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A quasi-conservative DG-ALE method for multi-component flows using the non-oscillatory kinetic flux

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arXiv 2021年

作者： Luo, Dongmi Li, Shiyi Huang, Weizhang Qiu, Jianxian Chen, Yibing Institute of Applied Physics and Computational Mathematics Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100088 China Department of Mathematics University of Kansas LawrenceKS66045 United States School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University XiamenFujian361005 China

A high-order quasi-conservative discontinuous Galerkin (DG) method is proposed for the numerical simulation of compressible multi-component flows. A distinct feature of the method is a predictor-corrector strategy to define the grid velocity. A Lagrangian mesh is first computed based on the flow velocity and then used as an initial mesh in a moving mesh method (the moving mesh partial differential equation or MMPDE method) to improve its quality. The fluid dynamic equations are discretized in the direct arbitrary Lagrangian-Eulerian framework using DG elements and the non-oscillatory kinetic flux while the species equation is discretized using a quasi-conservative DG scheme to avoid numerical oscillations near material interfaces. A selection of one- and two-dimensional examples are presented to verify the convergence order and the constant-pressure-velocity preservation property of the method. They also demonstrate that the incorporation of the Lagrangian meshing with the MMPDE moving mesh method works well to concentrate mesh points in regions of shocks and material interfaces. Copyright © 2021, The Authors. All rights reserved.

关键词： Galerkin methods

A MULTIFIDELITY MONTE CARLO METHOD FOR REALISTIC computational BUDGETS

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arXiv 2022年

作者： Gruber, Anthony Gunzburger, Max Ju, Lili Wang, Zhu Department of Scientific Computing Florida State University 400 Dirac Science Library TallahasseeFL32306 United States Oden Institute for Computational Engineering and Sciences University of Texas at Austin 201 E 24th Street AustinTX78712 United States Department of Mathematics University of South Carolina 1523 Greene Street ColumbiaSC29208 United States

A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing closed-form solution, this method extends the usability of a well known MFMC algorithm, recovering it when the computational budget is large enough. Theoretical results verify that the proposed approach is at least as optimal as its namesake and retains the benefits of multifidelity estimation with minimal assumptions on the budget or amount of available data, providing a notable reduction in variance over simple Monte Carlo *** Codes 62K05, 49M20 Copyright © 2022, The Authors. All rights reserved.

关键词： Monte Carlo methods

A NITSCHE HYBRID MULTISCALE METHOD WITH NON-MATCHING GRIDS

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arXiv 2021年

作者： Ming, Pingbing Song, Siqi 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

We propose a Nitsche method for multiscale partial differential equations, which retrieves the macroscopic information and the local microscopic information at one stroke. We prove the convergence of the method for second order elliptic problem with bounded and measurable coefficients. The rate of convergence may be derived for coefficients with further structures such as periodicity and ergodicity. Extensive numerical results confirm the theoretical predictions. Copyright © 2021, The Authors. All rights reserved.

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Verifiable blind quantum computation with identity authentication for different types of clients

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arXiv 2022年

作者： Quan, Junyu Li, Qin Li, Lvzhou School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China School of Computer Science Xiangtan University Xiangtan411105 China Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-sen University Guangzhou510006 China

Quantum computing has considerable advantages in solving some problems over its classical counterpart. Currently various physical systems are developed to construct quantum computers but it is still challenging and the first use of quantum computers may adopt the cloud style. Blind quantum computing (BQC) provides a solution for clients with limited quantum capabilities to delegate their quantum computation to remote quantum servers while keeping input, output, and even algorithm private. In this paper, we propose three multi-party verifiable blind quantum computing (VBQC) protocols with identity authentication to handle clients with varying quantum capabilities in quantum networks, such as those who can just make measurements, prepare single qubits, or perform a few single-qubit gates. They are client-friendly and flexible since the clients can achieve BQC depending on their own quantum devices and resist both insider outsider attacks in quantum networks. Furthermore, all the three proposed protocols are verifiable, namely that the clients can verify the correctness of their calculations. Copyright © 2022, The Authors. All rights reserved.

