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Viscosity in water from first-principles and deep-neural-network simulations

npj computational Materials 2022年第1期8卷 1318-1327页

作者： Cesare Malosso Linfeng Zhang Roberto Car Stefano Baroni Davide Tisi SISSA—Scuola Internazionale Superiore di Studi Avanzati 34136TriesteItaly Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJ08544USA DP Technology Beijing100080PR China Department of Chemistry Department of Physicsand Princeton Institute for the Science and Technology of MaterialsPrinceton UniversityPrincetonNJUSA CNR Istituto Officina dei Materiali SISSA Unit34136TriesteItaly

We report on an extensive study of the viscosity of liquid water at near-ambient conditions,performed within the Green-Kubo theory of linear response and equilibrium ab initio molecular dynamics(AIMD),based on density-functional theory(DFT).In order to cope with the long simulation times necessary to achieve an acceptable statistical accuracy,our ab initio approach is enhanced with deep-neural-network potentials(NNP).This approach is first validated against AIMD results,obtained by using the Perdew–Burke–Ernzerhof(PBE)exchange-correlation functional and paying careful attention to crucial,yet often overlooked,aspects of the statistical data ***,we train a second NNP to a dataset generated from the Strongly Constrained and Appropriately Normed(SCAN)*** the error resulting from the imperfect prediction of the melting line is offset by referring the simulated temperature to the theoretical melting one,our SCAN predictions of the shear viscosity of water are in very good agreement with experiments.

关键词： viscosity Strongly ambient

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Ab initio multi-scale modeling of ferroelectrics: The case of PbTiO3

arXiv

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arXiv 2022年

作者： Xie, Pinchen Chen, Yixiao Weinan, E. Car, Roberto Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics and Program in Applied and Computational Mathematics 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

We report an ab initio multi-scale study of lead titanate using the Deep Potential (DP) models, a family of machine learning-based atomistic models, trained on first-principles density functional theory data, to represent potential and polarization surfaces. Our approach includes anharmonic effects beyond the limitations of reduced models and of the linear approximation for the polarization. The calculated enthalpy, spontaneous polarization, specific heat and dielectric susceptibility agree well with experiments on single crystals. In addition, we study how the free energy depends on the polarization with enhanced sampling methods, further supporting the first-order and order-disorder character of the transition. The latter is evidenced by persistence of local dipoles above the transition temperature. The simulated free energy surface as a function of the global polarization leads to a Landau-Devonshire theory of the single domain crystal. © 2022, CC BY.

关键词： Free energy

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Characterization of maximally random jammed sphere packings: Voronoi correlation functions

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Physical Review E 2014年第5期90卷 052120-052120页

作者： Michael A. Klatt Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

We characterize the structure of maximally random jammed (MRJ) sphere packings by computing the Minkowski functionals (volume, surface area, and integrated mean curvature) of their associated Voronoi cells. The probability distribution functions of these functionals of Voronoi cells in MRJ sphere packings are qualitatively similar to those of an equilibrium hard-sphere liquid and partly even to the uncorrelated Poisson point process, implying that such local statistics are relatively structurally insensitive. This is not surprising because the Minkowski functionals of a single Voronoi cell incorporate only local information and are insensitive to global structural information. To improve upon this, we introduce descriptors that incorporate nonlocal information via the correlation functions of the Minkowski functionals of two cells at a given distance as well as certain cell-cell probability density functions. We evaluate these higher-order functions for our MRJ packings as well as equilibrium hard spheres and the Poisson point process. It is shown that these Minkowski correlation and density functions contain visibly more information than the corresponding standard pair-correlation functions. We find strong anticorrelations in the Voronoi volumes for the hyperuniform MRJ packings, consistent with previous findings for other pair correlations [A. Donev et al., Phys. Rev. Lett. 95, 090604 (2005)], indicating that large-scale volume fluctuations are suppressed by accompanying large Voronoi cells with small cells, and vice versa. In contrast to the aforementioned local Voronoi statistics, the correlation functions of the Voronoi cells qualitatively distinguish the structure of MRJ sphere packings (prototypical glasses) from that of not only the Poisson point process but also the correlated equilibrium hard-sphere liquids. Moreover, while we did not find any perfect icosahedra (the locally densest possible structure in which a central sphere contacts 12 neighbors) in th

关键词： RANDOM variables VORONOI polygons MINKOWSKI space POISSON processes FUNCTIONS (mathematics)

