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arXiv 2023年

作者： Cohl, Howard S. Costas-Santos, Roberto S. Durand, Loyal Montoya, Camilo Ólafsson, Gestur Applied and Computational Mathematics Division National Institute of Standards and Technology GaithersburgMD20899-8910 United States Department of Quantitative Methods Universidad Loyola Andalucía Sevilla Spain Department of Physics University of Wisconsin MadisonWI53706 United States Department of Mathematics Louisiana State University Baton RougeLA70803-4918 United States

In this paper we review and derive hyperbolic and trigonometric double summation addition theorems for Jacobi functions of the first and second kind. In connection with these addition theorems, we perform a full analysis of the relation between symmetric, antisymmetric and odd-half-integer parameter values for the Jacobi functions with certain Gauss hypergeometric functions which satisfy a quadratic transformation, including associated Legendre, Gegenbauer and Ferrers functions of the first and second kind. We also introduce Olver normalizations of the Jacobi functions which are particularly useful in the derivation of expansion formulas when the parameters are integers. We introduce an application of the addition theorems for the Jacobi functions of the second kind to separated eigenfunction expansions of a fundamental solution of the Laplace-Beltrami operator on the compact and noncompact rank one symmetric spaces. © 2023, CC0.

关键词： Polynomials

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computational design of anisotropic stealthy hyperuniform composites with engineered directional scattering properties

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Physical Review E 2023年第4期108卷 045306-045306页

作者： Wenlong Shi David Keeney Duyu Chen Yang Jiao Salvatore Torquato Materials Science and Engineering Arizona State University Tempe Arizona 85287 USA Materials Research Laboratory University of California Santa Barbara California 93106 USA Department of Physics Arizona State University Tempe Arizona 85287 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Disordered hyperuniform materials are an emerging class of exotic amorphous states of matter that endow them with singular physical properties, including large isotropic photonic band gaps, superior resistance to fracture, and nearly optimal electrical and thermal transport properties, to name but a few. Here we generalize the Fourier-space-based numerical construction procedure for designing and generating digital realizations of isotropic disordered hyperuniform two-phase heterogeneous materials (i.e., composites) developed by Chen and Torquato [Acta Mater. 142, 152 (2018)] to anisotropic microstructures with targeted spectral densities. Our generalized construction procedure explicitly incorporates the vector-dependent spectral density function χ̃V(k) of arbitrary form that is realizable. We demonstrate the utility of the procedure by generating a wide spectrum of anisotropic stealthy hyperuniform microstructures with χ̃V(k)=0 for k∈Ω, i.e., complete suppression of scattering in an “exclusion” region Ω around the origin in Fourier space. We show how different exclusion-region shapes with various discrete symmetries, including circular-disk, elliptical-disk, square, rectangular, butterfly-shaped, and lemniscate-shaped regions of varying size, affect the resulting statistically anisotropic microstructures as a function of the phase volume fraction. The latter two cases of Ω lead to directionally hyperuniform composites, which are stealthy hyperuniform only along certain directions and are nonhyperuniform along others. We find that while the circular-disk exclusion regions give rise to isotropic hyperuniform composite microstructures, the directional hyperuniform behaviors imposed by the shape asymmetry (or anisotropy) of certain exclusion regions give rise to distinct anisotropic structures and degree of uniformity in the distribution of the phases on intermediate and large length scales along different directions. Moreover, while the anisotropic exclusion regions

关键词： Amorphous materials Complex materials Simulated annealing

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Decoherence, entanglement negativity, and circuit complexity for an open quantum system

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Physical Review D 2023年第10期107卷 106007-106007页

作者： Arpan Bhattacharyya Tanvir Hanif S. Shajidul Haque Arpon Paul Indian Institute of Technology Gandhinagar Gujarat-382355 India Department of Theoretical Physics University of Dhaka Dhaka-1000 Bangladesh High Energy Physics Cosmology and Astrophysics Theory Group and The Laboratory for Quantum Gravity and Strings Department of Mathematics and Applied Mathematics University of Cape Town Cape Town-7700 South Africa National Institute for Theoretical and Computational Sciences (NITheCS) South Africa University of Minnesota Twin Cities Minneapolis Minnesota 55455 USA

In this paper, we compare the saturation timescales for complexity, linear entropy, and entanglement negativity for two open quantum systems. Our first model is a coupled harmonic oscillator, where we treat one of the oscillators as the bath. The second one is a type of Caldeira-Leggett model, where we consider a one-dimensional free scalar field as the bath. Using these open quantum systems, we discovered that both the complexity of purification and the complexity from operator-state mapping is always saturated for a completely mixed state. More explicitly, the saturation timescale for both types of complexity is smaller than the saturation timescale for linear entropy. On top of this, we found that the saturation timescale for linear entropy and entanglement negativity is of the same order for the Caldeira-Leggett model.

