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Time-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Bénard convection

Physical Review E 2015年第4期92卷 043012-043012页

作者： Baole Wen Gregory P. Chini Rich R. Kerswell Charles R. Doering Program in Integrated Applied Mathematics University of New Hampshire Durham New Hampshire 03824 USA Center for Fluid Physics University of New Hampshire Durham New Hampshire 03824 USA The Institute for Computational Engineering and Sciences The University of Texas at Austin Austin Texas 78712 USA Department of Mechanical Engineering University of New Hampshire Durham New Hampshire 03824 USA School of Mathematics University of Bristol University Walk Bristol BS8 1TW United Kingdom Department of Physics University of Michigan Ann Arbor Michigan 48109-1040 USA Department of Mathematics University of Michigan Ann Arbor Michigan 48109-1043 USA Center for the Study of Complex Systems University of Michigan Ann Arbor Michigan 48109-1107 USA

An alternative computational procedure for numerically solving a class of variational problems arising from rigorous upper-bound analysis of forced-dissipative infinite-dimensional nonlinear dynamical systems, including the Navier-Stokes and Oberbeck-Boussinesq equations, is analyzed and applied to Rayleigh-Bénard convection. A proof that the only steady state to which this numerical algorithm can converge is the required global optimal of the relevant variational problem is given for three canonical flow configurations. In contrast with most other numerical schemes for computing the optimal bounds on transported quantities (e.g., heat or momentum) within the “background field” variational framework, which employ variants of Newton's method and hence require very accurate initial iterates, the new computational method is easy to implement and, crucially, does not require numerical continuation. The algorithm is used to determine the optimal background-method bound on the heat transport enhancement factor, i.e., the Nusselt number (Nu), as a function of the Rayleigh number (Ra), Prandtl number (Pr), and domain aspect ratio L in two-dimensional Rayleigh-Bénard convection between stress-free isothermal boundaries (Rayleigh's original 1916 model of convection). The result of the computation is significant because analyses, laboratory experiments, and numerical simulations have suggested a range of exponents α and β in the presumed Nu∼PrαRaβ scaling relation. The computations clearly show that for Ra≤1010 at fixed L=22,Nu≤0.106Pr0Ra5/12, which indicates that molecular transport cannot generally be neglected in the “ultimate” high-Ra regime.

关键词： RAYLEIGH-Benard convection RESEARCH BOUNDS (mathematics) CONVECTIVE flow (Fluid dynamics) NATURAL heat convection NUSSELT number

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Performance Analysis of Interleaved Bidirectional DC-DC Converters for Battery Control in Islanded Microgrid

Performance Analysis of Interleaved Bidirectional DC-DC Conv...

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IEEE General Meeting Power& Energy Society

作者： Lindemberg Roberto de Lima Pedro A. de Alcântara Luana C. S. Soares Camila M. V. Barros Luciano S. Barros Mathematics and Computational Modeling Graduate Program João Pessoa Brazil Electrical Engineering Graduate Program Federal University of Paraíba João Pessoa Brazil Computer Systems Department Federal University of Paraíba João Pessoa Brazil

In this paper, considering photovoltaic/battery sourced microgrids with grid-forming droop control in the load interface converter for power management, two alternative converter topologies for the battery are tested: dual boost interleaved converter and three-phase interleaved converter. These topologies are based on the conventional bidirectional buckboost converter and their employment is to allow a reduction in component sizing, improvement in power quality, and higher output voltage. Analysis of the operation of these converters in different operation modes of the microgrid is carried out, including battery normal charging, battery normal discharging, battery charging limit, and maximum state-of-charge, through simulations in MATLAB/Simulink environment. Results suggest advantages such as reduced stress on switches and battery charging current ripple for the two interleaved converters tested and the potential implementation of higher output voltage for the dual boost converter.

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EQUATION OF STATE OF FLUID HE+H2 MIXTURES UNDER HIGH PRESSURE

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中国物理（英文版） 2001年第12期10卷 1144-1148页

作者： CHEN QI-FENG CAI LING-CANG SUN ZHI-HONG JING FU-QIAN CHEN DONG-QUAN Department of Physics Northwest Normal University Lanzhou 730070 China Laboratory for Shock Wave and Detonation Physics Research Institute of Fluid PhysicsCAEP Mianyang 621900 China Department of Basic Science Gansu University of Technology Lanzh Laboratory for Shock Wave and Detonation Physics Research Institute of Fluid PhysicsCAEP Mianyang 621900 China Department of Basic Science Gansu University of Technology Lanzhou 730050 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

A statistical mechanical variational theory and an improved van der Waals one-fluid model have been used to compute the equation of state of fluid He+H2 mixtures with different H2:He compositions under high pressure. The first-order quantum correction is included. Comparing the present results with Monte Carlo simulations indicates that the quantum corrections for calculating the thermodynamic properties become increasingly important at lower temperatures.

