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Hermite interpolation and its numerical differentiation formula involving symmetric functions

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Applied Mathematics(A Journal of Chinese Universities) 2009年第3期24卷 309-314页

作者： bai Hong-huan xu Ai-min Department of Mathematics Zhejiang University Hangzhou 310027 China Institute of Mathematics Zhejiang Wanli University Ningbo 315100 China

By utilizing symmetric functions,this paper presents explicit representations for Hermite interpolation and its numerical differentiation *** the corresponding error estimates are also provided.

关键词： Hermite interpolation numerical differentiation elementary symmetric function complete symmetric function

Impact of climate change on allowable bearing capacity on theQinghai-Tibetan Plateau

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Advances in Climate Change Research 2019年第2期10卷 99-108页

作者： xu Xiao-Ming WU Qing-bai State Key Laboratory of Frozen Soil Engineering Northwest Institute of Eco-Environment and Resources Chinese Academy o f Sciences Lanzhou 730000 China

Climate change has a substantial impact on infrastructures in the permafrost on the Qinghai-Tibetan Plateau (QTP). In this study, the mean annual ground temperature (MAGT) and permafrost evolution were investigated in both the historical (1950-2005) and projected (2006-2099) periods. Then, an allowable bearing capacity model was used to discuss the allowable bearing capacity change on the QTP. Results show that the MAGT increased by 0.36 ℃ during 1950-2005. The MAGT will increase by 0.40 (RCP2.6), 0.79 (RCP4.5), 1.07 (RCP6.0), and 1.75 (RCP8.5)℃C during 2006-2099. In addition, the permafrost area has decreased by 0.195 × 10^6 km2 in 1950-2005. The permafrost area will decrease by 0.232 × 10^6 (RCP2.6), 0.468 × 10^6 (RCP4.5), 0.564 × 10^6 (RCP6.0), and 0.803 × 10^6 (RCP8.5) km2 during 2006-2099. With the degradation of permafrost, the allowable bearing capacity in permafrost zones would decrease accordingly. The decreasing trend is 6 kPa per 10 years in 1950-2005, and will be 0.6 (RCP2.6), 5 (RCP4.5), 7 (RCP6.0), and 11 (RCP8.5) kPa per 10 years during 2006-2099. The most remarkable trend would be observed under RCP8.5. Meanwhile, some scientific advices for the design, construction, operation and maintenance of permafrost engineering in the context of climate change were provided.

关键词： Qinghai-Tibetan Plateau Climate change Permafrost Allowable bearing capacity

Numerical simulation on reho-diecasting mould filling of an automobile master brake cylinder

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International Journal of Minerals,Metallurgy and Materials 2009年第2期16卷 184-188页

作者： Yue-long bai Wei-min Mao Hong xu Jun xu School of Materials Science and Engineering University of Science and Technology Beijing Beijing 100083 China General Research Institute for Non-ferrous Metals Beijing 100088 China Research Center for Foundry Engineer North University of China Taiyuan 030051 China

An apparent viscosity model of semi-solid A356 aluminum alloy has been developed and the software Castsofl6.0 coupled with the model has been used to simulate the mould filling of an automobile master brake cylinder with the semi-solid A356 aluminum alloy slurry. The simulation results are in agreement with the practical filling process, indicating that the apparent viscosity model is feasible and can be used to simulate the mould filling of the semisolid A356 aluminum alloy slurry and can be used to optimize the filling process and the design of dies. A higher injection pressure, a higher ingate flow velocity of the semi-solid slurry, and a higher slurry temperature are advantageous to the mould filling of the automobile master brake cylinder.

