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Physical Review E 2012年第2期85卷 021130-021130页

作者： Adam B. Hopkins Frank H. Stillinger Salvatore Torquato Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The densest binary sphere packings in the α-x plane of small to large sphere radius ratio α and small sphere relative concentration x have historically been very difficult to determine. Previous research had led to the prediction that these packings were composed of a few known “alloy” phases including, for example, the AlB2 (hexagonal ω), HgBr2, and AuTe2 structures, and to XYn structures composed of close-packed large spheres with small spheres (in a number ratio of n to 1) in the interstices, e.g., the NaCl packing for n=1. However, utilizing an implementation of the Torquato-Jiao sphere-packing algorithm [Torquato and Jiao, Phys. Rev. E 82, 061302 (2010)], we have discovered that many more structures appear in the densest packings. For example, while all previously known densest structures were composed of spheres in small to large number ratios of one to one, two to one, and very recently three to one, we have identified densest structures with number ratios of seven to three and five to two. In a recent work [Hopkins et al., Phys. Rev. Lett. 107, 125501 (2011)], we summarized these findings. In this work, we present the structures of the densest-known packings and provide details about their characteristics. Our findings demonstrate that a broad array of different densest mechanically stable structures consisting of only two types of components can form without any consideration of attractive or anisotropic interactions. In addition, the structures that we have identified may correspond to currently unidentified stable phases of certain binary atomic and molecular systems, particularly at high temperatures and pressures.

关键词： SPHERE packings RADIUS (Geometry) PHASE transformations (Physics) ALGORITHMS TEMPERATURE effect ANISOTROPY PRESSURE

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Organizing principles for dense packings of nonspherical hard particles: Not all shapes are created equal

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Physical Review E 2012年第1期86卷 011102-011102页

作者： Salvatore Torquato Yang Jiao []Department of Chemistry Department of Physics Princeton Center for Theoretical Science Program of Applied and Computational Mathematics Princeton Institute of the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

We have recently devised organizing principles to obtain maximally dense packings of the Platonic and Archimedean solids and certain smoothly shaped convex nonspherical particles [Torquato and Jiao, Phys. Rev. E 81, 041310 (2010)]. Here we generalize them in order to guide one to ascertain the densest packings of other convex nonspherical particles as well as concave shapes. Our generalized organizing principles are explicitly stated as four distinct propositions. All of our organizing principles are applied to and tested against the most comprehensive set of both convex and concave particle shapes examined to date, including Catalan solids, prisms, antiprisms, cylinders, dimers of spheres, and various concave polyhedra. We demonstrate that all of the densest known packings associated with this wide spectrum of nonspherical particles are consistent with our propositions. Among other applications, our general organizing principles enable us to construct analytically the densest known packings of certain convex nonspherical particles, including spherocylinders, “lens-shaped” particles, square pyramids, and rhombic pyramids. Moreover, we show how to apply these principles to infer the high-density equilibrium crystalline phases of hard convex and concave particles. We also discuss the unique packing attributes of maximally random jammed packings of nonspherical particles.

关键词： PARTICLES (Nuclear physics) PACKINGS (Chromatography) CONCAVE functions CATALANS POLYHEDRA

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Critical slowing down and hyperuniformity on approach to jamming

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Physical Review E 2016年第1期94卷 012902-012902页

作者： Steven Atkinson Ge Zhang Adam B. Hopkins Salvatore Torquato Department of Chemistry Department of Physics Princeton Center for Theoretical Science Program of Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

