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Displaced Path Integral Formulation for the Momentum Distribution of Quantum Particles

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Physical Review Letters 2010年第11期105卷 110602-110602页

作者： Lin Lin Joseph A. Morrone Roberto Car Michele Parrinello Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Computational Science Department of Chemistry and Applied Biosciences ETH Zurich USI Campus Via Giuseppe Buffi 12 CH-6900 Lugano Switzerland

The proton momentum distribution, accessible by deep inelastic neutron scattering, is a very sensitive probe of the potential of mean force experienced by the protons in hydrogen-bonded systems. In this work we introduce a novel estimator for the end-to-end distribution of the Feynman paths, i.e., the Fourier transform of the momentum distribution. In this formulation, free particle and environmental contributions factorize. Moreover, the environmental contribution has a natural analogy to a free energy surface in statistical mechanics, facilitating the interpretation of experiments. The new formulation is not only conceptually but also computationally advantageous. We illustrate the method with applications to an empirical water model, ab initio ice, and one dimensional model systems.

关键词： Statistical mechanics

First-principles characterization of Ni diffusion kinetics in β-NiAl

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Physical Review B 2008年第18期78卷 184105-184105页

作者： Kristen A. Marino Emily A. Carter Department of Chemical Engineering Princeton University Princeton New Jersey 08544-5263 USA Department of Mechanical and Aerospace Engineering and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544-5263 USA

First-principles density functional theory calculations are performed to examine five postulated diffusion mechanisms for Ni in NiAl: next-nearest-neighbor (NNN) jumps, the triple defect mechanism, and three variants of the six-jump cycle. In contrast to most previous theoretical work, which employed empirical interatomic potentials, we provide a more accurate nonempirical description of the mechanisms. For each pathway, we calculate the activation energy and the pre-exponential factor for the diffusion constant. Although our quantum mechanics calculations are performed at 0 K, we show that it is critical to include the effect of temperature on the pre-exponential factor. We predict that the triple defect mechanism and [110] six-jump cycle both are likely contributors to Ni diffusion in NiAl since their activation energies and pre-exponential factors are in very good agreement with experimental data. Although the activation energy and pre-exponential factor of NNN jumps agree well with experiment, experimental evidence suggests that this is not a dominant contributor to Ni diffusion. Lastly, the activation energies of the [100] bent and straight six-jump cycles are 1 eV higher than the experimental value, allowing us to exclude both [100] cycle mechanisms.

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A fourth-order accurate finite volume method for ideal mhd via upwind constrained transport

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arXiv 2017年

作者： Felker, Kyle Gerard Stone, James Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Astrophysical Sciences Princeton University PrincetonNJ08544 United States

We present a fourth-order accurate finite volume method for the solution of ideal magnetohydrodynamics (MHD). The numerical method combines high-order quadrature rules in the solution of semi-discrete formulations of hyperbolic conservation laws with the upwind constrained transport (UCT) framework to ensure that the divergence-free constraint of the magnetic field is satisfied. A novel implementation of UCT that uses the piecewise parabolic method (PPM) for the reconstruction of magnetic fields at cell corners in 2D is introduced. The resulting scheme can be expressed as the extension of the second-order accurate constrained transport (CT) Godunov-type scheme that is currently used in the Athena astrophysics code. After validating the base algorithm on a series of hydrodynamics test problems, we present the results of multidimensional MHD test problems which demonstrate formal fourth-order convergence for smooth problems, robustness for discontinuous problems, and improved accuracy relative to the second-order scheme. Copyright © 2017, The Authors. All rights reserved.

关键词： Numerical methods

Dynamic Measure of Hyperuniformity and Nonhyperuniformity in Heterogeneous Media via the Diffusion Spreadability

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Physical Review applied 2022年第3期17卷 034022-034022页