关键词： equation of state fluid He+H2 mixtures fluid variational theory mixing rules

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An Immersed Peridynamics Model of Fluid-Structure Interaction Accounting for Material Damage and Failure

SSRN

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SSRN 2022年

作者： Kim, Keon Ho Bhalla, Amneet Pal Singh Griffith, Boyce E. Department of Mathematics University of North Carolina Chapel HillNC United States Department of Mechanical Engineering San Diego State University San DiegoCA 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 Chapel HillNC United States McAllister Heart Institute University of North Carolina Chapel HillNC United States

This paper develops and benchmarks an immersed peridynamics method to simulate the deformation, damage, and failure of hyperelastic materials within a fluid-structure interaction framework. The immersed peridynamics method describes an incompressible structure immersed in a viscous incompressible fluid. It expresses the momentum equation and incompressibility constraint in Eulerian form, and it describes the structural motion and resultant forces in Lagrangian form. Coupling between Eulerian and Lagrangian variables is achieved by integral transforms with Dirac delta function kernels, as in standard immersed boundary (IB) methods. The major difference between our approach and conventional IB methods is that we use peridynamics, instead of classical continuum mechanics, to determine the structural forces. We focus on non-ordinary state-based peridynamic material descriptions that allow us to use a constitutive correspondence framework that can leverage well characterized nonlinear constitutive models of soft materials. The convergence and accuracy of our approach are compared to both conventional and immersed finite element methods using widely used benchmark problems of nonlinear incompressible elasticity. We demonstrate that the immersed peridynamics method yields comparable accuracy with similar numbers of structural degrees of freedom for several choices of the size of the peridynamic horizon. We also demonstrate that the method can generate grid-converged simulations of fluid-driven material damage growth, crack formation and propagation, and rupture under large deformations. © 2022, The Authors. All rights reserved.

关键词： Fluid structure interaction

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Default network and intelligence difference

Default network and intelligence difference

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Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)

作者： Ming Song Yong Liu Yuan Zhou Kun Wang Chunshui Yu Tianzi Jiang Research Center of Computational Medicine Sino-French Laboratory in Computer Science Automation and Applied Mathematics Institution of Automation Chinese Academy and Sciences Beijing China Department of Radiology Xuanwu Hospital of Capital Medical University Beijing China

In the last few years, many studies in the cognitive and system neuroscience found that a consistent network of brain regions, referred to as the default network, showed high levels of activity when no explicit task was performed. Some scientists believed that the resting state activity might reflect some neural functions that consolidate the past, stabilize brain ensembles and prepare us for the future. Here, we modeled default network as undirected weighted graph and then used graph theory to investigate the topological properties of the default network of the two groups of people with different intelligence levels. We found that, in both groups, the posterior cingulate cortex showed the greatest degree in comparison to the other brain regions in the default network, and that the medial temporal lobes and cerebellar tonsils were topologically separations from the other brain regions in the default network. More importantly, we found that the strength of some functional connectivities and the global efficiency of default network were significantly different between the superior intelligence group and the average intelligence group, which indicates that the functional integration of the default network might be related to the individual intelligent performance.

关键词： Intelligent networks Humans Artificial intelligence Neuroscience Graph theory Temporal lobe Intelligent sensors Automation Hospitals Alzheimer's disease

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Variational joint filtering

arXiv

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arXiv 2017年

作者： Zhao, Yuan Park, Il Memming Department of Neurobiology and Behavior Stony Brook University Stony BrookNY11794 United States Department of Neurobiology and Behavior Department of Applied Mathematics and Statistics Institute for Advanced Computational Science Stony Brook University Stony BrookNY11794 United States

State space models provide an interpretable framework for complex time series by combining an intuitive dynamical system model with a probabilistic observation model. We developed a flexible online learning framework for latent nonlinear state dynamics and filtered latent states. Our method utilizes the stochastic gradient variational Bayes method to jointly optimize the parameters of the nonlinear dynamics, observation model, and the black-box recognition model. Unlike previous approaches, our framework can incorporate non-trivial observation noise models and has potential of inferring in real-time. We test our method on point process and Gaussian observations driven by continuous attractor dynamics and nonstationary systems, demonstrating its ability to recover the phase portrait, filtered trajectory, and produce long-term predictions for online machine learning. Copyright © 2017, The Authors. All rights reserved.

