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International Conference on Perspective Technologies and Methods in MEMS Design (MEMSTECH)

作者： Winfried Auzinger Roksolyana Stolyarchuk Yaroslav Pelekh Oksana Kozar Serhii Mentynskyi Mykola Ihnatyshyn Institute for Analysis and Scientific Computing Vienna University of Technology (TU Wien) Wien Austria Department of Computational Mathematics and Programming Lviv Polytechnic National University Lviv Ukraine Department of Mechanical Engineering Natural Sciences and Information Technologies Mukachevo State University Mukachevo Ukraine Department of Light Industry and Professional Education Mukachevo State University Mukachevo Ukraine

ISBN: (数字)9781728171807

ISBN: (纸本)9781728171814

In this paper we study an elastic-plastic isotropic body weakened by a rectilinear crack, directed along the abscissa axis, under the action of stresses symmetrical about its plane. An approximate (analytical and numerical) solution of this problem is constructed under the condition that the hydrostatic deformation of the split expansion is approximated by a parabola. The concentration of hydrogen near the top of the crack is calculated. Note that when using the above calculation formulas, at each node we get several approximations to the exact solution. In the proposed methods, only three appeals to the right-hand side of the differential equation are necessary to obtain both the third order accuracy method and the two approximations (upper and lower) of the second order of accuracy.

关键词： mathematical model elastic-plastic isotropic body hydrogen diffusion internal crack continued fractions two-sided approximations nonlinear methods diffusion of hydrogen internal cracks MEMS devices cracks Cocaine Fissure Mathematical Model Continued fraction Fields

On the spectrum of mesons in quenched Sp(2N) gauge theories

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arXiv 2023年

作者： Bennett, Ed Holligan, Jack Hong, Deog Ki Lee, Jong-Wan Lin, C.-J. David Lucini, Biagio Piai, Maurizio Vadacchino, Davide Swansea Academy of Advanced Computing Swansea University Fabian Way Swansea WalesSA1 8EN United Kingdom Biomedical and Physical Sciences Building Michigan State University East LansingMI48824 United States Department of Physics Pusan National University Busan46241 Korea Republic of Institute for Extreme Physics Pusan National University Busan46241 Korea Republic of Daejeon34126 Korea Republic of Institute of Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu30010 Taiwan Center for High Energy Physics Chung-Yuan Christian University Chung-Li32023 Taiwan Centre for Theoretical and Computational Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu30010 Taiwan Department of Mathematics Faculty of Science and Engineering Swansea University Fabian Way Swansea WalesSA1 8EN United Kingdom Department of Physics Faculty of Science and Engineering Swansea University Singleton Park Swansea WalesSA2 8PP United Kingdom Centre for Mathematical Sciences University of Plymouth PlymouthPL4 8AA United Kingdom

We report the findings of our extensive study of the spectra of flavoured mesons in lattice gauge theories with symplectic gauge group and fermion matter content treated in the quenched approximation. For the Sp(4), Sp(6), and Sp(8) gauge groups, the (Dirac) fermions transform in either the fundamental, or the 2-index, antisymmetric or symmetric, representations. This study sets the stage for future precision calculations with dynamical fermions in the low mass region of lattice parameter space. Our results have potential phenomenological applications ranging from composite Higgs models, to top (partial) compositeness, to dark matter models with composite, strong-coupling dynamical origin. Having adopted the Wilson flow as a scale-setting procedure, we apply Wilson chiral perturbation theory to extract the continuum and massless limits for the observables of interest. The resulting measurements are used to perform a simplified extrapolation to the large-N limit, hence drawing a preliminary connection with gauge theories with unitary groups. We conclude with a brief discussion of the Weinberg sum rules. © 2023, CC BY.

