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Deep neural network for the dielectric response of insulators

Physical Review B 2020年第4期102卷 041121(R)-041121(R)页

作者： Linfeng Zhang Mohan Chen Xifan Wu Han Wang Weinan E Roberto Car Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

We introduce a deep neural network to model in a symmetry preserving way the environmental dependence of the centers of the electronic charge. The model learns from ab initio density functional theory, wherein the electronic centers are uniquely assigned by the maximally localized Wannier functions. When combined with the deep potential model of the atomic potential energy surface, the scheme predicts the dielectric response of insulators for trajectories inaccessible to direct ab initio simulation. The scheme is nonperturbative and can capture the response of a mutating chemical environment. We demonstrate the approach by calculating the infrared spectra of liquid water at standard conditions, and of ice under extreme pressure, when it transforms from a molecular to an ionic crystal.

关键词： Electric polarization Electrical properties Electronic structure Ferroelectrics Liquids Piezoelectrics Density functional theory First-principles calculations Machine learning Molecular dynamics Multiscale modeling Wannier function methods

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Understanding degeneracy of two-point correlation functions via Debye random media

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Physical Review E 2021年第4期104卷 045306-045306页

作者： Murray Skolnick 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

It is well known that the degeneracy of two-phase microstructures with the same volume fraction and two-point correlation function S2(r) is generally infinite. To elucidate the degeneracy problem explicitly, we examine Debye random media, which are entirely defined by a purely exponentially decaying two-point correlation function S2(r). In this work, we consider three different classes of Debye random media. First, we generate the “most probable” class using the Yeong-Torquato construction algorithm [Yeong and Torquato, Phys. Rev. E 57, 495 (1998)]. A second class of Debye random media is obtained by demonstrating that the corresponding two-point correlation functions are effectively realized in the first three space dimensions by certain models of overlapping, polydisperse spheres. A third class is obtained by using the Yeong-Torquato algorithm to construct Debye random media that are constrained to have an unusual prescribed pore-size probability density function. We structurally discriminate these three classes of Debye random media from one another by ascertaining their other statistical descriptors, including the pore-size, surface correlation, chord-length probability density, and lineal-path functions. We also compare and contrast the percolation thresholds as well as the diffusion and fluid transport properties of these degenerate Debye random media. We find that these three classes of Debye random media are generally distinguished by the aforementioned descriptors, and their microstructures are also visually distinct from one another. Our work further confirms the well-known fact that scattering information is insufficient to determine the effective physical properties of two-phase media. Additionally, our findings demonstrate the importance of the other two-point descriptors considered here in the design of materials with a spectrum of physical properties.

关键词： Complex systems

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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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Generation and structural characterization of Debye random media

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Physical Review E 2020年第4期102卷 043310-043310页

In their seminal paper on scattering by an inhomogeneous solid, Debye and coworkers proposed a simple exponentially decaying function for the two-point correlation function of an idealized class of two-phase random media. Such Debye random media, which have been shown to be realizable, are singularly distinct from all other models of two-phase media in that they are entirely defined by their one- and two-point correlation functions. To our knowledge, there has been no determination of other microstructural descriptors of Debye random media. In this paper, we generate Debye random media in two dimensions using an accelerated Yeong-Torquato construction algorithm. We then ascertain microstructural descriptors of the constructed media, including their surface correlation functions, pore-size distributions, lineal-path function, and chord-length probability density function. Accurate semianalytic and empirical formulas for these descriptors are devised. We compare our results for Debye random media to those of other popular models (overlapping disks and equilibrium hard disks) and find that the former model possesses a wider spectrum of hole sizes, including a substantial fraction of large holes. Our algorithm can be applied to generate other models defined by their two-point correlation functions, and their other microstructural descriptors can be determined and analyzed by the procedures laid out here.