关键词： State space methods

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Dynamics of bond breaking and formation in polyethylene near shock front

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Physical Review E 2020年第2期102卷 023207-023207页

作者： Hao Liu Hao Zhou Wei Kang Ping Zhang Huiling Duan Weiyan Zhang X. T. He Department of Applied Physics School of Physics and Electronics Hunan University Changsha 410082 China HEDPS Center for Applied Physics and Technology and College of Engineering Peking University Beijing 100871 China Department of Mechanics and Engineering Science College of Engineering Peking University Beijing 100871 China Division of Engineering and Applied Science California Institute of Technology Pasadena California 91125 USA Institute of Applied Physics and Computational Mathematics Beijing 100088 China China Academy of Engineering Physics Mianyang 621900 China

In a systematic study of shock wave propagating in crystalline polyethylenes using molecular dynamics method and the electron force field (eFF) potential, we show that microscopic structure of shock front is significantly affected by the anisotropy of long carbon chain and the bond breaking and recombination dynamics. However, macroscopic properties measured in Hugoniot experiments, such as compression ratio and shock velocity, are not sensitive to carbon chain anisotropy and bond dynamics. Our work also display that hydrogen molecules are formed when the piston speed is in the region between 10 km/s and 30 km/s. However, carbon-hydrogen pair distribution function does not display an indication of carbon-hydrogen phase segregation.

关键词： High-energy-density plasmas Inertial confinement fusion Plasma production & heating by shock waves & compression Shock waves

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High-Frequency Volatility Estimation With Fast Multiple Change Points Detection

arXiv

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arXiv 2023年

作者： Ainasse, El Mehdi Balabhadra, Greeshma Polak, Pawel Center of Excellence in Wireless and Information Technology Stony Brook University United States Department of Applied Mathematics and Statistics Stony Brook University United States Institute for Advanced Computational Science Stony Brook University United States

We propose a method for constructing sparse high-frequency volatility estimators that are robust against change points in the spot volatility process. The estimators we propose are 1-regularized versions of existing volatility estimators. We focus on power variation estimators as they represent a fundamental class of volatility estimators. We establish consistency of these estimators for the true unobserved volatility and the change points locations, showing that minimax rates can be achieved for particular volatility estimators. The new estimators utilize the computationally efficient least angle regression algorithm for estimation purposes, followed by a reduced dynamic programming step to refine the final number of change points. In terms of numerical performance, these estimators are not only computationally fast but also accurately identify breakpoints near the end of the sample, both features highly desirable in today's electronic trading environment. In terms of out-of-sample volatility prediction, our new estimators provide more realistic and smoother volatility forecasts, outperforming a broad range of classical and recent volatility estimators across various frequencies and forecasting horizons. Copyright © 2023, The Authors. All rights reserved.

关键词： Change detection

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Distribution system voltage prediction from smart inverters using decentralized regression

arXiv

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arXiv 2021年

作者： Atkins, Zachary R. Vogl, Christopher J. Madduri, Achintya Duan, Nan Miedlar, Agnieszka K. Merl, Daniel Department of Mathematics University of Kansas Lawrence United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory Livermore United States Computational Engineering Division Lawrence Livermore National Laboratory Livermore United States

As photovoltaic (PV) penetration continues to rise and smart inverter functionality continues to expand, smart inverters and other distributed energy resources (DERs) will play increasingly important roles in distribution system power management and security. In this paper, it is demonstrated that a constellation of smart inverters in a simulated distribution circuit can enable precise voltage predictions using an asynchronous and decentralized prediction algorithm. Using simulated data and a constellation of 15 inverters in a ring communication topology, the COLA algorithm is shown to accomplish the learning task required for voltage magnitude prediction with far less communication overhead than fully connected P2P learning protocols. Additionally, a dynamic stopping criterion is proposed that does not require a regularizer like the original COLA stopping criterion. Copyright © 2021, The Authors. All rights reserved.

关键词： Smart power grids

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CONTINUOUS-TIME ANALYSIS OF ADAPTIVE OPTIMIZATION AND NORMALIZATION

arXiv

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arXiv 2024年

作者： Gould, Rhys Tanaka, Hidenori Department of Applied Mathematics and Theoretical Physics University of Cambridge United Kingdom CBS-NTT Physics of Intelligence Program Harvard University Physics & Informatics Laboratories NTT Research Inc United States

Adaptive optimization algorithms, particularly Adam and its variant AdamW, are fundamental components of modern deep learning. However, their training dynamics lack comprehensive theoretical understanding, with limited insight into why common practices—such as specific hyperparameter choices and normalization layers—contribute to successful generalization. This work presents a continuous-time formulation of Adam and AdamW, facilitating a tractable analysis of training dynamics that can shed light on such practical questions. We theoretically derive a stable region for Adam’s hyperparameters (β, γ) that ensures bounded updates, empirically verifying these predictions by observing unstable exponential parameter growth outside of this stable region. Furthermore, we theoretically justify the success of normalization layers by uncovering an implicit meta-adaptive effect of scale-invariant architectural components. This insight leads to an explicit optimizer, 2-Adam, which we generalize to k-Adam—an optimizer that applies an adaptive normalization procedure k times, encompassing Adam (corresponding to k = 1) and Adam with a normalization layer (corresponding to k = 2). Overall, our continuous-time formulation of Adam facilitates a principled analysis, offering deeper understanding of optimal hyperparameter choices and architectural decisions in modern deep learning. © 2024, CC BY.

关键词： Adaptive algorithms

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