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Variational solution to the lattice Boltzmann method for Couette flow

Physical Review E 2024年第5期109卷 055305-055305页

作者： Joseph T. Johnson Mahyar Madadi Daniel R. Ladiges Yong Shi Barry D. Hughes John E. Sader School of Mathematics and Statistics Department of Materials Physics Research School of Physics Center for Computational Sciences and Engineering Department of Mechanical Materials and Manufacturing Engineering Graduate Aerospace Laboratories and Department of Applied Physics

Literature studies of the lattice Boltzmann method (LBM) demonstrate hydrodynamics beyond the continuum limit. This includes exact analytical solutions to the LBM, for the bulk velocity and shear stress of Couette flow under diffuse reflection at the walls through the solution of equivalent moment equations. We prove that the bulk velocity and shear stress of Couette flow with Maxwell-type boundary conditions at the walls, as specified by two-dimensional isothermal lattice Boltzmann models, are inherently linear in Mach number. Our finding enables a systematic variational approach to be formulated that exhibits superior computational efficiency than the previously reported moment method. Specifically, the number of partial differential equations (PDEs) in the variational method grows linearly with quadrature order while the number of moment method PDEs grows quadratically. The variational method directly yields a system of linear PDEs that provide exact analytical solutions to the LBM bulk velocity field and shear stress for Couette flow with Maxwell-type boundary conditions. It is anticipated that this variational approach will find utility in calculating analytical solutions for novel lattice Boltzmann quadrature schemes and other flows.

关键词： Rarefied flows Boltzmann theory Lattice-Boltzmann methods

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Thermodynamics, Dynamics, and Kinetics of Nanostructured Fluid-Solid Interfaces

arXiv

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arXiv 2017年

作者： Colosqui, Carlos E. Department of Mechanical Engineering Stony Brook University Department of Applied Mathematics & Statistics Stony Brook University

This article covers thermodynamic, dynamic, and kinetic models that are suitable for the analysis of wetting, adsorption, and related interfacial phenomena in colloidal and multiphase systems. Particular emphasis is made on describing crucial physical assumptions and the validity range of the described theoretical approaches and predictive models. The classical sharp interface treatment of thermodynamic systems where a perfectly smooth surface is assumed to separate homogeneous phases can present significant limitations when analyzing systems that are subject to thermal motion and present multiple metastable states caused by interfacial heterogeneities of nanoscale dimensions. Mesoscopic approaches such as stochastic Langevin dynamics can extend the application of sharp interface models to a wide variety of systems exhibiting metastability as they undergo thermal motion. For such metastable systems, dynamic and kinetic equations can describe the evolution of observable (macroscopic) variables as the system approaches thermodynamic equilibrium. Sufficiently close to equilibrium, Kramers theory of thermally activated escape from metastable states can be effectively employed to describe diverse wetting and interfacial processes via kinetic equations. Future directions for further advancement and application of thermodynamic, dynamic, and kinetic models are briefly discussed in the context of current technological developments involving nanoparticles, nanofluidics, and nanostructured surfaces. Copyright © 2017, The Authors. All rights reserved.

关键词： Integral equations

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STATISTICAL ANALYSIS AND COMPUTATIONAL MODELLING OF SUPERFLUID HELIUM

STATISTICAL ANALYSIS AND COMPUTATIONAL MODELLING OF SUPERFLU...

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ASME 2024 International mechanical engineering Congress and Exposition, IMECE 2024

作者： Domenikos, George-Rafael Mantzaris, Alexander V. Laboratory of Applied Thermodynamics Thermal Engineering Sector Department of Mechanical Engineering National Technical University of Athens Heroon Polytechneiou 9 Athens15780 Greece University of Central Florida Department of Statistics and Data Science 4000 University Bvld OrlandoFL32816 United States