Hyperuniformity characterizes a state of matter that is poised at a critical point at which density or volume-fraction fluctuations are anomalously suppressed at infinite wavelengths. Recently, much attention has been given to the link between strict jamming (mechanical rigidity) and (effective or exact) hyperuniformity in frictionless hard-particle packings. However, in doing so, one must necessarily study very large packings in order to access the long-ranged behavior and to ensure that the packings are truly jammed. We modify the rigorous linear programming method of Donev et al. [J. Comput. Phys. 197, 139 (2004)] in order to test for jamming in putatively collectively and strictly jammed packings of hard disks in two dimensions. We show that this rigorous jamming test is superior to standard ways to ascertain jamming, including the so-called “pressure-leak” test. We find that various standard packing protocols struggle to reliably create packings that are jammed for even modest system sizes of N≈103 bidisperse disks in two dimensions; importantly, these packings have a high reduced pressure that persists over extended amounts of time, meaning that they appear to be jammed by conventional tests, though rigorous jamming tests reveal that they are not. We present evidence that suggests that deviations from hyperuniformity in putative maximally random jammed (MRJ) packings can in part be explained by a shortcoming of the numerical protocols to generate exactly jammed configurations as a result of a type of “critical slowing down” as the packing's collective rearrangements in configuration space become locally confined by high-dimensional “bottlenecks” from which escape is a rare event. Additionally, various protocols are able to produce packings exhibiting hyperuniformity to different extents, but this is because certain protocols are better able to approach exactly jammed configurations. Nonetheless, while one should not generally expect exact hyperuniformity for d

关键词： Granular materials Packing & jamming problems

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Maximally dense packings of two-dimensional convex and concave noncircular particles

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Physical Review E 2012年第3期86卷 031302-031302页

作者： Steven Atkinson Yang Jiao Salvatore Torquato Department of Chemistry Department of Physics Princeton Center for Theoretical Science Program of Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

Dense packings of hard particles have important applications in many fields, including condensed matter physics, discrete geometry, and cell biology. In this paper, we employ a stochastic search implementation of the Torquato-Jiao adaptive-shrinking-cell (ASC) optimization scheme [Nature (London) 460, 876 (2009)] to find maximally dense particle packings in d-dimensional Euclidean space Rd. While the original implementation was designed to study spheres and convex polyhedra in d≥3, our implementation focuses on d=2 and extends the algorithm to include both concave polygons and certain complex convex or concave nonpolygonal particle shapes. We verify the robustness of this packing protocol by successfully reproducing the known putative optimal packings of congruent copies of regular pentagons and octagons, then employ it to suggest dense packing arrangements of congruent copies of certain families of concave crosses, convex and concave curved triangles (incorporating shapes resembling the Mercedes-Benz logo), and “moonlike” shapes. Analytical constructions are determined subsequently to obtain the densest known packings of these particle shapes. For the examples considered, we find that the densest packings of both convex and concave particles with central symmetry are achieved by their corresponding optimal Bravais lattice packings; for particles lacking central symmetry, the densest packings obtained are nonlattice periodic packings, which are consistent with recently-proposed general organizing principles for hard particles. Moreover, we find that the densest known packings of certain curved triangles are periodic with a four-particle basis, and we find that the densest known periodic packings of certain moonlike shapes possess no inherent symmetries. Our work adds to the growing evidence that particle shape can be used as a tuning parameter to achieve a diversity of packing structures.

关键词： MAXIMAL functions DIMENSIONAL analysis CONVEX geometry CONCAVE functions PARTICLES (Nuclear physics) DISCRETE geometry POLYGONS

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Static structural signatures of nearly jammed disordered and ordered hard-sphere packings: Direct correlation function

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Physical Review E 2016年第3期94卷 032902-032902页

作者： Steven Atkinson Frank H. Stillinger Salvatore Torquato Department of Chemistry Department of Physics Princeton Center for Theoretical Science Program of Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

The nonequilibrium process by which hard-particle systems may be compressed into disordered, jammed states has received much attention because of its wide utility in describing a broad class of amorphous materials. While dynamical signatures are known to precede jamming, the task of identifying static structural signatures indicating the onset of jamming have proven more elusive. The observation that compressing hard-particle packings towards jamming is accompanied by an anomalous suppression of density fluctuations (termed “hyperuniformity”) has paved the way for the analysis of jamming as an “inverted critical point” in which the direct correlation function c(r), rather than the total correlation function h(r), diverges. We expand on the notion that c(r) provides both universal and protocol-specific information as packings approach jamming. By considering the degree and position of singularities (discontinuities in the nth derivative) as well as how they are changed by the convolutions found in the Ornstein-Zernike equation, we establish quantitative statements about the structure of c(r) with regards to singularities it inherits from h(r). These relations provide a concrete means of identifying features that must be expressed in c(r) if one hopes to reproduce various details in the pair correlation function accurately and provide stringent tests on the associated numerics. We also analyze the evolution of systems of three-dimensional monodisperse hard spheres of diameter D as they approach ordered and disordered jammed configurations. For the latter, we use the Lubachevsky-Stillinger (LS) molecular dynamics and Torquato-Jiao (TJ) sequential linear programming algorithms, which both generate disordered packings, but can show perceptible structural differences. We identify a short-ranged scaling c(r)∝−1/r as r→0 that accompanies the formation of the delta function at c(D) that indicates the formation of contacts in all cases, and show that this scaling behavior is,