作者： Haina Wang Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Time-dependent interphase diffusion processes in multiphase heterogeneous media are ubiquitous phenomena in physics, chemistry and biology. Examples of heterogeneous media include composites, geological media, gels, foams, and cell aggregates. The recently developed concept of spreadability, S(t), provides a direct link between time-dependent diffusive transport and the microstructure of two-phase media across length scales [Torquato, S., Phys. Rev. E., 104 054102 (2021)]. To investigate the capacity of S(t) to probe microstructures of real heterogeneous media, we explicitly compute S(t) for well-known two-dimensional and three-dimensional idealized model structures that span across nonhyperuniform and hyperuniform classes. Among the former class, we study fully penetrable spheres and equilibrium hard spheres, and in the latter class, we examine sphere packings derived from “perfect glasses,” uniformly randomized lattices (URLs), disordered stealthy hyperuniform point processes, and Bravais lattices. Hyperuniform media are characterized by an anomalous suppression of volume fraction fluctuations at large length scales compared to that of any nonhyperuniform medium. We further confirm that the small-, intermediate-, and long-time behaviors of S(t) sensitively capture the small-, intermediate-, and large-scale characteristics of the models. In instances in which the spectral density χ~V(k) has a power-law form B|k|α in the limit |k|→0, the long-time spreadability provides a simple means to extract the value of the coefficients α and B that is robust against noise in χ~V(k) at small wave numbers. For typical nonhyperuniform media, the intermediate-time spreadability is slower for models with larger values of the coefficient B=χ~V(0). Interestingly, the excess spreadability S(∞)−S(t) for URL packings has nearly exponential decay at small to intermediate t, but transforms to a power-law decay at large t, and the time for this transition has a logarithmic divergence in th

关键词： Complex systems Diffusion Flows in porous media Rocks Composite materials Glassy systems Porous materials Random & disordered media

Deep Potential generation scheme and simulation protocol for the Li10GeP2S12-type superionic conductors

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arXiv 2020年

作者： Huang, Jianxing Zhang, Linfeng Wang, Han Zhao, Jinbao Cheng, Jun Weinan, E. State Key Laboratory of Physical Chemistry of Solid Surfaces iChEM College of Chemistry and Chemical Engineering Xiamen University Xiamen361005 China 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 Mathematics Princeton University PrincetonNJ08544 United States

Solid-state electrolyte materials with superior lithium ionic conductivities are vital to the next-generation Li-ion batteries. Molecular dynamics could provide atomic scale information to understand the diffusion process of Li-ion in these superionic conductor materials. Here we implement the Deep Potential Generator (DP-GEN) to set up an efficient protocol to automatically generate interatomic potentials for Li10GeP2S12-type solid-state electrolyte materials (Li10GeP2S12, Li10SiP2S12 and Li10SnP2S12). The reliability and accuracy of the fast interatomic potentials are validated. With the potentials, we extend the simulation of diffusion process to a wide temperature range (300K-1000K) and systems with large size (~1000 atoms). Important technical aspects like the statistical error and size effect are carefully investigated and benchmark tests including the effect of density functional, thermal expansion and configurational disorder are performed. The computed data that considering these factors agrees well with the experimental results and we find that the 3 structures shows different behaviors with respect to configurational disorder. Our work paves the way for further research on computation screening of solid-state electrolyte materials. Copyright © 2020, The Authors. All rights reserved.

关键词： Solid electrolytes

Heat transport in liquid water from first-principles and deep neural network simulations

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Physical Review B 2021年第22期104卷 224202-224202页

作者： Davide Tisi Linfeng Zhang Riccardo Bertossa Han Wang Roberto Car Stefano Baroni SISSA–Scuola Internazionale Superiore di Studi Avanzati 34136 Trieste Italy Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing 100088 People's Republic of China Department of Chemistry Department of Physics and Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA CNR Istituto Officina dei Materiali SISSA unit 34136 Trieste Italy

We compute the thermal conductivity of water within linear response theory from equilibrium molecular dynamics simulations, by adopting two different approaches. In one, the potential energy surface (PES) is derived on the fly from the electronic ground state of density functional theory (DFT) and the corresponding analytical expression is used for the energy flux. In the other, the PES is represented by a deep neural network (DNN) trained on DFT data, whereby the PES has an explicit local decomposition and the energy flux takes a particularly simple expression. By virtue of a gauge invariance principle, established by Marcolongo, Umari, and Baroni, the two approaches should be equivalent if the PES were reproduced accurately by the DNN model. We test this hypothesis by calculating the thermal conductivity, at the GGA (PBE) level of theory, using the direct formulation and its DNN proxy, finding that both approaches yield the same conductivity, in excess of the experimental value by approximately 60%. Besides being numerically much more efficient than its direct DFT counterpart, the DNN scheme has the advantage of being easily applicable to more sophisticated DFT approximations, such as meta-GGA and hybrid functionals, for which it would be hard to derive analytically the expression of the energy flux. We find in this way that a DNN model, trained on meta-GGA (SCAN) data, reduces the deviation from experiment of the predicted thermal conductivity by about 50%, leaving the question open as to whether the residual error is due to deficiencies of the functional, to a neglect of nuclear quantum effects in the atomic dynamics, or, likely, to a combination of the two.