关键词： semi-solid A356 aluminum alloy reho-diecasting numerical simulation

Quantitative Analysis of Frosting Characteristics on the Drip Tray of A Cryogenic Valve for LNG Ships

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China Ocean Engineering 2024年第4期38卷 572-585页

作者： bai xu CHEN Guan-yu DU Yue xu Cao CHEN Jia-jing School of Naval Architecture&Ocean Engineering Jiangsu University of Science and TechnologyZhenjiang 212003China

Cryogenic valves play a crucial role in the production and transportation of liquefied natural gas(LNG),and are primarily responsible for efficiently controlling the inflow and outflow of LNG and regulating ***,due to their operation in low-temperature and high-humidity environments,crucial components such as drip trays are susceptible to frosting,which may lead to LNG leakage,thereby causing severe safety *** this study,the user-defined function(UDF)is employed to redevelop Fluent,which integrates the frost growth model with the Eulerian multiphase flow model,to conduct a quantitative analysis of frosting on drip trays of cryogenic *** effects of environmental parameters,such as wind speed,ambient temperature,air humidity,and cold surface temperature on the growth of the frost layer were *** study reveals a limiting wind speed between 1 m/s and 2 m/*** reaching this limit speed,the growth of the frost layer reaches its maximum,and further increases in the wind speed have no significant effect on the growth of the frost ***,the influence of the change in the flow field on droplet impingement and freezing during the growth of the frost layer is considered through the coupling method of the kinematic characteristics of water droplets and the collection coefficient of water *** study identifies the influence of different parameters on the droplet impact efficiency,leading to the modification of the frost layer on the drip tray.

关键词： LNG carrier drip tray frost effective impact coefficient

Objective Variation Simplex Algorithm for Continuous Piecewise Linear Programming

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Tsinghua Science and Technology 2017年第1期22卷 73-82页

作者： Yu bai Zhiming xu Xiangming Xi Shuning Wang Department of Automation Tsinghua National Laboratory for Information Science and Technology(TNList)Tsinghua UniversityBeijing100084China Faculty of College of Science Air Force Engineering UniversityXi'an 710051 Department of Automation Tsinghua UniversityBeijing 100084China

This paper works on a modified simplex algorithm for the local optimization of Continuous Piece Wise Linear（CPWL） programming with generalization of hinging hyperplane objective and linear constraints. CPWL programming is popular since it can be equivalently transformed into difference of convex functions programming or concave optimization. Inspired by the concavity of the concave CPWL functions, we propose an Objective Variation Simplex Algorithm（OVSA）, which is able to find a local optimum in a reasonable time. Computational results are presented for further insights into the performance of the OVSA compared with two other algorithms on random test problems.

关键词： local optimization continuous piecewise linear programming modified simplex algorithm

Simulation of the Dendrite Morphology and Microsegregation in Solidification of Al–Cu–Mg Aluminum Alloys

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Acta Metallurgica Sinica(English letters) 2015年第2期28卷 173-181页

作者： Rui Chen Qing-Yan xu bai-Cheng Liu Key Laboratory for Advanced Materials Processing Technology Ministry of Education School of Materials Science and Engineering Tsinghua University

Since most typical alloys in industrial applications are multicomponent with three or more components, and various CA models proposed in the past mainly focus on the binary alloys, a two-dimensional modified cellular automaton model allowing for the quantitatively predicting dendrite growth of multicomponent alloys in the low P6clet number regime is presented. The elimination of the mesh-induced anisotropy is achieved by adopting a modified virtual front tracking method. A new efficient method based on the lever rule is applied to calculate the solid fraction increment of the interfacial cells. The thermodynamic data such as liquidus temperature, the partition coefficients, and the slope of liquidus surface, needed for determining the dynamics of dendrite growth, are obtained by coupling with PanEngine. This model is applied to simulate the dendrite morphology and microsegregation of A1-Cu-Mg temary alloy both for single and multi- dendrites growth. The simulated results demonstrate that the difference of the concentration distribution profiles ahead of the dendrite tip for each alloying element mainly results from the different partition coefficients and solute diffusion coefficients. Comparison with the prediction of analytical model is carded out and it reveals the correctness of the model. Consequently, the difference in interdendritic microsegregation behavior of different components is analyzed.

