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arXiv 2022年

作者： Horák, Martin Gil, Antonio J. Ortigosa, Rogelio Kružík, Martin Faculty of Civil Engineering Czech Technical University Thákurova 7 Praha 6CZ-166 29 Czech Republic Zienkiewicz Centre for Computational Engineering Faculty of Science and Engineering Swansea University Bay Campus SA1 8EN United Kingdom Computational Mechanics and Scientific Computing Group Technical University of Cartagena Campus Muralla del Mar Cartagena Murcia30202 Spain Czech Academy of Sciences Institute of Information Theory and Automation Pod vodárenskou věží 4 Praha 8CZ-182 00 Czech Republic

The fabrication of evermore sophisticated miniaturised soft robotic components made up of Electro-Active Polymers (EAPs) is constantly demanding parallel development from the in-silico simulation point of view. The incorporation of crystallographic anisotropic micro-architectures, within an otherwise nearly uniform isotropic soft polymer matrix, has shown great potential in terms of advanced three-dimensional actuation (i.e. stretching, bending, twisting), especially at large strains, that is, beyond the onset of geometrical pull-in instabilities. To accommodate for this in-silico response, this paper presents a phenomenological invariant-based polyconvex transversely isotropic framework for the simulation of EAPs at large strains. This research expands previous work developed by Gil and Ortigosa for isotropic EAPs [40] with the help of the pioneering work by Schröeder and Neff [81] in the context of polyconvexity for materials endowed with crystallographic architectures in single physics mechanics. The paper also summarises key important results both in terms of the existence of minimisers and material stability. In addition, a series of numerical examples is presented in order to demonstrate the effect that the anisotropic orientation and the contrast of material properties, as well as the level of deformation and electric field, have upon the response of the EAP when subjected to large three-dimensional stretching, bending and torsion, including the possible development of wrinkling. Copyright © 2022, The Authors. All rights reserved.

关键词： Finite element method

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Phase transition analysis for covariance based massive random access with massive MIMO

arXiv

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arXiv 2020年

作者： Chen, Zhilin Sohrabi, Foad Liu, Ya-Feng Yu, Wei The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto TorontoONM5S 3G4 Canada 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

This paper considers a massive random access problem in which a large number of sporadically active devices wish to communicate with a base station (BS) equipped with massive multiple-input multiple-output (MIMO) antennas. Each device is preassigned a unique signature sequence, and the BS identifies the active devices by detecting which sequences are transmitted. This device activity detection problem can be formulated as a maximum likelihood estimation (MLE) problem for which the sample covariance matrix of the received signal is a sufficient statistic. The goal of this paper is to characterize the feasible set of problem parameters under which this covariance based approach is able to successfully recover the device activities in the massive MIMO regime. Through an analysis of the asymptotic behaviors of MLE via its associated Fisher information matrix, this paper derives a necessary and sufficient condition on the Fisher information matrix to ensure a vanishing probability of detection error as the number of antennas goes to infinity, based on which a numerical phase transition analysis is obtained. This condition is also examined from a perspective of covariance matching, which relates the phase transition analysis to a recently derived scaling law. Further, we provide a characterization of the distribution of the estimation error in MLE, based on which the error probabilities in device activity detection can be accurately predicted. Finally, this paper studies a random access scheme with joint device activity and data detection and analyzes its performance in a similar way. Copyright © 2020, The Authors. All rights reserved.

关键词： Maximum likelihood estimation

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Application of a dispersive wave hydro-sediment-morphodynamic model in the Ria Formosa lagoon

arXiv

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arXiv 2022年

作者： Kazhyken, Kazbek Valseth, Eirik Videman, Juha Dawson, Clint Oden Institute for Computational Engineering and Sciences The University of Texas at Austin AustinTX78712 United States CAMGSD Departamento de Matemática Universidade de Lisboa Lisbon1049-001 Portugal Department of Data Science The Norwegian University of Life Sciences Ås1433 Norway Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Oslo0164 Norway

