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Local order metrics for many-particle systems across length scales

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arXiv 2024年

作者： Maher, Charles Emmett Torquato, Salvatore Department of Chemistry Princeton University New Jersey08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in d-dimensional Euclidean space Rd across length scales is an outstanding challenge in physics, chemistry, and materials science. Since an infinite set of n-particle correlation functions is required to fully characterize a system, one must settle for a reduced set of structural information, in practice. We initiate a program to use the local number variance σN2 (R) associated with a spherical sampling window of radius R (which encodes pair correlations) and an integral measure derived from it ΣN(Ri, Rj) that depends on two specified radial distances Ri and Rj. Across the first three space dimensions (d = 1, 2, 3), we find these metrics can sensitively describe and categorize the degree of order/disorder of 41 different models of antihyperuniform, nonhyperuniform, disordered hyperuniform, and ordered hyperuniform many-particle systems at a specified length scale R. Using our local variance metrics, we demonstrate the importance of assessing order/disorder with respect to a specific value of R. These local order metrics could also aid in the inverse design of structures with prescribed length-scale-specific degrees of order/disorder that yield desired physical properties. In future work, it would be fruitful to explore the use of higher-order moments of the number of points within a spherical window of radius R [S. Torquato et al., Phys. Rev. X, 11, 021028 (2021)] to devise even more sensitive order metrics. © 2024, CC BY.

关键词： Inverse problems

Quantifying gender imbalance in East Asian academia: Research career and citation practice

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arXiv 2023年

作者： Nakajima, Kazuki Liu, Ruodan Shudo, Kazuyuki Masuda, Naoki Department of Mathematical and Computing Science Tokyo Institute of Technology Meguro-ku Tokyo152-8552 Japan Department of Mathematics State University of New York at Buffalo Buffalo14260 United States Academic Center for Computing and Media Studies Kyoto University Sakyo-ku Kyoto606-8501 Japan Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo Buffalo14260 United States Center for Computational Social Science Kobe University Kobe657-8501 Japan

Gender imbalance in academia has been confirmed in terms of a variety of indicators, and its magnitude often varies from country to country. Europe and North America, which cover a large fraction of research workforce in the world, have been the main geographical regions for research on gender imbalance in academia. However, the academia in East Asia, which accounts for a substantial fraction of research, may be exposed to strong gender imbalance because Asia has been facing persistent and stronger gender imbalance in society at large than Europe and North America. Here we use publication data between 1950 and 2020 to analyze gender imbalance in academia in China, Japan, and South Korea in terms of the number of researchers, their career, and citation practice. We found that, compared to the average of the other countries, gender imbalance is larger in these three East Asian countries in terms of the number of researchers and their citation practice and additionally in Japan in terms of research career. Moreover, we found that Japan has been exposed to the larger gender imbalance than China and South Korea in terms of research career and citation practice. Copyright © 2023, The Authors. All rights reserved.

关键词： Geographical regions

From Dyson models to many-body quantum chaos

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Physical Review B 2025年第3期111卷 035147-035147页

作者： Alexei Andreanov Matteo Carrega Jeff Murugan Jan Olle Dario Rosa Ruth Shir Center for Theoretical Physics of Complex Systems Institute for Basic Science (IBS) Daejeon 34126 Korea Basic Science Program Korea University of Science and Technology (UST) Daejeon 34113 Korea CNR-SPIN Via Dodecaneso 33 16146 Genova Italy The Laboratory for Quantum Gravity & Strings Department of Mathematics and Applied Mathematics University of Cape Town Cape Town 7701 South Africa The National Institute for Theoretical and Computational Sciences Private Bag X1 Matieland 7602 South Africa Max Planck Institute for the Science of Light 91058 Erlangen Germany ICTP South American Institute for Fundamental Research Instituto de Física Teórica UNESP—University of Estadual Paulista Rua Dr. Bento Teobaldo Ferraz 271 01140-070 São Paulo SP Brazil Department of Physics and Materials Science University of Luxembourg L-1511 Luxembourg Luxembourg

A deep understanding of the mechanisms underlying many-body quantum chaos is one of the big challenges in contemporary theoretical physics. We tackle this problem in the context of a set of perturbed quadratic Sachdev-Ye-Kitaev (SYK) Hamiltonians defined on graphs. This allows us to disentangle the geometrical properties of the underlying single-particle problem and the importance of the interaction terms, showing that the former is the dominant feature ensuring the single-particle to many-body chaotic transition. Our results are verified numerically with state-of-the-art numerical techniques, capable of extracting eigenvalues in a desired energy window of very large Hamiltonians. Our approach essentially provides a new way of viewing many-body chaos from a single-particle perspective.

