Parameter estimation for a three‐dimensional numerical barotropic tidal model with adjoint method

The parameters of a three‐dimensional (3‐D) barotropic tidal model are estimated using the adjoint method. The mode splitting technique is employed in both forward and adjoint models. In the external mode, the alternating direction implicit method is used to discretize the two‐dimensional depth‐averaged equations and a semi‐implicit scheme is used for the 3‐D internal mode computations. In this model the bottom friction is expressed in terms of bottom velocity which is different from the previous works. Besides, the bottom friction coefficients (BFCs) are supposed to be spatially varying, i.e. the BFC at some grid points are selected as the independent BFC, while the BFC at the other grid points can be obtained through linear interpolation with these independent BFCs. On the basis of the simulation of M₂ tide in the Bohai and North Yellow Seas (BNYS), twin experiments are carried out to invert the prescribed distributions of model parameters. The parameters inverted are the Fourier coefficients of open boundary conditions (OBCs), the BFC and the vertical eddy viscosity profiles. In these twin experiments, the real topography of BNYS is installed. The ‘observations’ are produced by the tidal model and recorded at the position of TOPEX/Poseidon altimeter data, tidal gauge data and current data. The experiments discuss the influence of initial guesses, model errors and data number. The inversion has obtained satisfactory results and the prescribed distributions have been successfully inverted. The results indicate that the inversion of BFC is more sensitive to data error than that of OBC and the vertical eddy viscosity profiles. Copyright © 2007 John Wiley & Sons, Ltd.     

二维潮波模式底摩擦效应参数化方案同化研究

基于伴随同化方法对二维潮波模式底摩擦效应的线性与非线性参数化方案进行了比较研究。采用拉格朗日乘子法推导了底摩擦效应两种参数化方案的伴随表达式,并借助孪生实验对所述方法的参数反演能力进行了验证.通过同化高度计资料和验潮站资料,分别使用线性和非线性参数化方案,以及常数底摩擦系数与空间分布底摩擦系数设置的两两组合,对模拟结果进行了比较和分析。经过同化,模拟结果与观测数据的差异均有了明显下降。结果表明,如果将底摩擦系数设置为全区常数,则非线性参数化方案的模拟结果远优于线性方案;然而,在空间分布设置下,两者模拟得到的水位场与潮流场仅有细微差别,并尝试从底摩擦引起的能量耗散角度对其原因进行了分析。     

LINEAR ACTIVE STRUCTURES AND MODES （ Ⅰ ） — BASIC CONCEPTS AND PROPERTIES

Some basic concepts about the active structures were firstly explained, and the main subjects to study in the field of active structure dynamics were synthesized. For the linear active structures, the annotations on the modes were done in detail. The physical meanings of the right and left eigenvectors were explained. The right eigenvectors are the modal shapes and the modal responses of an active structure depend on the left ones. The adjoint structure of an active structure was defined and the reciprocity theorem was interpreted. For two active structures, which are adjoint to each other and with the reciprocal gain-matrices, the right and left eigenvector are reciprocal The relationship between an active structure and the corresponding passive structure is expressed with the transfer functions, which is employed to resolve the estimation problems.     

New Explicit and Exact Travelling Wave Solutions for a Class of Nonlinear Evolution Equations

ＩｎｔｒｏｄｕｃｔｉｏｎＷｉｔｈｔｈｅｒａｐｉｄｄｅｖｅｌｏｐｍｅｎｔｏｆｓｃｉｅｎｃｅａｎｄｔｅｃｈｎｏｌｏｇｙ ,ｔｈｅｓｔｕｄｙｋｅｒｎｅｌｏｆｍｏｄｅｒｎｓｃｉｅｎｃｅｉｓｃｈａｎｇｅｄｆｒｏｍｌｉｎｅａｒｔｏｎｏｎｌｉｎｅａｒｓｔｅｐｂｙｓｔｅｐ .Ｍａｎｙｎｏｎｌｉｎｅａｒｓｃｉｅｎｃｅｐｒｏｂｌｅｍｓｃａｎｓｉｍｐｌｙａｎｄｅｘａｃｔｌｙｂｅｄｅｓｃｒｉｂｅｄｂｙｕｓｉｎｇｔｈｅｍａｔｈｅｍａｔｉｃａｌｍｏｄｅｌｏｆｎｏｎｌｉｎｅａｒｅｑｕａｔｉｏｎ .Ｕｐｔｏｎｏｗ ,ｍａｎｙｉｍｐｏｒ…     

The solution of weak formulation for axisymmetric problem of orthotropic cantilever cylindrical shell

