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arXiv 2021年

作者： Lee, Jae H. Griffith, Boyce E. Department of Mathematics University of North Carolina Chapel HillNC United States Department of Mechanical Engineering Johns Hopkins University BaltimoreMD United States Institute for Computational Medicine Johns Hopkins University BaltimoreMD United States Departments of Mathematics Applied Physical Sciences and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

The immersed boundary (IB) method is a non-body conforming approach to fluid-structure interaction (FSI) that uses an Eulerian description of the momentum, viscosity, and incompressibility of a coupled fluid-structure system and a Lagrangian description of the deformations, stresses, and resultant forces of the immersed structure. Integral transforms with Dirac delta function kernels couple the Eulerian and Lagrangian variables, and in practice, discretizations of these integral transforms use regularized delta function kernels. Many different kernel functions have been proposed, but prior numerical work investigating the impact of the choice of kernel function on the accuracy of the methodology has often been limited to simplified test cases or Stokes flow conditions that may not reflect the method’s performance in applications, particularly at intermediate-to-high Reynolds numbers, or under different loading conditions. This work systematically studies the effect of the choice of regularized delta function in several fluid-structure interaction benchmark tests using the immersed finite element/difference (IFED) method, which is an extension of the IB method that uses a finite element structural discretizations combined with a Cartesian grid finite difference method for the incompressible Navier-Stokes equations. Whereas the conventional IB method spreads forces from the nodes of the structural mesh and interpolates velocities to those nodes, the IFED formulation evaluates the regularized delta function on a collection of interaction points that can be chosen to be denser than the nodes of the Lagrangian mesh. This opens the possibility of using structural discretizations with wide node spacings that would produce gaps in the Eulerian force in nodally coupled schemes (e.g., if the node spacing is comparable to or broader than the support of the regularized delta function). Earlier work with this methodology suggested that such coarse structural meshes can yield imp

关键词： Fluid structure interaction

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Universal features of the stick-slip dynamics of an intruder moving through a confined granular medium

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Physical Review E 2022年第4期105卷 L042902-L042902页

作者： Luis A. Pugnaloni C. Manuel Carlevaro Ryan Kozlowski Hu Zheng Lou Kondic Joshua E. S. Socolar Departamento de Física Facultad de Ciencias Exactas y Naturales Universidad Nacional de La Pampa CONICET Uruguay 151 6300 Santa Rosa (La Pampa) Argentina Instituto de Física de Líquidos y Sistemas Biológicos CONICET 59 789 1900 La Plata Argentina and Departamento de Ingeniería Mecánica Universidad Tecnológica Nacional Facultad Regional La Plata Avenida 60 Esquina 124 1900 La Plata Argentina Physics Department Berea College Berea Kentucky 40404 USA Department of Geotechnical Engineering College of Civil Engineering Tongji University Shanghai 200092 China Department of Mathematical Sciences and Center for Applied Mathematics and Statistics New Jersey Institute of Technology Newark New Jersey 07102 USA Department of Physics Duke University Durham North Carolina 27708 USA

Experiments and simulations of an intruder dragged by a spring through a two-dimensional annulus of granular material exhibit robust force fluctuations. At low packing fractions (ϕ<ϕ0), the intruder clears an open channel. Above ϕ0, stick-slip dynamics develop, with an average energy release that is independent of the particle-particle and particle-base friction coefficients but does depend on the width W of the annulus and the diameter D of the intruder. A simple model predicts the dependence of ϕ0 on W and D, allowing for a data collapse for the average energy release as a function of ϕ/ϕ0. These results pose challenges for theories of mechanical failure in amorphous materials.

