, 000 nodes) are narrower, have larger peaks, and smaller tails than a Gaussian distribution implies that in the thermodynamic limit the distributions should exhibit compact suppo

关键词： Gaussian distribution

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Commercial Versus Natural Activated Carbon Fabricated Sheets: applied to Dyes Removal Application

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Macromolecular Symposia 2024年第2期413卷 2300046-2300046页

作者： Alrefaey, Khlood A. Mohamed, Nora Husien, Sh. Fahim, Irene Samy Said, Lobna A. Radwan, Ahmed G. School of Engineering and Applied Sciences Nile University Giza12613 Egypt Industrial Engineering program SESC Research Center Nile University Giza12613 Egypt Nile University Giza12613 Egypt Engineering Mathematics and Physics Department Faculty of Engineering Cairo University Giza12613 Egypt

Industrial dyes are considered one of the main causes of increased water pollution of water. Many businesses, such as steel and paper, are located along riverbanks because they require large amounts of water in their manufacturing processes, and their wastes, which contain acids, alkalis, dyes, and other chemicals, are dumped and poured into rivers as effluents. For example, chemical enterprises producing aluminum emit a significant quantity of fluoride into the air and effluents into water bodies. Fertilizer facilities produce a lot of ammonia, whereas steel plants produce cyanide. Many nations consider employing wastewater treatment plants using physical, biological, and chemical methods to clean the wastewater to address environmental crises. The treated water can be used for targeting the irrigation systems in its majority, as it is biologically acceptable for that specific use, industrial dyes are considered one of the leading causes of increased water pollution of water. Many businesses, such as steel and paper, are located along riverbanks because they require large amounts of water in their manufacturing processes, and their wastes, which contain acids, alkalis, dyes, and other chemicals, are dumped and poured into rivers as effluents. For example, chemical enterprises producing aluminum emit a significant quantity of fluoride into the air and effluents into water bodies. Fertilizer facilities produce much ammonia, whereas steel plants produce cyanide. Chromium salts are used in. Many nations consider employing wastewater treatment plants using physical, biological, and chemical methods to clean the wastewater to address environmental crises. The treated water can target the majority of irrigation systems, as it is biologically acceptable for that specific use, which economizes the use of freshwater sources for municipal use. This study presents a novel method for fabricating an efficient adsorbent sheet for wastewater treatment. The sheets are fabricated by

关键词： Activated carbon

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DATA-DRIVEN MORI-ZWANZIG: REDUCED ORDER MODELING OF SPARSE SENSORS MEASUREMENTS FOR BOUNDARY LAYER TRANSITION

arXiv

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arXiv 2023年

作者： Woodward, Michael Tian, Yifeng Mohan, Arvind Lin, Yen Ting Hader, Christoph Fasel, Hermann Chertkov, Michael Livescu, Daniel Computer Computational and Statistical Sciences Division Los Alamos National Laboratory Los AlamosNM87544 United States Graduate Interdisciplinary Program in Applied Mathematics Department of Mathematics University of Arizona TucsonAZ85721 United States Department of Aerospace and Mechanical Engineering University of Arizona TucsonAZ85721 United States

Understanding, predicting and controlling laminar-turbulent boundary-layer transition is crucial for the next generation aircraft design. However, in real flight experiments, or wind tunnel tests, often only sparse sensor measurements can be collected at fixed locations. Thus, in developing reduced models for predicting and controlling the flow at the sensor locations, the main challenge is in accounting for how the surrounding field of unobserved (or unresolved) variables interacts with the observed (or resolved) variables at the fixed sensor locations. This makes the Mori-Zwanzig (MZ) formalism a natural choice, as it results in the Generalized Langevin Equations which provides a mathematically sound framework for constructing non-Markovian reduced-order models that include the effects the unresolved variables have on the resolved variables. These effects are captured in the so called memory kernel and orthogonal dynamics, which, when using Mori's linear projection, provides a higher order approximation to the traditional approximate Koopman learning methods. In this work, we explore recently developed data-driven methods for extracting the MZ operators to two boundary-layer flows obtained from high resolution data;a low speed incompressible flow over a flat plate exhibiting bypass transition;and a high speed compressible flow over a flared cone at Mach 6 and zero angle of attack where transition was initiated using a broadband forcing approach ("natural" transition). In each case, an array of "sensors" are placed near the surface of the solid boundary, and the MZ operators are learned and the predictions are compared to the Extended Dynamic Mode Decomposition (EDMD), both using delay embedded coordinates. Further comparisons are made with Long Short-Term Memory (LSTM) and a regression based projection framework using neural networks for the MZ operators. First, we compare the effects of including delay embedded coordinates with EDMD and Mori based MZ and provide

关键词： Dynamic mode decomposition

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Classical and machine learning interatomic potentials for BCC vanadium

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Physical Review Materials 2022年第11期6卷 113603-113603页

