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arXiv 2022年

作者： Svolos, Lampros Mourad, Hashem M. Manzini, Gianmarco Garikipati, Krishna Fluid Dynamics and Solid Mechanics T-3 Theoretical Division Los Alamos National Laboratory Los AlamosNM United States Applied Mathematics and Plasma Physics T-5 Theoretical Division Los Alamos National Laboratory Los AlamosNM United States Department of Mechanical Engineering University of Michigan Ann ArborMI United States Department of Mathematics University of Michigan Ann ArborMI United States Michigan Institute for Computational Discovery & Engineering University of Michigan Ann ArborMI United States

Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability to capture the formation of complex fracture patterns, e.g. via crack merging and branching, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models have also been proposed to increase the regularity of the exact solution and thus increase the spatial convergence rate of its numerical approximation. However, they require special numerical techniques to enforce the necessary continuity of the phase field solution. In this paper, we derive a fourth-order phase-field model of fracture in two independent ways;namely, from Hamilton's principle and from a higher-order micromechanics-based approach. The latter approach is novel, and provides a physical interpretation of the higher-order terms in the model. In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution. This method employs Lagrange polynomial shape functions to guarantee C0-continuity of the solution at inter-element boundaries, and enforces the required C1regularity with the aid of additional variational and interior penalty terms in the weak form. The phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials. Two benchmark problems are presented to compare the numerical behavior of the C/DG method with mixed finite element methods. Copyright © 2022, The Authors. All rights reserved.

关键词： Galerkin methods

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A Quantum Computing View on Unitary Coupled Cluster Theory

arXiv

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arXiv 2021年

作者： Anand, Abhinav Schleich, Philipp Alperin-Lea, Sumner Jensen, Phillip W. K. Sim, Sukin Díaz-Tinoco, Manuel Kottmann, Jakob S. Degroote, Matthias Izmaylov, Artur F. Aspuru-Guzik, Alán Chemical Physics Theory Group Department of Chemistry University of Toronto Canada 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 Department of Chemistry and Chemical Biology Harvard University United States Department of Physical and Environmental Sciences University of Toronto Scarborough Canada Lebovic Fellow Toronto Canada

We present a review of the Unitary Coupled Cluster (UCC) ansatz and related ansätze which are used to variationally solve the electronic structure problem on quantum computers. A brief history of coupled cluster (CC) methods is provided, followed by a broad discussion of the formulation of CC theory. This includes touching on the merits and difficulties of the method and several variants, UCC among them, in the classical context, to motivate their applications on quantum computers. In the core of the text, the UCC ansatz and its implementation on a quantum computer are discussed at length, in addition to a discussion on several derived and related ansätze specific to quantum computing. The review concludes with a unified perspective on the discussed ansätze, attempting to bring them under a common framework, as well as with a reflection upon open problems within the field. © 2021, CC BY.

关键词： Cluster analysis

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Inferring solar differential rotation through normal-mode coupling using bayesian statistics

arXiv

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arXiv 2021年

作者： Kashyap, Samarth Ganesh Bharati Das, Srijan Hanasoge, Shravan M. Woodard, Martin F. Tromp, Jeroen Department of Astronomy and Astrophysics Tata Institute of Fundamental Research Mumbai India Department of Geosciences Princeton University PrincetonNJ United States NorthWest Research Associates Boulder Office 3380 Mitchell Lane BoulderCO United States Department of Geosciences and Program in Applied & Computational Mathematics Princeton University PrincetonNJ United States

Normal-mode helioseismic data analysis uses observed solar oscillation spectra to infer perturbations in the solar interior due to global and local-scale flows and structural asphericity. Differential rotation, the dominant global-scale axisymmetric perturbation, has been tightly constrained primarily using measurements of frequency splittings via "a-coefficients". However, the frequency-splitting formalism invokes the approximation that multiplets are isolated. This assumption is inaccurate for modes at high angular degrees. Analysing eigenfunction corrections, which respect cross coupling of modes across multiplets, is a more accurate approach. However, applying standard inversion techniques using these cross-spectral measurements yields a-coefficients with a significantly wider spread than the well-constrained results from frequency splittings. In this study, we apply Bayesian statistics to infer a-coefficients due to differential rotation from cross spectra for both f-modes and p-modes. We demonstrate that this technique works reasonably well for modes with angular degrees ` = 50 − 291. The inferred a3−coefficients are found to be within 1 nHz of the frequency splitting values for ` > 200. We also show that the technique fails at ` © 2021, CC BY.

