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Numerical Mathematics(Theory,Methods and Applications) 2012年第3期5卷 333-358页

作者： Xia Ji Huazhong Tang LSEC Institute of Computational MathematicsChinese Academy of SciencesP.O.Box 2719Beijing 100190China hedps CAPT and LMAMSchool of Mathematical SciencesPeking UniversityBeijing 100871China

As the generalization of the integer order partial differential equations(PDE),the fractional order PDEs are drawing more and more attention for their applications in fluid flow,finance and other *** paper presents high-order accurate Runge-Kutta local discontinuous Galerkin(DG)methods for one-and two-dimensional fractional diffusion equations containing derivatives of fractional order in *** Caputo derivative is chosen as the representation of spatial derivative,because it may represent the fractional derivative by an integral *** numerical examples show that the convergence orders of the proposed local Pk–DG methods are O(hk+1)both in one and two dimensions,where Pk denotes the space of the real-valued polynomials with degree at most k.

关键词： Discontinuous Galerkin method Runge-Kutta time discretization fractional derivative Caputo derivative diffusion equation

Finite Indentation of Pressurized Elastic Fluid Nano vesicles by a Rigid Cylindrical Indenter

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Acta Mechanica Solida Sinica 2019年第5期32卷 633-642页

作者： Xingyi Tang Jianxiang Wang Xin Yi Department of Mechanics and Engineering Science College of EngineeringPeking UniversityBeijing 100871China capt HEDPS and IFSA Collaborative Innovation Center of MoEPeking UniversityBeijing 100871China Beijing Innovation Center for Engineering Science and Advanced Technology Peking UniversityBeijing 100871China

Nanovesicles have been demonstrated to be the key agents in therapeutic encapsulations for drug delivery and diagnostic area,and the effectiveness and efficiency of these applications strongly depend on the mechanical properties of *** on the Helfrich membrane theory,a theoretical investigation is conducted to explore the mechanical behaviors of pressurized elastic fluid nanovesicles during the indentation by a rigid cylindrical *** effects of osmotic pressure,membrane bending rigidity,energy of adhesion bet ween the vesicle and substrate on the mechanical responses of the vesicle to the indentation are *** is found that the osmotic pressure dominates the mechanical behaviors of strongly pressurized nanovesicles as well as the effective vesicle stiffness and Young's *** results may have important implications on regulating the mechanical behaviors of inter-and intracellular nanovesicles which are crucial for particle-based drug delivery systems.

关键词： Nanovesicles Indentation Osmotic pressure Young's modulus Stiffness Forcedepth curves

Mechanical properties of irradiated multi-phase polycrystalline BCC materials

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Acta Mechanica Sinica 2015年第2期31卷 191-204页

作者： Dingkun Song Xiazi Xiao Jianming Xue Haijian Chu Huiling Duan State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering ScienceCollege of EngineeringPeking University capt HEDPS and IFSA Collaborative Innovation Center of MoEPeking University Department of Mechanics College of SciencesShanghai University Shanghai Institute of Applied Mathematics and Mechanics

Structure materials under severe irradiations in nuclear environments are known to degrade because of irradiation hardening and loss of ductility,resulting from irradiation-induced defects such as vacancies,interstitials and dislocation loops,*** this paper,we develop an elastic-viscoplastic model for irradiated multi-phase polycrystalline BCC materials in which the mechanical behaviors of individual grains and polycrystalline aggregates are both *** the microscopic grain scale,we use the internal variable model and propose a new tensorial damage descriptor to represent the geometry character of the defect loop,which facilitates the analysis of the defect loop evolutions and dislocation-defect *** the macroscopic polycrystal scale,the self-consistent scheme is extended to consider the multiphase problem and used to bridge the individual grain behavior to polycrystal *** on the proposed model,we found that the work-hardening coefficient decreases with the increase of irradiation-induced defect loops,and the orientation/loading dependence of mechanical properties is mainly attributed to the different Schmid *** the polycrystalline scale,numerical results for pure Fe match well with the irradiation experiment *** model is further extended to predict the hardening effect of dispersoids in oxide-dispersed strengthened steels by the considering the Orowan *** influences of grain size and irradiation are found to compete to dominate the strengthening behaviors of materials.