关键词： Perturbation techniques

Towards provably efficient quantum algorithms for large-scale machine-learning models

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arXiv 2023年

作者： Liu, Junyu Liu, Minzhao Liu, Jin-Peng Ye, Ziyu Wang, Yunfei Alexeev, Yuri Eisert, Jens Jiang, Liang Pritzker School of Molecular Engineering The University of Chicago ChicagoIL60637 United States Department of Computer Science The University of Chicago ChicagoIL60637 United States Chicago Quantum Exchange ChicagoIL60637 United States Kadanoff Center for Theoretical Physics The University of Chicago ChicagoIL60637 United States qBraid Co. ChicagoIL60615 United States SeQure ChicagoIL60615 United States Department of Physics The University of Chicago ChicagoIL60637 United States Computational Science Division Argonne National Laboratory LemontIL60439 United States Simons Institute for the Theory of Computing University of California BerkeleyCA94720 United States Department of Mathematics University of California BerkeleyCA94720 United States Center for Theoretical Physics Massachusetts Institute of Technology CambridgeMA02139 United States Martin A. Fisher School of Physics Brandeis University WalthamMA02453 United States Dahlem Center for Complex Quantum Systems Free University Berlin Berlin14195 Germany

Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as O(T2 × polylog(n)), where n is the size of the models and T is the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse, with small learning rates. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that faulttolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems. Copyright © 2023, The Authors. All rights reserved.

关键词： Differential equations

Sp(2N) Lattice Gauge Theories and Extensions of the Standard Model of Particle Physics

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arXiv 2023年

作者： Bennett, Ed Holligan, Jack Hong, Deog Ki Hsiao, Ho Lee, Jong-Wan Lin, C.-J. David Lucini, Biagio Mesiti, Michele Piai, Maurizio Vadacchino, Davide Fabian Way SwanseaSA1 8EN United Kingdom Michigan State University Biomedical and Physical Sciences Building East LansingMI48824 United States Physical Sciences Complex University of Maryland College ParkMD20742 United States Department of Physics Pusan National University Busan46241 Korea Republic of Institute of Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu30010 Taiwan Institute for Extreme Physics Pusan National University Busan46241 Korea Republic of Daejeon34126 Korea Republic of Center for High Energy Physics Chung-Yuan Christian University Chung-Li32023 Taiwan Centre for Theoretical and Computational Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu30010 Taiwan Fabian Way SwanseaSA1 8EN United Kingdom Steinbuch Centre for Computing Karlsruher Institut für Technologie Zirkel 2 Karlsruhe76131 Germany Department of Physics Faculty of Science and Engineering Swansea University Singleton Park Campus Singleton Park SwanseaSA2 8PP United Kingdom School of Mathematics Hamilton Mathematics Institute Trinity College Dublin 2 Ireland Centre for Mathematical Sciences University of Plymouth PlymouthPL4 8AA United Kingdom

We review the current status of the long-term programme of numerical investigation of Sp(2N) gauge theories with and without fermionic matter content. We start by introducing the phenomenological as well as theoretical motivations for this research programme, which are related to composite Higgs models, models of partial top compositeness, dark matter models, and in general to the physics of strongly coupled theories and their approach to the large-N limit. We summarise the results of lattice studies conducted so far in the Sp(2N) Yang-Mills theories, measuring the string tension, the mass spectrum of glueballs and the topological susceptibility, and discuss their large-N extrapolation. We then focus our discussion on Sp(4), and summarise numerical measurements of mass and decay constant of mesons in the theories with fermion matter in either the fundamental or the antisymmetric representation, first in the quenched approximation, and then with dynamical fermions. We finally discuss the case of dynamical fermions in mixed representations, and exotic composite fermion states such as the chimera baryons. We conclude by sketching the future stages of the programme. And we describe our approach to open access. © 2023, CC BY.

关键词： Mass spectrometry

Adaptive step size strategies for orthogonality constrained line search methods

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arXiv 2019年

作者： Dai, Xiaoying Zhang, Liwei Zhou, Aihui LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In this paper, we propose an adaptive step size strategy for a class of line search methods for orthogonality constrained minimization problems, which avoids the classic backtracking procedure. We prove the convergence of the line search methods equipped with our adaptive step size strategy under some mild *** then apply the adaptive algorithm to electronic structure calculations, which show that our strategy is efficient and recommended. Copyright © 2019, The Authors. All rights reserved.