关键词： Eigenvalues and eigenfunctions

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Inference of phase field fracture models

arXiv

引用

arXiv 2025年

作者： Livingston, Elizabeth Srivastava, Siddhartha Holber, Jamie Mourad, Hashem M. Garikipati, Krishna Department of Mechanical Engineering University of Michigan United States Michigan Institute for Computational Discovery & Engineering University of Michigan United States Applied Physics University of Michigan United States Department of Mathematics University of Michigan United States T-3 Theoretical Division Los Alamos National Laboratory United States

The phase field approach to modeling fracture uses a diffuse damage field to represent a crack. This addresses the singularities that arise at the crack tip in computations with sharp interface models, mollifying some of the difficulties associated with the mathematical and numerical treatment of fracture. The introduction of the diffuse field helps with crack propagation dynamics, enabling phase-field approaches to model all phases of damage from crack initiation to propagation, branching, and merging. Specific formulations, beginning with brittle fracture, have also been shown to converge to classical solutions. Extensions to cover the range of material failure, including ductile and cohesive fracture, leads to an array of possible models. There exists a large body of studies of these models and their consequences for crack evolution. However, there have not been systematic studies into how optimal models may be chosen. Here we take a first step in this direction by developing formal methods for identification of the best parsimonious model of phase field fracture given full-field data on the damage and deformation fields. We consider some of the main models that have been used to model damage, its degradation of elastic response, and its propagation. Our approach builds upon Variational System Identification (VSI), a weak form variant of the Sparse Identification of Nonlinear Dynamics (SINDy). In this first communication we focus on synthetically generated data but we also consider central issues associated with the use of experimental full-field data, such as data sparsity and noise. © 2025, CC BY-NC-SA.

关键词： Crack tips

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Multipartite Entanglement in Rabi-Driven Superconducting Qubits

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PRX Quantum 2022年第4期3卷 040322-040322页

作者： Marie Lu Jean-Loup Ville Joachim Cohen Alexandru Petrescu Sydney Schreppler Larry Chen Christian Jünger Chiara Pelletti Alexei Marchenkov Archan Banerjee William P. Livingston John Mark Kreikebaum David I. Santiago Alexandre Blais Irfan Siddiqi Department of Physics University of California Berkeley California 94720 USA Institut Quantique and Département de Physique Université de Sherbrooke Sherbrooke Québec J1K 2R1 Canada Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory University of California Berkeley California 94720 USA Bleximo Corporation 701 Heinz Avenue Berkeley California 94710 USA Canadian Institute for Advanced Research Toronto Ontario M5G1M1 Canada

Exploring highly connected networks of qubits is invaluable for implementing various quantum algorithms and simulations. All-to-all connectivity allows for entangling qubits with reduced gate depth. On trapped ion quantum processors, the shared motional degree of freedom is routinely used to simultaneously entangle over a dozen qubits with high fidelity in the Mølmer-Sørensen gate. Here, we demonstrate the first implementation of a Mølmer-Sørensen-like interaction in circuit quantum electrodynamics through assisted by a shared photonic mode and Rabi driven qubits, which relaxes restrictions on qubit frequencies during fabrication and supports scalability. We achieve a two-qubit entangled state with maximum state fidelity or 97% in 310 ns and a three-qubit GHZ state with fidelity 90.5% in 217 ns, and a four-qubit GHZ state with 66% fidelity. The four-qubit gate is limited by shared resonator losses and the spread of qubit-resonator couplings, which must be addressed for high fidelity operations. Exploring highly connected networks of qubits is invaluable for implementing various quantum algorithms and simulations as it allows for entangling qubits with reduced circuit depth. Here, we demonstrate a multi-qubit STAR (Sideband Tone Assisted Rabi driven) gate. Our scheme is inspired by the ion qubit Mølmer-Sørensen gate and is mediated by a shared photonic mode and Rabi-driven superconducting qubits, which relaxes restrictions on qubit frequencies during fabrication and supports scalability. We achieve a two-qubit gate with maximum state fidelity of 95% in 310 ns, a three-qubit gate with state fidelity 90.5% in 217 ns, and a four-qubit gate with state fidelity 66% in 200 ns. Furthermore, we develop a model of the gate that show the four-qubit gate is limited by shared resonator losses and the spread of qubit-resonator couplings, which must be addressed to reach high-fidelity operations.