关键词： Irradiation Self-consistent method Multi-phase polycrystal Dislocation density

Viscous Rayleigh-Taylor instability with and without diffusion effect

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Applied Mathematics and Mechanics(English Edition) 2017年第2期38卷 263-270页

作者： Chenyue XIE Jianjun TAO Ji LI Center for Applied Physics and Technology (capt)-MOE Key Laboratory of High Energy Density Physics Simulation (hedps) State Key Laboratory for Turbulence and Complex System (SKLTCS) Department of Mechanics and Engineering ScienceCollege of Engineering Peking University Department of Engineering University of Cambridge

The approximate but analytical solution of the viscous Rayleigh-Taylor insta- bility （RTI） has been widely used recently in theoretical and numerical investigations due to its clarity. In this paper, a modified analytical solution of the growth rate for the viscous RTI of incompressible fluids is obtained based on an approximate method. Its accuracy is verified numerically to be significantly improved in comparison with the previous one in the whole wave number range for different viscosity ratios and Atwood numbers. Fur- thermore, this solution is expanded for viscous RTI including the concentration-diffusion effect.

关键词： viscous Rayleigh-Taylor instability (RTI) dispersion relation diffusioneffect

Advances in the kinetics of heat and mass transfer in near-continuous complex flows

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Frontiers of physics 2024年第4期19卷 187-234页

作者：许爱国张德佳甘延标 National Key Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsP.O.Box 8009-26Beijing 100088China State Key Laboratory of Explosion Science and Technology Beijing Institute of TechnologyBeijing 100081China hedps Center for Applied Physics and Technologyand College of EngineeringPeking UniversityBeijing 100871China State Key Laboratory for GeoMechanics and Deep Underground Engineering China University of Mining and TechnologyBeijing 100083China National Key Laboratory of Shock Wave and Detonation Physics Mianyang 621999China Hebei Key Laboratory of Trans-Media Aerial Underwater Vehicle School of Liberal Arts and SciencesNorth China Institute of Aerospace EngineeringLangfang 065000China

The study of macro continuous flow has a long ***,the exploration of heat and mass transfer in small systems with a particle number of several hundred or less has gained significant interest in the fields of statistical physics and nonlinear ***,due to absence of suitable methods,the understanding of mesoscale behavior situated between the aforementioned two scenarios,which challenges the physical function of traditional continuous fluid theory and exceeds the simulation capability of microscopic molecular dynamics method,remains considerably *** greatly restricts the evaluation of effects of mesoscale behavior and impedes the development of corresponding regulation *** access the mesoscale behaviors,there are two ways:from large to small and from small to *** the necessity to interface with the prevailing macroscopic continuous modeling currently used in the mechanical engineering community,our study of mesoscale behavior begins from the side closer to the macroscopic continuum,that is from large to *** on some fundamental challenges encountered in modeling and analysis of near-continuous flows,we review the research progress of discrete Boltzmann method(DBM).The ideas and schemes of DBM in coarse-grained modeling and complex physical field analysis are *** relationships,particularly the differences,between DBM and traditional fluid modeling as well as other kinetic methods are *** verification and validation of the method,some applied researches including the development of various physical functions associated with discrete and non-equilibrium effects are *** directions of DBM related studies are indicated.

关键词： near-continuous flow non-equilibrium kinetics discrete Boltzmann method complex physical field analysis

Theoretical models of void nucleation and growth for ductile metals under dynamic loading: A review

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Matter and Radiation at Extremes 2022年第1期7卷 64-78页

作者： Haonan Sui Long Yu Wenbin Liu Ying Liu Yangyang Cheng Huiling Duan State Key Laboratory for Turbulence and Complex System Department of Mechanics and Engineering ScienceBIC-ESATCollege of EngineeringPeking UniversityBeijing 100871People’s Republic of China capt HEDPS and IFSACollaborative Innovation Center of MoEPeking UniversityBeijing 100871People’s Republic of China

Void nucleation and growth under dynamic loading are essential for damage initiation and evolution in ductile *** the past few decades,the development of experimental techniques and simulation methods has helped to reveal a wealth of information about the nucleation and growth process from its microscopic aspects to macroscopic *** and effective theoretical approaches have been developed based on this information and have helped in the analysis of the damage states of structures,thereby making an important contribution to the design of damageresistant *** Review presents a brief overview of theoretical models related to the mechanisms of void nucleation and growth under dynamic *** work and recent research progress are summarized,together with discussion of some aspects deserving further study.