关键词： Jamming

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ABACUS: An Electronic Structure Analysis Package for the AI Era

arXiv

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arXiv 2025年

作者： Zhou, Weiqing Zheng, Daye Liu, Qianrui Lu, Denghui Liu, Yu Lin, Peize Huang, Yike Peng, Xingliang Bao, Jie J. Cai, Chun Jin, Zuxin Wu, Jing Zhang, Haochong Jin, Gan Ji, Yuyang Shen, Zhenxiong Liu, Xiaohui Sun, Liang Cao, Yu Sun, Menglin Liu, Jianchuan Chen, Tao Liu, Renxi Li, Yuanbo Han, Haozhi Liang, Xinyuan Bao, Taoni Chen, Nuo Ren, Hongxu Zhang, Xiaoyang Liu, Zhaoqing Fu, Yiwei Liu, Maochang Li, Zhuoyuan Wen, Tongqi Tang, Zechen Xu, Yong Duan, Wenhui Wang, Xiaoyang Gu, Qiangqiang Dai, Fu-Zhi Zheng, Qijing Zhao, Jin Zhang, Yuzhi Ou, Qi Jiang, Hong Liu, Shi Xu, Ben Xu, Shenzhen Ren, Xinguo He, Lixin Zhang, Linfeng Chen, Mohan AI for Science Institute Beijing100080 China HEDPS CAPT School of Physics College of Engineering Peking University Beijing100871 China College of Engineering Peking University Beijing100871 China Institute of Artificial Intelligence Hefei Comprehensive National Science Center Hefei230026 China Key Laboratory of Quantum Information University of Science and Technology of China Hefei230026 China Supercomputing Center University of Science and Technology of China Anhui Hefei230026 China Institute of Physics Chinese Academy of Sciences Beijing100190 China School of Materials Science and Engineering Peking University Beijing100871 China School of Electrical Engineering and Electronic Information Xihua University Chengdu610039 China Academy for Advanced Interdisciplinary Studies Peking University Beijing100871 China College of Chemistry and Molecular Engineering Peking University Beijing100871 China International Research Center for Renewable Energy State Key Laboratory of Multiphase Flow Xi’an Jiaotong University Shaanxi Xi’an710049 China Suzhou Academy of Xi’an Jiaotong University Jiangsu Suzhou215123 China Center for Structural Materials Department of Mechanical Engineering The University of Hong Kong Hong Kong The University of Hong Kong Shenzhen China State Key Laboratory of Low Dimensional Quantum Physics Department of Physics Tsinghua University Beijing100084 China Frontier Science Center for Quantum Information Beijing China Saitama Wako351-0198 Japan Institute for Advanced Study Tsinghua University Beijing100084 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China School of Artificial Intelligence and Data Science University of Science and Technology of China Hefei230026 China School of Materials Science and Engineering University of Science and Technology Beijing Beijing100083 China Department of Physics University of Science and

ABACUS (Atomic-orbital Based Ab-initio Computation at USTC) is an open-source software for first-principles electronic structure calculations and molecular dynamics simulations. It mainly features density functional theory (DFT) and is compatible with both plane-wave basis sets and numerical atomic orbital basis sets. ABACUS serves as a platform that facilitates the integration of various electronic structure methods, such as Kohn-Sham DFT, stochastic DFT, orbital-free DFT, and real-time time-dependent DFT, etc. In addition, with the aid of high-performance computing, ABACUS is designed to perform efficiently and provide massive amounts of first-principles data for generating general-purpose machine learning potentials, such as DPA models. Furthermore, ABACUS serves as an electronic structure platform that interfaces with several AI-assisted algorithms and packages, such as DeePKS-kit, DeePMD, DP-GEN, DeepH, DeePTB, etc. Copyright © 2025, The Authors. All rights reserved.