关键词： Adaptive algorithms

Rubric-based holistic review: A promising route to equitable graduate admissions in physics

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arXiv 2021年

作者： Young, Nicholas T. Tollefson, K. Zegers, Remco G.T. Caballero, Marcos D. Department of Physics and Astronomy Michigan State University East LansingMI48824 United States Department of Computational Mathematics Science and Engineering Michigan State University East LansingMI48824 United States National Superconducting Cyclotron Laboratory Michigan State University East LansingMI48824 United States Joint Institute for Nuclear Astrophysics Michigan State University East LansingMI48824 United States Center for Computing in Science Education Department of Physics University of Oslo OsloN-0316 Norway Create for Stem Institute Michigan State University East LansingMI48824 United States

As systematic inequities in higher education and society have been brought to the forefront, graduate programs are interested in increasing the diversity of their applicants and enrollees. Yet, structures in place to evaluate applicants may not support such aims. One potential solution to support those aims is rubric-based holistic review. Starting in 2018, our physics department implemented a rubric-based holistic review process for all applicants to our graduate program. The rubric assessed applicants on 18 metrics covering their grades, test scores, research experiences, noncognitive competencies, and fit with the program. We then compared faculty's ratings of applicants by admission status, sex, and undergraduate program over a three-year period. We find that the rubric scores show statistically significant differences between admitted and non-admitted students as hoped and that statistically significant differences based on sex or undergraduate program aligned with known disparities in GRE scores and service work expectations. Our results then suggest rubric-based holistic review as a possible route to making graduate admissions in physics more equitable. Copyright © 2021, The Authors. All rights reserved.

关键词： Students

Gradient flow based discretized kohn-sham density functional theory

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arXiv 2019年

作者： Dai, Xiaoying Wang, Qiao Zhou, Aihui LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In this paper, we propose and analyze a gradient ow based Kohn-Sham density functional theory. First, we prove that the critical point of the gradient ow based model can be a local minimizer of the Kohn-Sham total energy. Then we apply a midpoint scheme to carry out the temporal discretization. It is shown that the critical point of the Kohn-Sham energy can be well-approximated by the scheme. In particular, based on the midpoint scheme, we design an orthogonality preserving iteration scheme to minimize the Kohn-Sham energy and show that the orthogonality preserving iteration scheme produces approximations that are orthogonal and conver- gent to a local minimizer under reasonable assumptions. Finally, we report numerical experiments that support our theory. Copyright © 2019, The Authors. All rights reserved.

关键词： Dynamical systems

Modeling subgrid-scale force and divergence of heat flux of compressible isotropic turbulence by artificial neural network

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Physical Review Fluids 2019年第10期4卷 104605-104605页

作者： Chenyue Xie Ke Li Chao Ma Jianchun Wang Shenzhen Key Laboratory of Complex Aerospace Flows Center for Complex Flows and Soft Matter Research Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Shenzhen 518055 People's Republic of China Institute of Computational Mathematics and Scientific Engineering Computing Chinese Academy of Sciences Beijing 100190 People's Republic of China The Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

In this paper, the subgrid-scale (SGS) force and the divergence of SGS heat flux of compressible isotropic turbulence are modeled directly by an artificial neural network (ANN), which serves as a data-driven SGS modeling tool for large-eddy simulations (LESs). The unclosed SGS force and divergence of SGS heat flux are modeled based on the local stencil geometry with Galilean invariance. The input features include the first-order and second-order derivatives of filtered velocity and temperature, filtered density, and its first-order derivative. It is shown that the proposed ANN-F7 model shows an advantage over the gradient model in the a priori test. Specifically, the ANN-F7 model gives larger correlation coefficients and smaller relative errors than the gradient model. In an a posteriori analysis, the ANN-F7 model performs better than the dynamic Smagorinsky model (DSM) and dynamic mixed model (DMM) in the prediction of the statistical properties of flow fields at the Taylor microscale Reynolds number Reλ ranging from 180 to 250. The DSM and DMM models lead to the typical tilted spectral distribution of velocity, where low wave numbers are too energy rich, while those near the cutoff are damped too strongly. In contrast, it is shown that the velocity spectrum predicted by the ANN-F7 model almost overlaps with the filtered direct numerical simulation data. Besides, the ANN-F7 model reconstructs the probability density functions of SGS force and divergence of SGS heat flux much better than the DSM and DMM models. An artificial neural network with reasonable physical input features can deepen our understanding of turbulence modeling.

