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arXiv 2025年

作者： Field, Scott E. Varma, Vijay Blackman, Jonathan Gadre, Bhooshan Galley, Chad R. Islam, Tousif Mitman, Keefe Pürrer, Michael Ravichandran, Adhrit Scheel, Mark A. Stein, Leo C. Yoo, Jooheon Department of Mathematics Center for Scientific Computing & Data Science Research University of Massachusetts DartmouthMA02747 United States Theoretical Astrophysics 350-17 California Institute of Technology PasadenaCA91125 United States Utrecht University Utrecht3584 CC Netherlands Kavli Institute for Theoretical Physics University of California Santa BarbaraCA93106 United States Department of Physics Center for Computational Research East Hall University of Rhode Island KingstonRI02881 United States Department of Physics and Astronomy The University of Mississippi UniversityMS38677 United States Cornell Center for Astrophysics and Planetary Science Cornell University IthacaNY14853 United States

Gravitational waves are ripples in space-time caused by the motion of massive objects. One of the most astrophysically important sources of gravitational radiation is caused by two orbiting compact objects, such as black holes and neutron stars, that slowly inspiral and merge. The motion of these massive objects generates gravitational waves that radiate to the far field where gravitational-wave detectors can observe them. Complicated partial or ordinary differential equations govern the entire process. Traditionally, the dynamics of compact binary systems and the emitted gravitational waves have been computed by expensive simulation codes that can take days to months to run. A key simulation output is the gravitational wave signal for a particular set of parameter values describing the system, such as the black holes’ masses and spins. The computed signal is required for a diverse range of multiple-query applications, such as template bank generation for searches, parameter estimation, mock data analysis, studies of model bias, and tests of general relativity, to name a few. In such settings, the high-fidelity signal computed from differential equations is often too slow to be directly used. Surrogate models offer a practical way to dramatically accelerate model evaluation while retaining the high-fidelity accuracy of the expensive simulation code;an example is shown in Fig. 1. Surrogate models can be constructed in various ways, but what separates these models from other modeling frameworks is that they are primarily data-driven. Given a training set of gravitational waveform data sampling the parameter space, a model is built by following three steps: 1. Feature extraction: the waveform is decomposed into data pieces that are simple to model, 2. Dimensionality reduction: each data piece is approximated by a low-dimensional vector space, which reduces the degrees of freedom we need to model, and 3. Regression: fitting and regression techniques are applied to the l

关键词： Gravitational effects

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Phenomenology and origin of late-time tails in eccentric binary black hole mergers

arXiv

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arXiv 2024年

作者： Islam, Tousif Faggioli, Guglielmo Khanna, Gaurav Field, Scott E. van de Meent, Maarten Buonanno, Alessandra Kavli Institute for Theoretical Physics University of California Santa Barbara Kohn Hall Lagoon Rd Santa BarbaraCA93106 United States Department of Physics University of Massachusetts DartmouthMA02747 United States Department of Mathematics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Data Science Research University of Massachusetts DartmouthMA02747 United States Max Planck Institute for Gravitational Physics Albert Einstein Institute Am M¨uhlenberg 1 Potsdam14476 Germany Department of Physics Center for Computational Research University of Rhode Island KingstonRI02881 United States Niels Bohr International Academy Niels Bohr Institute Blegdamsvej 17 Copenhagen2100 Denmark

We investigate the late-time tail behavior in gravitational waves from merging eccentric binary black holes (BBH) using black hole perturbation theory. For simplicity, we focus only on the dominant quadrupolar mode of the radiation. We demonstrate that such tails become more prominent as eccentricity increases. Exploring the phenomenology of the tails in both spinning and non-spinning eccentric binaries, with the spin magnitude varying from χ = −0.6 to χ = +0.6 and eccentricity as high as e = 0.98, we find that these tails can be well approximated by a slowly decaying power law. We study the power law for varying systems and find that the power law exponent lies close to the theoretically expected value −4. Finally, using both plunge geodesic and radiation-reaction-driven orbits, we perform a series of numerical experiments to understand the origin of the tails in BBH simulations. Our results suggest that the late-time tails are strongly excited in eccentric BBH systems when the smaller black hole is in the neighborhood of the apocenter, as opposed to any structure in the strong field of the larger black hole. Our analysis framework is publicly available through the gwtails Python package. Copyright © 2024, The Authors. All rights reserved.

