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Designer Pair Statistics of Disordered Many-Particle Systems with Novel Properties

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arXiv 2023年

作者： Wang, Haina Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Materials Institute Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States School of Natural Sciences Institute for Advanced Study 1 Einstein Drive PrincetonNJ08540 United States

Knowledge of exact analytical functional forms for the pair correlation function g2(r) and its corresponding structure factor S(k) of disordered many-particle systems is limited. For fundamental and practical reasons, it is highly desirable to add to the existing data base of analytical functional forms for such pair statistics. Here, we design a plethora of such pair functions in direct and Fourier spaces across the first three Euclidean space dimensions that are realizable by diverse many-particle systems with varying degrees of correlated disorder across length scales, spanning a wide spectrum of hyperuniform, typical nonhyperuniform and antihyperuniform ones. This is accomplished by utilizing an efficient inverse algorithm that determines equilibrium states with up to pair interactions at positive temperature that precisely match targeted forms for both g2(r) and S(k). Among other results, we realize an example with the strongest hyperuniform property among known positive-temperature equilibrium states, critical-point systems (implying unusual 1D systems with phase transitions) that are not in the Ising universality class, systems that attain self-similar pair statistics under Fourier transformation, and an experimentally feasible polymer model. We show that our pair functions enable one to achieve systems with a wide range of translational order and self-diffusion coefficients D, which are inversely related to one another. One can design other realizable pair statistics via linear combinations of our functions or by applying our inverse procedure to other desirable functional forms. Our approach facilitates the inverse design of materials with desirable physical and chemical properties by tuning their pair statistics. © 2023, CC BY.

关键词： Statistics

Unbiased Approximations for Stationary Distributions of McKean-Vlasov SDEs

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arXiv 2024年

作者： Awadelkarim, Elsiddig Chada, Neil K. Jasra, Ajay Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Mathematics City University of Hong Kong Hong Kong School of Data Science The Chinese University of Hong Kong Shenzhen Shenzhen China

We consider the development of unbiased estimators, to approximate the stationary distribution of Mckean-Vlasov stochastic differential equations (MVSDEs). These are an important class of processes, which frequently appear in applications such as mathematical finance, biology and opinion dynamics. Typically the stationary distribution is unknown and indeed one cannot simulate such processes exactly. As a result one commonly requires a time-discretization scheme which results in a discretization bias and a bias from not being able to simulate the associated stationary distribution. To overcome this bias, we present a new unbiased estimator taking motivation from the literature on unbiased Monte Carlo. We prove the unbiasedness of our estimator, under assumptions. In order to prove this we require developing ergodicity results of various discrete time processes, through an appropriate discretization scheme, towards the invariant measure. Numerous numerical experiments are provided, on a range of MVSDEs, to demonstrate the effectiveness of our unbiased estimator. Such examples include the Currie-Weiss model, a 3D neuroscience model and a parameter estimation problem. © 2024, CC BY-NC-SA.

关键词： Stochastic systems

A General Positivity-Preserving Algorithm for Implicit High-Order Finite Volume Schemes Solving the Euler and Navier-Stokes Equations

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SSRN

SSRN 2023年

作者： Huang, Qian-Min Ren, Yu-Xin Wang, Qian Department of Engineering Mechanics Tsinghua University Beijing100084 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100088 China Beijing Computational Science Research Center Beijing100193 China