关键词： Compressible flows Turbulence Artificial neural networks

Uplink-downlink duality between multiple-access and broadcast channels with compressing relays

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arXiv 2020年

作者： Liu, Liang Liu, Ya-Feng Patil, Pratik Yu, Wei the Department of Electronic and Information Engineering The Hong Kong Polytechnic University Hong Kong the State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Edward S. Rogers Sr. Department of Electrical and Computer Engineering the University of Toronto the Department of Statistics and Data Science and the Machine Learning Department Carnegie Mellon University PittsburghPA15213 United States The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto 10 King’s College Road TorontoONM5S3G4 Canada

—Uplink-downlink duality refers to the fact that under a sum-power constraint, the capacity regions of a Gaussian multiple-access channel and a Gaussian broadcast channel with Hermitian transposed channel matrices are identical. This paper generalizes this result to a cooperative cellular network, in which remote access-points are deployed as relays in serving the users under the coordination of a central processor (CP). In this model, the users and the relays are connected over noisy wireless links, while the relays and the CP are connected over noiseless but rate-limited fronthaul links. Based on a Lagrangian technique, this paper establishes a duality relationship between such a multiple-access relay channel and broadcast relay channel, under the assumption that the relays use compression-based strategies. Specifically, we show that under the same total transmit power constraint and individual fronthaul rate constraints, the achievable rate regions of the Gaussian multiple-access and broadcast relay channels are identical, when either independent compression or Wyner-Ziv and multivariate compression strategies are used. The key observations are that if the beamforming vectors at the relays are fixed, the sum-power minimization problems under the achievable rate and fronthaul constraints in both the uplink and the downlink can be transformed into either a linear programming or a semidefinite programming problem depending on the compression technique, and that the uplink and downlink problems are Lagrangian duals of each other. Moreover, the dual variables corresponding to the downlink rate constraints become the uplink powers;the dual variables corresponding to the downlink fronthaul constraints become the uplink quantization noises. This duality relationship enables an efficient algorithm for optimizing the downlink transmission and relaying strategies based on the uplink. Copyright © 2020, The Authors. All rights reserved.

关键词： Linear programming

Considerations for a Distributed GraphBLAS API

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Considerations for a Distributed GraphBLAS API

IEEE International Symposium on Parallel and Distributed Processing Workshops and Phd Forum (IPDPSW)

作者： Benjamin Brock Aydin Buluç Timothy G. Mattson Scott McMillan José E. Moreira Roger Pearce Oguz Selvitopi Trevor Steil EECS Department University of California Berkeley CA Computational Research Department Lawrence Berkeley National Laboratory Berkeley CA Parallel Computing Labs Intel Hillsboro OR Software Engineering Institute Carnegie Mellon University Pittsburgh PA IBM Thomas J. Watson Research Center Yorktown Heights NY Center for Applied Scientific Computing Lawrence Livermore National Laboratory Livermore CA School of Mathematics University of Minnesota Minneapolis MN

ISBN: (数字)9781728174457

ISBN: (纸本)9781728174570

The GraphBLAS emerged from an international effort to standardize linear-algebraic building blocks for computing on graphs and graph-structured data. The GraphBLAS is expressed as a C API and has paved the way for multiple implementations. The GraphBLAS C API, however, does not define how distributed-memory parallelism should be handled. This paper reviews various approaches for a GraphBLAS API for distributed computing. This work is guided by our experience with existing distributed memory libraries. Our goal for this paper is to highlight the pros and cons of different approaches rather than to advocate for one particular choice.

关键词： Context Parallel processing Libraries Data structures Task analysis Message systems Electronics packaging