关键词： Patterns in complex systems

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Ground states of stealthy hyperuniform potentials. II. Stacked-slider phases

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Physical Review E 2015年第2期92卷 022120-022120页

作者： G. Zhang F. H. Stillinger S. 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

Stealthy potentials, a family of long-range isotropic pair potentials, produce infinitely degenerate disordered ground states at high densities and crystalline ground states at low densities in d-dimensional Euclidean space Rd. In the previous paper in this series, we numerically studied the entropically favored ground states in the canonical ensemble in the zero-temperature limit across the first three Euclidean space dimensions. In this paper, we investigate using both numerical and theoretical techniques metastable stacked-slider phases, which are part of the ground-state manifold of stealthy potentials at densities in which crystal ground states are favored entropically. Our numerical results enable us to devise analytical models of this phase in two, three, and higher dimensions. Utilizing this model, we estimated the size of the feasible region in configuration space of the stacked-slider phase, finding it to be smaller than that of crystal structures in the infinite-system-size limit, which is consistent with our recent previous work. In two dimensions, we also determine exact expressions for the pair correlation function and structure factor of the analytical model of stacked-slider phases and analyze the connectedness of the ground-state manifold of stealthy potentials in this density regime. We demonstrate that stacked-slider phases are distinguishable states of matter; they are nonperiodic, statistically anisotropic structures that possess long-range orientational order but have zero shear modulus. We outline some possible future avenues of research to elucidate our understanding of this unusual phase of matter.

关键词： Ground state

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Characterization of maximally random jammed sphere packings. II. Correlation functions and density fluctuations

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Physical Review E 2016年第2期94卷 022152-022152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

In the first paper of this series, we introduced Voronoi correlation functions to characterize the structure of maximally random jammed (MRJ) sphere packings across length scales. In the present paper, we determine a variety of different correlation functions that arise in rigorous expressions for the effective physical properties of MRJ sphere packings and compare them to the corresponding statistical descriptors for overlapping spheres and equilibrium hard-sphere systems. Such structural descriptors arise in rigorous bounds and formulas for effective transport properties, diffusion and reactions constants, elastic moduli, and electromagnetic characteristics. First, we calculate the two-point, surface-void, and surface-surface correlation functions, for which we derive explicit analytical formulas for finite hard-sphere packings. We show analytically how the contact Dirac delta function contribution to the pair correlation function g2(r) for MRJ packings translates into distinct functional behaviors of these two-point correlation functions that do not arise in the other two models examined here. Then we show how the spectral density distinguishes the MRJ packings from the other disordered systems in that the spectral density vanishes in the limit of infinite wavelengths; i.e., these packings are hyperuniform, which means that density fluctuations on large length scales are anomalously suppressed. Moreover, for all model systems, we study and compute exclusion probabilities and pore size distributions, as well as local density fluctuations. We conjecture that for general disordered hard-sphere packings, a central limit theorem holds for the number of points within an spherical observation window. Our analysis links problems of interest in material science, chemistry, physics, and mathematics. In the third paper of this series, we will evaluate bounds and estimates of a host of different physical properties of the MRJ sphere packings that are based on the structural

关键词： Jamming

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Detailed characterization of rattlers in exactly isostatic, strictly jammed sphere packings

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Physical Review E 2013年第6期88卷 062208-062208页

作者： Steven Atkinson Frank H. Stillinger 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 generate jammed disordered packings of 100≤N≤2000 monodisperse hard spheres in three dimensions whose strictly jammed backbones are demonstrated to be exactly isostatic with unprecedented numerical accuracy. This is accomplished by using the Torquato-Jiao (TJ) packing algorithm as a means of studying the maximally random jammed (MRJ) state. The rattler fraction of these packings converges towards 0.015 in the infinite-system limit, which is markedly lower than previous estimates for the MRJ state using the Lubachevsky-Stillinger protocol. This is because the packings that the TJ algorithm creates are closer to the true MRJ state, as shown using bond-orientational and translational order metrics. The rattler pair correlation statistics exhibit strongly correlated behavior contrary to the conventional understanding that they be randomly (Poisson) distributed. Dynamically interacting “polyrattlers” may be found imprisoned in shared cages as well as interacting through “bottlenecks” in the backbone and these clusters are mainly responsible for the sharp increase in the rattler pair correlation function near contact. We discover the surprising existence of polyrattlers with cluster sizes of up to five rattlers (which is expected to increase with system size) and present a distribution of polyrattler occurrence as a function of cluster size and system size. We also enumerate all of the rattler interaction topologies we observe and present images of several examples, showing that MRJ packings of monodisperse spheres can contain large rattler cages while still obeying the strict jamming criterion. The backbone spheres that encage the rattlers are significantly hypostatic, implying that correspondingly hyperstatic regions must exist elsewhere in these isostatic packings. We also observe that rattlers in hard-sphere packings share an apparent connection with the low-temperature two-level system anomalies that appear in real amorphous insulators and semiconductors.