Weak formulation of equilibrium equations including boundary conditions of laminated cylindrical shell is presented, and thermal stresses mixed state equation for axisymmetric problem of closed cantilever cylindrical shell is established. A unified approach and weak solutions are obtained for closed laminated cantilever cylindrical shell of arbitrary thickness under thermal and mechanical loadings. The equation and boundary conditions proposed in this paper are weakened, the method of this paper would be easy to popularize in dynamics analysis of elasticity. Foundation item: the National Natural Science Foundation of China (19392305)     

A class of nonlinear boundary value problems for the second-order<Emphasis Type="Italic">E</Emphasis><Subscript>2</Subscript> class elliptic systems in general form

A class of nonlinear boundary value problems (BVP) for the second-order E₂ class elliptic systems in general form is discussed. By introducing a kind of transformation, this kind of BVP is reduced to a class of generalized nonlinear Riemann-Hilbert BVP. And then some singular integral operators are introduced to establish the equivalent nonlinear singular integral equations. The solvability is proved under some suitable hypotheses by means of the properties of singular integral operators and the function theoretic methods. Foundation items: the National Natural Science Foundation of China (19671056); Shanghai Municipal Natural Scientific Foundation (99ZA14030, 01ZA14023); Jiangxi Provincial Natural Scientific Foundation (981102, 0211014) Biographies: LI Ming-zhong (1935−); XU Ding-hua (1967−)     

LINEAR ACTIVE STRUCTURES AND MODES （ Ⅱ ） — DISCRETE SYSTEMS AND BEAMS

The basic concepts about the active structures and some attributes of the modes were presented in paper “Liner Active Structures and Modes ( Ⅰ ) “. The characteristics of the active discrete systems and active beams were discussed, especially, the stability of the active structures and the orthogonality of the eigenvectors. The notes about modes were portrayed by a model of a seven-storeyed building with sensors and actuators. The concept of the adjoint active structure was extended from the discrete systems to the beams that were the representations of the continuous structures. Two types of beams with different placements of the measuring and actuating systems were discussed in detail. One is the beam with the discrete sensors and actuators, and the other is the beam with distributed sensor and actuator function. The orthogonality conditions were derived with the modal shapes of the active beam and its adjoint active beam. An example shows that the variation of eigenvalues with feedback amplitude for the homo-configuration and non-homo-configuration active structures.     

Extended self-similar scaling law of multi-scale eddy structure in wall turbulence

ＩｎｔｒｏｄｕｃｔｉｏｎＭｕｃｈｗｏｒｋｈａｓｂｅｅｎｄｅｖｏｔｅｄｉｎｔｈｅｌａｓｔｆｅｗｄｅｃａｄｅｓｔｏｔｈｅｍｅａｓｕｒｅｍｅｎｔａｎｄｍｏｄｅｌｉｎｇｏｆｔｈｅｓｃａｌｉｎｇｌａｗｏｆｓｔｒｕｃｔｕｒｅｆｕｎｃｔｉｏｎｏｆｔｕｒｂｕｌｅｎｔｆｌｏｗｓ.Ｔｈｅｓｏ＿ｃａｌｌｅｄ“ｖｅｌｏｃｉｔｙｓｔｒｕｃｔｕｒｅｆｕｎｃｔｉｏｎｏｆｏｒｄｅｒｎ”ｆｏｒｔｕｒｂｕｌｅｎｔｆｌｏｗｓｉｓｄｅｆｉｎｅｄａｓ〈ΔＶ(ｒ) ｎ〉 ,ｗｈｅｒｅΔＶ(ｒ) =Ｖ(ｘ ｒ) -Ｖ(ｘ)ｉｓｔｈｅｖｅｌｏｃｉｔｙｃｏｍｐ…     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅴ)——POLAR THERMOMECHANICAL CONTINUA

The purpose is to reestablish rather complete basic balance equations and boundary conditions for polar thermomechanical continua based on the restudy of the traditional theories of micropolar thermoelasticity and thermopiezoelectricity. The equations of motion and the local balance equation of energy rate for micropolar thermoelasticity are derived from the rather complete principle of virtual power. The equations of motion, the balance equation of entropy and all boundary conditions are derived from the rather complete Hamilton principle. The new balance equations of momentum and energy rate which are essentially different from the existing results are presented. The corresponding results of micromorphic thermoelasticity and couple stress elastodynamics may be naturally obtained by the transition and the reduction from the micropolar case, respectively. Finally, the results of micropolar thermopiezoelectricity are directly given. Contributed by DAI Tian-min, Original Member of Editorial Committee, AMM Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001) Biography: DAI Tian-min (1931-)     

MIXED FINITE ELEMENT METHODS FOR THE SHALLOW WATER EQUATIONS INCLUDING CURRENT AND SILT SEDIMENTATION （Ⅰ）——THE CONTINUOUS-TIME CASE

An initial-boundary value problem for shallow equation system consisting of water dynamics equations, silt transport equation, the equation of bottom topography change, and of some boundary and initial conditions is studied, the existence of its generalized solution and semidiscrete mixed finite element (MFE) solution was discussed, and the error estimates of the semidiscrete MFE solution was derived. The error estimates are optimal.     