ISBN: (纸本)9780791888643

Superfluidity as a state of matter is a complex phenomenon that can be studied from different perspectives. In this work the authors aim to describe superfluidity in Helium-4 through a microscopical computational approach. Through the quantum mechanical states of Helium a statistical model is created in order to transverse from the microscopical to the macroscopical spectrum. The Bose-Einstein statistics and the Maxwell-Boltzmann are then calculated for different temperatures to investigate the divergence between them in the microscopic view of the system, and explore the macroscopic system phase transitions to superfluidity. Through this computational model the probability distributions of the different energy states are presented, giving the ability to compare the statistical behavior of the ideal and non-ideal parts of superfluid Helium, and how superfluidity can be associated with the phenomenon of Bose-Einstein condensation computationally. The excitation spectrum of the superfluid is studied, through which the entropy of the excitations is shown to be the total entropy of the superfluid below the lambda line, connecting these finding with Landau’s quasiparticle approach. Through these computations the authors are now able to showcase this microscopical behavior directly, without making use of macroscopical thermodynamic data as done previously, and derive the basic thermodynamic behaviors of superfluid Helium-4 to near absolute zero without the need of experimental data. Copyright © 2024 by ASME.

关键词： Bose-Einstein condensation

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Triangle formation design in eccentric orbits using pseudospectral optimal control

Triangle formation design in eccentric orbits using pseudosp...

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作者： Gong, Qi Ross, I. Michael Alfriendz, K.T. Department of Applied Mathematics and Statistics University of California Santa Cruz CA 95064 United States Department of Mechanical and Astronautical Engineering Naval Postgraduate School Monterey CA 93943 United States Department of Aerospace Engineering Texas A and M University College Station TX 77843 United States

ISBN: (纸本)9781563479458

In this paper, we further a general framework for the formation design of distributed space systems. Based on constrained nonlinear optimal control theory, the formation of multi-spacecraft is designed by pseudospectral methods. The approach deals with the full nonlinear dynamics without using any linearization/approximation techniques;and is applicable to elliptical reference orbits. The method is tested on various formation problems including equilateral triangular formation over eccentric orbits. This framework provides a unified and straightforward way to design large-scale formation for distributed space systems.

关键词： Orbits

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Optimization of a joint sensor placement and robust estimation scheme for distributed parameter processes subject to worst case spatial disturbance distributions

Optimization of a joint sensor placement and robust estimati...

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Proceedings of the 2004 American Control Conference (AAC)

作者： Demetriou, Michael A. Borggaard, Jeff Department of Mechanical Engineering Worcester Polytechnic Institute Worcester MA 01609 United States Interdisc. Center for Applied Math Virginia Tech Blacksburg VA 24061-0531 United States

In this paper, we consider the development of a systematic optimization process that can be used to locate sensors in distributed parameter systems. We focus on two components in this process: developing a performance metric, and invoking optimization algorithms to find the best location of sensors according to this metric. In choosing a metric, we incorporate the notion of a worst-case, spatially distributed disturbance. The included numerical study uses a variety of second-order parabolic problems.

关键词： Sensors

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Global and Local Reduced Models for Interacting, Heterogeneous Agents

Global and Local Reduced Models for Interacting, Heterogeneo...

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2021 AIChE Annual Meeting

作者： Thiem, Thomas N. Kemeth, Felix P. Bertalan, Tom Laing, Carlo R. Kevrekidis, Ioannis G. Department of Chemical and Biological Engineering Princeton University United States Department of Chemical and Biomolecular Engineering Whiting School of Engineering Johns Hopkins University United States Department of Mechanical Engineering Massachusetts Institute of Technology United States School of Natural and Computational Sciences Massey University New Zealand Department of Applied Mathematics and Statistics Johns Hopkins University United States