关键词： Packing

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Extracting spatial information from networks with low-order eigenvectors

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Physical Review E 2013年第3期87卷 032803-032803页

作者： Mihai Cucuringu Vincent D. Blondel Paul Van Dooren Program in Applied and Computational Mathematics (PACM) Princeton University Fine Hall Princeton NJ 08544-1000 Washington Road United States Department of Applied Mathematics Université Catholique de Louvain B-1348 Louvain-la-Neuve Belgium

We consider the problem of inferring meaningful spatial information in networks from incomplete information on the connection intensity between the nodes of the network. We consider two spatially distributed networks: a population migration flow network within the US, and a network of mobile phone calls between cities in Belgium. For both networks we use the eigenvectors of the Laplacian matrix constructed from the link intensities to obtain informative visualizations and capture natural geographical subdivisions. We observe that some low-order eigenvectors localize very well and seem to reveal small geographically cohesive regions that match remarkably well with political and administrative boundaries. We discuss possible explanations for this observation by describing diffusion maps and localized eigenfunctions. In addition, we discuss a possible connection with the weighted graph cut problem, and provide numerical evidence supporting the idea that lower-order eigenvectors point out local cuts in the network. However, we do not provide a formal and rigorous justification for our observations.

关键词： Eigenvalues and eigenfunctions

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Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations

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Physical Review E 2015年第2期92卷 022119-022119页

Systems of particles interacting with “stealthy” pair potentials have been shown to possess infinitely degenerate disordered hyperuniform classical ground states with novel physical properties. Previous attempts to sample the infinitely degenerate ground states used energy minimization techniques, introducing algorithmic dependence that is artificial in nature. Recently, an ensemble theory of stealthy hyperuniform ground states was formulated to predict the structure and thermodynamics that was shown to be in excellent agreement with corresponding computer simulation results in the canonical ensemble (in the zero-temperature limit). In this paper, we provide details and justifications of the simulation procedure, which involves performing molecular dynamics simulations at sufficiently low temperatures and minimizing the energy of the snapshots for both the high-density disordered regime, where the theory applies, as well as lower densities. We also use numerical simulations to extend our study to the lower-density regime. We report results for the pair correlation functions, structure factors, and Voronoi cell statistics. In the high-density regime, we verify the theoretical ansatz that stealthy disordered ground states behave like “pseudo” disordered equilibrium hard-sphere systems in Fourier space. The pair statistics obey certain exact integral conditions with very high accuracy. These results show that as the density decreases from the high-density limit, the disordered ground states in the canonical ensemble are characterized by an increasing degree of short-range order and eventually the system undergoes a phase transition to crystalline ground states. In the crystalline regime (low densities), there exist aperiodic structures that are part of the ground-state manifold but yet are not entropically favored. We also provide numerical evidence suggesting that different forms of stealthy pair potentials produce the same ground-state ensemble in the zero-temperatur

关键词： Ground state

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Time-frequency analysis and determinantal point processes 13

Time-frequency analysis and determinantal point processes

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13th International Conference on Theoretical and computational Acoustics, ICTCA 2017

作者： Abreu, Luís Daniel Gröchenig, Karlheinz Pereira, João M. Romero, José L. Torquato, Salvatore Acoustics Research Institute Austrian Academy of Sciences Vienna Austria NuHAG Faculty of Mathematics University of Vienna Vienna Austria Program in Applied and Computational Mathematics Princeton University New Jersey United States Princeton Materials Institute Department of Chemistry Princeton University New Jersey United States

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