Results of an application of a dispersive wave hydro-sediment-morphodynamic model in the western circulation cell of the Ria Formosa lagoon located in the Algarve region of the southern Portugal are presented. This area of interest has a couple of features that complicate the application of the dispersive wave model: (1) the area has a complex irregular geometry with a number of barrier islands that separate the lagoon from the Atlantic Ocean, artificial and naturally occurring tidal inlets, and a number of curling channels inside the lagoon that interconnect the inlets and serve as waterways between the lagoon settlements;(2) the tidal range in the area can reach up to 3.5 m;therefore, the terrain inside the lagoon is characterized by vast salt marshes and tidal flats, and the wetting-drying process is a key component of any hydrodynamic simulation in this area. A model representation of the area has been developed by generating an unstructured finite element mesh of the circulation cell, and collecting data on parameters that characterize the tidal waves in the area, and bottom friction and sediment transport models used in the simulations. The results of the simulations indicate that the dispersive wave model can be applied in coastal areas with nontrivial underlying physical processes, and complex irregular geometries. Moreover, the dispersive term of the model is capable of capturing additional flow characteristics that are otherwise not present in hydrodynamic simulations that involve the nonlinear shallow water equations;and these additional flow features can, in their turn, affect the resulting sediment transport and bed morphodynamic process simulations. Copyright © 2022, The Authors. All rights reserved.

关键词： Equations of motion

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Higher-order rich-club phenomenon in collaborative research grant networks

arXiv

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arXiv 2022年

作者： Nakajima, Kazuki Shudo, Kazuyuki Masuda, Naoki Department of Mathematical and Computing Science Tokyo Institute of Technology Meguro-ku Tokyo152-8552 Japan Department of Mathematics State University of New York at Buffalo Buffalo14260 United States Academic Center for Computing and Media Studies Kyoto University Sakyo-ku Kyoto606-8501 Japan Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo Buffalo14260 United States Faculty of Science and Engineering Waseda University Tokyo169-8555 Japan

Modern scientific work, including writing papers and submitting research grant proposals, increasingly involves researchers from different institutions. In grant collaborations, it is known that institutions involved in many collaborations tend to densely collaborate with each other, forming rich clubs. Here we investigate higher-order rich-club phenomena in networks of collaborative research grants among institutions and their associations with research impact. Using publicly available data from the National Science Foundation in the US, we construct a bipartite network of institutions and collaborative grants, which distinguishes among the collaboration with different numbers of institutions. By extending the concept and algorithms of the rich club for dyadic networks to the case of bipartite networks, we find rich clubs both in the entire bipartite network and the bipartite subnetwork induced by the collaborative grants involving a given number of institutions up to five. We also find that the collaborative grants within rich clubs tend to be more productive in a per-dollar sense than the control. Our results highlight advantages of collaborative grants among the institutions in the rich clubs. Copyright © 2022, The Authors. All rights reserved.

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RIGIDITY OF STEADY SOLUTIONS TO THE NAVIER-STOKES EQUATIONS IN HIGH DIMENSIONS AND ITS APPLICATIONS

arXiv

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arXiv 2023年

作者： Bang, Jeaheang Gui, Changfeng Liu, Hao Wang, Yun Xie, Chunjing Department of Mathematics The University of Texas at San Antonio One UTSA Circle San AntonioTX78249 United States Department of Mathematics Faculty of Science and Technology University of Macau Taipa China School of Mathematical Sciences Institute of Natural Sciences Shanghai Jiao Tong University 800 Dongchuan Road Shanghai China School of Mathematical Sciences Center for dynamical systems and differential equations Soochow University Suzhou China School of Mathematical Sciences Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing CMA-Shanghai Shanghai Jiao Tong University 800 Dongchuan Road Shanghai China

Solutions with scaling-invariant bounds such as self-similar solutions, play an important role in the understanding of the regularity and asymptotic structures of solutions to the Navier-Stokes equations. In this paper, we prove that any steady solution satisfying |u(x)| ≤ C/|x| for any constant C in n \ {0} with n ≥ 4, must be zero. Our main idea is to analyze the velocity field and the total head pressure via weighted energy estimates with suitable multipliers so that the proof is pretty elementary and short. These results not only give the Liouville-type theorem for steady solutions in higher dimensions with neither smallness nor self-similarity type assumptions, but also help to remove a class of singularities of solutions and give the optimal asymptotic behaviors of solutions at infinity in the exterior domains. Copyright © 2023, The Authors. All rights reserved.