关键词： Quantum computation Quantum control Quantum entanglement Quantum gates Quantum information processing Superconductors

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Characterization of a microsecond pulsed non-equilibrium atmospheric pressure Ar plasma using laser scattering and optical emission spectroscopy

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Plasma Science and Technology 2020年第6期22卷 120-127页

作者： Fengdong JIA Yong WU Qi MIN Maogen SU Keigo TAKEDA Kenji ISHIKAWA Hiroki KONDO Makoto SEKINE Masaru HORI Zhiping ZHONG School of Physical Sciences University of Chinese Academy of SciencesBeijing 100049People's Republic of China Institute of Applied Physics and Computational Mathematics Beijing 100088People's Republic of China Key Laboratory of Atomic and Molecular Physics&Functional Material of Gansu Province College of Physics and Electronic EngineeringNorthwest Normal UniversityLanzhou 730070People's Republic of China Department of Electrical and Electronic Engineering Faculty of Science and TechnologyMeijo UniversityNagoya 468-8502Japan Graduate School of Engineering Nagoya UniversityNagoya 464-8603Japan CAS Center for Excellence in Topological Quantum Computation University of Chinese Academy of SciencesBeijing 100190People's Republic of China

A non-equilibrium atmospheric pressure argon(Ar)plasma excited by microsecond pulse is studied experimentally by laser scattering and optical emission spectroscopy(OES),and theoretically by collisional-radiative(CR)*** specifically,the electron temperature and electron density of plasma are obtained directly by the laser Thomson scattering,the gas temperature is measured by laser Raman scattering,the optical emissions of excited Ar states of plasma are measured by *** laser scattering results show that the electron temperature is about 1 eV which is similar to that excited by 60 Hz AC power,but the gas temperature is as low as 300 K compared to about 700 K excited by 60 Hz AC *** is shown that the microsecond pulsed power supply,rather than nanosecond ones,is short enough to reduce the gas temperature of atmospheric pressure plasma to near room *** electron temperature and electron density are also obtained by CR model based on OES,and find that the intensities of the optical emission intensity lines of 727.41,811.73,841.08,842.83,852.44 and 912.86 nm of Ar can be used to characterize the behavior of electron density and electron temperature,it is very useful to quickly estimate the activity of the atmospheric pressure Ar plasma in many applications.

关键词： plasma diagnosis laser Thomson scattering atmospheric pressure plasma

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Applicability of 9Be global optical potential to reactions of 7,10,11,12Be

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Chinese physics C 2019年第9期43卷 55-61页

作者： Yong-Li Xu Yin-Lu Han Hai-Ying Liang Zhen-Dong Wu Hai-Rui Guo Chong-Hai Cai College of Physics and Electronic Science Shanxi Datong UniversityDatong 037009China Key Laboratory of Nuclear Data China Institute of Atomic EnergyP.O.BOX(275-41)Beijing 102413China Institute of Applied Physics and Computational Mathematics Beijing 100094China Department of Physics Nankai UniversityTianjin 300071China

Elastic scattering angular distributions and total reaction cross-sections of 7,10,11,12Be projectiles are predicted by the systematic 9Be global phenomenological optical model potential for target mass numbers ranging from 24 to *** predictions provide a detailed analysis by their comparison with the available experimental ***,these elastic scattering observables are also predicted for some targets out of the mass number *** results are in reasonable agreement with the existing experimental data,and they are presented in this study.

