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Physics of Fluids 2023年第1期35卷

作者： Jonathan L. Palafoutas William A. Sirignano 1Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA 2Department of Mechanical and Aerospace Engineering University of California Irvine Irvine California 92697 USA

This article was published online on 2 December 2022 with errors throughout the paper. All the derivative terms had the wrong denominator; the denominators were

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Manifestations of metastable criticality in the long-range structure of model water glasses

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arXiv 2021年

作者： Gartner, Thomas E. Torquato, Salvatore Car, Roberto Debenedetti, Pablo G. Department of Chemistry Princeton University PrincetonNJ United States Department of Physics Princeton University PrincetonNJ United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ United States Department of Chemical and Biological Engineering Princeton University PrincetonNJ United States

Much attention has been devoted to water’s metastable phase behavior, including polyamorphism (multiple amorphous solid phases), and the hypothesized liquid-liquid transition and associated critical point. However, the possible relationship between these phenomena remains incompletely understood. Using molecular dynamics simulations of the realistic TIP4P/2005 model, we found a striking signature of the liquid-liquid critical point in the structure of water glasses, manifested as a pronounced increase in long-range density fluctuations at pressures proximate to the critical pressure. By contrast, these signatures were absent in glasses of two model systems that lack a critical point. We also characterized the departure from equilibrium upon vitrification via the non-equilibrium index;water-like systems exhibited a strong pressure dependence in this metric, whereas simple liquids did not. These results reflect a surprising relationship between the metastable equilibrium phenomenon of liquid-liquid criticality and the non-equilibrium structure of glassy water, with implications for our understanding of water phase behavior and glass physics. Our calculations suggest a possible experimental route to probing the existence of the liquid-liquid transition in water and other fluids. © 2021, CC BY.

关键词： Criticality (nuclear fission)

Threshold and decay properties of transient isolated turbulent band in plane Couette flow

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applied mathematics and Mechanics(English Edition) 2019年第10期40卷 1449-1456页

作者： Jianzhou LU Jianjun TAO Weitao ZHOU Xiangming XIONG CAPT-HEDPS SKLTCS Collaborative Innovation Center of IFSA Department of Mechanics and Engineering Science College of Engineering Peking University Beijing 100871 China The Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 U. S.A.

By direct numerical simulations of the plane Couette flow (PCF) in a large computational domain, it is shown that an isolated turbulent band decays monotonically at low Reynolds numbers but experiences transient growth before the eventual relaminarization at moderate Reynolds numbers. The lower bound Reynolds number of the transient-growth regime is determined as 286. The width, length, and tilt angle of the iso- lated band structure are defined based on the disturbance kinetic energy in the mid-plane, and the geometric characteristics of the band can be described with a tilted rectangle. It is illustrated that before its eventual fragmentation, the isolated turbulent band decays in a style of longitudinal contraction, where the center, width, and tilt angle of the band keep almost constant but the band length contracts with a statistically constant velocity.

关键词： plane Couette flow (PCF) subcritical transition turbulent band

On the approximability of random-hypergraph MAX-3-XORSAT problems with quantum algorithms

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arXiv 2023年

作者： Kapit, Eliot Barton, Brandon A. Feeney, Sean Grattan, George Patnaik, Pratik Sagal, Jacob Carr, Lincoln D. Oganesyan, Vadim Department of Physics Colorado School of Mines 1523 Illinois St GoldenCO80401 United States Department of Applied Mathematics and Statistics Colorado School of Mines 1500 Illinois St GoldenCO80401 United States Quantum Engineering Program Colorado School of Mines 1523 Illinois St GoldenCO80401 United States Department of Physics and Astronomy College of Staten Island CUNY Staten IslandNY10314 United States Physics Program and Initiative for the Theoretical Sciences The Graduate Center CUNY New YorkNY10016 United States Center for Computational Quantum Physics Flatiron Institute 162 5th Avenue New YorkNY10010 United States

A canonical feature of the constraint satisfaction problems in NP is approximation hardness, where in the worst case, finding sufficient-quality approximate solutions is exponentially hard for all known methods. Fundamentally, the lack of any guided local minimum escape method ensures both exact and approximate classical approximation hardness, but the equivalent mechanism(s) for quantum algorithms are poorly understood. For algorithms based on Hamiltonian time evolution, we explore this question through the prototypically hard MAX-3-XORSAT problem class. We conclude that the mechanisms for quantum exact and approximation hardness are fundamentally distinct. We review known results from the literature, and identify mechanisms that make conventional quantum methods (such as Adiabatic Quantum Computing) weak approximation algorithms in the worst case. We construct a family of "spectrally filtered" quantum algorithms that escape these issues, and develop analytical theories for their performance. We show that, for random hypergraphs in the approximation-hard regime, if we define the energy to be E = Nunsat - Nsat, spectrally filtered quantum optimization will return states with E ≤ qmEGS (where EGS is the ground state energy) in sub-quadratic time, where conservatively, qm 0.59. This is in contrast to qm → 0 for the hardest instances with classical searches. We test all of these claims with extensive numerical simulations. We do not claim that this approximation guarantee holds for all possible hypergraphs, though our algorithm’s mechanism can likely generalize widely. These results suggest that quantum computers are more powerful for approximate optimization than had been previously assumed. © 2023, CC BY.