关键词： Navier Stokes equations

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An adjoint-free algorithm for conditional nonlinear optimal perturbations (CNOPs) via sampling

arXiv

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arXiv 2022年

作者： Shi, Bin Sun, Guodong State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing100029 China University of Chinese Academy of Sciences Beijing100049 China

In this paper, we propose a sampling algorithm based on state-of-the-art statistical machine learning techniques to obtain conditional nonlinear optimal perturbations (CNOPs), which is different from traditional (deterministic) optimization methods.1 Specifically, the traditional approach is unavailable in practice, which requires numerically computing the gradient (first-order information) such that the computation cost is expensive since it needs a large number of times to run numerical models. However, the sampling approach directly reduces the gradient to the objective function value (zeroth-order information), which also avoids using the adjoint technique that is unusable for many atmosphere and ocean models and requires large amounts of storage. We show an intuitive analysis for the sampling algorithm from the law of large numbers and further present a Chernoff-type concentration inequality to rigorously characterize the degree to which the sample average probabilistically approximates the exact gradient. The experiments are implemented to obtain the CNOPs for two numerical models, the Burgers equation with small viscosity and the Lorenz-96 model. We demonstrate the CNOPs obtained with their spatial patterns, objective values, computation times and nonlinear error growth. Compared with the performance of the three approaches, all the characters for quantifying the CNOPs are nearly consistent, while the computation time using the sampling approach with fewer samples is extremely shorter. In other words, the new sampling algorithm shortens the computation time to the utmost at the cost of losing little accuracy. © 2022, CC BY-NC-SA.

关键词： Numerical models

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Thermodynamics up to the melting point in a TaVCrW high entropy alloy: Systematic ab initio study aided by machine learning potentials

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Physical Review B 2022年第21期105卷 214302-214302页

作者： Ying Zhou Prashanth Srinivasan Fritz Körmann Blazej Grabowski Roger Smith Pooja Goddard Andrew Ian Duff School of Science Loughborough University LE11 3TU United Kingdom Institute of Materials Science University of Stuttgart Pfaffenwaldring 55 D-70569 Stuttgart Germany Materials Science and Engineering Delft University of Technology 2628 CD Delft The Netherlands Department for Computational Materials Design Max-Planck-Institut für Eisenforschung GmbH 40237 Düsseldorf Germany Scientific Computing Department STFC Daresbury Laboratory Warrington WA4 4AD United Kingdom

Multi-principal-component alloys have attracted great interest as a novel paradigm in alloy design, with often unique properties and a vast compositional space auspicious for materials discovery. High entropy alloys (HEAs) belong to this class and are being investigated for prospective nuclear applications with reported superior mechanical properties including high-temperature strength and stability compared to conventional alloys. computational materials design has the potential to play a key role in screening such alloys, yet for high-temperature properties, challenges remain in finding an appropriate balance between accuracy and computational cost. Here we develop an approach based on density-functional theory (DFT) and thermodynamic integration aided by machine learning based interatomic potential models to address this challenge. We systematically evaluate and compare the efficiency of computing the full free energy surface and thermodynamic properties up to the melting point at different stages of the thermodynamic integration scheme. Our new approach provides a ×4 speed-up with respect to comparable free energy approaches at the level of DFT, with errors on high-temperature free energy predictions less than 1 meV/atom. Calculations are performed on an equiatomic HEA, TaVCrW—a low-activation composition and therefore of potential interest for next generation fission and fusion reactors.