关键词： Qubits

Lattice Construction C∗ from Self-Dual Codes

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Lattice Construction C∗ from Self-Dual Codes

2020 IEEE International Symposium on Information Theory, ISIT 2020

作者： Bollauf, Maiara F. Costa, Sueli I. R. Zamir, Ram University of Campinas Institute of Mathematics Statistic and Scientific Computing São Paulo13083-859 Brazil Tel Aviv University Deptartment Electrical Engineering-Systems Tel Aviv Israel

ISBN: (纸本)9781728164328

Construction C∗ was recently introduced as a generalization of the multilevel Construction C (or Forney's code-formula), such that the coded levels may be dependent. Both constructions do not produce a lattice in general, hence the central idea of this paper is to present a 3-level lattice Construction C∗ scheme that admits an efficient nearest-neighborhood decoding. In order to achieve this objective, we choose coupled codes for levels 1 and 3, and set the second level code C 2 as an independent linear binary self-dual code, which is known to have a rich mathematical structure among families of linear codes. Our main result states a necessary and sufficient condition for this construction to generate a lattice. We then present examples of efficient lattices and also non-lattice constellations with good packing properties. © 2020 IEEE.

关键词： C (programming language)

Machine learning for elliptic PDEs: Fast rate generalization bound, neural scaling law and minimax optimality

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arXiv 2021年

作者： Lu, Yiping Chen, Haoxuan Lu, Jianfeng Ying, Lexing Blanchet, Jose Institute for Computational and Mathematical Engineering Stanford University StanfordCA United States Department of Computing and Mathematical Sciences Caltech Mathematics Department Duke University United States Department of Mathematics Institute for Computational and Mathematical Engineering Stanford University StanfordCA United States Department of Management Science & Engineering Stanford University StanfordCA United States

In this paper, we study the statistical limits of deep learning techniques for solving elliptic partial differential equations (PDEs) from random samples using the Deep Ritz Method (DRM) and Physics-Informed Neural Networks (PINNs). To simplify the problem, we focus on a prototype elliptic PDE: the Schrödinger equation on a hypercube with zero Dirichlet boundary condition, which has wide application in the quantum-mechanical systems. We establish upper and lower bounds for both methods, which improves upon concurrently developed upper bounds for this problem via a fast rate generalization bound. We discover that the current Deep Ritz Methods is sub-optimal and propose a modified version of it. We also prove that PINN and the modified version of DRM can achieve minimax optimal bounds over Sobolev spaces. Empirically, following recent work which has shown that the deep model accuracy will improve with growing training sets according to a power law, we supply computational experiments to show a similar behavior of dimension dependent power law for deep PDE solvers. © 2021, CC BY.

关键词： Optimization

DisTRaC: Accelerating High Performance Compute Processing for Temporary Data Storage

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arXiv 2022年

作者： Mason-Williams, Gabryel Bond, Dave Basham, Mark Diamond Light Source Scientific Computing SSCC Oxfordshire Didcot United Kingdom The University of Plymouth School of Engineering Computing and Mathematics Devon Plymouth United Kingdom The Rosalind Franklin Institute Artificial Intelligence and Informatics Oxfordshire Didcot United Kingdom Diamond Light Source Data Analysis Group SSCC Oxfordshire Didcot United Kingdom

High Performance Compute (HPC) clusters often produce intermediate files as part of code execution and message passing is not always possible to supply data to these cluster jobs. In these cases, I/O goes back to central distributed storage to allow cross node data sharing. These systems are often high performance and characterised by their high cost per TB and sensitivity to workload type such as being tuned to small or large file I/O. However, compute nodes often have large amounts of RAM, so when dealing with intermediate files where longevity or reliability of the system is not as important, local RAM disks can be used to obtain performance benefits. In this paper we show how this problem was tackled by creating a RAM block that could interact with the object storage system Ceph, as well as creating a deployment tool to deploy Ceph on HPC infrastructure effectively. This work resulted in a system that was more performant than the central high performance distributed storage system used at Diamond reducing I/O overhead and processing time for Savu, a tomography data processing application, by 81.04% and 8.32% respectively. © 2022, CC BY.

