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Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective pair interactions

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Physical Review E 2020年第3期101卷 032124-032124页

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

The capacity to identify realizable many-body configurations associated with targeted functional forms for the pair correlation function g2(r) or its corresponding structure factor S(k) is of great fundamental and practical importance. While there are obvious necessary conditions that a prescribed structure factor at number density ρ must satisfy to be configurationally realizable, sufficient conditions are generally not known due to the infinite degeneracy of configurations with different higher-order correlation functions. A major aim of this paper is to expand our theoretical knowledge of the class of pair correlation functions or structure factors that are realizable by classical disordered ensembles of particle configurations, including exotic “hyperuniform” varieties. We first introduce a theoretical formalism that provides a means to draw classical particle configurations from canonical ensembles with certain pairwise-additive potentials that could correspond to targeted analytical functional forms for the structure factor. This formulation enables us to devise an improved algorithm to construct systematically canonical-ensemble particle configurations with such targeted pair statistics, whenever realizable. As a proof of concept, we test the algorithm by targeting several different structure factors across dimensions that are known to be realizable and one hyperuniform target that is known to be nontrivially unrealizable. Our algorithm succeeds for all realizable targets and appropriately fails for the unrealizable target, demonstrating the accuracy and power of the method to numerically investigate the realizability problem. Subsequently, we also target several families of structure-factor functions that meet the known necessary realizability conditions but are not known to be realizable by disordered hyperuniform point configurations, including d-dimensional Gaussian structure factors, d-dimensional generalizations of the two-dimensional one-component plas

关键词： Classical statistical mechanics

Isotope effects in liquid water via deep potential molecular dynamics

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arXiv 2019年

作者： Ko, Hsin-Yu Zhang, Linfeng Santra, Biswajit Wang, Han Weinan, E. DiStasio, Robert A. Cara, Roberto Department of Chemistry Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Physics Temple University PhiladelphiaPA19122 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China Department of Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry and Chemical Biology Cornell University IthacaNY14853 United States Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States

A comprehensive microscopic understanding of ambient liquid water is a major challenge for ab initio simulations as it simultaneously requires an accurate quantum mechanical description of the underlying potential energy surface (PES) as well as extensive sampling of configuration space. Due to the presence of light atoms (e.g., H or D), nuclear quantum fluctuations lead to observable changes in the structural properties of liquid water (e.g., isotope effects), and therefore provide yet another challenge for ab initio approaches. In this work, we demonstrate that the combination of dispersion-inclusive hybrid density functional theory (DFT), the Feynman discretized path-integral (PI) approach, and machine learning (ML) constitutes a versatile ab initio based framework that enables extensive sampling of both thermal and nuclear quantum fluctuations on a quite accurate underlying PES. In particular, we employ the recently developed deep potential molecular dynamics (DPMD) model - a neural-network representation of the ab initio PES - in conjunction with a PI approach based on the generalized Langevin equation (PIGLET) to investigate how isotope effects influence the structural properties of ambient liquid H2O and D2O. Through a detailed analysis of the interference differential cross sections as well as several radial and angular distribution functions, we demonstrate that this approach can furnish a semi-quantitative prediction of these subtle isotope effects. Copyright © 2019, The Authors. All rights reserved.

关键词： Deep neural networks

Quantum phase transitions in long-range interacting hyperuniform spin chains in a transverse field

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Physical Review B 2021年第1期103卷 014118-014118页

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

Hyperuniform states of matter are characterized by anomalous suppression of long-wavelength density fluctuations. While most of the interesting cases of disordered hyperuniformity are provided by complex many-body systems such as liquids or amorphous solids, classical spin chains with certain long-range interactions have been shown to demonstrate the same phenomenon. Such spin-chain systems are ideal models for exploring the effects of quantum mechanics on hyperuniformity. It is well-known that the transverse field Ising model shows a quantum phase transition (QPT) at zero temperature. Under the quantum effects of a transverse magnetic field, classical hyperuniform spin chains are expected to lose their hyperuniformity. High-precision simulations of these cases are complicated because of the presence of highly nontrivial long-range interactions. We perform an extensive analysis of these systems using density matrix renormalization group simulations to study the possibilities of phase transitions and the mechanism by which they lose hyperuniformity. Even for a spin chain of length 30, we see discontinuous changes in properties like the “τ order metric” of the ground state, the measure of hyperuniformity, and the second cumulant of the total magnetization along the x-direction, all suggestive of first-order QPTs. An interesting feature of the phase transitions in these disordered hyperuniform spin chains is that, depending on the parameter values, the presence of a transverse magnetic field may lead remarkably to an increase in the order of the ground state as measured by the “τ order metric,” even if hyperuniformity is lost. Therefore, it would be possible to design materials to target specific novel quantum behaviors in the presence of a transverse magnetic field. Our numerical investigations suggest that these spin chains can show no more than two QPTs. We further analyze the long-range interacting spin chains via the Jordan-Wigner mapping onto a system of spinless