关键词： Constraint satisfaction problems

Fast-slow neural networks for learning singularly perturbed dynamical systems

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Journal of computational Physics 2025年 537卷

作者： Serino, Daniel A. Alvarez Loya, Allen Burby, J.W. Kevrekidis, Ioannis G. Tang, Qi Los Alamos National Laboratory Los AlamosNM United States Department of Physics University of Texas at Austin AustinTX United States Department of Chemical and Biomolecular Engineering and Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD United States School of Computational Science and Engineering Georgia Institute of Technology AtlantaGA United States

Singularly perturbed dynamical systems play a crucial role in climate dynamics and plasma physics. A powerful and well-known tool to address these systems is the Fenichel normal form, which significantly simplifies fast dynamics near slow manifolds through a transformation. However, this normal form is difficult to realize in conventional numerical algorithms. In this work, we explore an alternative way of realizing it through structure-preserving machine learning. Specifically, a fast-slow neural network (FSNN) is proposed for learning data-driven models of singularly perturbed dynamical systems with dissipative fast timescale dynamics. Our method enforces the existence of a trainable, attracting invariant slow manifold as a hard constraint. Closed-form representation of the slow manifold enables efficient integration on the slow time scale and significantly improves prediction accuracy beyond the training data. We demonstrate the FSNN on examples including the Grad moment system, two-scale Lorenz96 equations, and Abraham-Lorentz dynamics modeling radiation reaction of electrons. © 2025 Elsevier Inc.

关键词： Plant shutdowns

Iterative quantum optimization of spin glass problems with rapidly oscillating transverse fields

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arXiv 2024年

作者： Barton, Brandon Sagal, Jacob Feeney, Sean Grattan, George Patnaik, Pratik Oganesyan, Vadim Carr, Lincoln D. Kapit, Eliot Quantum Engineering Program Colorado School of Mines 1523 Illinois St GoldenCO80401 United States Department of Applied Mathematics and Statistics Colorado School of Mines 1500 Illinois St GoldenCO80401 United States Center for Computational Quantum Physics Flatiron Institute 162 5th Avenue New YorkNY10010 United States Department of Physics Colorado School of Mines 1523 Illinois St GoldenCO80401 United States Department of Computer Science Colorado School of Mines 1500 Illinois St GoldenCO80401 United States Department of Physics and Astronomy College of Staten Island City University of New York Staten IslandNY10314 United States Physics program and Initiative for the Theoretical Sciences The Graduate Center City University of New York New YorkNY10016 United States

In this work, we introduce a new iterative quantum algorithm, called Iterative Symphonic Tunneling for Satisfiability problems (IST-SAT), which solves quantum spin glass optimization problems using high-frequency oscillating transverse fields. IST-SAT operates as a sequence of iterations, in which bitstrings returned from one iteration are used to set spin-dependent phases in oscillating transverse fields in the next iteration. Over several iterations, the novel mechanism of the algorithm steers the system toward the problem ground state. We benchmark IST-SAT on sets of hard MAX-3-XORSAT problem instances with exact state vector simulation, and report polynomial speedups over trotterized adiabatic quantum computation (TAQC) and the best known semi-greedy classical algorithm. When IST-SAT is seeded with a sufficiently good initial approximation, the algorithm converges to exact solution(s) in a polynomial number of iterations. Our numerical results identify a critial Hamming radius(CHR), or quality of initial approximation, where the time-to-solution crosses from exponential to polynomial scaling in problem size. By combining IST-SAT with future classical or quantum approximation algorithms, larger gains may be achieved. The mechanism we present in this work thus presents a new path toward achieving quantum advantage in optimization. © 2024, CC BY.

关键词： Combinatorial optimization

A Model of Fluid-Structure and Biochemical Interactions for Applications to Subclinical Leaflet Thrombosis

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arXiv 2022年

作者： Barrett, Aaron Brown, Jordan A. Smith, Margaret Anne Woodward, Andrew Vavalle, John P. Kheradvar, Arash Griffith, Boyce E. Fogelson, Aaron L. Department of Mathematics University of Utah Salt Lake CityUT United States Department of Mathematics University of North Carolina Chapel HillNC United States Advanced Medical Imaging Lab University of North Carolina Medical Center Chapel HillNC United States University of North Carolina School of Medicine Chapel HillNC United States Division of Cardiology Department of Medicine University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of California Irvine IrvineCA United States Department of Mathematics Applied Physical Sciences and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina Chapel HillNC United States McAllister Heart Institute University of North Carolina Chapel HillNC United States Department of Mathematics and Biomedical Engineering University of Utah Salt Lake CityUT United States

