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Traveling wave solutions of the nonlinear Gilson-Pickering equation in crystal lattice theory

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Journal of Ocean Engineering and Science 2024年第1期9卷 40-49页

作者： A.T.Nguyen O.Nikan Z.Avazzadeh Division of applied {1. Science and Technology Advanced InstituteVan Lang UniversityHo Chi Minh CityVietnam Faculty of Technology Van Lang UniversityHo Chi Minh CityVietnam School of mathematics Iran University of Science and TechnologyNarmakTehranIran Department of applied {1. Xi’an Jiaotong-Liverpool UniversitySuzhou 215123China

This paper focuses on obtaining the traveling wave solutions of the nonlinear Gilson-Pickering equa-tion(GPE),which describes the prorogation of waves in crystal lattice theory and plasma *** solution of the GPE is approximated via the finite difference technique and the localized meshless radial basis function generated finite *** association of the technique results in a meshless approach that does not require linearizing the nonlinear *** the first step,the PDE is converted to a system of nonlinear ODEs with the help of the radial *** the second step,a high-order ODE solver is adopted to discretize the nonlinear ODE *** global collocation techniques pose a considerable computationl burden due to the calculation of the dense algebraic *** proposed method approx-imates differential operators over the local support domain,leading to sparse differentiation matrices and decreasing the computational *** results and comparisons are provided to confirm the efficiency and accuracy of the method.

关键词： Nonlinear Gilson–Pickering equation Soliton wave solutions Meshless technique RBF LRBF-FD Optimal shape parameter

Natural vibration and critical velocity of translating Timoshenko beam with non-homogeneous boundaries

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applied {1. and Mechanics(English Edition) 2024年第9期45卷 1523-1538页

作者： Yanan LI Jieyu DING Hu DING Liqun CHEN Shanghai institute of {1. mathematics and Mechanics Shanghai Key Laboratory of Mechanics in Energy EngineeringShanghai Frontier Science Center of MechanoinformaticsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200072China School of mathematics and Statistics Qingdao UniversityQingdao 266071Shandong ProvinceChina

In most practical engineering applications,the translating belt wraps around two fixed *** boundary conditions of the dynamic model are typically specified as simply supported or fixed *** this paper,non-homogeneous boundaries are introduced by the support *** the translating belt as the mechanical prototype,the vibration characteristics of translating Timoshenko beam models with nonhomogeneous boundaries are investigated for the first *** governing equations of Timoshenko beam are deduced by employing the generalized Hamilton's *** effects of parameters such as the radius of wheel and the length of belt on vibration characteristics including the equilibrium deformations,critical velocities,natural frequencies,and modes,are numerically calculated and *** numerical results indicate that the beam experiences deformation characterized by varying curvatures near the *** radii of the wheels play a pivotal role in determining the change in trend of the relative difference between two beam *** the results unearths that the relative difference in equilibrium deformations between the two beam models is more pronounced with smaller-sized *** the two wheels are of equal size,the critical velocities of both beam models reach their respective *** addition,the relative difference in natural frequencies between the two beam models exhibits nonlinear variation and can easily exceed 50%.Furthermore,as the axial velocities increase,the impact of non-homogeneous boundaries on modal shape of translating beam becomes more *** dealing with non-homogeneous boundaries is challenging,beam models with non-homogeneous boundaries are more sensitive to parameters,and the differences between the two types of beams undergo some interesting variations under the influence of non-homogeneous boundaries.

关键词： translating beam Timoshenko beam non-homogeneous boundary natural frequency critical velocity

Revealing excited states of rotational Bose-Einstein condensates

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The Innovation 2024年第1期5卷 41-48页

作者： Jianyuan Yin Zhen Huang Yongyong Cai Qiang Du Lei Zhang School of Mathematical Sciences Laboratory of Mathematics and Applied MathematicsPeking UniversityBeijing 100871China Department of mathematics National University of SingaporeSingapore 119076Singapore Department of mathematics University of CaliforniaBerkeleyBerkeleyCA 94720USA School of Mathematical Sciences Beijing Normal UniversityBeijing 100875China Department of applied Physics and applied mathematics and Data Science institute Columbia UniversityNew YorkNY 10027USA Beijing International Center for Mathematical Research Center for Quantitative BiologyCenter for Machine Learning ResearchPeking UniversityBeijing 100871China

Rotational Bose-Einstein condensates can exhibit quantized vortices as topological *** this study,the ground and excited states of the rotational Bose-Einstein condensates are systematically studied by calculating the stationary points of the Gross-Pitaevskii energy *** excited states and their connections at different rotational frequencies are revealed in solution landscapes constructed with the constrained high-index saddle dynamics *** excitation mechanisms are identified:vortex addition,rearrangement,merging,and *** demonstrate changes in the ground state with increasing rotational frequencies and decipher the evolution of the stability of ground states.

