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Cloaking the underlying long-range order of randomly perturbed lattices

Physical Review E 2020年第3期101卷 032118-032118页

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

Random, uncorrelated displacements of particles on a lattice preserve the hyperuniformity of the original lattice, that is, normalized density fluctuations vanish in the limit of infinite wavelengths. In addition to a diffuse contribution, the scattering intensity from the the resulting point pattern typically inherits the Bragg peaks (long-range order) of the original lattice. Here we demonstrate how these Bragg peaks can be hidden in the effective diffraction pattern of independent and identically distributed perturbations. All Bragg peaks vanish if and only if the sum of all probability densities of the positions of the shifted lattice points is a constant at all positions. The underlying long-range order is then “cloaked” in the sense that it cannot be reconstructed from the pair correlation function alone. On the one hand, density fluctuations increase monotonically with the strength of perturbations a, as measured by the hyperuniformity order metric Λ¯. On the other hand, the disappearance and reemergence of long-range order, depending on whether the system is cloaked as the perturbation strength increases, is manifestly captured by the τ order metric. Therefore, while the perturbation strength a may seem to be a natural choice for an order metric of perturbed lattices, the τ order metric is a superior choice. It is noteworthy that cloaked perturbed lattices allow one to easily simulate very large samples (with at least 106 particles) of disordered hyperuniform point patterns without Bragg peaks.

关键词： Classical statistical mechanics

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Raman spectrum and polarizability of liquid water from deep neural networks

arXiv

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arXiv 2020年

作者： Sommers, Grace M. Calegari Andrade, Marcos F. Zhang, Linfeng Wang, Han Car, Roberto Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States 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

We introduce a scheme based on machine learning and deep neural networks to model the environmental dependence of the electronic polarizability in insulating materials. Application to liquid water shows that training the network with a relatively small number of molecular configurations is sufficient to predict the polarizability of arbitrary liquid configurations in close agreement with ab initio density functional theory calculations. In combination with a neural network representation of the interatomic potential energy surface, the scheme allows us to calculate the Raman spectra along 2-nanosecond classical trajectories at different temperatures for H2O and D2O. The vast gains in efficiency provided by the machine learning approach enable longer trajectories and larger system sizes relative to ab initio methods, reducing the statistical error and improving the resolution of the low-frequency Raman spectra. Decomposing the spectra into intramolecular and intermolecular contributions elucidates the mechanisms behind the temperature dependence of the low-frequency and stretch modes. Copyright © 2020, The Authors. All rights reserved.

关键词： Liquids

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Global well-posedness of a three-dimensional Brinkman-Forchheimer-Bénard convection model in porous media

arXiv

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arXiv 2022年

作者： Titi, Edriss S. Trabelsi, Saber Department of Mathematics Texas A&M University College StationTX77843 United States Department of Applied Mathematics and Theoretical Physics University of Cambridge CambridgeCB3 0WA United Kingdom Science Program Texas A&M University at Qatar P.O. Box Doha23874 Qatar

We consider three-dimensional (3D) Boussinesq convection system of an incompressible fluid in a closed sample of a porous medium. Specifically, we introduce and analyze a 3D Brinkman-Forchheimer-Bénard convection problem describing the behavior of an incompressible fluid in a porous medium between two plates heated from the bottom and cooled from the top. We show the existence and uniqueness of global in-time solutions, and the existence of absorbing balls in L2 and H1. Eventually, we comment on the applicability of a data assimilation algorithm to our *** Codes 35Q30, 35Q35, 76B03, 86A10, 93C20, 37C50, 76B75, 34D06 © 2022, CC BY.

关键词： Porous materials

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Phonon dispersion throughout the iron spin crossover in ferropericlase

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Physical Review B 2020年第10期102卷 104112-104112页

作者： Michel L. Marcondes Fawei Zheng Renata M. Wentzcovitch Department of Earth and Environmental Sciences Columbia University Lamont-Doherty Earth Observatory Palisades New York 10964 USA Institute of Applied Physics and Computational Mathematics Beijing 100088 China Department of Applied Physics and Applied Mathematics Columbia University New York New York 10027 USA

Ferropericlase (Fp), (Mg1−xFex)O, is the second most abundant phase in the Earth's lower mantle. At relevant pressure-temperature conditions, iron in Fp undergoes a high spin (HS), S = 2, to low spin (LS), S = 0, state change. The nature of this phenomenon is quite well understood now, but there are still basic questions regarding the structural stability and the existence of soft phonon modes during this iron state change. General theories exist to explain the volume reduction, the significant thermoelastic anomalies, and the broad nature of this HS-LS crossover. These theories make extensive use of the quasiharmonic approximation. Therefore, dynamical and structural stability is essential to their validity. Here, we investigate the vibrational spectrum of Fp throughout this spin crossover using ab initio density-functional theory +Usc calculations. We address vibrational modes associated with isolated and (second-)nearest-neighbor iron ions undergoing the HS-LS state change. As expected, acoustic modes of this solid solution are resilient, while optical modes are the most affected. We show that there are no soft phonon modes across this HS-LS crossover, and Fp is dynamically stable at all relevant pressures.