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Effect of dimensionality on the percolation thresholds of various d-dimensional lattices

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Physical Review E 2013年第3期87卷 032149-032149页

作者： S. Torquato Y. Jiao []Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

We show analytically that the [0,1], [1,1], and [2,1] Padé approximants of the mean cluster number S(p) for site and bond percolation on general d-dimensional lattices are upper bounds on this quantity in any Euclidean dimension d, where p is the occupation probability. These results lead to certain lower bounds on the percolation threshold pc that become progressively tighter as d increases and asymptotically exact as d becomes large. These lower-bound estimates depend on the structure of the d-dimensional lattice and whether site or bond percolation is being considered. We obtain explicit bounds on pc for both site and bond percolation on five different lattices: d-dimensional generalizations of the simple-cubic, body-centered-cubic, and face-centered-cubic Bravais lattices as well as the d-dimensional generalizations of the diamond and kagomé (or pyrochlore) non-Bravais lattices. These analytical estimates are used to assess available simulation results across dimensions (up through d=13 in some cases). It is noteworthy that the tightest lower bound provides reasonable estimates of pc in relatively low dimensions and becomes increasingly accurate as d grows. We also derive high-dimensional asymptotic expansions for pc for the 10 percolation problems and compare them to the Bethe-lattice approximation. Finally, we remark on the radius of convergence of the series expansion of S in powers of p as the dimension grows.

关键词： Solvents

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Effect of dimensionality on the percolation threshold of overlapping nonspherical hyperparticles

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Physical Review E 2013年第2期87卷 022111-022111页

We study the effect of dimensionality on the percolation threshold ηc of identical overlapping nonspherical convex hyperparticles in d-dimensional Euclidean space Rd. This is done by formulating a scaling relation for ηc that is based on a rigorous lower bound [Torquato, J. Chem. Phys. 136, 054106 (2012)] and a conjecture that hyperspheres provide the highest threshold, for any d, among all convex hyperparticle shapes (that are not a trivial affine transformation of a hypersphere). This scaling relation also exploits the recently discovered principle that low-dimensional continuum percolation behavior encodes high-dimensional information. We derive an explicit formula for the exclusion volume vex of a hyperparticle of arbitrary shape in terms of its d-dimensional volume v, surface area s, and radius of mean curvature R¯ (or, equivalently, mean width). These basic geometrical properties are computed for a wide variety of nonspherical hyperparticle shapes with random orientations across all dimensions, including, among other shapes, various polygons for d=2, Platonic solids, spherocylinders, parallepipeds, and zero-volume plates for d=3 and their appropriate generalizations for d≥4. Using this information, we compute the lower bound and scaling relation for ηc for this comprehensive set of continuum percolation models across dimensions. We demonstrate that the scaling relation provides accurate upper-bound estimates of the threshold ηc across dimensions and becomes increasingly accurate as the space dimension increases.

关键词： DIMENSIONAL analysis PERCOLATION (Statistical physics) EUCLIDEAN geometry SCALING laws (Statistical physics) POLYGONS SHAPES

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Instantaneous radar polarimetry with multiple dually-polarized antennas

Instantaneous radar polarimetry with multiple dually-polariz...

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40th Asilomar Conference on Signals, Systems, and Computers, ACSSC '06

作者： Calderbank, A.R. Howard, S.D. Moran, W. Pezeshki, A. Zoltowski, M. Program in Applied and Computational Mathematics Princeton University Princeton NJ United States Defence Science and Technology Organization Edinburgh Australia Electrical Engineering and Computer Science University of Melbourne Melbourne Australia Electrical and Computer Engineering Purdue University West Lafayette IN United States

ISBN: (纸本)1424407850

Fully Polarimetric radar systems are capable of simultaneously transmitting and receiving in two orthogonal polarizations. Instantaneous radar polarimetry exploits both polarization modes of a dually-polarized radar transmitter and receiver on a pulse by pulse basis, and can improve the radar detection performance and suppress range sidelobes. In this paper, we extend the use of instantaneous radar polarimetry for radar systems with multiple dually-polarized transmit and receive antennas. Alamouti signal processing is used to coordinate transmission of Golay pairs of phase codes waveforms across polarizations and multiple antennas. The integration of multi-antenna signal processing with instantaneous radar polarimetry can further improve the detection performance, at a computational cost comparable to single channel matched filtering.