关键词： Confinement Creep Earthquake statistics & scaling Granular flows Granular materials Jamming Dry granular materials Granular solids Molecular dynamics Tension tests

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A second-order accurate numerical scheme for a time-fractional Fokker-Planck equation

arXiv

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arXiv 2021年

作者： Mustapha, Kassem Knio, Omar M. Le Maître, Olivier P. Department of Mathematics and Statistics King Fahd University of Petroleum and Minerals Dhahran31261 Saudi Arabia Computer Electrical Mathermatical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia CNRS LIMSI Université Paris-Scalay Campus Universitaire - BP 133 OrsayF-91403 France

A time-stepping L1 scheme for solving a time fractional Fokker-Planck equation of order α ∈ (0, 1), with a general driving force, is investigated. A stability bound for the semi-discrete solution is obtained for α ∈ (1/2, 1) via a novel and concise approach. Our stability estimate is α-robust in the sense that it remains valid in the limiting case where α approaches 1 (when the model reduces to the classical Fokker-Planck equation), a limit that presents practical importance. Concerning the error analysis, we obtain an optimal second-order accurate estimate for α ∈ (1/2, 1). A time-graded mesh is used to compensate for the singular behavior of the continuous solution near the origin. The L1 scheme is associated with a standard spatial Galerkin finite element discretization to numerically support our theoretical contributions. We employ the resulting fully-discrete computable numerical scheme to perform some numerical tests. These tests suggest that the imposed time-graded meshes assumption could be further relaxed, and we observe second-order accuracy even for the case α ∈ (0, 1/2], that is, outside the range covered by the *** Fokker-Planck, L1 approximations, finite elements, stability and error analysis, graded meshes. © 2021, CC BY.

关键词： Error analysis

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RETRACTED ARTICLE: Some properties of the generalized autoregressive moving average (GARMA(1, 2;δ, 1)) model

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Communications in statistics - Theory and Methods 2023年第14期52卷 i-xv页

作者： Thulasyammal R. Pillai Mahendran Shitan a Laboratory of Computational Statistics and Operations Research Institute for Mathematical Research Universiti Putra Malaysia Serdang Malaysiab Faculty of Engineering and Computer Technology AIMST University Bedong Malaysia a Laboratory of Computational Statistics and Operations Research Institute for Mathematical Research Universiti Putra Malaysia Serdang Malaysiac Department of Mathematics Faculty of Science Universiti Putra Malaysia Serdang Malaysia

Recently, the GARMA(1, 2; δ, 1) time series model has been introduced in the literature. In this paper, the variance and autocovariance of the GARMA(1, 2; δ, 1) model are derived. Some numerical results are also provided. It appears from the simulation study that the HRA and WE estimation procedures are relatively good for GARMA(1, 2; δ,1) model. The GARMA(1, 2; δ, 1) model was also applied to model a real data set, namely Dow Jones Utility Index. We believe that this model would also be useful for modeling many other time series data.

关键词： Autocorrelation autocovariance generalized ARMA model GAR GMA time series 62M10

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Better Algorithm of Ordinal Online Schedule for Jobs with Similar Sizes on Two Machines

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American Journal of Operations Research 2019年第5期9卷 235-243页

作者： Limin Wang Rongheng Li Yunxia Zhou Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education) Department of Mathematics School of Mathematics and Statistics Hunan Normal University Changsha China College of Information Science and Engineering Hunan Normal University Changsha China

Ordinal online schedule for jobs with similar sizes in on two parallel machines system is considered. Firstly it is proved that the worst case performance ratio of the existing algorithm P2 cannot be improved even if the job processing times are known in for any . Then a better algorithm named S is developed and its worst case performance ratio is given for? .

关键词： Semi-Online Scheduling Pm Algorithm S Algorithm Worst Performance Ratio

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Large-scale structure with superhorizon isocurvature dark energy

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Physical Review D 2022年第8期105卷 083531-083531页

作者： Koki Yamashita Yue Nan Yuuki Sugiyama Kazuhiro Yamamoto Department of Physics Kyushu University Motooka 744 Fukuoka 819-0395 Japan Physics Program Graduate School of Advanced Science and Engineering Hiroshima University 1-3-1 Kagamiyama Higashi-hiroshima 739-8526 Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI) The University of Tokyo Institutes for Advanced Study The University of Tokyo Kashiwa Chiba 277-8583 Japan Research Center for Advanced Particle Physics Kyushu University 744 Motooka Nishi-ku Fukuoka 819-0395 Japan