关键词： Random access storage

Measuring kinetic inductance and superfluid stiffness of two-dimensional superconductors using high-quality transmission-line resonators

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Physical Review Research 2024年第4期6卷 043245-043245页

作者： Mary Kreidel Xuanjing Chu Jesse Balgley Abhinandan Antony Nishchhal Verma Julian Ingham Leonardo Ranzani Raquel Queiroz Robert M. Westervelt School of Engineering and Applied Sciences Harvard University Cambridge Massachusetts 02138 USA Department of Applied Physics and Applied Mathematics Columbia University New York New York 10027 USA Department of Mechanical Engineering Columbia University New York New York 10027 USA Department of Physics Columbia University New York New York 10027 USA RTX BBN Technologies Quantum Engineering and Computing Group Cambridge Massachusetts 02138 USA Center for Computational Quantum Physics Flatiron Institute New York New York 10010 USA Department of Physics Harvard University Cambridge Massachusetts 02138 USA

The discovery of van der Waals superconductors in recent years has generated a lot of excitement for their potentially novel pairing mechanisms. However, their typical atomic-scale thickness and micrometer-scale lateral dimensions impose severe challenges to investigations of pairing symmetry by conventional methods. We demonstrate an improved technique that employs high-quality-factor superconducting resonators to measure the kinetic inductance—up to one part per million—and loss of a van der Waals superconductor. We analyze the equivalent circuit model to extract the kinetic inductance, superfluid stiffness, penetration depth, and ratio of imaginary and real parts of the complex conductivity. We validate the technique by measuring aluminum and finding excellent agreement in both the zero-temperature superconducting gap as well as the complex conductivity data when compared with BCS theory. We then demonstrate the utility of the technique by measuring the kinetic inductance of multilayered niobium diselenide and discuss the limits to the accuracy of our technique when the transition temperature of the sample, NbSe2 at 7.06 K, approaches our Nb probe resonator at 8.59 K. Our method will be useful for practitioners in the growing fields of superconducting physics, materials science, and quantum sensing, as a means of characterizing superconducting circuit components and studying pairing mechanisms of the novel superconducting states which arise in layered two-dimensional materials and heterostructures.

关键词： Quantum circuits Superconducting order parameter Superconductivity 2-dimensional systems Van der Waals systems Methods in superconductivity Microwave techniques

Influence of Material Parameter Variability on the Predicted Coronary Artery Biomechanical Environment via Uncertainty Quantification

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arXiv 2024年

作者： Berggren, Caleb C. Jiang, David Wang, Y.F. Jack Bergquist, Jake A. Rupp, Lindsay C. Liu, Zexin MacLeod, Rob S. Narayan, Akil Timmins, Lucas H. Department of Biomedical Engineering University of Utah Salt Lake CityUT United States Scientific Computing and Imaging Institute University of Utah Salt Lake CityUT United States Nora Eccles Cardiovascular Research and Training Institute University of Utah Salt Lake CityUT United States Department of Mathematics University of Utah Salt Lake CityUT United States School of Engineering Medicine Texas A&M University HoustonTX United States Department of Biomedical Engineering Texas A&M University College StationTX United States

Central to the clinical adoption of patient-specific modeling strategies is demonstrating that simulation results are reliable and safe. Indeed, simulation frameworks must be robust to uncertainty in model input(s), and levels of confidence should accompany results. In this study, we applied a coupled uncertainty quantification-finite element (FE) framework to understand the impact of uncertainty in vascular material properties on variability in predicted stresses. Univariate probability distributions were fit to material parameters derived from layer-specific mechanical behavior testing of human coronary tissue. Parameters were assumed to be probabilistically independent, allowing for efficient parameter ensemble sampling. In an idealized coronary artery geometry, a forward FE model for each parameter ensemble was created to predict tissue stresses under physiologic loading. An emulator was constructed within the UncertainSCI software using polynomial chaos techniques, and statistics and sensitivities were directly computed. Results demonstrated that material parameter uncertainty propagates to variability in predicted stresses across the vessel wall, with the largest dispersions in stress within the adventitial layer. Variability in stress was most sensitive to uncertainties in the anisotropic component of the strain energy function. Moreover, unary and binary interactions within the adventitial layer were the main contributors to stress variance, and the leading factor in stress variability was uncertainty in the stress-like material parameter that describes the contribution of the embedded fibers to the overall artery stiffness. Results from a patient-specific coronary model confirmed many of these findings. Collectively, these data highlight the impact of material property variation on uncertainty in predicted artery stresses and present a pipeline to explore and characterize forward model uncertainty in computational biomechanics. © 2024, CC BY.

关键词： Uncertainty analysis