Subclinical leaflet thrombosis (SLT) is a potentially serious complication of aortic valve replacement with a bioprosthetic valve in which blood clots form on the replacement valve. SLT is associated with increased risk of transient ischemic attacks and strokes and can progress to clinical leaflet thrombosis. SLT following aortic valve replacement also may be related to subsequent structural valve deterioration, which can impair the durability of the valve replacement. Because of the difficulty in clinical imaging of SLT, models are needed to determine the mechanisms of SLT and could eventually predict which patients will develop SLT. To this end, we develop methods to simulate leaflet thrombosis that combine fluid-structure interaction and a simplified thrombosis model that allows for deposition along the moving leaflets. Additionally, this model can be adapted to model deposition or absorption along other moving boundaries. We present convergence results and quantify the model's ability to realize changes in valve opening and pressures. These new approaches are an important advancement in our tools for modeling thrombosis in which they incorporate both adhesion to the surface of the moving leaflets and feedback to the fluid-structure interaction. © 2022, CC BY-SA.

关键词： Deposition

Exclusion Volumes of Convex Bodies in High Space Dimensions: Applications to Virial Coefficients and Continuum Percolation

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arXiv 2022年

作者： Torquato, Salvatore Jiao, Yang Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Materials Science and Engineering Arizona State University TempeAZ85287 United States Department of Physics Arizona State University TempeAZ85287 United States

Using the concepts of mixed volumes and quermassintegrals of convex geometry, we derive an exact formula for the exclusion volume vex(K) for a general convex body K that applies in any space dimension. While our main interests concern the rotationally-averaged exclusion volume of a convex body with respect to another convex body, we also describe some results for the exclusion volumes for convex bodies with the same orientation. We show that the sphere minimizes the dimensionless exclusion volume vex(K)/v(K) among all convex bodies, whether randomly oriented or uniformly oriented, for any d, where v(K) is the volume of K. When the bodies have the same orientation, the simplex maximizes the dimensionless exclusion volume for any d with a large-d asymptotic scaling behavior of 22d/d3/2, which is to be contrasted with the corresponding scaling of 2d for the sphere. We present explicit formulas for quermassintegrals W0(K), . . ., Wd(K) for many different nonspherical convex bodies, including cubes, parallelepipeds, regular simplices, cross-polytopes, cylinders, spherocylinders, ellipsoids as well as lower-dimensional bodies, such as hyperplates and line segments. These results are utilized to determine the rotationally-averaged exclusion volume vex(K) for these convex-body shapes for dimensions 2 through 12. While the sphere is the shape possessing the minimal dimensionless exclusion volume, we show that, among the convex bodies considered that are sufficiently compact, the simplex possesses the maximal vex(K)/v(K) with a scaling behavior of 21.6618...d. Subsequently, we apply these results to determine the corresponding second virial coefficient B2(K) of the aforementioned hard hyperparticles. Our results are also applied to compute estimates of the continuum percolation threshold ηc derived previously by the authors for systems of identical overlapping convex bodies. We conjecture that overlapping spheres possess the maximal value of ηc among all identical nonzero-vol

关键词： Spheres

Modeling liquid water by climbing up Jacob’s ladder in density functional theory facilitated by using deep neural network potentials

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arXiv 2021年

作者： Zhang, Chunyi Tang, Fujie Chen, Mohan Zhang, Linfeng Qiu, Diana Y. Perdew, John P. Klein, Michael L. Wu, Xifan Department of Physics Temple University PhiladelphiaPA19122 United States HEDPS Center for Applied Physics and Technology College of Engineering Peking University Beijing100871 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mechanical Engineering and Materials Science Yale University New HavenCT06520 United States Department of Chemistry Temple University PhiladelphiaPA19122 United States Institute for Computational Molecular Science Temple University PhiladelphiaPA19122 United States

Within the framework of Kohn-Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent years. Here, we further advance the modeling of water by building a more accurate model on the fourth rung of Jacob’s ladder with the hybrid functional, SCAN0. In particular, we carry out both classical and Feynman path-integral molecular dynamics calculations of water with the SCAN0 functional and the isobaric-isothermal ensemble. In order to generate the equilibrated structure of water, a deep neural network potential is trained from the atomic potential energy surface based on ab initio data obtained from SCAN0 DFT calculations. For the electronic properties of water, a separate deep neural network potential is trained using the Deep Wannier method based on the maximally localized Wannier functions of the equilibrated trajectory at the SCAN0 level. The structural, dynamic, and electric properties of water were analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion coefficients, and dielectric constants of water, in the electronic ground state, are computed using a large simulation box and long simulation time. For the properties involving electronic excitations, we apply the GW approximation within many-body perturbation theory to calculate the quasiparticle density of states and bandgap of water. Compared to the SCAN functional, mixing exact exchange mitigates the self-interaction error in the meta-generalized-gradient approximation and further softens liquid water towards the experimental direction. For most of the water properties, the SCAN0 functional shows a systematic improvement over the SCAN functional. © 2021, CC BY.

关键词： Deep neural networks

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