关键词： Gauge-gravity dualities Open quantum systems & decoherence computational complexity

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Generating large disordered stealthy hyperuniform systems with ultrahigh accuracy to determine their physical properties

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Physical Review Research 2023年第3期5卷 033190-033190页

作者： Peter K. Morse Jaeuk Kim Paul J. Steinhardt Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute of Materials Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Hyperuniform many-particle systems are characterized by a structure factor S(k) that is precisely zero as |k|→0; and stealthy hyperuniform systems have S(k)=0 for the finite range 0<|k|≤K, called the “exclusion region.” Through a process of collective-coordinate optimization, energy-minimizing disordered stealthy hyperuniform systems of moderate size have been made to high accuracy, and their novel physical properties have shown great promise. However, minimizing S(k) in the exclusion region is computationally intensive as the system size becomes large. In this paper, we present an improved methodology to generate such states using double-double precision calculations on graphical processing units (GPUs) that reduces the deviations from zero within the exclusion region by a factor of approximately 1030 for system sizes more than an order of magnitude larger. We further show that this ultrahigh accuracy is required to draw conclusions about their corresponding characteristics, such as the nature of the associated energy landscape and the presence or absence of Anderson localization, which might be masked, even when deviations are relatively small.

关键词： Exotic phases of matter

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Phase Diagram of a Deep Potential Water Model

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Physical Review Letters 2021年第23期126卷 236001-236001页

作者： Linfeng Zhang Han Wang Roberto Car Weinan E Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA and Beijing Institute of Big Data Research Beijing 100871 People’s Republic of China

Using the Deep Potential methodology, we construct a model that reproduces accurately the potential energy surface of the SCAN approximation of density functional theory for water, from low temperature and pressure to about 2400 K and 50 GPa, excluding the vapor stability region. The computational efficiency of the model makes it possible to predict its phase diagram using molecular dynamics. Satisfactory overall agreement with experimental results is obtained. The fluid phases, molecular and ionic, and all the stable ice polymorphs, ordered and disordered, are predicted correctly, with the exception of ice III and XV that are stable in experiments, but metastable in the model. The evolution of the atomic dynamics upon heating, as ice VII transforms first into ice VII′′ and then into an ionic fluid, reveals that molecular dissociation and breaking of the ice rules coexist with strong covalent fluctuations, explaining why only partial ionization was inferred in experiments.

关键词： Classical statistical mechanics First order phase transitions Interatomic & molecular potentials Phase diagrams Potential energy surfaces Water First-principles calculations Machine learning Molecular dynamics

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Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with physics Prior

Gaussian Process Port-Hamiltonian Systems: Bayesian Learning...

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IEEE Conference on Decision and Control

作者： Thomas Beckers Jacob Seidman Paris Perdikaris George J. Pappas Department of Electrical and Systems Engineering University of Pennsylvania Philadelphia PA USA graduate program in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia PA USA Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia PA USA

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

Data-driven approaches achieve remarkable results for the modeling of complex dynamics based on collected data. However, these models often neglect basic physical principles which determine the behavior of any real-world system. This omission is unfavorable in two ways: The models are not as data-efficient as they could be by incorporating physical prior knowledge, and the model itself might not be physically correct. We propose Gaussian Process Port-Hamiltonian systems (GPPHS) as a physics-informed Bayesian learning approach with uncertainty quantification. The Bayesian nature of GP-PHS uses collected data to form a distribution over all possible Hamiltonians instead of a single point estimate. Due to the underlying physics model, a GP-PHS generates passive systems with respect to designated inputs and outputs. Further, the proposed approach preserves the compositional nature of Port-Hamiltonian systems.

关键词： Uncertainty Gaussian processes Probabilistic logic Data models Bayes methods Behavioral sciences Kernel

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CMGC: a CAD to Monte Carlo geometry conversion code

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Nuclear Science and Techniques 2020年第8期31卷 104-115页

作者： Xin Wang Jun-Li Li Zhen Wu Shen-Shen Gao Rui Qiu Li Deng Gang Li Institute of Applied Physics and Computational Mathematics Beijing 100088China CAEP Software Center for High Performance Numerical Simulation Beijing 100088China Department of Engineering Physics Tsinghua UniversityBeijing 100084China Nuctech Company Limited Beijing 100084China

Automatic conversion from a computer-aided design(CAD) model to Monte Carlo geometry is one of the most effective methods for large-scale and detailed Monte Carlo modeling. The CAD to Monte Carlo geometry converter(CMGC) is a newly developed conversion code based on the boundary representation to constructive solid geometry(BRep→CSG) conversion method. The goal of the conversion process in the CMGC is to generate an appropriate CSG representation to achieve highly efficient Monte Carlo simulations. We designed a complete solid decomposition scheme to split a complex solid into as few nonoverlapping simple sub-solids as possible. In the complete solid decomposition scheme, the complex solid is successively split by so-called direct, indirect, and auxiliary splitting surfaces. We defined the splitting edge and designed a method for determining the direct splitting surface based on the splitting edge, then provided a method for determining indirect and auxiliary splitting surfaces based on solid vertices. Only the sub-solids that contain concave boundary faces need to be supplemented with auxiliary surfaces because the solid is completely decomposed, which will reduce the redundancy in the CSG expression. After decomposition, these sub-solids are located on only one side of their natural and auxiliary surfaces;thus, each sub-solid can be described by the intersections of a series of half-spaces or geometrical primitives. The CMGC has a friendly graphical user interface and can convert a CAD model into geometry input files for several Monte Carlo codes. The reliability of the CMGC was evaluated by converting several complex models and calculating the relative volume errors. Moreover, JMCT was used to test the efficiency of the Monte Carlo simulation. The results showed that the converted models performed well in particle transport calculations.

