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Gravitational waves from black hole emission

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arXiv 2024年

作者： Islam, Tousif Khanna, Gaurav Liebling, Steven L. Kavli Institute of Theoretical Physics University of California Santa Barbara Santa BarbaraCA93106 United States Theoretical Astrophysics Walter Burke Institute for Theoretical Physics California Institute of Technology PasadenaCA91125 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 Department of Physics Center for Computational Research University of Rhode Island KingstonRI02881 United States Long Island University BrookvilleNY11548 United States

Using adiabatic point-particle black hole perturbation theory, we simulate plausible gravitational wave (GW) signatures in two exotic scenarios (i) where a small black hole is emitted by a larger one (‘black hole emission’) and (ii) where a small black hole is emitted by a larger one and subsequently absorbed back (‘black hole absorption’). While such scenarios are forbidden in general relativity!(GR), alternative theories (such as certain quantum gravity scenarios obeying the weak gravity conjecture, white holes, and Hawking radiation) may allow them. By leveraging the phenomenology of black hole emission and absorption signals, we introduce straightforward modifications to existing gravitational waveform models to mimic gravitational radiation associated with these exotic events. We anticipate that these (incomplete but) initial simulations, coupled with the adjusted waveform models, will aid in the development of null tests for GR using GWs. Copyright © 2024, The Authors. All rights reserved.

关键词： Black holes

Sparse approximation of data-driven polynomial chaos expansions: An induced sampling approach

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arXiv 2020年

作者： Guo, Ling Narayan, Akil Liu, Yongle Zhou, Tao Department of Mathematics Shanghai Normal University Shanghai China Department of Mathematics Scientific Computing and Imaging Institute University of Utah Salt Lake CityUT United States Department of Mathematics Southern University of Science and Technology Shenzhen China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

One of the open problems in the field of forward uncertainty quantification (UQ) is the ability to form accurate assessments of uncertainty having only incomplete information about the distribution of random inputs. Another challenge is to efficiently make use of limited training data for UQ predictions of complex engineering problems, particularly with high dimensional random parameters. We address these challenges by combining data-driven polynomial chaos expansions with a recently developed preconditioned sparse approximation approach for UQ problems. The first task in this two-step process is to employ the procedure developed in (Ahlfeld et al. 2016, [1]) to construct an "arbitrary" polynomial chaos expansion basis using a finite number of statistical moments of the random inputs. The second step is a novel procedure to effect sparse approximation via 1 minimization in order to quantify the forward uncertainty. To enhance the performance of the preconditioned 1 minimization problem, we sample from the so-called induced distribution, instead of using Monte Carlo (MC) sampling from the original, unknown probability measure. We demonstrate on test problems that induced sampling is a competitive and often better choice compared with sampling from asymptotically optimal measures (such as the equilibrium measure) when we have incomplete information about the distribution. We demonstrate the capacity of the proposed induced sampling algorithm via sparse representation with limited data on test functions, and on a Kirchoff plating bending problem with random Young’s modulus. Copyright © 2020, The Authors. All rights reserved.

关键词： Probability distributions

Complexity Analysis and Algorithm Design of Pooling Problem

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Journal of the Operations Research Society of China 2018年第2期6卷 249-266页

作者： Yu-Hong Dai Rui Diao Kai Fu State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The pooling problem,also called the blending problem,is fundamental in production planning of *** can be formulated as an optimization problem similar with the minimum-cost flow ***,Alfaki and Haugland(J Glob Optim 56:897–916,2013)proved the strong NP-hardness of the pooling problem in general *** also pointed out that it was an open problem to determine the computational complexity of the pooling problem with a fixed number of *** this paper,we prove that the pooling problem is still strongly NP-hard even with only one *** means the quality is an essential difference between minimum-cost flow problem and the pooling *** solving large-scale pooling problems in real applications,we adopt the non-monotone strategy to improve the traditional successive linear programming *** convergence of the algorithm is *** numerical experiments show that the non-monotone strategy is effective to push the algorithm to explore the global minimizer or provide a good local *** results for real problems from factories show that the proposed algorithm is competitive to the one embedded in the famous commercial software Aspen PIMS.

关键词： Pooling problem Complexity analysis Successive linear programming Non-monotone

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

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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

Circumferential crack modeling of thin cylindrical shells in modal deformation

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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

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

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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

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

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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

The Basics of Quantum computing for Chemists

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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

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

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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