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The elastic inclusion problem in the (amplitude) phase field crystal model

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arXiv 2021年

作者： Salvalaglio, Marco Chockalingam, Karthikeyan Voigt, Axel Dörfler, Willy Institute of Scientific Computing TU Dresden Dresden01062 Germany Dresden Center for Computational Materials Science TU Dresden Dresden01062 Germany Science and Technology Facilities Council Daresbury Laboratory Daresbury Science and Innovation Campus Warrington Cheshire WA4 4AD United Kingdom Institute for Applied and Numerical Mathematics Karlsruhe Institute of Technology Karlsruhe76131 Germany

In many processes for crystalline materials such as precipitation, heteroepitaxy, alloying, and phase transformation, lattice expansion or compression of embedded domains occurs. This can significantly alter the mechanical response of the material. Typically, these phenomena are studied macroscopically, thus neglecting the underlying microscopic structure. Here we present the prototypical case of an elastic inclusion described by a mesoscale model, namely a coarse-grained phase-field crystal model. A spatially-dependent parameter is introduced into the free energy functional to control the local spacing of the lattice structure, effectively prescribing an eigenstrain. The stress field obtained for an elastic inclusion in a 2D triangular lattice is shown to match well with the analytic solution of the Eshelby inclusion problem. Copyright © 2021, The Authors. All rights reserved.

关键词： Free energy

Overview of couplet scoring in content-focused physics assessments

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arXiv 2023年

作者： Vignal, Michael Geschwind, Gayle Caballero, Marcos D. Lewandowski, H.J. JILA National Institute of Standards and Technology the University of Colorado BoulderCO80309 United States Department of Physics University of Colorado 390 UCB BoulderCO80309 United States Department of Physics Willamette University 900 State Street SalemOR97301 United States Department of Physics & Astronomy CREATE for STEM Institute Michigan State University East LansingMI48824 United States Department of Computational Mathematics Science & Engineering Michigan State University East LansingMI48824 United States Department of Physics Center for Computing in Science Education University of Oslo Oslo0315 Norway

Content-focused research-based assessment instruments typically use items (i.e., questions) as the unit of assessment for scoring, reporting, and validation. Couplet scoring employs an alternative unit of assessment called a couplet, which is essentially an item viewed and scored through the lens of a specific assessment objective. With couplet scoring, a single item may have more than one assessment objective and therefore more than one couplet and thus more than one score. We outline the components of traditional item scoring, discuss couplet scoring and its benefits, and use both a recently developed content research-based assessment instrument and an existing one to ground our discussion. © 2023, CC BY.

关键词： Uncertainty analysis

On the implementation of a robust and efficient finite element-based parallel solver for the compressible Navier-Stokes equations

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arXiv 2021年

作者： Guermond, Jean-Luc Kronbichler, Martin Maier, Matthias Popov, Bojan Tomas, Ignacio Department of Mathematics Texas A&M University 3368 College StationTX77843 United States Institute for Computational Mechanics Department for Mechanical Engineering Technical University of Munich Germany Division of Scientific Computing Department of Information Technology Uppsala University Sweden Sandia National Laboratories P.O. Box 5800 MS 1320 AlbuquerqueNM87185-1320 United States

This paper describes in detail the implementation of a finite element technique for solving the compressible Navier-Stokes equations that is provably robust and demonstrates excellent performance on modern computer hardware. The method is second-order accurate in time and space. Robustness here means that the method is proved to be invariant domain preserving under the hyperbolic CFL time step restriction, and the method delivers results that are reproducible. The proposed technique is shown to be accurate on challenging 2D and 3D realistic *** Codes 35L65, 65M60, 65M12, 65N30 Copyright © 2021, The Authors. All rights reserved.

关键词： Finite element method

ParaDiag: Parallel-in-time algorithms based on the diagonalization technique

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arXiv 2020年

作者： Gander, Martin J. Liu, Jun Wu, Shu-Lin Yue, Xiaoqiang Zhou, Tao Section of Mathematics University of Geneva GenevaCH-1211 Switzerland Department of Mathematics and Statistics Southern Illinois University Edwardsville EdwardsvilleIL62026 United States School of Mathematics and Statistics Northeast Normal University Changchun130024 China School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing China