关键词： Cellular automaton Multicomponent Dendrite growth Microsegregation

Transition study of 3D aerodynamic configures using improved transport equations modeling

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Chinese Journal of Aeronautics 2016年第4期29卷 874-881页

作者： xu Jiakuan bai Junqiang Zhang Yang Qiao lei School of Aeronautics Northwestern Polytechnical University

As boundary layer transition plays an important role in aerodynamic drag prediction, the proposal and study of transition prediction methods simulating the complex flow phenomena are prerequisite for aerodynamic design. In this paper, with the application of the linear stability theory based on amplification factor transport transition equations on the two-equation shear stress transport (SST) eddy-viscosity model, a new method, the SST-NTS-NCF model, is yielded. The new amplification factor transport equation for the crossflow instability induced transition is proposed to add to the NTS equation proposed by Coder, which simulates Tollmien-Schlichting wave transition. The turbulent kinetic energy equation is modified by introducing a new source term that simulates the transition process without the intermittency factor equation. Finally, coupled with these two amplification factor transport equations and SST turbulence model, a four-equation transition turbulence model is built. Comparisons between predictions using the new model and wind-tunnel experiments of NACA64(2) A015, NLF(2)-0415 and ONERA-D infinite swept wing and ONERAM6 swept wing validate the predictive quality of the new SST-NTS-NCF model. (C) 2016 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd.

关键词： Boundary layer CFD Crossflow instability Linear stability theory Transition Turbulence

Potential Application of Entangled Porous Titanium Alloy Metal Rubber in Artificial Lumbar Disc Prostheses

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Journal of Bionic Engineering 2021年第3期18卷 584-599页

作者： Zhiying Ren Jingfei Huang Hongbai bai Rui Jin Fangqi xu Jie xu College of Mechanical Engineering and Automation Fuzhou UniversityFuzhou 350116China Metal Rubber Engineering Research Center Fuzhou UniversityFuzhou 350116China Department of Orthopedics Fujian Provincial HospitalFuzhou 350001China

Entangled Porous Titanium Alloy Metal Rubber(EPTA-MR)was used as a nucleus pulposus material in the design of non-fusion intervertebral disc prosthesis for the first time.A novel artificial lumbar intervertebral disc prosthesis was designed by reconstructing the lumbar model with reverse engineering technology,and the biomechanical behavior of the prosthesis was simulated under varied working *** nucleus pulposus size was determined by the actual size of human ***-MR samples with different densities were prepared by medical titanium alloy wire experimental studies were conducted on static stiffness,damping energy consumption,and fatigue *** results indicated that the static stiffness of EPTA-MR could reach approximately 1500 N mm and its loss factor remained higher than 0.2,and the variation range was relatively small,with excellent vibration damping capacity and bearing *** them,the overall performance of EPTA-MR with a density of 2.5 g em 3 was closer to that of the physiologic intervertebral disc.A macro experiment of five million fatigue vibration tests combined with microstructure observation exhibited a wear rate of only 0.9396 g-MC with no noticeable change in the internal ***,the EPTA-MR has a broad application prospect as the nucleus pulposus material of artificial intervertebral disc prosthesis.

关键词： artificial intervertebral disc prosthesis biomechanical properties entangled porous titanium alloy metal rubber(EPTA-MR) fatigue life vibration damping

Method of Hill Tunneling via Weighted Simplex Centroid for Continuous Piecewise Linear Programming

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Tsinghua Science and Technology 2019年第3期24卷 301-316页

作者： Zhiming xu Yu bai Kuangyu Liu Shuning Wang the National Laboratory for Information Science and Technology Department of Automation Tsinghua University Faculty of Air Force Engineering University

This paper works on a heuristic algorithm with determinacy for the global optimization of Continuous PieceWise Linear(CPWL) programming. The widely applied CPWL programming can be equivalently transformed into D.C. programming and concave optimization over a polyhedron. Considering that the super-level sets of concave piecewise linear functions are polyhedra, we propose the Hill Tunneling via Weighted Simplex Centroid(HTWSC) algorithm, which can escape a local optimum to reach the other side of its contour surface by cutting across the super-level set. The searching path for hill tunneling is established via the weighted centroid of a constructed simplex. In the numerical experiments, different weighting methods are studied first, and the best is chosen for the proposed HTWSC algorithm. Then, the HTWSC algorithm is compared with the hill detouring method and the software CPleX for the equivalent mixed integer programming, with results indicating its superior performance in terms of numerical efficiency and the global search capability.

关键词： global optimization piecewise linear concave minimization cutting plane method hill tunneling