关键词： Quantum chaos

Artificial neural network approach for turbulence models: A local framework

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Physical Review Fluids 2021年第8期6卷 084612-084612页

作者： Chenyue Xie Xiangming Xiong Jianchun Wang Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Shenzhen 518055 People's Republic of China

A local artificial neural network (LANN) framework is developed for turbulence modeling. The Reynolds-averaged Navier-Stokes (RANS) unclosed terms are reconstructed by the artificial neural network based on the local coordinate system which is orthogonal to the curved walls. We verify the proposed model in the flows over periodic hills. The correlation coefficients of the RANS unclosed terms predicted by the LANN model can be made larger than 0.96 in an a priori analysis, and the relative error of the unclosed terms can be made smaller than 18%. In an a posteriori analysis, detailed comparisons are made on the results of RANS simulations using the LANN, global artificial neural network (GANN), Spalart-Allmaras (SA), and shear stress transport (SST) k−ω models. It is shown that the LANN model performs better than the GANN, SA, and SST k−ω models in the prediction of the average velocity, wall-shear stress, and average pressure, which gives the results that are essentially indistinguishable from the direct numerical simulation data. The LANN model trained at low Reynolds number, Re=2800, can be directly applied to the cases of high Reynolds numbers, Re=5600, 10 595, 19 000, and 37 000, with accurate predictions. Furthermore, the LANN model is verified for flows over periodic hills with varying slopes. These results suggest that the LANN framework has a great potential to be applied to complex turbulent flows with curved walls.

关键词： Compressible boundary layers Turbulence Artificial neural networks

The Effect of Avian Eggshell Membrane Structure on Microbial Penetration: A Simulation Study

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SSRN

SSRN 2024年

作者： Sim, Seungwoo Park, Cheol-Min Lee, Sang-Hee Cho, Haeun Ji, Youngheum Noh, Heeso Lee, Sang-Im Ecological Technology Research Team National Institute of Ecology Chungnam Seocheon Korea Republic of Division of Industrial Mathematics National Institute for Mathematical Sciences Daejeon Korea Republic of Laboratory of Behaviour and Ecology Interdisciplinary Program of EcoCreative Ewha Womans University Seoul Korea Republic of School of Undergraduate Studies Daegu Gyeongbuk Institute of Science and Technology Daegu Korea Republic of Department of Nano and Electronic Physics Kookmin University Seoul Korea Republic of Department of New Biology Daegu Gyeongbuk Institute of Science and Technology Daegu Korea Republic of

Avian eggshells exhibit excellent antimicrobial properties. In this study, we conducted simulation experiments to explore the defense mechanisms of eggshell membranes with regards to their physical features. We developed a mathematical model for the movement of microorganisms and estimated their penetration ratio into eggshell membranes based on several factors, including membrane thickness, microbial size, directional drift, and attachment probability to membrane fibers. These results not only suggest that an eggshell membrane with multiple layers and low porosity indicates high antimicrobial performance, but also imply that the fibrous network structure of the membrane might contribute to effective defense. Our simulation results aligned with experimental findings, specifically in measuring the penetration time of Escherichia coli through the eggshell membrane. We briefly discuss the significance and limitations of this pilot study, as well as the potential for these results, to serve as a foundation for the development of antimicrobial materials. © 2024, The Authors. All rights reserved.