关键词： ductile loading damage

A HYBRID EXPLICIT-IMPLICIT SCHEME FOR THE TIME-DEPENDENT WIGNER EQUATION

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Journal of Computational Mathematics 2021年第1期39卷 22-42页

作者： Haiyan Jiang Tiao Lu Xu Yin Department of Mathematics and Statistics Beijing Institute of TechnologyBeiing 100081China capt HEDPSLMAMIFSA Collaborative Innovation Center of MoESchool of Mathematical SciencesPeking UniversityBeijing 100871China Department of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China

This paper designs a hybrid scheme based on finite difference methods and a spectral method for the time-dependent Wigner equation,and gives the error analysis for the full discret ization of its initial value *** explicit-implicit time-splitting scheme is used for time integration and the second-order upwind finite difference scheme is used to dis-cretize the advection *** consistence error and the stability of the full discretization are analyzed.A Fourier spectral method is used to approximate the pseudo-differential operator term and the corresponding error is studied in *** final convergence result shows clearly how the regularity of the solution affects the convergence order of the pro-posed scheme.N umerical results are presented for confirming the sharpness of the *** scattering effects of a Gaussian wave packet tunneling through a Gaussian potential barrier are *** evolution of the density function shows that a larger portion of the wave is reflected when the height and the width of the barrier *** subject classification:65M06,65M70.

关键词： Finite diference method Spectral method Hybrid scheme Error analysis Wigner equation.

Threshold and decay properties of transient isolated turbulent band in plane Couette flow

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Applied Mathematics and Mechanics(English Edition) 2019年第10期40卷 1449-1456页

作者： Jianzhou LU Jianjun TAO Weitao ZHOU Xiangming XIONG capt-hedps SKLTCS Collaborative Innovation Center of IFSA Department of Mechanics and Engineering Science College of Engineering Peking University Beijing 100871 China The Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 U. S.A.

By direct numerical simulations of the plane Couette flow (PCF) in a large computational domain, it is shown that an isolated turbulent band decays monotonically at low Reynolds numbers but experiences transient growth before the eventual relaminarization at moderate Reynolds numbers. The lower bound Reynolds number of the transient-growth regime is determined as 286. The width, length, and tilt angle of the iso- lated band structure are defined based on the disturbance kinetic energy in the mid-plane, and the geometric characteristics of the band can be described with a tilted rectangle. It is illustrated that before its eventual fragmentation, the isolated turbulent band decays in a style of longitudinal contraction, where the center, width, and tilt angle of the band keep almost constant but the band length contracts with a statistically constant velocity.

关键词： plane Couette flow (PCF) subcritical transition turbulent band

Editorial:Recent advances in hydrodynamic instability and transition to turbulence

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Theoretical & Applied Mechanics Letters 2015年第3期5卷 101-102,I0004页

作者： Luca Brandt Jianjun Tao Linné FLOW Centre KTH Mechanics capt HEDPSand IFSA Collaborative Innovation Center of MoEDepartment of Mechanics and Engineering ScienceCollege of EngineeringPeking University

Hydrodynamic instability and the mechanisms for turbulence onset and self-sustaining are two research questions that have puzzled the scientists for over a century, yet renewed interest and significant progress occurred in the last decade or so. We know only few exact analytical solutions of the Navier-Stokes equations, the equations governing the flow of simple fluids like water and air, and most of these are never observed in applications or laboratory experiments since these configurations are prone to instabilities that quickly bring the flow to the turbulent regime.

关键词： Editorial

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石墨烯热学性能及表征技术

力学进展 2014年第1期44卷 236-259页

作者：白树林赵云红北京大学工学院材料科学与工程系 HEDPS/CAPT/LTCS北京100871

2004年石墨烯的发现立刻引起了全球科技界的高度关注,掀起了从碳纳米管问世以来对于碳族材料的又一个研究高潮,人们迅速开展了针对石墨烯的制备、性能表征、甚至应用的研究工作.从石墨烯问世到目前,主要研究工作集中在石墨烯电学性能的... 详细信息

2004年石墨烯的发现立刻引起了全球科技界的高度关注,掀起了从碳纳米管问世以来对于碳族材料的又一个研究高潮,人们迅速开展了针对石墨烯的制备、性能表征、甚至应用的研究工作.从石墨烯问世到目前,主要研究工作集中在石墨烯电学性能的研究,特别是集中在用石墨烯制备超级电容器方面.相比之下,人们对于石墨烯热学性能的研究还比较少.然而,鉴于石墨烯具有极高的热导率和负的热膨胀系数,以及作为热界面材料的工程应用价值,对其热学性能的研究正逐渐成为研究的一个重要分支.以石墨烯热学性能如热导率到热膨胀系数为研究对象,全面总结国际上的发展现状.内容涉及单层石墨烯、多层石墨烯和石墨烯泡沫.研究手段包括理论研究、数值模拟和实验测定3个方面.在综合研究成果的基础上,最后对于存在的问题和可能的发展方向给出了合理的建议.

关键词：石墨烯热学性能表征技术数值模拟