关键词： Monte Carlo CAD Geometry converter Complete solid decomposition

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Elasticity and acoustic velocities of δ-AlOOH at extreme conditions: a methodology assessment

arXiv

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arXiv 2024年

作者： Luo, Chenxing Sun, Yang Wentzcovitch, Renata M. Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States Department of Physics Xiamen University Xiamen361005 China Department of Earth and Environmental Sciences Columbia University New YorkNY10027 United States Lamont–Doherty Earth Observatory Columbia University PalisadesNY10964 United States Data Science Institute Columbia University New YorkNY10027 United States Center for Computational Quantum Physics Flatiron Institute New YorkNY10010 United States

Hydrous phases play a fundamental role in the deep-water cycle on Earth. Understanding their stability and thermoelastic properties is essential for constraining their abundance using seismic tomography. However, determining their elastic properties at extreme conditions is notoriously challenging. The challenges stem from the complex behavior of hydrogen bonds under high pressures and temperatures (P, Ts). In this study, we evaluate how advanced molecular dynamics simulation techniques can address these challenges by investigating the adiabatic elasticity and acoustic velocities of δ-AlOOH, a critical and prototypical high-pressure hydrous phase. We compared the performances of three methods to assess their viability and accuracy. The thermoelastic tensor was computed up to 140 GPa and temperatures up to 2,700 K using molecular dynamics with a DeePMD machine-learning interatomic potential based on the SCAN meta-GGA functional. The excellent agreement with ambient condition single-crystal ultrasound measurements and the correct description of velocity changes induced by H-bond disorder-symmetrization transition observed at 10 GPa in Brillouin scattering measurements underscores the accuracy and efficacy of our approach. Copyright © 2024, The Authors. All rights reserved.

关键词： Elasticity

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Viscosity Solutions for McKean-Vlasov Control I: one-dimensional torus

arXiv

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arXiv 2022年

作者： Soner, H. Mete Yan, Qinxin Department of Operations Research and Financial Engineering Princeton University PrincetonNJ08540 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States

An optimal control problem in the space of probability measures, and the viscosity solutions of the corresponding dynamic programming equations defined using the intrinsic linear derivative are studied. The value function is shown to be Lipschitz continuous with respect to a novel smooth Fourier-Wasserstein metric. A comparison result between the Lipschitz viscosity sub and super solutions of the dynamic programming equation is proved using this metric, characterizing the value function as the unique Lipschitz viscosity *** Codes 35Q89, 35D40, 49L25, 60G99 © 2022, CC BY-NC-ND.

关键词： Viscosity

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Minuscule corrections to near-surface solar internal rotation using mode-coupling

arXiv

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arXiv 2023年

作者： Das, Srijan Bharati Kashyap, Samarth G. Oktay, Deniz Hanasoge, Shravan M. Tromp, Jeroen Department of Geosciences Princeton University PrincetonNJ United States Department of Astronomy and Astrophysics Tata Institute of Fundamental Research Mumbai India Department of Computer Science Princeton University PrincetonNJ United States Department of Geosciences and Program in Applied & Computational Mathematics Princeton University PrincetonNJ United States

The observed solar oscillation spectrum is influenced by internal perturbations such as flows and structural asphericities. These features induce splitting of characteristic frequencies and distort the resonant-mode eigenfunctions. Global axisymmertric flow — differential rotation — is a very prominent perturbation. Tightly constrained rotation profiles as a function of latitude and radius are products of established helioseismic pipelines that use observed Dopplergrams to generate frequency-splitting measurements at high precision. However, the inference of rotation using frequency-splittings do not consider the effect of mode-coupling. This approximation worsens for high-angular-degree modes, as they become increasingly proximal in frequency. Since modes with high angular degrees probe the near-surface layers of the Sun, inversions considering coupled modes could potentially lead to more accurate estimates of rotation very close to the surface. In order to investigate if this is indeed the case, we perform inversions for solar differential rotation, considering coupling of modes for angular degrees 160 ≤ ` ≤ 300 in the surface gravity f-branch and first-overtone p modes. In keeping with the character of mode coupling, we carry out a non-linear inversion using an eigenvalue solver. Differences in inverted profiles for frequency splitting measurements from MDI and HMI are compared and discussed. We find that corrections to the near-surface differential rotation profile, when accounting for mode-coupling effects, are smaller than 0.003 nHz and hence are insignificant. These minuscule corrections are found to be correlated with the solar cycle. We also present corrections to even-order splitting coefficients, which could consequently impact inversions for structure and magnetic fields. © 2023, CC BY.

关键词： Rotation

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