关键词： method rotational excited

MONOTONICITY CORRECTIONS FOR NINE-POINT SCHEME OF DIFFUSION EQUATIONS

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Journal of Computational mathematics 2024年第5期42卷 1305-1327页

作者： Wang Kong Zhenying Hong Guangwei Yuan Zhiqiang Sheng School of mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing 211106China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China HEDPS Center for Applied Physics and TechnologyPeking UniversityBeijing 100871China

In this paper,we present a nonlinear correction technique to modify the nine-point scheme proposed in[SIAM ***.,30:3(2008),1.41.1.61.such that the resulted scheme preserves the *** first express the flux by the cell-centered unknowns and edge unknowns based on the stencil of the nine-point ***,we use a nonlinear combination technique to get a monotone *** order to obtain a cell-centered finite volume scheme,we need to use the cell-centered unknowns to locally approximate the auxiliary *** present a new method to approximate the auxiliary unknowns by using the idea of an improved multi-points flux *** numerical results show that the new proposed scheme is robust,can handle some distorted grids that some existing finite volume schemes could not handle,and has higher numerical accuracy than some existing positivity-preserving finite volume schemes.

关键词： Monotonicity corrections Diffusion equation Improved MPFA Distorted meshes

A CELL-CENTERED GODUNOV METHOD BASED ON STAGGERED DATA DISTRIBUTION,PART Ⅰ:ONE-DIMENSIONAL CASE

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Journal of Computational mathematics 2024年第4期42卷 1172-1196页

作者： Jiayin Zhai Xiao Li Zhijun Shen institute of {1. Physics and Computational mathematics LCPP.O.Box 8009-26Beijing 100088China College of Big Data and Internet Shenzhen Technology UniversityShenzhen 518118China Center for applied Physics and Technology HEDPSPeking UniversityChina

This paper presents a cell-centered Godunov method based on staggered data distribu-tion in Eulerian *** motivation is to reduce the intrinsic entropy dissipation of classical Godunov methods in the calculation of an isentropic or rarefaction *** the same time,the property of accurate shock capturing is also *** analyzing the factors that cause nonphysical entropy in the conventional Godunov methods,we introduce two velocities rather than a single velocity in a cell to reduce kinetic energy dissipation.A series of redistribution strategies are adopted to update subcell quantities in order to improve *** examples validate that the present method can dramatically reduce nonphysical entropy *** subject classification:35Q35,76N1.,76M1..

关键词： Godunov method Riemann solver Rarefaction wave Nonphysical entropy increase.

Phase-field simulations of the effect of temperature and interface for zirconiumδ-hydrides

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Chinese Physics B 2024年第4期33卷 701-710页

作者：陈子航盛杰刘瑜施小明黄厚兵许可王越超武帅孙博刘海风宋海峰 School of Materials Science and Engineering Beijing Institute of TechnologyBeijing 100081China Advanced Research institute of Multidisciplinary Science Beijing Institute of TechnologyBeijing 100081China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China Department of Physics University of Science and Technology BeijingBeijing 100083China

Hydride precipitation in zirconium cladding materials can damage their integrity and *** temperature and material defects have a significant effect on the dynamic growth of *** this study,we have developed a phasefield model based on the assumption of elastic behaviour within a specific temperature range(61. K-653 K).This model allows us to study the influence of temperature and interfacial effects on the morphology,stress,and average growth rate of zirconium *** results suggest that changes in temperature and interfacial energy influence the length-to-thickness ratio and average growth rate of the hydride *** ultimate determinant of hydride orientation is the loss of interfacial coherency,primarily induced by interfacial dislocation defects and quantifiable by the mismatch degree *** escalation in interfacial coherency loss leads to a transition of hydride growth from horizontal to vertical,accompanied by the onset of redirection ***,redirection occurs at a critical mismatch level,denoted as qc,and remains unaffected by variations in temperature and interfacial ***,this redirection leads to an increase in the maximum stress,which may influence the direction of hydride crack *** research highlights the importance of interfacial coherency and provides valuable insights into the morphology and growth kinetics of hydrides in zirconium alloys.