This paper presents a general positivity-preserving algorithm for implicit high-order finite volume schemes solving Euler and Navier-Stokes equations. Previous positivity-preserving algorithms are mainly based on mathematical analyses, being highly dependent on the existence of low-order positivity-preserving numerical schemes for specific governing equations. This dependency poses serious restrictions on extending these algorithms to temporally implicit schemes, since it is difficult to know if a low-order implicit scheme is positivity-preserving. The present positivity-preserving algorithm is based on an asymptotic analysis of the solutions near local vacuum minimum points. The asymptotic analysis shows that the solutions decay exponentially with time to maintain non-negative density and pressure at a local vacuum minimum point. In its neighborhood, the exponential evolution leads to a modification of the linear evolution process, which can be modelled by a direct correction of the linear residual to ensure positivity. This correction however destroys the conservation of the numerical scheme. Therefore, a second correction procedure is proposed to recover conservation. The proposed positivity-preserving algorithm is considerably less restrictive than existing algorithms. It does not rely on the existence of low-order positivity-preserving baseline schemes and the convex decomposition of volume integrals of flow quantities. It does not need to reduce the time step size for maintaining the stability either. Furthermore, it can be implemented iteratively in the implicit dual time-stepping schemes to preserve positivity of the intermediate and converged states of the sub-iterations. It is proved that the present positivity-preserving algorithm is accuracy-preserving. Numerical results demonstrate that the proposed algorithm preserve the positive density and pressure in all test cases, and considerably improve the robustness of the numerical schemes. © 2023, The Author

关键词： Finite volume method

Dynamics of particles near the surface of amedium under ultra-strong shocks

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Matter and Radiation at Extremes 2021年第2期6卷 46-53页

作者： Zixiang Yan Hao Liu Xinyu Zhang Guoli Ren Jie Liu Wei Kang Weiyan Zhang Xiantu He HEDPS Center for Applied Physics and Technologyand School of PhysicsPeking UniversityBeijing 100871China Department of Applied Physics School of Physics and ElectronicsHunan UniversityChangsha 410082China HEDPS Center for Applied Physics and Technologyand College of EngineeringPeking UniversityBeijing 100871China Institute of Applied Physics and Computational Mathematics Beijing 100088China Graduate School China Academy of Engineering PhysicsBeijing 100193China China Academy of Engineering Physics Mianyang 621900China

Through nonequilibrium molecular dynamics simulations,we provide an atomic-scale picture of the dynamics of particles near the surface of a medium under ultra-strong *** shows that the measured surface velocity v_(f)under ultra-strong shocks is actually the velocity of the critical surface at which the incident probe light is reflected,and v_(f)has a single-peaked *** doubling rule commonly used in the case of relatively weak shocks to determine particle velocity behind the shock front is generally not valid under ultra-strong *** a short period of acceleration,v_(f)exhibits a long slowly decaying tail,which is not sensitive to the atomic mass of the medium.A scaling law for v_(f)is also proposed,and this may be used to improve the measurement of particle velocity u in future experiments.

关键词： structure. surface doubling

A general positivity-preserving algorithm for implicit high-order finite volume schemes solving the Euler and Navier-Stokes equations

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arXiv 2023年

关键词： Finite volume method

Characterizing the mechanical response of metallic glasses to uniaxial tension using a spring network model

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Physical Review Materials 2023年第7期7卷 073605-073605页

作者： Aya Nawano Weiwei Jin Jan Schroers Mark D. Shattuck Corey S. O'Hern Department of Mechanical Engineering and Materials Science Yale University New Haven Connecticut 06520 USA Benjamin Levich Institute and Physics Department The City College of New York New York New York 10031 USA Department of Physics Yale University New Haven Connecticut 06520 USA Department of Applied Physics Yale University New Haven Connecticut 06520 USA Graduate Program in Computational Biology and Bioinformatics Yale University New Haven Connecticut 06520 USA

A coarse-grained spring network model is proposed for the prediction of the mechanical response of metallic glasses as a function of the microstructure prior to loading. This model describes the mechanical response of metallic glasses using a network of parallel springs that can break and reform, mimicking atomic rearrangements during deformation. We compare predictions of the spring network model for stress versus strain to results from numerical simulations of athermal quasistatic, uniaxial tensile deformation of Cu50Zr50 metallic glasses using Lennard-Jones (LJ) and embedded atom method (EAM) atomic interactions. We show that both the LJ and EAM models possess qualitatively similar stress σ versus strain γ curves. By specifying five parameters [ultimate strength, strain at ultimate strength, slopes of σ(γ) at γ=0 and at large strain, and strain at fracture where σ=0], we demonstrate that the spring network model can accurately describe the form of the stress-strain curves during uniaxial tension for the computational studies of Cu50Zr50, as well as recent experimental studies of several Zr-based metallic glasses.