ISBN: (纸本)9781713852834

Large collections of coupled, heterogeneous agents can manifest complex dynamical behavior presenting difficulties for simulation and analysis. However, if the collective dynamics lie on a low-dimensional manifold then the original agent-based model may be approximated with a simplified surrogate model on and near the low-dimensional space where the dynamics live. Analytically identifying such simplified models can be challenging or impossible, but here we present a data-driven coarse-graining methodology for discovering such reduced models. We consider two types of reduced models: globally-based models which use global information and predict dynamics using information from the whole ensemble, and locally-based models that use local information, that is, information from just a subset of agents close (close in heterogeneity space, not physical space) to an agent, to predict the dynamics of an agent. For both approaches we are able to learn laws governing the behavior of the reduced system on the low-dimensional manifold directly from time series of states from the agent-based system. These laws take the form of either a system of ordinary differential equations (ODEs), for the globally-based approach, or a partial differential equation (PDE) in the locally-based case. For each technique we employ a specialized artificial neural network integrator that has been templated on an Euler time stepper (i.e. a ResNet) to learn the laws of the reduced model. As part of our methodology, we utilize the proper orthogonal decomposition (POD) to identify the low-dimensional space of the dynamics. Our globally-based technique uses the resulting POD basis to define a set of coordinates for the agent states in this space, and then seeks to learn the time evolution of these coordinates as a system of ODEs. For the locally-based technique, we propose a methodology for learning a partial differential equation representation of the agents;the PDE law depends on the state variables and

关键词： Dynamics

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Predictive study of combustion temperature of liquefied petroleum gas (LPG) on the spherical packed-bed porous burner

Predictive study of combustion temperature of liquefied petr...

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International Symposium on Advanced Materials and Application, ISAMA 2019

作者： Peamsuwan, Rapeepong Klamnoi, Anucha Yotha, Narongsak Krittacom, Bundit Department of Applied Physics Faculty of Science and Liberal Arts Rajamangala University of Technology Isan Nakhonrachasima Thailand Department of Applied Mathematics and Statistics Faculty of Science and Liberal Arts Rajamangala University of Technology Isan Nakhonrachasima Thailand Department of Mechanical Engineering Faculty of Engineering and Architecture Rajamangala University of Technology Isan Nakhonrachasima Thailand Rajamangala University of Technology Isan Nakhonrachasima Thailand

ISBN: (纸本)9783035713152

The relation between the significant factors and the combustion temperature (T) of Liquid Petroleum Gas (LPG) on the spherical packed-bed porous burner is investigated. Alumina-Cordierite ceramic balls having the average diameter (d) of 3 mm. and the porosity (Ε) of 0.322 are employed as porous media. The multiple-linear and multiple-quadratic regressions are used to analyze the data at the equivalence ratio (Φ) of 0.58 – 0.66 and volumetric premixed-gas flow rate (Vmix) in a range of 10 – 25 m3/h. The porous thickness (H) is in the range of 2.5 – 7.5 cm. Thus, independent variables are Φ, Vmix and H. The dependent variable is the maximum temperature (T) of combustion LPG on the porous burner. For statistical analysis, both main and interaction of independent variables effecting to the combustion temperature are investigated. The results showed that, for the case of multiple-linear regression, an equations recommended in prediction of the T on porous burner is T = 1375.603(Φ) +179.636(H) – 295.028(ΦH) – 9.628(HVmix) + 16.368(ΦVmixH) with a coefficient of determination (R2) of 0.998 and the standard error of the estimation of 42.7365. In the case of multiple-quadratic regression, a proper equation used in predicting T on porous burner is T = 2133.184(Φ)2 + 1.247(Vmix)2 + 17.248(H)2 –2.916(ΦVmix)2 – 42.107(ΦH)2 – 0.049(VmixH)2 + 0.123(ΦVmixH)2 with R2 of 0.997 and standard error of the estimation of 44.2979. In addition, the comparison between the experimental results and the predicted estimation is reported that different percentage of both regressions and experimental results is satisfied. © 2019 Trans Tech Publications Ltd, Switzerland.

关键词： Multiple linear regression

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On a control design to an AFM microcantilever beam, operating in a tapping-mode, with irregular behavior

On a control design to an AFM microcantilever beam, operatin...