The standard cosmological model assumes a homogeneous and isotropic universe as the background spacetime on large scales called the cosmological principle. However, some observations suggest the possibility of an inhomogeneous and anisotropic universe at large scales. In this paper, we investigate a model of the Universe with random inhomogeneities and anisotropies on very large scales, motivated by the supercurvature dark energy model in Nan et al. [Phys. Rev. D 99, 103512 (2019)]. In this model, the authors introduced a scalar field with O(1) inhomogeneities on a scale sufficiently larger than the current horizon scale (superhorizon scale), and the potential energy of the scalar field explains the accelerating expansion, with slight deviations from the cosmological principle. We aim at clarifying the theoretical prediction on the large-scale structure (LSS) of the matter component in this model. Based on the work on the superhorizon scale fluctuations (superhorizon mode) presented in Y. Nan and K. Yamamoto [Phys. Rev. D 105, 063518 (2022)], we derive the equations that the perturbative components to the LSS obey as a generalization of the cosmological perturbations theory, which is solved to find the influence of the dark energy inhomogeneities on the formation of the LSS. Finally, we show that the model can be consistent with observations by comparing the σ8 predicted by the numerical solution of the model with the σ8 indicated by observations such as Planck and the Sloan Digital Sky Survey.

关键词： Cosmology Dark energy Evolution of the Universe Large scale structure of the Universe

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Non-bipartite k-common graphs

arXiv

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arXiv 2020年

作者： Král, Daniel Noel, Jonathan A. Norin, Sergey Volec, Jan Wei, Fan Faculty of Informatics Masaryk University Botanická 68A Brno602 00 Czech Republic Mathematics Institute DIMAP Department of Computer Science University of Warwick CoventryCV4 7AL United Kingdom Department of Mathematics and Statistics University of Victoria David Turpin Building A425 3800 Finnerty Road VictoriaV8P 5C2 Canada Mathematics Institute and DIMAP University of Warwick CoventryCV4 7AL United Kingdom Department of Mathematics and Statistics McGill University Montreal Canada Department of Mathematics Faculty of Nuclear Sciences and Physical Engineering Czech Technical University in Prague Trojanova 13 Prague120 00 Czech Republic Department of Mathematics Princeton University PrincetonNJ United States School of Mathematics Institute for Advanced Study Princeton United States

A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of Kn is asymptotically minimized by a random coloring. For every k, we construct a connected non-bipartite k-common graph. This resolves a problem raised by Jagger, Št’ovíček and Thomason [Combinatorica 16 (1996), 123–141]. We also show that a graph H is k-common for every k if and only if H is Sidorenko and that H is locally k-common for every k if and only if H is locally Sidorenko. Copyright © 2020, The Authors. All rights reserved.

关键词： Graph theory

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Time series forecasting using manifold learning

arXiv

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arXiv 2021年

作者： Papaioannou, Panagiotis Talmon, Ronen Kevrekidis, Ioannis G. Siettos, Constantinos Dipartimento di Matematica e Applicazioni Università degli Studi di Napoli Federico II Naples Italy Department of Electrical Engineering Technion-Israel Institute of Technology Haifa Israel Department of Chemical and Biomolecular Engineering Department of Applied Mathematics and Statistics Department of Medicine Johns Hopkins University BaltimoreMD United States Dipartimento di Matematica e Applicazioni & Scuola Superiore Meridionale Università degli Studi di Napoli Federico II Naples Italy