关键词： Long-range interactions Quantum phase transitions Spin chains

DATA-DRIVEN MORI-ZWANZIG: REDUCED ORDER MODELING OF SPARSE SENSORS MEASUREMENTS FOR BOUNDARY LAYER TRANSITION

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arXiv 2023年

作者： Woodward, Michael Tian, Yifeng Mohan, Arvind Lin, Yen Ting Hader, Christoph Fasel, Hermann Chertkov, Michael Livescu, Daniel Computer Computational and Statistical Sciences Division Los Alamos National Laboratory Los AlamosNM87544 United States Graduate Interdisciplinary Program in Applied Mathematics Department of Mathematics University of Arizona TucsonAZ85721 United States Department of Aerospace and Mechanical Engineering University of Arizona TucsonAZ85721 United States

Understanding, predicting and controlling laminar-turbulent boundary-layer transition is crucial for the next generation aircraft design. However, in real flight experiments, or wind tunnel tests, often only sparse sensor measurements can be collected at fixed locations. Thus, in developing reduced models for predicting and controlling the flow at the sensor locations, the main challenge is in accounting for how the surrounding field of unobserved (or unresolved) variables interacts with the observed (or resolved) variables at the fixed sensor locations. This makes the Mori-Zwanzig (MZ) formalism a natural choice, as it results in the Generalized Langevin Equations which provides a mathematically sound framework for constructing non-Markovian reduced-order models that include the effects the unresolved variables have on the resolved variables. These effects are captured in the so called memory kernel and orthogonal dynamics, which, when using Mori's linear projection, provides a higher order approximation to the traditional approximate Koopman learning methods. In this work, we explore recently developed data-driven methods for extracting the MZ operators to two boundary-layer flows obtained from high resolution data;a low speed incompressible flow over a flat plate exhibiting bypass transition;and a high speed compressible flow over a flared cone at Mach 6 and zero angle of attack where transition was initiated using a broadband forcing approach ("natural" transition). In each case, an array of "sensors" are placed near the surface of the solid boundary, and the MZ operators are learned and the predictions are compared to the Extended Dynamic Mode Decomposition (EDMD), both using delay embedded coordinates. Further comparisons are made with Long Short-Term Memory (LSTM) and a regression based projection framework using neural networks for the MZ operators. First, we compare the effects of including delay embedded coordinates with EDMD and Mori based MZ and provide

关键词： Dynamic mode decomposition

Methodology to construct large realizations of perfectly hyperuniform disordered packings

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Physical Review E 2019年第5期99卷 052141-052141页

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

Disordered hyperuniform packings (or dispersions) are unusual amorphous two-phase materials that are endowed with exotic physical properties. Such hyperuniform systems are characterized by an anomalous suppression of volume-fraction fluctuations at infinitely long-wavelengths, compared to ordinary disordered materials. While there has been growing interest in such singular states of amorphous matter, a major obstacle has been an inability to produce large samples that are perfectly hyperuniform due to practical limitations of conventional numerical and experimental methods. To overcome these limitations, we introduce a general theoretical methodology to construct perfectly hyperuniform packings in d-dimensional Euclidean space Rd. Specifically, beginning with an initial general tessellation of space by disjoint cells that meets a “bounded-cell” condition, hard particles of general shape are placed inside each cell such that the local-cell particle packing fractions are identical to the global packing fraction. We prove that the constructed packings with a polydispersity in size are perfectly hyperuniform in the infinite-sample-size limit, regardless of particle shapes, positions, and numbers per cell. We use this theoretical formulation to devise an efficient and tunable algorithm to generate extremely large realizations of such packings. We employ two distinct initial tessellations: Voronoi as well as sphere tessellations. Beginning with Voronoi tessellations, we show that our algorithm can remarkably convert extremely large nonhyperuniform packings into hyperuniform ones in R2 and R3. Implementing our theoretical methodology on sphere tessellations, we establish the hyperuniformity of the classical Hashin-Shtrikman multiscale coated-spheres structures, which are known to be two-phase media microstructures that possess optimal effective transport and elastic properties. A consequence of our work is a rigorous demonstration that packings that have identical tessella

关键词： Fluctuations & noise

Random Measures, ANOVA Models and Quantifying Uncertainty in Randomized Controlled Trials