作者： Rui Wang Xiaoxiao Ma Linfeng Zhang Han Wang David J. Srolovitz Tongqi Wen Zhaoxuan Wu Department of Materials Science and Engineering City University of Hong Kong Hong Kong China AI for Science Institute Beijing 100080 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 China Department of Mechanical Engineering The University of Hong Kong Hong Kong China Hong Kong Institute for Advanced Study City University of Hong Kong Hong Kong China

BCC transition metals (TMs) exhibit complex temperature and strain-rate dependent plastic deformation behavior controlled by individual crystal lattice defects. Classical empirical and semiempirical interatomic potentials have limited capability in modeling defect properties such as the screw dislocation core structures and Peierls barriers in the BCC structure. Machine learning (ML) potentials, trained on DFT-based datasets, have shown some successes in reproducing dislocation core properties. However, in group VB TMs, the most widely used DFT functionals produce erroneous shear moduli C44 which are undesirably transferred to machine-learning interatomic potentials, leaving current ML approaches unsuitable for this important class of metals and alloys. Here, we develop two interatomic potentials for BCC vanadium (V) based on (i) an extension of the partial electron density and screening parameter in the classical semiempirical modified embedded-atom method (XMEAM-V) and (ii) a recent hybrid descriptor in the ML Deep Potential framework (DP-HYB-V). We describe distinct features in these two disparate approaches, including their dataset generation, training procedure, weakness and strength in modeling lattice and defect properties in BCC V. Both XMEAM-V and DP-HYB-V reproduce a broad range of defect properties (vacancy, self-interstitials, surface, dislocation) relevant to plastic deformation and fracture. In particular, XMEAM-V reproduces nearly all mechanical and thermodynamic properties at DFT accuracies and with C44 near the experimental value. XMEAM-V also naturally exhibits the anomalous slip at 77 K widely observed in group VB and VIB TMs and outperforms all existing, publically available interatomic potentials for V. The XMEAM thus provides a practical path to developing accurate and efficient interatomic potentials for nonmagnetic BCC TMs and possibly multiprincipal element TM alloys.

关键词： Interatomic & molecular potentials Materials modeling

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Structural characterization of many-particle systems on approach to hyperuniform states

arXiv

引用

arXiv 2021年

作者： Torquato, Salvatore Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The study of hyperuniform states of matter is an emerging multidisciplinary field, impinging on topics in the physical sciences, mathematics and biology. The focus of this work is the exploration of quantitative descriptors that herald when a many-particle system in d-dimensional Euclidean space Rd approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative criteria to ascertain the extent of hyperuniform and nonhyperuniform distance-scaling regimes as well as the crossover point between them in terms of the "volume" coefficient A and "surface-area" coefficient B associated with the local number variance σ2(R) for a spherical window of radius R. The larger the ratio B/A, the larger the hyperuniform scaling regime, which becomes of infinite extent in the limit B/A → ∞. To complement the known direct-space representation of the coefficient B in terms of the total correlation function h(r), we derive its corresponding Fourier representation in terms of the structure factor S(k), which is especially useful when scattering information is available experimentally or theoretically. We also demonstrate that the free-volume theory of the pressure of equilibrium packings of identical hard spheres that approach a strictly jammed state either along the stable crystal or metastable disordered branch dictates that such end states be exactly hyperuniform. Using the ratio B/A, as well as other diagnostic measures of hyperuniformity, including the hyperuniformity index H and the direct-correlation function length scale ξc, we study three different exactly solvable models as a function of the relevant control parameter, either density or temperature, with end states that are perfectly hyperuniform. Specifically, we analyze equilibrium systems of hard rods and "sticky" hard-sphere systems in arbitrary space dimension d as a function of density. We also examine low-temperature excited states of many-particle systems interacting with "steal

关键词： Temperature

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DECOUPLING FOR CONVEX HYPERSURFACES OF FINITE TYPE IN HIGHER DIMENSIONS

arXiv

引用

arXiv 2022年

作者： Gao, Chuanwei Li, Zhuoran Zhao, Tengfei Zheng, Jiqiang School of Mathematical Sciences Capital Normal University Beijing100048 China Department of Mathematics Taizhou University Taizhou225300 China School of Mathematics and Physics University of Science and Technology Beijing Beijing100083 China Institute of Applied Physics and Computational Mathematics Beijing100088 China

In this paper, we establish an 2 decoupling inequality for the convex hypersurface{ (ξ1, ..., ξn−1, ξ1m + ... + ξmn−1): (ξ1, ..., ξn−1) ∈ [0, 1]n−1} associated with the decomposition adapted to hypersurfaces of finite type, where n ≥ 2 and m ≥ 4 is an even number. The key ingredients of the proof include 2 decoupling inequalities for convex hypersurfaces of the form { (ξ1, ..., ξn−1, φ1(ξ1)+...+φs(ξs)+ξms+1+...+ξmn−1): (ξ1, ..., ξn−1) ∈ [0, 1]n−1} , 0 ≤ s ≤ n − 1, with φ1, ..., φs being m-nondegenerate. © 2022, CC BY.