关键词： Phase transitions Phonons Pressure effects Spin state transition

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Magnon thermal conductivity in multiferroics with spin cycloids

arXiv

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arXiv 2025年

作者： Park, Hyeon Woo Zhang, Shu Meisenheimer, Peter Ramesh, Maya Husain, Sajid Harris, Isaac Íñiguez-González, Jorge Yao, Zhi Ramesh, Ramamoorthy Kim, Se Kwon Department of Physics Korea Advanced Institute of Science and Technology Daejeon34141 Korea Republic of Institute for Theoretical Solid State Physics IFW Dresden Helmholtzstrasse 20 Dresden01069 Germany Department of Materials Science and Engineering University of California BerkeleyCA94720 United States Department of Materials Science and Engineering Cornell University IthacaNY14853 United States Materials Science Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Department of Physics University of California BerkeleyCA94720 United States Esch-sur-Alzette Luxembourg Department of Physics and Materials Science University of Luxembourg Belvaux Esch-sur-Alzette1511 Luxembourg Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Departments of Physics and Astronomy and Materials Science and Nano Engineering Rice Advanced Materials Institute Rice University HoustonTX77005 United States

Multiferroic materials, characterized by the occurrence of two or more ferroic properties, hold potential in future technological applications and also exhibit intriguing phenomena caused by the interplay of multiple orders. One such example is the formation of spin cycloid structures within multiferroic materials, which we investigate in this work by focusing on their magnon excitations and transport based on a general multiferroic Hamiltonian with an antiferromagnetic order. More specifically, we identify the ground state and explore the dynamics of magnon modes, revealing distinct in-plane and out-of-plane modes with anisotropic dispersion relations. The magnon modes include a massless excitation, known as the Goldstone boson, originating from the spontaneous breaking of the translational symmetry by the formation of the cycloid structures. By employing the Boltzmann transport formalism, the magnonic thermal conductivity with spin cycloids and low-temperature anisotropic behaviors is discussed. This work provides pathways to envision the spin-textured multiferroics, which may serve as a fertile ground to look for novel thermal and spin transport with the rich interplay of quasiparticles such as magnons and phonons. Copyright © 2025, The Authors. All rights reserved.

关键词： Anisotropy

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An Energy-Based Discontinuous Galerkin Method with Tame CFL Numbers for the Wave Equation

arXiv

引用

arXiv 2021年

作者： Appelö, Daniel Zhang, Lu Hagstrom, Thomas Li, Fengyan Department of Computational Mathematics Science & Engineering Department of Mathematics Michigan State University East LansingMI48824 United States Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States Department of Mathematics Southern Methodist University DallasTX75275 United States Department of Mathematical Sciences Rensselaer Polytechnic Institute TroyNY12180 United States

We extend and analyze the energy-based discontinuous Galerkin method for second order wave equations on staggered and structured meshes. By combining spatial staggering with local time-stepping near boundaries, the method overcomes the typical numerical stiffness associated with high order piecewise polynomial approximations. In one space dimension with periodic boundary conditions and suitably chosen numerical fluxes, we prove bounds on the spatial operators that establish stability for CFL numbers c∆ht MSC Codes 65M12, 65M60 Copyright © 2021, The Authors. All rights reserved.

关键词： Galerkin methods

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Constraining f(R) models with cosmic chronometers and the HII galaxy Hubble diagram

arXiv

引用

arXiv 2022年

作者： Sultana, Joseph Yennapureddy, Manoj K. Melia, Fulvio Kazanas, Demosthenes Department of Mathematics Faculty of Science University of Malta MSD Msida2080 Malta Department of Physics The University of Arizona TucsonAZ85721 United States Department of Physics The Applied Math Program Department of Astronomy The University of Arizona TucsonAZ85721 United States Astrophysics Science Division NASA/Goddard Space Flight Center GreenbeltMD20771 United States

We consider several well-known f(R) cosmological models and constrain their parameters, namely the deviation parameter b and the cosmological parameters Ωm and h. We first obtain analytical approximations for the Hubble rate H(z) and the luminosity distance dL(z) in terms of these parameters, and then test these against the observational expansion rate derived from cosmic chronometers and the distance modulus in the HII galaxy Hubble diagram, obtained in a model-independent way using Gaussian Processes (GP). We first optimize the models based solely on the cosmic chronometers and then repeat this process with a joint analysis using both the cosmic chronometers and HII galaxies. Copyright © 2022, The Authors. All rights reserved.