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arXiv 2023年

作者： Bastian, Caleb Deen Rabitz, Herschel Rempala, Grzegorz A. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Mathematics The Ohio State University ColumbusOH43210 United States Division of Biostatistics The Ohio State University ColumbusOH43210 United States

This short paper introduces a novel approach to global sensitivity analysis, grounded in the variance-covariance structure of random variables derived from random measures. The proposed methodology facilitates the application of information-theoretic rules for uncertainty quantification, offering several advantages. Specifically, the approach provides valuable insights into the decomposition of variance within discrete subspaces, similar to the standard ANOVA analysis. To illustrate this point, the method is applied to datasets obtained from the analysis of randomized controlled trials on evaluating the efficacy of the COVID-19 vaccine and assessing clinical endpoints in a lung cancer *** Codes 92-05, 92-11 Copyright © 2023, The Authors. All rights reserved.

关键词： Sensitivity analysis

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

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arXiv 2021年

作者： Tisi, Davide Zhang, Linfeng Bertossa, Riccardo Wang, Han Car, Roberto Baroni, Stefano SISSA - Scuola Internazionale Superiore di Studi Avanzati Trieste34136 Italy Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States CNR Istituto Officina Dei Materiali SISSA Unit Trieste34136 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, reduce 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. Copyright © 2021, The Authors. All rights reserved.

关键词： Deep neural networks

On the uniqueness of FROG methods

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arXiv 2017年

作者： Bendory, Tamir Sidorenko, Pavel Eldar, Yonina C. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Physics and Solid State Institute Technion-Israel Institute of Technology Haifa Israel Department of Electrical Engineering Technion-Israel Institute of Technology Haifa Israel

The problem of recovering a signal from its power spectrum, called phase retrieval, arises in many scientific fields. One of many examples is ultra-short laser pulse characterization in which the electromagnetic field is oscillating with ∼ 1015 Hz and phase information cannot be measured directly due to limitations of the electronic sensors. Phase retrieval is ill-posed in most cases as there are many different signals with the same Fourier transform magnitude. To overcome this fundamental ill-posedness, several measurement techniques are used in practice. One of the most popular methods for complete characterization of ultra-short laser pulses is the Frequency-Resolved Optical Gating (FROG). In FROG, the acquired data is the power spectrum of the product of the unknown pulse with its delayed replica. Therefore the measured signal is a quartic function of the unknown pulse. A generalized version of FROG, where the delayed replica is replaced by a second unknown pulse, is called blind FROG. In this case, the measured signal is quadratic with respect to both pulses. In this letter we introduce and formulate FROG-type techniques. We then show that almost all band-limited signals are determined uniquely, up to trivial ambiguities, by blind FROG measurements (and thus also by FROG), if in addition we have access to the signals power spectrum. Copyright © 2017, The Authors. All rights reserved.

关键词： Power spectrum

Mori–Zwanzig Modal Decomposition

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arXiv 2023年

作者： Woodward, Michael Tian, Yifeng Lin, Yen Ting Hader, Christoph Fasel, Hermann Livescu, Daniel Graduate Interdisciplinary Program in Applied Mathematics Department of Mathematics University of Arizona TucsonAZ85721 United States Computer Computational and Statistical Sciences Division Los Alamos National Laboratory Los AlamosNM87544 United States Department of Aerospace and Mechanical Engineering University of Arizona TucsonAZ85721 United States

We introduce the Mori-Zwanzig (MZ) Modal Decomposition (MZMD), a novel technique for performing modal analysis of large scale spatio-temporal structures in complex dynamical systems, and show that it represents an efficient generalization of Dynamic Mode Decomposition (DMD). The MZ formalism provides a mathematical framework for constructing non-Markovian reduced-order models of resolved variables from high-dimensional dynamical systems, incorporating the effects of unresolved dynamics through the memory kernel and orthogonal dynamics. We present a formulation and analysis of the modes and spectrum from MZMD and compare it to DMD when applied to a complex flow: a Direct Numerical Simulation (DNS) data-set of laminar-turbulent boundary-layer transition flow over a flared cone at Mach 6. We show that the addition of memory terms by MZMD improves the resolution of spatio-temporal structures within the transitional/turbulent regime, which contains features that arise due to nonlinear mechanisms, such as the generation of the so-called "hot" streaks on the surface of the flared cone. As a result, compared to DMD, MZMD improves future state prediction accuracy, while requiring nearly the same computational cost. Copyright © 2023, The Authors. All rights reserved.

关键词： Dynamic mode decomposition