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Ordered and disordered stealthy hyperuniform point patterns across spatial dimensions

arXiv

引用

arXiv 2024年

作者： Morse, Peter K. Steinhardt, Paul J. Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute of Materials Princeton University PrincetonNJ08544 United States Princeton Center for Theoretical Science Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

In previous work [Phys. Rev. X 5, 021020 (2015)], it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier-space in the sense that the the structure factor is exactly zero in a spherical region around the origin in analogy with the pair-correlation function of real-space hard spheres. In this work, we exploit this correspondence to confirm that the densest Fourier-space hard-sphere system is that of a Bravais lattice. This is in contrast to real-space hard-spheres, whose densest configuration is conjectured to be disordered. We also extend the virial series previously suggested for disordered stealthy hyperuniform systems to higher dimensions in order to predict spatial decorrelation as function of dimension. This prediction is then borne out by numerical simulations of disordered stealthy hyperuniform ground states in dimensions d = 2-8. © 2024, CC BY.

关键词： Ground state

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A Multi-Technique Study of C2H4 Adsorption on Fe3O4(001)

arXiv

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arXiv 2023年

作者： Puntscher, Lena Sombut, Panukorn Wang, Chunlei Ulreich, Manuel Pavelec, Jiri Rafsanjani-Abbasi, Ali Meier, Matthias Lagin, Adam Setvin, Martin Diebold, Ulrike Franchini, Cesare Schmid, Michael Parkinson, Gareth S. Institute of Applied Physics TU Wien Vienna Austria Faculty of Physics Center for Computational Materials Science University of Vienna Vienna Austria Department of Surface and Plasma Science Faculty of Mathematics and Physics Charles University Prague Czech Republic Dipartimento di Fisica e Astronomia Università di Bologna Bologna Italy

The adsorption/desorption of ethene (C2H4), also commonly known as ethylene, on Fe3O4(001) was studied under ultrahigh vacuum conditions using temperature programmed desorption (TPD), scanning tunneling microscopy, x-ray photoelectron spectroscopy, and density functional theory (DFT) based computations. To interpret the TPD data, we have employed a new analysis method based on equilibrium thermodynamics. C2H4 adsorbs intact at all coverages and interacts most strongly with surface defects such as antiphase domain boundaries and Fe adatoms. On the regular surface, C2H4 binds atop surface Fe sites up to a coverage of 2 molecules per (√2×√2)R45° unit cell, with every second Fe occupied. A desorption energy of 0.36 eV is determined by analysis of the TPD spectra at this coverage, which is approximately 0.1-0.2 eV lower than the value calculated by DFT+U with van der Waals corrections. Additional molecules are accommodated in between the Fe rows. These are stabilized by attractive interactions with the molecules adsorbed at Fe sites. The total capacity of the surface for C2H4 adsorption is found to be close to 4 molecules per (√2×√2)R45° unit cell. © 2023, CC BY.

关键词： Ethylene

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Scaling law of mixing layer in cylindrical Rayleigh-Taylor turbulence

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Physical Review E 2021年第5期104卷 055104-055104页

作者： Zhiye Zhao Pei Wang Nan-Sheng Liu Xi-Yun Lu Department of Modern Mechanics University of Science and Technology of China Hefei Anhui 230026 China Institute of Applied Physics and Computational Mathematics Beijing 10094 China

The nonlinear evolution of mixing layer in cylindrical Rayleigh-Taylor (RT) turbulence is studied theoretically and numerically. The scaling laws including the hyperbolic cosine growth for outward mixing layer and the cosine growth for inward mixing layer of the cylindrical RT turbulence are proposed for the first time and verified reliably by direct numerical simulation of the Navier-Stokes equations. It is identified that the scaling laws for the cylindrical RT turbulence transcend the classical power law for the planar RT turbulence and can be recovered to the quadratic growth as cylindrical geometry effect vanishes. Further, characteristic time- and length scales are reasonably obtained based on the scaling laws to reveal the self-similar evolution features for the cylindrical RT turbulence.

关键词： Flow instability Rayleigh-Taylor instability Turbulence Turbulent mixing

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Random Measures, ANOVA Models and Quantifying Uncertainty in Randomized Controlled Trials

arXiv

引用

arXiv 2023年

作者： Bastian, Caleb Deen Rabitz, Herschel Rempala, Grzegorz A. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Mathematics The Ohio State University ColumbusOH43210 United States Division of Biostatistics The Ohio State University ColumbusOH43210 United States

This short paper introduces a novel approach to global sensitivity analysis, grounded in the variance-covariance structure of random variables derived from random measures. The proposed methodology facilitates the application of information-theoretic rules for uncertainty quantification, offering several advantages. Specifically, the approach provides valuable insights into the decomposition of variance within discrete subspaces, similar to the standard ANOVA analysis. To illustrate this point, the method is applied to datasets obtained from the analysis of randomized controlled trials on evaluating the efficacy of the COVID-19 vaccine and assessing clinical endpoints in a lung cancer *** Codes 92-05, 92-11 Copyright © 2023, The Authors. All rights reserved.

关键词： Sensitivity analysis

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