关键词： Stochastic systems

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The phase diagram of a deep potential water model

arXiv

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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

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A Runge Kutta Discontinuous Galerkin Method for Lagrangian Compressible Euler Equations in Two-Dimensions

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Communications in computational Physics 2014年第4期15卷 1184-1206页

作者： Zhenzhen Li Xijun Yu Jiang Zhu Zupeng Jia School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026P.R.China Graduate School China Academy of Engineering PhysicsBeijing 100088P.R.China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088P.R.China National Laboratory for Scientific Computing LNCC/MCTIAvenida Getúlio Vargas 33325651-075 PetrópolisRJBrazil

This paper presents a new Lagrangian type scheme for solving the Euler equations of compressible gas *** this new scheme the system of equations is discretized by Runge-Kutta Discontinuous Galerkin(RKDG)method,and the mesh moves with the fluid *** scheme is conservative for the mass,momentum and total energy and maintains second-order *** scheme avoids solving the geometrical part and has free *** of some numerical tests are presented to demonstrate the accuracy and the non-oscillatory property of the scheme.

关键词： Lagrangian type scheme compressible Euler equations RKDG method conservative scheme

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Survival window for atomic tunneling ionization with elliptically polarized laser fields

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Physical Review A 2013年第3期87卷 033415-033415页

作者： Kai-yun Huang Qin-zhi Xia Li-Bin Fu National Laboratory of Science and Technology on Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 China Graduate School China Academy of Engineering Physics Beijing 100088 China HEDPS Center for Applied Physics and Technology Peking University Beijing 100084 China

We find a fraction of atoms remain unionized after the laser pulse when the tunneled electrons are released in a certain window of initial field phase and transverse velocity. The survival window shifts with laser polarization ellipticity and its width varies with respect to laser intensity and atomic ionization potential. Neutral atom yield can be calculated by summing up tunneling probabilities in the window. Our theory can quantitatively reproduce the distribution of the survival yields vs laser ellipticity observed for helium in experiment. For other atom species with smaller ionization potential such as magnesium, our theory predicts a wider distribution than the strong-field approximation model while closer to the three-dimensional semiclassical electron ensemble simulations, indicating the important role of the Coulomb effects.

关键词： TUNNELING (Physics) IONIZATION (Atomic physics) POLARIZATION (Nuclear physics) LASERS in physics LASER pulses PHYSICS experiments POTENTIAL theory (Physics)

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Monte Carlo simulation of prompt γ-ray spectra from depleted uranium under D-T neutron irradiation and electron recoil spectra in a liquid scintillator detector

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Chinese Physics C 2016年第3期40卷 115-119页

作者：秦建国赖财锋刘荣朱通华张信威叶邦角 Department of Modern Physics University of Science and Technology of China Hefei 230026 China Institute of Nuclear Physics and Chemistry China Academy of Engineering Physics P.O.Box 213 Mianyang 621900 China Graduate School China Academy of Engineering Physics Mianyang 621900 China Institute of Applied Physics and Computational Mathematics P.O.Box 8009 Beijing 100088 China

To overcome the problem of inefficient computing time and unreliable results in MCNP5 calculation, a two-step method is adopted to calculate the energy deposition of prompt γ-rays in detectors for depleted uranium spherical shells under D-T neutron irradiation. In the first step, the γ-ray spectrum for energy below 7 MeV is calculated by MCNP5 code; secondly, the electron recoil spectrum in a BC501 A liquid scintillator detector is simulated based on EGSnrc Monte Carlo Code with the γ-ray spectrum from the first step as input. The comparison of calculated results with experimental ones shows that the simulations agree well with experiment in the energy region 0.4–3 MeV for the prompt γ-ray spectrum and below 4 MeVee for the electron recoil spectrum. The reliability of the two-step method in this work is validated.

关键词： Monte Carlo simulation depleted uranium prompt γ-ray energy spectrum recoil electron spectrum

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