MIXED FINITE ELEMENT METHODS FOR THE SHALLOWWATER EQUATIONS INCLUDING CURRENT AND SILTSEDIMENTATION （Ⅱ）——THE DISCRETE-TIMECASE ALONG CHARACTERISTICS

The mixed finite element(MFE) methods for a shallow water equation systemconsisting of water dynamics equations, silt transport equation, and the equation of bottomtopography change were derived. A fully discrete MFE scheme for the discrete-time alongcharacteristics is presented and error estimates are established. The existence andconvergence of MFE solution of the discrete current velocity, elevation of the bottomtopography, thickness of fluid column, and mass rate of sediment is demonstrated.     

Crack problems of piezoelectric materials

This paper presents an analysis of crack problems in homogeneous piezoelectrics or on the interfaces between two dissimilar piezoelectric materials based on the continuity of normal electric displacement and electric potential across the crack faces. The explicit analytic solutions are obtained for a single crack in piezoelectrics or on the interfaces of piezoelectric bimaterials. A class of boundary problems involving many cracks is also solved. For homogeneous materials it is found that the normal electric displacementD ₂ induced by the crack is constant along the crack faces which depends only on the applied remote stress field. Within the crack slit, the electric fields induced by the crack are also constant and not affected by the applied electric field. For the bimaterials with realH, the normal electric displacementD ₂ is constant along the crack faces and electric fieldE ₂ has the singularity ahead of the crack tip and a jump across the interface. The project is supported by the National Natural Science Foundation of China(No. 19704100) and the Natural Science Foundation of Chinese Academy of Sciences(No. KJ951-1-201).     

On the formal solution of initial value problem of Navier-Stokes equation

Ｉｎｒｅｆｅｒｅｎｃｅ [1 ] ,ｗｅｄｉｓｃｕｓｓｅｄｔｈｅｉｎｓｔａｂｉｌｉｔｙｏｆＮａｖｉｅｒ＿ＳｔｏｋｅｓｅｑｕａｔｉｏｎｏｎＲ3×Ｒ ,ａｎｄ ,ｉｎｔｈｅｉｌｌｕｓｔｒａｔｉｏｎｏｆｉｔ,ｗｅｐｒｅｓｅｎｔｅｄｓｏｍｅｅｘａｍｐｌｅｓｉｎｔｈｅｆｏｒｍｏｆｅｘａｃｔｓｏｌｕｔｉｏｎ .Ｔｈｅｂａｓｉｓｏｆｔｈｅｃｏｎｓｔｒｕｃｔｉｏｎｏｆｔｈｅｍｉｓｔｈｅ“ｅｑｕａｔｉｏｎｓｅｃｏｎｄａｉｒｅ”ｏｆｔｈｅｅｑｕａｔｉｏｎ .Ｉｎｆａｃｔ,ｔｈｅｓｅｅｘａｃｔｓｏｌｕｔｉｏｎｓａｒｅｓｏｍｅｌｉｍｉｔ…     

RESTUDY OF COUPLED FIELD THEORIES FOR MICROPOLAR CONTINUA (Ⅱ)-THERMOPIEZOELECTRICITY AND MAGNETOTHERMOELASTICITY

The theories of thermopiezoelectricity and magnetoelasticity for micropolar continua have been systematically developed by W. Nowacki. In this paper, the theories are restudied. The reason why they were restricted to linear cases is analyzed. The more general conservation principle of energy, energy balance equation and Hamilton principle of thermopiezoelectricity and magnetoelasticity for micropolar continua are established. The corresponding complete equations of motion and boundary conditions as well as balance equations of energy rate for local and nonlocal micropolar thermopiezoelectricity and magnetothermoelasticity are naturally derived. By means of two new functionals and total variation the boundary conditions of displacement, microrotation, electric potential and temperature are also given. Foundation item: the National Natural Science Foundation of China (10072024); the International Cooperation Project of the NSFC (10011130235) and the DFG (51520001); the Research Foundation of the Liaoning Education Committee (990111001) Biography: DAI Tian-min (1931-)     