关键词： zirconium hydride phase-field method temperature effect mismatch degree

Self-consistent and precise measurement of time-dependent radiative albedo of gold based on specially symmetrical triple-cavity Hohlraum

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Matter and Radiation at Extremes 2024年第3期9卷 57-64页

作者： Zhiyu Zhang Yang Zhao Xiaoying Han Liling Li Bo Qing Lifei Hou Yulong Li YuXue Zhang Huan Zhang Xiangming Liu Bo Deng Gang Xiong Min Lv Tuo Zhu Chengwu Huang Tianming Song Yan Zhao Yingjie Li Lu Zhang Xufei Xie Jiyan Zhang Jiamin Yang Laser Fusion Research Center China Academy of Engineering PhysicsMianyang 621900China National Key Laboratory of Plasma Physcis Mianyang 621900China institute of {1. Physics and Computational mathematics Beijing 100088China

A self-consistent and precise method to determine the time-dependent radiative albedo,i.e.,the ratio of the reemission flux to the incident flux,for an indirect-drive inertial confinement fusion Hohlraum wall material is proposed.A specially designed symmetrical triple-cavity gold Hohlraum is used to create approximately constant and near-equilibrium uniform radiation with a peak temperature of 1.0 *** incident flux at the secondary cavity waist is obtained from flux balance analysis and from the shock velocity of a standard *** results agree well owing to the symmetrical radiation in the secondary cavity.A self-consistent and precise time-dependent radiative albedo is deduced from the reliable reemission flux and the incident flux,and the result from the shock velocity is found to have a smaller uncertainty than that from the multi-angle flux balance analysis,and also to agree well with the result of a simulation using the HYADES opacity.

关键词： precise cavity radiative

Attractor for the Extensible Beam Equation with Nonlocal Weak Damping on Time–Dependent Space

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Acta Mathematica Sinica,English Series 2024年第4期40卷 1115-1126页

作者： Chun Xiang ZHAO Feng Juan MENG institute of {1. System Analysis Jiangsu UniversityZhenjiang 212013P.R.China School of mathematics and Physics Jiangsu University of TechnologyChangzhou 213001P.R.China

In this article,we consider the long-time behavior of extensible beams with nonlocal weak damping:ε(t)u_(tt)+Δ^(2)u-m(‖▽u‖^(2))Δu+‖u_(t)‖^(p_(u_(t)))+f(u)=h,whereε(t)is a decreasing function vanishing at *** the theory of process on time-dependent spaces,we investigate the existence of the time-dependent attractor by using the Condition(C_(t))method and more detailed *** results obtained essentially improve and complete some previous works.

关键词： Time-dependent attractor extensible beams equation nonlocal weak damping

An improved interval model updating method via adaptive Kriging models

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applied {1. and Mechanics(English Edition) 2024年第3期45卷 497-514页

作者： Sha WEI Yifeng CHEN Hu DING Liqun CHEN Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai Frontier Science Center of MechanoinformaticsShanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200072China Shanghai institute of Aircraft Mechanics and Control Shanghai 200092China

Interval model updating(IMU)methods have been widely used in uncertain model updating due to their low requirements for sample ***,the surrogate model in IMU methods mostly adopts the one-time construction *** makes the accuracy of the surrogate model highly dependent on the experience of users and affects the accuracy of IMU ***,an improved IMU method via the adaptive Kriging models is *** method transforms the objective function of the IMU problem into two deterministic global optimization problems about the upper bound and the interval diameter through universal grey *** optimization problems are addressed through the adaptive Kriging models and the particle swarm optimization(PSO)method to quantify the uncertain parameters,and the IMU is *** the construction of these adaptive Kriging models,the sample space is gridded according to sensitivity *** sampling is then performed in key subspaces based on the maximum mean square error(MMSE)*** interval division coefficient and random sampling coefficient are adaptively adjusted without human interference until the model meets accuracy *** effectiveness of the proposed method is demonstrated by a numerical example of a three-degree-of-freedom mass-spring system and an experimental example of a butted cylindrical *** results show that the updated results of the interval model are in good agreement with the experimental results.

关键词： interval model updating(IMU) non-probabilistic uncertainty adaptive Kriging model surrogate model grey number