关键词： Black holes

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Circumferential crack modeling of thin cylindrical shells in modal deformation

arXiv

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arXiv 2021年

作者： Alijani, Ali Barrera, Olga Bordas, Stéphane P.A. Department of Mechanical Engineering Bandar Anzali Branch Islamic Azad University Bandar Anzali Iran School of Engineering Computing and Mathematics Oxford Brookes University United Kingdom Institute of Computational Engineering Faculty of Sciences and Technology University of Luxembourg Luxembourg City Luxembourg

An innovative technique, called conversion, is introduced to model circumferential cracks in thin cylindrical shells. The semi-analytical finite element method is applied to investigate the modal deformation of the cylinder. An element including the crack is divided into three sub-elements with four nodes in which the stiffness matrix is enriched. The crack characteristics are included in the finite element method relations through conversion matrices and a rotational spring corresponding to the crack. Conversion matrices obtained by applying continuity conditions at the crack tip are used to transform displacements of the middle nodes to those of the main nodes. Moreover, another technique, called spring set, is represented based on a set of springs to model the crack as a separated element. Components of the stiffness matrix related to the separated element are incorporated while the geometric boundary conditions at the crack tip are satisfied. The effects of the circumferential mode number, the crack depth and the length of the cylinder on the critical buckling load are investigated. Experimental tests, ABAQUS modeling and results from literature are used to verify and validate the results and derived relations. In addition, the crack effect on the natural frequency is examined using the vibration analysis based on the conversion technique. Copyright © 2021, The Authors. All rights reserved.

关键词： Deformation

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General liquid-crystal theory for anisotropically shaped molecules: Symmetry, orientational order parameters, and system free energy

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Physical Review E 2020年第6期102卷 062701-062701页

作者： Jie Xu Jeff Z. Y. Chen LSEC & NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing (ICMSEC) Academy of Mathematics and Systems Science (AMSS) Chinese Academy of Sciences Beijing 100190 China Department of Physics and Astronomy University of Waterloo Ontario Canada N2L 3G1

A general theory of liquid crystals is presented, starting from the group-theory symmetry analysis of the constituting molecules. A particular attention is paid to the type of elastic free-energies and their relationships with the molecular symmetries. The orientational order-parameter tensors are identified for each molecular symmetry, in a consideration of consistently keeping the leading, characteristic elastic free energies in a model. The order parameters are expressed in terms of symmetric traceless tensors, some of high orders, for all major molecular symmetries, including seven groups of axial symmetries and seven groups of polyhedral symmetries. For spatially inhomogeneous liquid crystals, the couplings of these tensors in the elastic energies are derived by expanding the interaction energies between these molecules. The aim is to provide a general view of the molecular symmetries of individual molecules, orientational order parameters characterizing the orientational distribution functions, and the elastic free energies, all under one single group-theory approach.

关键词： Bent-core liquid crystals Liquid crystals Lyotropic liquid crystals Nematic liquid crystals

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Extending the limit of molecular dynamics with ab initio accuracy to 10 billion atoms

arXiv

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arXiv 2022年

作者： Guo, Zhuoqiang Lu, Denghui Yan, Yujin Hu, Siyu Liu, Rongrong Tan, Guangming Sun, Ninghui Jiang, Wanrun Liu, Lijun Chen, Yixiao Zhang, Linfeng Chen, Mohan Wang, Han Jia, Weile Institute of Computing Technology Chinese Academy of Sciences Beijing China University of Chinese Academy of Sciences Beijing China State Key Laboratory of Computer Architecture ICT Chinese Academy of Sciences Beijing China HEDPS CAPT College of Engineering Peking University Beijing China AI for Science Institute Beijing China Osaka University Osaka Japan Princeton University Princeton United States DP Technology Beijing China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing China