In 2008, Maday and Rønquist introduced an interesting new approach for the direct parallel-in-time (PinT) solution of time-dependent PDEs. The idea is to diagonalize the time stepping matrix, keeping the matrices for the space discretization unchanged, and then to solve all time steps in parallel. Since then, several variants appeared, and we call these closely related algorithms ParaDiag algorithms. ParaDiag algorithms in the literature can be classified into two groups: We will explain the basic features of each group in this note. To have concrete examples, we will introduce ParaDiag-I and ParaDiag-II for the advection-diffusion equation. We will also introduce ParaDiag-II for the wave equation and an optimal control problem for the wave equation. We could have used the advection-diffusion equation as well to illustrate ParaDiag-II, but wave equations are known to cause problems for certain PinT algorithms and thus constitute an especially interesting example for which ParaDiag algorithms were tested. We show the main known theoretical results in each case, and also provide Matlab codes for testing. The goal of the Matlab codes is to help the interested reader understand the key features of the ParaDiag algorithms, without intention to be highly tuned for efficiency and/or low memory use. We also provide speedup measurements of ParaDiag algorithms for a 2D linear advection-diffusion equation. These results are obtained on the Tianhe-1 supercomputer in China and the SIUE Campus Cluster in the US, which is a multi-array, configurable and cooperative parallel system, and we compare these results to the performance of parareal and MGRiT, two widely used PinT algorithms. In a forthcoming update of this note, we will provide more material on ParaDiag algorithms, in particular further Matlab codes and parallel computing results, also for more realistic applications. Copyright © 2020, The Authors. All rights reserved.

关键词： Advection

Doubly degenerate diffuse interface models of anisotropic surface diffusion

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arXiv 2020年

作者： Salvalaglio, Marco Selch, Maximilian Voigt, Axel Wise, Steven M. Institute of Scientific Computing Department of Mathematics Tu Dresden Dresden01062 Germany Dresden Center for Computational Materials Science Tu Dresden Dresden01062 Germany Department of Mathematics University of Tennessee KnoxvilleTN37996 United States

We extend the doubly degenerate Cahn-Hilliard (DDCH) models for isotropic surface diffusion1, which yield more accurate approximations than classical degenerate Cahn-Hilliard (DCH) models, to the anisotropic case. We consider both weak and strong anisotropies and demonstrate the capabilities of the approach for these cases numerically. The proposed model provides a variational and energy dissipative approach for anisotropic surface diffusion, enabling large scale simulations with material-specific parameters. Copyright © 2020, The Authors. All rights reserved.

关键词： Anisotropy

***: A Comprehensive Genomic Visualisation Database for Malaysian Species

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***: A Comprehensive Genomic Visualisation Database for Mala...

computing (ICOCO), IEEE International Conference on

作者： Vei Siang Chan Farhan Bin Mohamed Faezah Mohd Salleh Andres Iglesias Alina Binti Wagiran Ali Bin Selamat School of Computing Faculty of Engineering Universiti Teknologi Malaysia Johor Bahru Malaysia Media and Game Innovation Center of Excellence Universiti Teknologi Malaysia Johor Bahru Malaysia Dept. of Biosciences Faculty of Science Universiti Teknologi Malaysia Johor Bahru Malaysia Dept. of Applied Mathematics and Computational Sciences University of Cantabria Santander Spain Malaysia-Japan International Institute of Technology University of Technology Malaysia Kuala Lumpur Malaysia

ISBN: (纸本)9781665489973

Malaysia is one of the most megadiverse regions in the world. Therefore, it is important to record these rich biodiversity data to safeguard and improve national conservation efforts. However, the lack of nationwide genomic sequencing hampers a more sophisticated species identification, data management, and analytics activities. Thus, this project aims to design and implement ***, a comprehensive one-stop online DNA reference database with integrated DNA visualisation and digital references to allow the users to search, retrieve and analyse the collected DNA sequencing data interactively. This paper documented the system architecture and implementation methods to create ***. The results of *** can display taxonomy information of biodiversity in the web’s user interfaces and visualise the complex set of DNA data to allow new insights. Lastly, the authors identified several future works to improve *** including improve user interaction, add visualisation methods to support more bioinformatics tasks, and conduct formal user evaluation.