关键词： global phenomenological optical model potential elastic scattering angular distributions total reaction cross sections

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Exploring the nexus of many-body theories through neural network techniques: the tangent model

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Machine Learning: Science and Technology 2025年第2期6卷

作者： Liang, Senwei Kowalski, Karol Yang, Chao Bauman, Nicholas P Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Physical Sciences Division Pacific Northwest National Laboratory RichlandWA99354 United States Department of Physics University of Washington SeattleWA98195 United States

In this paper, we present a physically informed neural network (NN) representation of the effective interactions associated with coupled-cluster downfolding models to describe chemical systems and processes. The NN representation not only allows us to evaluate the effective interactions efficiently for various geometrical configurations of chemical systems corresponding to various levels of complexity of the underlying wave functions, but also reveals that the bare and effective interactions are related by a tangent function of some latent variables. We refer to this characterization of the effective interaction as a tangent model. We discuss the connection between this tangent model for the effective interaction with the previously developed theoretical analysis that examines the difference between the bare and effective Hamiltonians in the corresponding active spaces. © 2025 The Author(s). Published by IOP Publishing Ltd.

关键词： Hamiltonians

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Hyperuniformity order metric of Barlow packings

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Physical Review E 2019年第2期99卷 022111-022111页

作者： T. M. Middlemas 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 New Jersey 08544 USA

The concept of hyperuniformity has been a useful tool in the study of density fluctuations at large length scales in systems ranging across the natural and mathematical sciences. One can rank a large class of hyperuniform systems by their ability to suppress long-range density fluctuations through the use of a hyperuniformity order metric Λ¯. We apply this order metric to the Barlow packings, which are the infinitely degenerate densest packings of identical rigid spheres that are distinguished by their stacking geometries and include the commonly known fcc lattice and hcp crystal. The “stealthy stacking” theorem implies that these packings are all stealthy hyperuniform, a strong type of hyperuniformity, which involves the suppression of scattering up to a wave vector K. We describe the geometry of three classes of Barlow packings, two disordered classes and small-period packings. In addition, we compute a lower bound on K for all Barlow packings. We compute Λ¯ for the aforementioned three classes of Barlow packings and find that, to a very good approximation, it is linear in the fraction of fcc-like clusters, taking values between those of least-ordered hcp and most-ordered fcc. This implies that the value of Λ¯ of all Barlow packings is primarily controlled by the local cluster geometry. These results highlight the special nature of anisotropic stacking disorder, which provides impetus for future research on the development of anisotropic order metrics and hyperuniformity properties.

关键词： Classical statistical mechanics

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Schwarzschild and Ledoux are equivalent on evolutionary timescales

arXiv

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arXiv 2022年

作者： Anders, Evan H. Jermyn, Adam S. Lecoanet, Daniel Fraser, Adrian E. Cresswell, Imogen G. Joyce, Meridith Fuentes, J.R. CIERA Northwestern University EvanstonIL60201 United States Kavli Institute for Theoretical Physics University of California Santa BarbaraCA93106 United States Center for Computational Astrophysics Flatiron Institute New YorkNY10010 United States Department of Engineering Sciences and Applied Mathematics Northwestern University EvanstonIL60208 United States Department of Applied Mathematics Baskin School of Engineering University of California Santa CruzCA95064 United States Department Astrophysical and Planetary Sciences & LASP University of Colorado BoulderCO80309 United States Space Telescope Science Institute 3700 San Martin Drive BaltimoreMD21218 United States Department of Physics McGill Space Institute McGill University 3600 rue University MontrealQCH3A 2T8 Canada

Stellar evolution models calculate convective boundaries using either the Schwarzschild or Ledoux criterion, but confusion remains regarding which criterion to use. Here we present a 3D hydrodynamical simulation of a convection zone and adjacent radiative zone, including both thermal and compositional buoyancy forces. As expected, regions which are unstable according to the Ledoux criterion are convective. Initially, the radiative zone adjacent to the convection zone is Schwarzschild-unstable but Ledoux-stable due to a composition gradient. Over many convective overturn timescales the convection zone grows via entrainment. The convection zone saturates at the size originally predicted by the Schwarzschild criterion, although in this final state the Schwarzschild and Ledoux criteria agree. Therefore, the Schwarzschild criterion should be used to determine the size of stellar convection zones, except possibly during short-lived evolutionary stages in which entrainment persists. © 2022, CC BY.

关键词： Stars

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