High-performance computing, together with a neural network model trained from data generated with first-principles methods, has greatly boosted applications of ab initio molecular dynamics in terms of spatial and temporal scales on modern supercomputers. Previous state-of-the-art can achieve 1 − 2 nanoseconds molecular dynamics simulation per day for 100-million atoms on the entire Summit supercomputer. In this paper, we have significantly reduced the memory footprint and computational time by a comprehensive approach with both algorithmic and system innovations. The neural network model is compressed by model tabulation, kernel fusion, and redundancy removal. Then optimizations such as acceleration of customized kernel, tabulation of activation function, MPI+OpenMP parallelization are implemented on GPU and ARM architectures. Testing results of the copper system show that the optimized code can scale up to the entire machine of both Fugaku and Summit, and the corresponding system size can be extended by a factor of 134 to an © 2022, CC BY-NC-SA.

关键词： Supercomputers

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A constrained transport divergence-free finite element method for incompressible MHD equations

arXiv

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arXiv 2020年

作者： Li, Lingxiao Zhang, Donghang Zheng, Weiying Institute of Applied Physics and Computational Mathematics Beijing100094 China LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Science University of Chinese Academy of Sciences Beijing100049 China

In this paper we study finite element method for three-dimensional incompressible resistive magnetohydrodynamic equations, in which the velocity, the current density, and the magnetic induction are divergence-free. It is desirable that the discrete solutions should also satisfy divergence-free conditions exactly especially for the momentum equations. Inspired by constrained transport method, we devise a new stable mixed finite element method that can achieve the goal. We also prove the well-posedness of the discrete solutions. To solve the resulting linear algebraic equations, we propose a GMRES solver with an augmented Lagrangian block preconditioner. By numerical experiments, we verify the theoretical results and demonstrate the quasi-optimality of the discrete solver with respect to the number of degrees of freedom. Copyright © 2020, The Authors. All rights reserved.

关键词： Finite element method

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The Basics of Quantum computing for Chemists

arXiv

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arXiv 2022年

作者： Claudino, Daniel Quantum Computing Institute Oak Ridge National Laboratory Oak RidgeTN37831 United States Computational Sciences and Engineering Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States

The rapid and successful strides in quantum chemistry in the past decades can be largely credited to a conspicuous synergy between theoretical and computational advancements. However, the architectural computer archetype that enabled such a progress is approaching a state of more stagnant development. One of the most promising technological avenues for the continuing progress of quantum chemistry is the emerging quantum computing paradigm. This revolutionary proposal comes with several challenges, which span a wide array of disciplines. In chemistry, it implies, among other things, a need to reformulate some of its long established cornerstones in order to adjust to the operational demands and constraints of quantum computers. Due to its relatively recent emergence, much of quantum computing may still seem fairly nebulous and largely unknown to most chemists. It is in this context that here we review and illustrate the basic aspects of quantum information and their relation to quantum computing insofar as enabling simulations of quantum chemistry. We consider some of the most relevant developments in light of these aspects and discuss the current landscape when of relevance to quantum chemical simulations in quantum computers. © 2022, CC BY.

关键词： Quantum optics

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H2−Korn⇔s inequality and the nonconforming elements for the strain gradient elastic model

arXiv

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arXiv 2021年

作者： Li, Hongliang Ming, Pingbing Wang, Huiyu Department of Mathematics Sichuan Normal University Chengdu610066 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences No. 55 East Road Zhong-Guan-Cun Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Middle School Beijing101 China

We establish a new H2−Korn’s inequality and its discrete analog, which greatly simplify the construction of nonconforming elements for a linear strain gradient elastic model. The Specht triangle [41] and the NZT tetrahedron [45] are analyzed as two typical representatives for robust nonconforming elements in the sense that the rate of convergence is independent of the small material parameter. We construct new regularized interpolation estimate and the enriching operator for both elements, and prove the error estimates under minimal smoothness assumption on the solution. Numerical results are consistent with the theoretical prediction. © 2021, CC BY.