关键词： Thermodynamics Disordered alloys Ab initio molecular dynamics Density functional theory

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PARALLEL ELEMENT-BASED ALGEBRAIC MULTIGRID FOR H(curl) AND H(div) PROBLEMS USING THE PARELAG LIBRARY

arXiv

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arXiv 2021年

作者： Kalchev, Delyan Z. Vassilevski, Panayot S. Villa, Umberto Center for Applied Scientific Computing Lawrence Livermore National Laboratory P.O. Box 808 L-561 LivermoreCA94551 United States Department of Mathematics and Statistics Portland State University PortlandOR97207 United States Oden Institute for Computational Engineering & Sciences The University of Texas at Austin AustinTX78712 United States

This paper presents the use of element-based algebraic multigrid (AMGe) hierarchies, implemented in the ParELAG (Parallel Element Agglomeration Algebraic Multigrid Upscaling and Solvers) library, to produce multilevel preconditioners and solvers for H(curl) and H(div) formulations. ParELAG constructs hierarchies of compatible nested spaces, forming an exact de Rham sequence on each level. This allows the application of hybrid smoothers on all levels and AMS (Auxiliary-space Maxwell Solver) or ADS (Auxiliary-space Divergence Solver) on the coarsest levels, obtaining complete multigrid cycles. Numerical results are presented, showing the parallel performance of the proposed methods. As a part of the exposition, this paper demonstrates some of the capabilities of ParELAG and outlines some of the components and procedures within the library. © 2021, CC BY.

关键词： Finite element method

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WAVEx: Stabilized Finite Elements for Spectral Wind Wave Models Using FEniCSx

arXiv

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arXiv 2023年

作者： Loveland, Mark Valseth, Eirik Meixner, Jessica Dawson, Clint Oden Institute for Computational Engineering and Sciences University of Texas at Austin 201 E. 24th St. AustinTX78712 United States The Department of Data Science The Norwegian University of Life Science Drøbakveien 31 Ås1433 Norway Department of Scientific Computing and Numerical Analysis Simula Research Laboratory Kristian Augusts gate 23 Oslo0164 Norway NWS NCEP EMC 830 University Research Court College ParkMD20740 United States

The prediction of the wind wave spectrum of the ocean using numerical models are an important tool for researchers, engineers, and communities living in coastal areas. The governing equation of the wind wave models, the Wave Action Balance Equation, presents unique challenges for implementing reliable numerical models because it is highly advective, highly nonlinear and high dimensional. Historically, most operational models have utilized finite difference methods, others have used finite volume methods but relatively few attempts at using finite element methods. In this work, we seek to fill this gap by investigating several different finite element discretizations of the Wave Action Balance Equation. The methods, which include streamline upwind Petrov-Galerkin (SUPG), least squares, and discontinuous Galerkin, are implemented and convergence properties are examined for some simplified 2-D test cases. Then, a new spectral wind wave model, WAVEx, is formulated and implemented for the full problem setting. WAVEx uses continuous finite elements along with SUPG stabilization in geographic/spectral space that allows for fully unstructured triangular meshes in both geographic and spectral space. For propagation in time, a second order fully implicit finite difference method is used. When source terms are active, a second order operator splitting scheme is used to linearize the problem. In the splitting scheme, propagation is solved using the implicit method and the nonlinear source terms are treated explicitly. Several test cases, including analytic tests and laboratory experiments, are demonstrated and results are compared to analytic solutions, observations, as well as output from another model that is used operationally. © 2023, CC BY.

关键词： Python

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Topical Issue scientific Machine Learning (1/2)

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GAMM Mitteilungen 2021年第1期44卷 e202100010-e202100010页

作者： Benner, Peter Klawonn, Axel Stoll, Martin Computational Methods in Systems and Control Theory Max Planck institute for Dynamics of Complex Technical Systems Magdeburg Germany Fakultät für Mathematik Otto-von-Guericke Universität Magdeburg Germany Department of Mathematics and Computer Science University of Cologne Germany Center for Data and Simulation Science University of Cologne Germany Chair of Scientific Computing Department of Mathematics TU Chemnitz Germany

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