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Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations

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arXiv 2021年

作者： Cao, Waixiang Li, Dongfang Zhang, Zhimin School of Mathematical Sciences Beijing Normal University Beijing100875 China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Beijing Computational Science Research Center Beijing100193 China Department of Mathematics Wayne State University DetroitMI48202 United States

In this paper, we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations. Optimal error estimates in time and superconvergent error estimates in space are established without time-step dependent on the spatial mesh size. The key is to estimate directly the solution bounds in the H2-norm for both the nonlinear wave equation and the corresponding fully discrete scheme, while the previous investigations rely on the temporal-spatial error splitting approach. Numerical examples are presented to confirm energy-conserving properties, unconditional convergence, and optimal error estimates, respectively, of the proposed fully discrete *** Codes 65M60, 65M12, 65N12 © 2021, CC0.

关键词： Wave equations

***: 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

GLOBAL SOLVABILITY AND ASYMPTOTICAL BEHAVIOR IN A TWO-SPECIES CHEMOTAXIS MODEL WITH SIGNAL ABSORPTION

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arXiv 2021年

作者： Ren, Guoqiang Xiang, Tian School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China Institute for Mathematical Sciences Renmin University of China Bejing100872 China

In this work, we study global existence, eventual smoothness and asymptotical behavior of positive solutions for the following two-species chemotaxis consumption model: ut = ∆u - χ1∇ · (u∇w), x ∈ Ω, t > 0, {{{{{{{ vt = ∆v - χ2∇ · (u∇w), x ∈ Ω, t > 0, wt = ∆w - (αu + βv)w, x ∈ Ω, t > 0, in a bounded smooth but not necessarily convex domain Ω ⊂ Rn(n = 2, 3, 4, 5) with nonnegative initial data u0, v0, w0 and homogeneous Neumann boundary data. Here, the parameters χ1, χ2 are positive and α, β are nonnegative. Under a smallness condition max{χ1, χ2}kw0kL∞ MSC Codes 35K59, 35K57 © 2021, CC BY.

关键词： Biochemistry

GLOBAL SOLVABILITY IN A TWO-SPECIES CHEMOTAXIS SYSTEM WITH SIGNAL PRODUCTION

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arXiv 2021年

In this paper, we study the following prototypical two-species chemotaxis system with Lotka-Volterra competition and signal production: (Equation presented). We show that if (Equation presented). the associated Neumann initial-boundary value problem for (∗) admits a global generalized solutions in a bounded and smooth domain Ω ⊂ N (N ≥ 2) under merely integrable initial *** Codes 35A01, 35K57, 35Q92, 92C17 © 2021, CC BY.

关键词： Initial value problems

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

Multiobjective Forecasting Model Based on the Interval Discrete Type-2 Fuzzy Sets and Genetic Algorithm 34

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Multiobjective Forecasting Model Based on the Interval Discr...

34th International Conference on Information Technologies, InfoTech 2020

作者： Demidova, Liliya Anatolievna Stepanov, Maksim Anatolievich Institute of Integrated Safety and Special Instrumentation Russian Technological University - MIREA Department of Intelligent Systems of Information Security Vernadsky Avenue78 Moscow119454 Russia Faculty of Computing Engineering Ryazan State Radio Engineering University Named after V.F. Utkin Department of Computational and Applied Mathematics Gagarin Str. 59/1 Ryazan390005 Russia

ISBN: (纸本)9781728169149

The forecasting task for the short time series has been investigated. The main problem of this task is the availability of a small amount of relevant information. Such tasks can be considered as the tasks in the conditions of uncertainty, fuzziness of the initial data. We suggest to develop the multiobjective forecasting model based on the interval discrete type-2 fuzzy sets. As the criteria which should be minimized, it is proposed to use the average relative forecasting error and the tendency mismatch indicator. The search for the optimal parameters values of the forecasting model is implemented using the genetic algorithm. The examples showing the possibilities of the proposed forecasting model have been discussed. © 2020 IEEE.

关键词： Genetic algorithms

Framework for evaluating statistical models in physics education research

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Physical Review Physics Education Research 2021年第2期17卷 020104-020104页

作者： John M. Aiken Riccardo De Bin H. J. Lewandowski Marcos D. Caballero Center for Computing in Science Education & Department of Physics University of Oslo N-0316 Oslo Norway Department of Mathematics University of Oslo N-0316 Oslo Norway Department of Physics University of Colorado Boulder Boulder Colorado 80309 USA JILA National Institute of Standards and Technology and the University of Colorado Boulder Colorado 80309 USA Department of Physics and Astronomy Department of Computational Mathematics Sciences and Engineering and CREATE for STEM Institute Michigan State University East Lansing Michigan 48824 USA

Across the field of education research there has been an increased focus on the development, critique, and evaluation of statistical methods and data usage due to recently created, very large datasets and machine learning techniques. In physics education research (PER), this increased focus has recently been shown through the 2019 Physical Review PER Focused Collection examining quantitative methods in PER. Quantitative PER has provided strong arguments for reforming courses by including interactive engagement, demonstrated that students often move away from scientistlike views due to science education, and has injected robust assessment into the physics classroom via concept inventories. The work presented here examines the impact that machine learning may have on physics education research, presents a framework for the entire process including data management, model evaluation, and results communication, and demonstrates the utility of this framework through the analysis of two types of survey data.

关键词： Research methodology