关键词： Thermal conductivity Thermal properties Water Density functional theory Linear response theory Machine learning Molecular dynamics

Heterogeneous multireference alignment for images with application to 2-D classification in single particle reconstruction

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arXiv 2018年

作者： Ma, Chao Bendory, Tamir Boumal, Nicolas Sigworth, Fred Singer, Amit Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Mathematics Princeton University PrincetonNJ United States Department of Cellular and Molecular Physiology Yale University School of Medicine New HavenCT United States

Motivated by the task of 2-D classification in single particle reconstruction by cryo-electron microscopy (cryo-EM), we consider the problem of heterogeneous multireference alignment of images. In this problem, the goal is to estimate a (typically small) set of target images from a (typically large) collection of observations. Each observation is a rotated, noisy version of one of the target images. For each individual observation, neither the rotation nor which target image has been rotated are known. As the noise level in cryo-EM data is high, clustering the observations and estimating individual rotations is challenging. We propose a framework to estimate the target images directly from the observations, completely bypassing the need to cluster or register the images. The framework consists of two steps. First, we estimate rotation-invariant features of the images, such as the bispectrum. These features can be estimated to any desired accuracy, at any noise level, provided sufficiently many observations are collected. Then, we estimate the images from the invariant features. Numerical experiments on synthetic cryo-EM datasets demonstrate the effectiveness of the method. Ultimately, we outline future developments required to apply this method to experimental data. Copyright © 2018, The Authors. All rights reserved.

关键词： Alignment

A deep potential model with long-range electrostatic interactions

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arXiv 2021年

作者： Zhang, Linfeng Wang, Han Muniz, Maria Carolina Panagiotopoulos, Athanassios Z. Car, Roberto Weinan, E. DP Technology Beijing China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China HEDPS CAPT College of Engineering Peking University Beijing100871 China Department of Chemical and Biological Engineering Princeton University PrincetonNJ08544 United States 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 School of Mathematical Sciences Peking University Beijing100871 China AI for Science Institute Beijing China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make possible molecular simulations with the accuracy of quantum mechanical density functional theory, at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei+core electrons) and valence electrons with that of distributions of spherical Gaussian charges located at ionic and electronic sites. The latter are rigorously defined in terms of the centers of the maximally localized Wannier distributions, whose dependence on the local atomic environment is modeled accurately by a deep neural network. In the deep potential long-range (DPLR) model, the electrostatic energy of the Gaussian charge system is added to short-range interactions that are represented as in the standard DP model. The resulting potential energy surface is smooth and possesses analytical forces and virial. Missing effects in the standard DP scheme are recovered, improving on accuracy and predictive power. By including long-range electrostatics, DPLR correctly extrapolates to large systems the potential energy surface learned from quantum mechanical calculations on smaller systems. We illustrate the approach with three examples, the potential energy profile of the water dimer, the free energy of interaction of a water molecule with a liquid water slab, and the phonon dispersion curves of the NaCl crystal. © 2021, CC BY.

关键词： Electrostatics

Angular-Momentum-Dependent Orbital-Free Density Functional Theory

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Physical Review Letters 2013年第6期111卷 066402-066402页

作者： Youqi Ke Florian Libisch Junchao Xia Lin-Wang Wang Emily A. Carter Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics and Andlinger Center for Energy and the Environment Princeton University Princeton New Jersey 08544 USA Material Science Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA

Orbital-free (OF) density functional theory (DFT) directly solves for the electron density rather than the wave function of many electron systems, greatly simplifying and enabling large scale first principles simulations. However, the required approximate noninteracting kinetic energy density functionals and local electron-ion pseudopotentials severely restrict the general applicability of conventional OFDFT. Here, we present a new generation of OFDFT called angular-momentum-dependent (AMD)-OFDFT to harness the accuracy of Kohn-Sham DFT and the simplicity of OFDFT. The angular momenta of electrons are explicitly introduced within atom-centered spheres so that the important ionic core region can be accurately described. In addition to conventional OF total energy functionals, we introduce a crucial nonlocal energy term with a set of AMD energies to correct errors due to the kinetic energy density functional and the local pseudopotential. We find that our AMD-OFDFT formalism offers substantial improvements over conventional OFDFT, as we show for various properties of the transition metal titanium.

关键词： DENSITY functional theory ELECTRON density KINETIC energy PSEUDOPOTENTIAL method TRANSITION metal compounds ELECTRON-ion collisions