关键词： Finite element method

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Space-time hp finite elements for heat evolution in laser-based additive manufacturing

arXiv

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arXiv 2021年

作者： Kopp, Philipp Calo, Victor Rank, Ernst Kollmannsberger, Stefan Computational Modeling and Simulation Technische Universität München Munich Germany Computational Geoscience & Applied Mathematics School of Electrical Engineering Computing & Mathematical Science Curtin University Perth Australia Institute for Advanced Study Technische Universität München Munich Germany

The direct numerical simulation of metal additive manufacturing processes such as laser powder bed fusion is challenging due to the vast differences in spatial and temporal scales. Classical approaches based on locally refined finite elements combined with time-stepping schemes can only address the spatial multi-scale nature and provide only limited scaling potential for massively parallel computations. We address these shortcomings in a space-time Galerkin framework where the finite element interpolation also includes the temporal dimension. In this setting, we construct four-dimensional meshes that are locally refined towards the laser spot and allow for varying temporal accuracy depending on the position in space. By splitting the mesh into conforming time-slabs, we recover a stepwise solution to solve the space-time problem locally in time at this slab;additionally, we can choose time-slab sizes significantly larger than classical time-stepping schemes. As a result, we believe this setting to be well suited for large-scale parallelization. In our work, we use a continuous Galerkin-Petrov formulation of the nonlinear heat equation with an apparent heat capacity model to account for the phase change. We validate our approach by computing the AMB2018-02 benchmark, where we obtain an excellent agreement with the measured melt pool shape. Using the same setup, we demonstrate the performance potential of our approach by hatching a square area with a laser path length of about one meter. © 2021, CC BY.

关键词： 3D printers

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Evidence of Large Recoil Velocity from a Black Hole Merger Signal

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Physical Review Letters 2022年第19期128卷 191102-191102页

作者： Vijay Varma Sylvia Biscoveanu Tousif Islam Feroz H. Shaik Carl-Johan Haster Maximiliano Isi Will M. Farr Scott E. Field Salvatore Vitale Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am Mühlenberg 1 Potsdam 14476 Germany LIGO Laboratory Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Department of Physics and Kavli Institute for Astrophysics and Space Research Massachusetts Institute of Technology 77 Massachusetts Ave Cambridge Massachusetts 02139 USA Department of Mathematics University of Massachusetts Dartmouth Massachusetts 02747 USA Center for Scientific Computing and Data Science Research University of Massachusetts Dartmouth Massachusetts 02747 USA Center for Computational Astrophysics Flatiron Institute New York New York 10010 USA Department of Physics and Astronomy Stony Brook University Stony Brook New York 11794 USA

The final black hole left behind after a binary black hole merger can attain a recoil velocity, or a “kick,” reaching values up to 5000 km/s. This phenomenon has important implications for gravitational wave astronomy, black hole formation scenarios, testing general relativity, and galaxy evolution. We consider the gravitational wave signal from the binary black hole merger GW200129_065458 (henceforth referred to as GW200129), which has been shown to exhibit strong evidence of orbital precession. Using numerical relativity surrogate models, we constrain the kick velocity of GW200129 to vf∼1542−1098+747 km/s or vf≳698 km/s (one-sided limit), at 90% credibility. This marks the first identification of a large kick velocity for an individual gravitational wave event. Given the kick velocity of GW200129, we estimate that there is a less than 0.48% (7.7%) probability that the remnant black hole after the merger would be retained by globular (nuclear star) clusters. Finally, we show that kick effects are not expected to cause biases in ringdown tests of general relativity for this event, although this may change in the future with improved detectors.

关键词： Gravitational waves

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