关键词： Polarimeters

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

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Physical Review E 2021年第5期103卷 052126-052126页

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

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 “stealt

关键词： Fluctuations & noise

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Hyperuniformity of generalized random organization models

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Physical Review E 2019年第2期99卷 022115-022115页

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

Studies of random organization models of monodisperse (i.e., identical) spherical particles have shown that a hyperuniform state is achievable when the system goes through an absorbing phase transition to a critical state. Here we investigate to what extent hyperuniformity is preserved when the model is generalized to particles with a size distribution and/or nonspherical shapes. We begin by examining binary disks in two dimensions and demonstrate that their critical states are hyperuniform as two-phase media, but not hyperuniform nor multihyperuniform as point patterns formed by the particle centroids. We further confirm the generality of our findings by studying particles with a continuous size distribution. Finally, to study the effect of rotational degrees of freedom, we extend our model to noncircular particles, namely, hard rectangles with various aspect ratios, including the hard-needle limit. Although these systems exhibit only short-range orientational order, hyperuniformity is still preserved. Our analysis reveals that the redistribution of the “mass” of the particles rather than the particle centroids is central to this dynamical process. The consideration of the “active volume fraction” of generalized random organization models may help to resolve which universality class they belong to and hence may lead to a deeper theoretical understanding of absorbing-state models. Our results suggest that general particle systems subject to random organization can be a robust way to fabricate a wide class of hyperuniform states of matter by tuning the structures via different particle-size and -shape distributions. This in turn potentially enables the creation of multifunctional hyperuniform materials with desirable optical, transport, and mechanical properties.

关键词： Classical statistical mechanics

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Characterization of maximally random jammed sphere packings. III. Transport and electromagnetic properties via correlation functions

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Physical Review E 2018年第1期97卷 012118-012118页

In the first two papers of this series, we characterized the structure of maximally random jammed (MRJ) sphere packings across length scales by computing a variety of different correlation functions, spectral functions, hole probabilities, and local density fluctuations. From the remarkable structural features of the MRJ packings, especially its disordered hyperuniformity, exceptional physical properties can be expected. Here we employ these structural descriptors to estimate effective transport and electromagnetic properties via rigorous bounds, exact expansions, and accurate analytical approximation formulas. These property formulas include interfacial bounds as well as universal scaling laws for the mean survival time and the fluid permeability. We also estimate the principal relaxation time associated with Brownian motion among perfectly absorbing traps. For the propagation of electromagnetic waves in the long-wavelength limit, we show that a dispersion of dielectric MRJ spheres within a matrix of another dielectric material forms, to a very good approximation, a dissipationless disordered and isotropic two-phase medium for any phase dielectric contrast ratio. We compare the effective properties of the MRJ sphere packings to those of overlapping spheres, equilibrium hard-sphere packings, and lattices of hard spheres. Moreover, we generalize results to micro- and macroscopically anisotropic packings of spheroids with tensorial effective properties. The analytic bounds predict the qualitative trend in the physical properties associated with these structures, which provides guidance to more time-consuming simulations and experiments. They especially provide impetus for experiments to design materials with unique bulk properties resulting from hyperuniformity, including structural-color and color-sensing applications.

关键词： Classical statistical mechanics

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Optimized Large Hyperuniform Binary Colloidal Suspensions in Two Dimensions

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Physical Review Letters 2020年第6期125卷 068002-068002页

作者： Zheng Ma Enrique Lomba Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The creation of disordered hyperuniform materials with extraordinary optical properties (e.g., large complete photonic band gaps) requires a capacity to synthesize large samples that are effectively hyperuniform down to the nanoscale. Motivated by this challenge, we propose a feasible equilibrium fabrication protocol using binary paramagnetic colloidal particles confined in a 2D plane. The strong and long-ranged dipolar interaction induced by a tunable magnetic field is free from screening effects that attenuate long-ranged electrostatic interactions in charged colloidal systems. Specifically, we numerically find a family of optimal size ratios that makes the two-phase system effectively hyperuniform. We show that hyperuniformity is a general consequence of low isothermal compressibilities, which makes our protocol suitable to treat more general systems with other long-ranged interactions, dimensionalities, and/or polydispersity. Our methodology paves the way to synthesize large photonic hyperuniform materials that function in the visible to infrared range and hence may accelerate the discovery of novel photonic materials.

关键词： Applications of soft matter Colloids Disordered systems

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