关键词： Chronometers

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How many simulations do we need for simulation-based inference in cosmology?

arXiv

引用

arXiv 2025年

作者： Bairagi, Anirban Wandelt, Benjamin Villaescusa-Navarro, Francisco UMR 7095 98 bis bd Arago ParisF-75014 France Center for Computational Astrophysics Flatiron Institute 162 5th Avenue New YorkNY10010 United States Department of Physics and Astronomy Johns Hopkins University 3400 North Charles Street BaltimoreMD21218 United States Department of Applied Mathematics and Statistics Johns Hopkins University 3400 North Charles Street BaltimoreMD21218 United States Department of Astrophysical Sciences Princeton University Peyton Hall PrincetonNJ08544-0010 United States

How many simulations do we need to train machine learning methods to extract information available from summary statistics of the cosmological density field? Neural methods have shown the potential to extract non-linear information available from cosmological data. Success depends critically on having sufficient simulations for training the networks and appropriate network architectures. In the first detailed convergence study of neural network training for cosmological inference, we show that currently available simulation suites, such as the Quijote Latin Hypercube(LH) with 2000 simulations, do not provide sufficient training data for a generic neural network to reach the optimal regime, even for the dark matter power spectrum, and in an idealized case. We discover an empirical neural scaling law that predicts how much information a neural network can extract from a highly informative summary statistic, the dark matter power spectrum, as a function of the number of simulations used to train the network, for a wide range of architectures and hyperparameters. We combine this result with the Cramer-Rao information bound to forecast the number of training simulations needed for near-optimal information extraction. To verify our method we created the largest publicly released simulation data set in cosmology, the Big Sobol Sequence(BSQ), consisting of 32,768 ΛCDM n-body simulations uniformly covering the ΛCDM parameter space. Our method enables efficient planning of simulation campaigns for machine learning applications in cosmology, while the BSQ dataset provides an unprecedented resource for studying the convergence behavior of neural networks in cosmological parameter inference. Our results suggest that new large simulation suites or new training approaches will be necessary to achieve information-optimal parameter inference from non-linear simulations. © 2025, CC BY-SA.

关键词： Dark Matter

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Improving the Accuracy of the Variational Quantum Eigensolver for Molecular Systems by the Explicitly-Correlated Perturbative R12-Correction

arXiv

引用

arXiv 2021年

作者： Schleich, Philipp Kottmann, Jakob S. Aspuru-Guzik, Alan Department of Computer Science University of Toronto Canada Applied and Computational Mathematics Department of Mathematics Rwth Aachen University Aachen Germany Vector Institute for Artificial Intelligence Toronto Canada Chemical Physics Theory Group Department of Chemistry University of Toronto Canada Toronto Canada

We provide an integration of the universal, perturbative explicitly correlated [2]R12-correction in the context of the Variational Quantum Eigensolver (VQE). This approach is able to increase the accuracy of the underlying reference method significantly while requiring no additional quantum resources. The proposed approach only requires knowledge of the one- and two-particle reduced density matrices (RDMs) of the reference wavefunction;these can be measured after having reached convergence in the VQE. This computation comes at a cost that scales as the sixth power of the number of electrons. We explore the performance of the VQE+[2]R12approach using both conventional Gaussian basis sets and our recently proposed directly determined pair-natural orbitals obtained by multiresolution analysis (MRA-PNOs). Both Gaussian orbital and PNOs are investigated as a potential set of complementary basis functions in the computation of [2]R12. In particular the combination of MRA-PNOs with [2]R12has turned out to be very promising - persistently throughout our data, this allowed very accurate simulations at a quantum cost of a minimal basis set. Additionally, we found that the deployment of PNOs as complementary basis can greatly reduce the number of complementary basis functions that enter the computation of the correction at a complexity. Copyright © 2021, The Authors. All rights reserved.

关键词： Functions

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Representation formulas and pointwise properties for Barron functions

arXiv

引用

arXiv 2020年

作者： Weinan, E. Wojtowytsch, Stephan Department of Mathematics Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Princeton University Program in Applied and Computational Mathematics 205 Fine Hall - Washington Road PrincetonNJ08544 United States

We study the natural function space for infinitely wide two-layer neural networks with ReLU activation (Barron space) and establish different representation formulae. In two cases, we describe the space explicitly up to isomorphism. Using a convenient representation, we study the pointwise properties of two-layer networks and show that functions whose singular set is fractal or curved (for example distance functions from smooth submanifolds) cannot be represented by infinitely wide two-layer networks with finite path-norm. We use this structure theorem to show that the only C1-diffeomorphisms which Barron space are affine. Furthermore, we show that every Barron function can be decomposed as the sum of a bounded and a positively one-homogeneous function and that there exist Barron functions which decay rapidly at infinity and are globally Lebesgue-integrable. This result suggests that two-layer neural networks may be able to approximate a greater variety of functions than commonly *** Codes 68T07, 46E15, 26B35, 26B40 Copyright © 2020, The Authors. All rights reserved.

关键词： Network layers

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