We address a three-tier numerical framework based on manifold learning for the forecasting of high-dimensional time series. At the first step, we embed the time series into a reduced low-dimensional space using a nonlinear manifold learning algorithm such as Locally Linear Embedding and Diffusion Maps. At the second step, we construct reduced-order regression models on the manifold, in particular Multivariate Autoregressive (MVAR) and Gaussian Process Regression (GPR) models, to forecast the embedded dynamics. At the final step, we lift the embedded time series back to the original high-dimensional space using Radial Basis Functions interpolation and Geometric Harmonics. For our illustrations, we test the forecasting performance of the proposed numerical scheme with four sets of time series: three synthetic stochastic ones resembling EEG signals produced from linear and nonlinear stochastic models with different model orders, and one real-world data set containing daily time series of 10 key foreign exchange rates (FOREX) spanning the time period 03/09/2001-29/10/2020. The forecasting performance of the proposed numerical scheme is assessed using the combinations of manifold learning, modelling and lifting approaches. We also provide a comparison with the Principal Component Analysis algorithm as well as with the naive random walk model and the MVAR and GPR models trained and implemented directly in the high-dimensional *** Codes 37Mxx, 58D30, 60G15, 37C05 Copyright © 2021, The Authors. All rights reserved.

关键词： Time series

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Machine learning-integrated computational analysis on a blood-based ternary nanofluid flow in a stenosed artery with the artificial neural networks and modified finite difference approach

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Chaos, Solitons & Fractals 2025年 199卷

作者： Mohib Hussain Du Lin Hassan Waqas Bagh Ali Nehad Ali Shah School of Mathematics and Statistics Northwestern Polytechnical University Xian 710072 China MIIT Key Laboratory of Dynamics and Control Complex System Northwestern Polytechnical University Xi’an 710072 China School of Naval Architecture Ocean and Energy Power Engineering Wuhan University of Technology Wuhan Hubei 430063 China Department of Software Engineering Faculty of Science & Technology ILMA University 75190 Karachi Pakistan Department of Mechanical Engineering Sejong University Seoul 05006 Republic of Korea

Heart failure and stroke continue to be the most common cause of global death, with atherosclerosis artery stenosis becoming a significant contributor. Although prior research has progressed in comprehending blood circulation behaviour, however, the incorporation of artificial intelligence (AI) and machine learning (ML) in the examination of ternary nanofluids for stenosed arterial diseases signifies a notable breakthrough in this domain. We proposes an integration of ML technique with computational fluid dynamics (CFD) to analyse the non-linear dynamics of thermal characterization in blood-based tri-hybrid nano-fluid flow, influenced by thermal radiation, variable heat sources and sinks, and aligned magnetic field effects within a blood artery exhibiting cosine stenosis. The investigation is based on AI approach, the Levenberg–Marquardt algorithm (LMA), with back propagation Artificial Neural Network (ANN-BP). The mathematical model is developed in the form of partial differentia equations and transformed into ordinary differential equation by similarity scaling, and then numerically evaluated by a modified finite difference approach, the Keller-Box method. The suggested ANN-LMA accuracy is compared to the ML solution for boundary layer flow. Regression values indicate an excellent fit between the predictions and the real data. It is observed that the inclined magnetic angle affects the drag force and heat transfer rate. There is a 27.9% increase in the heat transfer rate for ternary nano-fluid. Conclusively, the non-linear interaction between the magnetic field and nanofluid flow may significantly enhance heat transfer rates, which could have potential applications in biomedical sciences.

关键词： Artificial intelligence Blood-integrated nano-fluid Machine learning Neural networks Non-linear differential equations Thermal analysis

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Corrigendum to “I-divergence based statistical inference for heteroscedasticity and compounds of arsenic contamination in Chile” [Chemometr. Intell. Lab. Syst. 226 (2022) 104579]

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Chemometrics and Intelligent Laboratory Systems 2023年 234卷

作者： M. Stehlík R. Sabolová V. Sečkárová L. Núñez Soza J. Kiseľák Department of Applied Statistics Johannes Kepler University in Linz Austria Institute of Statistics Universidad de Valparaíso Valparaíso Chile Facultad de Ingeniería Universidad Andrés Bello Valparaíso Chile Department of Mathematics Faculty of Electrical Engineering Czech Technical University in Prague Czech Republic School of Mathematics Monash University Melbourne Australia Departamento de Matemática Facultad de Ciencias Universidad de Tarapacá Arica Chile P.J.Šafárik University in Košice Slovakia

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