关键词： Alloys Amorphous materials Glasses Packing & jamming problems Molecular dynamics

Cross sections for valence-shell excitations of H2O in the 9.85–12.15-eV energy-loss range studied by high-energy inelastic electron scattering

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Physical Review A 2022年第3期105卷 032801-032801页

作者： Wei-Qing Xu Yi-Geng Peng Jian-Hui Zhu Xiao-Jiao Du Yuan-Chen Xu Li-Han Wang Bo Li Hao-Ran Zhang Bei-Yuan Zhang Zi-Ru Ma Shu-Xing Wang Yong Wu Jian-Guo Wang Lin-Fan Zhu Center for Transformative Science ShanghaiTech University Shanghai 201210 China Department of Applied Physics Nanjing University of Science and Technology Nanjing 210094 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics University of Science and Technology of China Hefei Anhui 230026 China HEDPS Center for Applied Physics and Technology and College of Engineering Peking University Beijing 100871 China

The recent measurement of the generalized oscillator strengths (GOSs) for ÃB11 and B̃A11 of H2O exhibits the apparent deviations from the first Born approximation calculations in the large squared momentum transfer region [W. Q. Xu et al., Phys. Rev. A 103, 032808 (2021)]. Here a simplified theoretical model was proposed to calculate the GOSs of the two excitations at large momentum transfer within the second Born approximation. The accord of the experimental GOSs and the theoretical ones is improved, but the differences still exist. In addition, the GOSs and the integral cross sections for the higher excitations of H2O in 9.85–12.15 eV are presented, which could be used to complete the database of electron-impact excitation cross sections of H2O and be beneficial for modeling interaction processes between electrons and H2O in the earth's atmosphere, plasmas, radiation physics, biology, etc.

关键词： Electron & positron scattering Electronic excitation & ionization Electronic structure of atoms & molecules Molecular spectra Molecules Configuration interaction High-resolution electron energy loss spectroscopy

MULTI-TARGET DETECTION WITH ROTATIONS

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arXiv 2021年

作者： Bendory, Tamir Lan, Ti-Yen Marshall, Nicholas F. Rukshin, Iris Singer, Amit School of Electrical Engineering Tel Aviv University Tel Aviv Israel Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Mathematics Oregon State University Corvallis OR USA Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Program in Applied and Computational Mathematics and the Department of Mathematics Princeton University Princeton NJ USA

We consider the multi-target detection problem of estimating a two-dimensional target image from a large noisy measurement image that contains many randomly rotated and translated copies of the target image. Motivated by single-particle cryo-electron microscopy, we focus on the low signal-to-noise regime, where it is difficult to estimate the locations and orientations of the target images in the measurement. Our approach uses autocorrelation analysis to estimate rotationally and translationally invariant features of the target image. We demonstrate that, regardless of the level of noise, our technique can be used to recover the target image when the measurement is sufficiently large. Copyright © 2021, The Authors. All rights reserved.

关键词： Signal to noise ratio

On The Mechanism of Nucleation in Pulsed-laser Quenched Si Films on SiO 2

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MRS Online Proceedings Library 2021年第1期1245卷 1-6页

作者： Y. Deng Q. Hu U. J. Chung A. M. Chitu A. B. Limanov S. James Im Program in Materials Science and Engineering Department of Applied Physics and Applied Mathematics Columbia University New York USA

We have investigated the solid nucleation mechanism in laser-quenched Si films on SiO2. Previously neglected experimental steps, consisting of BHF-etching and irradiation in vacuum, were implemented to reduce potential extrinsic influences. The resulting experimental findings and computational analysis lead us to conclude that solid nucleation consistently takes place heterogeneously at, and only at, the bottom liquid Si-SiO2 interface.

关键词： Si thin film nucleation & growth