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ASME 2011 International Design engineering Technical Conferences and Computers and Information in engineering Conference, IDETC/CIE 2011

作者： Dos Santos Rodrigues, Kleber Balthazar, José Manoel Tusset, Angelo Marcelo Pontes Jr., Bento Rodrigues UNESP: Univ Estadual Paulista Department of Mechanical Engineering FEB Bauru São Paulo Brazil UNESP: Univ Estadual Paulista Department of Statistics Applied Mathematics and Computation DEMAC Rio Claro São Paulo Brazil Department of Engineering Science UTFPR Ponta Grossa Parana Brazil

ISBN: (纸本)9780791854846

In last decades, control of nonlinear dynamic systems became an important and interesting problem studied by many authors, what results the appearance of lots of works about this subject in the scientific literature. In this paper, an Atomic Force Microscope micro cantilever operating in tapping mode was modeled, and its behavior was studied using bifurcation diagrams, phase portraits, time history, Poincare maps and Lyapunov exponents. Chaos was detected in an interval of time;those phenomena undermine the achievement of accurate images by the sample surface. In the mathematical model, periodic and chaotic motion was obtained by changing parameters. To control the chaotic behavior of the system were implemented two control techniques. The SDRE control (State Dependent Riccati Equation) and Time-delayed feedback control. Simulation results show the feasibility of the bothmethods, for chaos control of an AFM system. Copyright © 2011 by ASME.

关键词： Chaos control

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FAD-SAR: A Novel Fishing Activity Detection System via Synthetic Aperture Radar Images Based on Deep Learning Method

FAD-SAR: A Novel Fishing Activity Detection System via Synth...

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2024 International Symposium on Intelligent Signal Processing and Communication Systems, ISPACS 2024

作者： Bai, Yanbing Li, Siao Ju, Rui-Yang Yang, Zihao Yu, Jinze Chiang, Jen-Shiun Center for Applied Statistics School of Statistics Renmin University of China Beijing100872 China Graduate Institute of Networking and Multimedia National Taiwan University Taipei City106335 Taiwan Department of Mechanical Systems Engineering Tokyo University of Agriculture and Technology Tokyo183-8538 Japan Department of Electrical and Computer Engineering Tamkang University New Taipei City251301 Taiwan

ISBN: (纸本)9798350389210

Illegal, unreported, and unregulated (IUU) fishing activities seriously affect various aspects of human life. However, traditional methods for detecting and monitoring IUU fishing activities at sea have limitations. Although synthetic aperture radar (SAR) can complement existing vessel detection systems, extracting useful information from SAR images using traditional methods remains a challenge, especially in IUU fishing. This paper proposes a deep learning based fishing activity detection system, which is implemented on the xView3 dataset using six classical object detection models: SSD, RetinaNet, FSAF, FCOS, Faster R-CNN, and Cascade R-CNN. In addition, this work employs different enhancement techniques to improve the performance of the Faster R-CNN model. The experimental results demonstrate that training the Faster R-CNN model using the Online Hard Example Mining (OHEM) strategy increases the Avg-F1 value from 0.212 to 0.216. © 2024 IEEE.

关键词： Deep learning

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Synchronization of Chaos in Fully Developed Turbulence

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Physical Review Letters 2013年第8期110卷 084102-084102页

作者： Cristian C. Lalescu Charles Meneveau Gregory L. Eyink Department of Applied Mathematics & Statistics The Johns Hopkins University Baltimore Maryland 21218 USA Department of Mechanical Engineering The Johns Hopkins University Baltimore Maryland 21218 USA

We investigate chaos synchronization of small-scale motions in the three-dimensional turbulent energy cascade, via pseudospectral simulations of the incompressible Navier-Stokes equations. The modes of the turbulent velocity field below about 20 Kolmogorov dissipation lengths are found to be slaved to the chaotic dynamics of larger-scale modes. The dynamics of all dissipation-range modes can be recovered to full numerical precision by solving small-scale dynamical equations with the given large-scale solution as an input, regardless of initial condition. The synchronization rate exponent scales with the Kolmogorov dissipation time scale, with possible weak corrections due to intermittency. Our results suggest that all sub-Kolmogorov length modes should be fully recoverable from numerical simulations with standard, Kolmogorov-length grid resolutions.

关键词： Synchronization

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