关键词： Sequential analysis Annotations Taxonomy Data visualization DNA Genomics Systems architecture

High-Precision Ringdown Surrogate Model for Non-Precessing Binary Black Holes

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arXiv 2024年

作者： Zertuche, Lorena Magaña Stein, Leo C. Mitman, Keefe Field, Scott E. Varma, Vijay Boyle, Michael Deppe, Nils Kidder, Lawrence E. Moxon, Jordan Pfeiffer, Harald P. Scheel, Mark A. Nelli, Kyle C. Throwe, William Vu, Nils L. Department of Physics and Astronomy University of Mississippi UniversityMS38677 United States Theoretical Astrophysics 350-17 California Institute of Technology PasadenaCA91125 United States Department of Mathematics Center for Scientific Computing & Visualization Research University of Massachusetts DartmouthMA02747 United States Department of Physics Center for Computational Research East Hall University of Rhode Island KingstonRI02881 United States Cornell Center for Astrophysics and Planetary Science Cornell University IthacaNY14853 United States Laboratory for Elementary Particle Physics Cornell University IthacaNY14853 United States Department of Physics Cornell University IthacaNY14853 United States Am Mühlenberg 1 Potsdam14476 Germany

Highly precise and robust waveform models are required as improvements in detector sensitivity enable us to test general relativity with more precision than ever before. In this work, we introduce a spin-aligned surrogate ringdown model. This ringdown surrogate, NRSur3dq8_RD, is built with numerical waveforms produced using Cauchy-characteristic evolution. In addition, these waveforms are in the superrest frame of the remnant black hole allowing us to do a correct analysis of the ringdown spectrum. The novel prediction of our surrogate model is complex-valued quasinormal mode (QNM) amplitudes, with median relative errors of 10−2 − 10−3 over the parameter space. Like previous remnant surrogates, we also predict the remnant black hole’s mass and spin. The QNM mode amplitude errors translate into median errors on ringdown waveforms of ∼ 10−4. The high accuracy and QNM mode content provided by our surrogate will enable high-precision ringdown analyses such as tests of general relativity. Our ringdown model is publicly available through the python package surfinBH. Copyright © 2024, The Authors. All rights reserved.

关键词： Relativity

TWO-WELL LINEARIZATION FOR SOLID-SOLID PHASE TRANSITIONS

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arXiv 2020年

作者： Davoli, Elisa Friedrich, Manuel Institute of Analysis and Scientific Computing Vienna University of Technology Wiedner Hauptstrasse 8-10 Vienna1040 Austria Institute for Computational and Applied Mathematics University of Münster Einsteinstrasse 62 MünsterD-48149 Germany

In this paper we consider nonlinearly elastic, frame-indifferent, and singularly perturbed two-well models for materials undergoing solid-solid phase transitions in any space dimensions, and we perform a simultaneous passage to sharp-interface and small-strain limits. Sequences of deformations with equibounded energies are decomposed via suitable Caccioppoli partitions into the sum of piecewise constant rigid movements and suitably rescaled displacements. These converge to limiting partitions, deformations, and displacements, respectively. Whereas limiting deformations are simple laminates whose gradients only attain two values, the limiting displacements belong to the class of special functions with bounded variation (SBV). The latter feature elastic contributions measuring the distance to simple laminates, as well as jumps associated to two consecutive phase transitions having vanishing distance, and thus not being detected by the limiting deformations. By Γ-convergence we identify an effective limiting model given by the sum of a quadratic linearized elastic energy in terms of displacements along with two surface terms. The first one is proportional to the total length of interfaces created by jumps in the gradient of the limiting deformation. The second one is proportional to twice the total length of interfaces created by jumps in the limiting displacement, as well as by the boundaries of limiting partitions. A main tool of our analysis is a novel two-well rigidity estimate which has been derived in [32] for a model with anisotropic second-order perturbation. Copyright © 2020, The Authors. All rights reserved.

关键词： Linearization

Positive definiteness of real quadratic forms resulting from the variable-step approximation of convolution operators

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arXiv 2020年

作者： Liao, Hong-Lin Tang, Tao Zhou, Tao Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing211106 China Division of Science and Technology BNU-HKBU United International College ZhuhaiGuangdong Province China NCMIS & LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

The positive definiteness of real quadratic forms with convolution structures plays an important role in stability analysis for time-stepping schemes for nonlocal operators. In this work, we present a novel analysis tool to handle discrete convolution kernels resulting from variable-step approximations for convolution operators. More precisely, for a class of discrete convolution kernels relevant to variable-step time discretizations, we show that the associated quadratic form is positive definite under some easy-to-check algebraic conditions. Our proof is based on an elementary constructing strategy using the properties of discrete orthogonal convolution kernels and complementary convolution kernels. To the best of our knowledge, this is the first general result on simple algebraic conditions for the positive definiteness of variable-step discrete convolution kernels. Using the unified theory, the stability for some simple non-uniform time-stepping schemes can be obtained in a straightforward *** Codes 65M06, 65M12, 65R20. © 2020, CC BY-NC-SA.

关键词： Number theory