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On two-dimensional large-scale primitive equations in oceanic dynamics (Ⅱ)

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applied mathematics and Mechanics(English Edition) 2007年第5期28卷 581-592页

作者：黄代文郭柏灵 institute of applied Physics and Computational mathematics

The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered. It is assumed that the depth of the ocean is a positive constant. Firstly, if the initial data are square integrable, then by Fadeo-Galerkin method, the existence of the global weak solutions for the problem is obtained. Secondly, if the initial data and their vertical derivatives are all square integrable, then by Faedo-Galerkin method and anisotropic inequalities, the existerce and uniqueness of the global weakly strong solution for the above initial boundary problem are obtained.

关键词： primitive equations of the ocean global weakly strong solution existence uniqueness

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Lagrangian cell-centered conservative scheme

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applied mathematics and Mechanics(English Edition) 2012年第10期33卷 1329-1350页

作者：葛全文 institute of applied Physics and Computational mathematics

This paper presents a Lagrangian cell-centered conservative gas dynamics scheme. The piecewise constant pressures of cells arising from the current time sub-cell densities and the current time isentropic speed of sound are introduced. Multipling the initial cell density by the initial sub-cell volumes obtains the sub-cell Lagrangian masses, and dividing the masses by the current time sub-cell volumes gets the current time sub- cell densities. By the current time piecewise constant pressures of cells, a scheme that conserves the momentum and total energy is constructed. The vertex velocities and the numerical fluxes through the cell interfaces are computed in a consistent manner due to an original solver located at the nodes. The numerical tests are presented, which are representative for compressible flows and demonstrate the robustness and accuracy of the Lagrangian cell-centered conservative scheme.

关键词： sub-cell force Lagrange cell-centered scheme Lagrangian cell-centeredconservative gas dynamics scheme piecewise constant pressure of cell

MESH FREE METHOD BASED ON LOCAL CARTESIAN FRAME

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applied mathematics and Mechanics(English Edition) 2006年第1期27卷 1-6页

作者：刘高联李孝伟 Shanghai institute of applied mathematics and Mechanics

A new mesh free method proposed by the authors was presented, in which the derivatives at each node were constructed using whole derivative formulas through the nodes selected around the node using local Cartesian frame in an autonomous manner, so that without any element it could be considered as a completely mesh free method. The method was tested with a numerical example, and reliable solution was obtained with high accuracy and efficiency.

关键词： mesh free whole derivative Cartesian frame

High-order Lagrangian cell-centered conservative scheme on unstructured meshes

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applied mathematics and Mechanics(English Edition) 2014年第9期35卷 1203-1222页

作者：葛全文 institute of applied Physics and Computational mathematics

A high-order Lagrangian cell-centered conservative gas dynamics scheme is presented on unstructured meshes. A high-order piecewise pressure of the cell is intro- duced. With the high-order piecewise pressure of the cell, the high-order spatial discretiza- tion fluxes are constructed. The time discretization of the spatial fluxes is performed by means of the Taylor expansions of the spatial discretization fluxes. The vertex velocities are evaluated in a consistent manner due to an original solver located at the nodes by means of momentum conservation. Many numerical tests are presented to demonstrate the robustness and the accuracy of the scheme.

关键词： high-order sub-cell force high-order Lagrangian cell-centered conservativescheme high-order piecewise pressure of cell unstructured mesh

EFFECT OF HEAD SHAPE ON THE ADHESION CAPABILITY OF MUSHROOM-LIKE BIOLOGICAL ADHESIVE STRUCTURES

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Acta Mechanica Solida Sinica 2011年第4期24卷 318-325页

作者： Tienchong Chang Shanghai institute of applied mathematics and Mechanics

Theoretical studies have been extensively performed to reveal the mechanism of the biological adhesive structure with a flat ***,most biological adhesive structures have a big *** we investigate the effect of the head shape on the adhesion capability of a mushroomlike adhesion structure based on a finite element *** show that a mushroom-like head produces significant adhesion *** investigate also the effect of the elastic modulus of the adhesive structure on the *** results are consistent with existing experimental results.

关键词： biological adhesion effect of head shape fracture mechanics FEM

Some Large Sample Results for a Class of Functionals of Kaplan-Meier Estimator

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Acta Mathematica Sinica,English Series 1998年第2期14卷 191-200页

作者： Wang Qihua (institute of applied mathematics,Academia Sinica,Beijing 100080,China) institute of applied mathematics Academia Sinica

In this paper,a class of functionals of Kaplan-Meier estimator is *** process martingale methods are used to show the asymptotic normality,and we establish a mean square error inequality and a probability inequality of them without the assumption that F,G are continuous,where F,G are survival time distribution and censoring time distribution respectively.

关键词： Counting Process Martingale Asymptotic normality Mean square error Probability inequality

ON THE CONVERGENCE RATE OF A CLASS OF REACTION HYPERBOLIC SYSTEMS FOR AXONAL TRANSPORT

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Acta Mathematica Scientia 2015年第4期35卷 945-954页

作者：曹文涛黄飞敏 institute of applied mathematics AMSS CAS

In this paper, we consider a class of reaction hyperbolic systems for axonal trans- port arising in neuroscience which can be regarded as hyperbolic systems with relaxation. We prove the BV entropy solutions of the hyperbolic systems converge toward to the unique entropy solution of the equilibrium equation at the optimal rate O（√δ） in L1 norm as the relaxation time δ tends to zero.

关键词： axonal transport relaxation equilibrium convergence rate

Exact solutions for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit

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Acta Mechanica Sinica 2009年第2期25卷 181-186页

作者： J. Kang M. Xu School of mathematics, institute of applied mathematics,Shandong University, 250100 Jinan, China M. Xu School of mathematics Institute of Applied Mathematics Shandong University 250100 Jinan China

The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit. The fractional calculus in the constitutive relationship of a non-Newtonian fluid is introduced. We construct the solutions by means of Fourier transform and the discrete Laplace transform of the sequential derivatives and the double finite Fourier transform. The solutions for Newtonian fluid between two infinite parallel plates appear as limiting cases of our solutions.

关键词： Generalized second-order fluid - Rectangularconduit Fractional calculus Exact solutions

Studying Validity of Single-Fluid Model in Inertial Confinement Fusion

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Communications in Theoretical Physics 2014年第3期61卷 370-376页

作者：谷建法范证锋戴振生叶文华裴文兵朱少平 institute of applied Physics and Computational mathematics

The validity of single-fluid model in inertial confinement fusion simulations is studied by comparing the results of the multi- and single-fluid models. The multi-fluid model includes the effects of collision and interpenetration between fluid species. By simulating the collision of fluid species, steady-state shock propagation into the thin DT gas and expansion of hohlraum Au wall heated by lasers, the results show that the validity of single-fluid model is strongly dependent on the ratio of the characteristic length of the simulated system to the particle mean free path. When the characteristic length L is one order larger than the mean free path A, the single-fluid model＇s results are found to be in good agreement with the multi-fluid model＇s simulations, and the modeling of single-fluid remains valid. If the value of L/A is lower than 10, the interpenetration between fluid species is significant, and the single-fluid simulations show some unphysical results; while the multi-fluid model can describe well the interpenetration and mix phenomena, and give more reasonable results.

关键词： multi-fluid model interpenetration mixing inertial confinement fusion