关键词： Escherichia coli

A double explosive Kuramoto transition in hypergraphs

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arXiv 2024年

作者： Dutta, Sangita Kundu, Prosenjit Khanra, Pitambar Minati, Ludovico Boccaletti, Stefano Pal, Pinaki Hens, Chittaranjan Department of Mathematics National Institute of Technology Durgapur713209 India Dhirubhai Ambani Institute of Information and Communication Technology Gujarat Gandhinagar382007 India Department of Chemical and Biological Engineering The State University of New York at Buffalo BuffaloNY14260 United States School of Life Science and Technology University of Electronic Science and Technology of China Chengdu611731 China University of Trento Trento38123 Italy Research Institute of Interdisciplinary Intelligent Science Ningbo University of Technology 315104 China Sino-Europe Complexity Science Center North University of China Taiyuan030051 China CNR Institute of Complex Systems Via Madonna del Piano 10 Sesto FiorentinoI-50019 Italy Center for Computational Natural Science and Bioinformatics International Institute of Informational Technology Gachibowli Hyderabad500032 India

This study aims to develop a generalised concept that will enable double explosive transitions in the forward and backward directions or a combination thereof. We found two essential factors for generating such phase transitions: the use of higher-order (triadic) interactions and the partial adaptation of a global order parameter acting on the triadic coupling. A compromise between the two factors may result in a double explosive transition. To reinforce numerical observations, we employed the Ott–Antonsen ansatz. We observed that for a wide class of hypergraphs, combining two elements can result in a double explosive transition. © 2024, CC BY.

关键词： Explosives

Diffusion spreadability as a probe of the microstructure of complex media across length scales

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arXiv 2021年

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

Understanding time-dependent diffusion processes in multiphase media is of great importance in physics, chemistry, materials science, petroleum engineering and biology. Consider the time-dependent problem of mass transfer of a solute between two phases and assume that the solute is initially distributed in one phase (phase 2) and absent from the other (phase 1). We desire the fraction of total solute present in phase 1 as a function of time, S(t), which we call the spreadability, since it is a measure of the spreadability of diffusion information as a function of time. We derive exact direct-space formulas for S(t) in any Euclidean space dimension d in terms of the autocovariance function as well as corresponding Fourier representations of S(t) in terms of the spectral density, which are especially useful when scattering information is available experimentally or theoretically. These are singular results because they are rare examples of mass transport problems where exact solutions are possible. We derive closed-form general formulas for the short- and long-time behaviors of the spreadability in terms of crucial small- and large-scale microstructural information, respectively. The long-time behavior of S(t) enables one to distinguish the entire spectrum of microstructures that span from hyperuniform to nonhyperuniform media. For hyperuniform media, disordered or not, we show that the "excess" spreadability, S(∞) − S(t), decays to its long-time behavior exponentially faster than that of any nonhyperuniform two-phase medium, the "slowest" being antihyperuniform media. The stealthy hyperuniform class is characterized by an excess spreadability with the fastest decay rate among all translationally invariant microstructures. We obtain exact results for S(t) for a variety of specific ordered and disordered model microstructures across dimensions that span from hyperuniform to antihyperuniform media. Moreover, we establish a remarkable connection between the spreadability

关键词： Microstructure

The phase diagram of a deep potential water model

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arXiv 2021年

作者： Zhang, Linfeng Wang, Han Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Beijing Institute of Big Data Research Beijing100871 China

Using the Deep Potential methodology, we construct a model that reproduces accurately the potential energy surface of the SCAN approximation of density functional theory for water, from low temperature and pressure to about 2400 K and 50 GPa, excluding the vapor stability region. The computational efficiency of the model makes it possible to predict its phase diagram using molecular dynamics. Satisfactory overall agreement with experimental results is obtained. The fluid phases, molecular and ionic, and all the stable ice polymorphs, ordered and disordered, are predicted correctly, with the exception of ice III and XV that are stable in experiments, but metastable in the model. The evolution of the atomic dynamics upon heating, as ice VII transforms first into ice VII′′ and then into an ionic fluid, reveals that molecular dissociation and breaking of the ice rules coexist with strong covalent fluctuations, explaining why only partial ionization was inferred in experiments. © 2021, CC BY-NC-ND.

关键词： Phase diagrams

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

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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