On the stability boundary of hamiltonian systems

The criterion for the points in the parameter space being on the stability boundary of linear Hamiltonian system depending on arbitrary numbers of parameters was given, through the sensitivity analysis of eigenvalues and eigenvectors. The results show that multiple eigenvalues with Jordan chain take a very important role in the stability of Hamiltonian systems. Foundation item: the National Natural Science Foundation of China (10072012); the National Natural Science Foundation of Russia Biography: QI Zhao-hui (1964-)     

Generalized fatigue constant life curve and two-dimensional probability distribution of fatigue limit

ＩｎｔｒｏｄｕｃｔｉｏｎＷｈｅｎａｃｏｍｐｏｎｅｎｔｆｏｒｉｎｓｔａｎｃｅｔｈｅｔｒａｎｓｍｉｓｓｉｏｎｓｈａｆｔａｎｄｔｈｅｖｉｂｒａｔｉｏｎｃｏｍｐｏｎｅｎｔ,ｅｔｃ.ｅｎｄｕｒｅｒａｔｈｅｒｌｏｗｓｔｒｅｓｓｌｅｖｅｌａｎｄｌｏｎｇｓｔｒｅｓｓｃｙｃｌｅｓ,ｉｔｓｓａｆｅｔｙｉｓｃｏｎｔｒｏｌｌｅｄｂｙｆａｔｉｇｕｅｓｔｒｅｓｓａｎｄｉｔｃａｎｂｅｄｅｓｉｇｎｅｄａｃｃｏｒｄｉｎｇｔｏｔｈｅｉｎｆｉｎｉｔｅｌｉｆｅｄｅｓｉｇｎｍｅｔｈｏｄｏｆｈｉｇｈｃｙｃｌｅｆａｔｉｇｕｅ .Ｗｈｅｎａｃｏｍ…     

A NOTE ON BIFURCATIONS OF u″+μ(u-uk)=0(4≤k∈Z+)

Bifurcations of one kind of reaction-diffusion equations, u″+μ(u-u^k)=0(μ is a parameter,4≤k∈Z⁺), with boundary value condition u(0)=u(π)=0 are discussed. By means of singularity theory based on the method of Liapunov-Schmidt reduction, satisfactory results can be acquired.     

MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H∞ DECENTRALIZED CONTROL SYSTEMS （ I ）

When using H∞ techniques to design decentralized controllers for large systems,the whole system is divided into subsystems, which are analysed using H∞ control theorybefore being recombined. An analogy was established with substructural analysis instructural mechanics, in which H∞ decentralized control theory corresponds to substructuralmodal synthesis theory so that the optimal H∞ norm of the whole system corresponds to thefundamental vibration frequency of the whole structure. Hence, modal synthesismethodology and the extended Wittrick-Williams algorithm were transplanted from structuralmechanics to compute the optimal H∞ norm of the control system. The orthogonality and theexpansion theorem of eigenfunctions of the subsystems H∞ control are presented in part(I) of the paper. The modal synthesis method for computation of the optimal H∞ norm ofdecentralized control systems and numerical examples are presented in part (Ⅱ).     

Asymptotic fields for interface crack in elastic-plastic material

Exact mathematical analyses are presented for interface crack between dissimilar elastic-plastic materials. The deformation theory of plasticity is used. For two kinds of boundary conditions on crack faces: (1) traction free and (2) frictionless contact, the asymptotic separable solutions of the HRR type with full continuity are obtained, which exist only for special mixity parameterM ^p. For any assignedM ^p, the separable solutions of the HRR type which contained weak discontinued line are further obtained. All of our results not only satisfy the continuity of displacements and that of tractions on the interface, but also they are free of oscillatory singularity and interpenetration of crack faces.This investigation is supported by the National Natural Science Foundation of China     

Three dimensional tide‐induced circulation model on a triangular mesh

In this paper a triangular mesh, which is generated by an automatic triangular mesh generator, is used to calculate the tide‐induced residual current in the Bohai Sea, China. The generator can modify the distribution of the node according to the water depth, thus ensuring the uniform distribution of the Courant number. The three dimensional nonlinear tide equation is employed to get the Eularian residual current and Stokes' drift. Then the Lagrangian residual current is obtained by adding the above two values. It has been proved in other papers that the Lagrangian residual current is more proper to represent the circulation and a numerical example is given. The application of these methods to the Bohai Sea shows that the results are in accordance with those obtained before. Copyright © 2002 John Wiley & Sons, Ltd.