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| 1 | High-Order Models of Nonlinear and Dispersive Wave in Water of Varying Depth with Arbitrary Sloping Bottom显示文摘High-order models with a dissipative term for nonlinear and dispersive wave in water of va-rying depth with an arbitrary sloping bottom are presented in this article.First,the formal derivations toany high order of μ(=h/λ,depth to deep-water wave length ratio)and ε(=α/h,wave amplitude todepth ratio)for velocity potential,particle velocity vector,pressure and the Boussinesq-type equations forsurface elevation η and horizontal velocity vector U at any given level in water are given.Then,the exactexplicit expressions to the fourth order of μ are derived.Finally,the linear solutions of η,U,C(phase ce-lerity)and C_g(group velocity)for a constant water depth are obtained.Compared with the Airy theory,excellent results can be found even for a water depth as large as the wave legnth.The present high-ordermodels are applicable to nonlinear regular and irregular waves in water of any varying depth(from shal-low to deep)and bottom slope(from mild to steep). | Hong Guangwen Professor, Coastal and Ocean Engineering Research Institute, Hohai University, Nanjing 210024, P. R. China. | 1997 | China Ocean Engineering1997，12，3： | 26 |
| 2 | A Survey of Unbalanced Flow Diagnostics and Their Application显示文摘This paper presents an extensive survey of the most commonly used tools for diagnosing unbalanced flow in the atmosphere, namely the Lagrangian Rossby number, Psi vector, divergence equation, nonlinear balance equation, generalized omega-equation, and departure from fields obtained by potential vorticity (PV) inversion. The basic thoery, assumptions as well as implementation and limitations for each of the tools are all discussed. These tools are applied to high-resolution mesoscale model data to assess the role of unbalanced dynamics in the generation of a mesoscale gravity wave event over the East Coast of the United States. Comparison of these tools in this case study shows that these various methods agree to a large extent with each other though they differ in details. | Fuqing Zhang Steven E. Koch Christopher A. Davis and Michael L. Kaplan | 2000 | Advances in Atmospheric Sciences2000，17，2： | 22 |
| 3 | MAXIMUM PRINCIPLE FOR OPTIMAL CONTROLPROBLEM OF FULLY COUPLEDFORWARD-BACKWARD STOCHASTIC SYSTEMS显示文摘The optimal control problem of fully coupled forward-backward stochastic systems is put forward. A necessary condition, called maximum principle, for an optimal control of the problem with the control domain being convex is proved. | WU Zhen(College of Mathematics and System Sciences, Shandong University, Ji’nan 250100, China) | 1998 | Systems Science and Mathematical Sciences1998，11，3： | 21 |
| 4 | Finite difference scheme based on proper orthogonal decomposition for the nonstationary Navier-Stokes equations显示文摘The proper orthogonal decomposition(POD)and the singular value decomposition(SVD) are used to study the finite difference scheme(FDS)for the nonstationary Navier-Stokes equations. Ensembles of data are compiled from the transient solutions computed from the discrete equation system derived from the FDS for the nonstationary Navier-Stokes equations.The optimal orthogonal bases are reconstructed by the elements of the ensemble with POD and SVD.Combining the above procedures with a Galerkin projection approach yields a new optimizing FDS model with lower dimensions and a high accuracy for the nonstationary Navier-Stokes equations.The errors between POD approximate solutions and FDS solutions are analyzed.It is shown by considering the results obtained for numerical simulations of cavity flows that the error between POD approximate solution and FDS solution is consistent with theoretical results.Moreover,it is also shown that this validates the feasibility and efficiency of POD method. | Zhen-dong LUO Rui-wen WANG Jiang ZHU | 2007 | Science China Mathematics2007，50，8： | 20 |
| 5 | Convergence on the iteration of Halley family in weak conditions显示文摘WE have obtained the convergence theorems of the iteration of Halley family by the point estimate of Smale. In the point estimate, map f which is desired to be solved is presumed to be analytic in some proper neighborhood at the initial value z0. From the viewpoint of | WANG XinghuaDepartment of Mathematics, Hangzhou University, Hangzhou 310028, China | 1997 | Chinese Science Bulletin1997，42，7： | 19 |
| 6 | NONLINEAR STABILITY OF NATURAL RUNGE-KUTTA METHODS FOR NEUTRAL DELAY DIFFERENTIAL EQUATIONS显示文摘This paper first presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDEs). Then the numerical analogous results, of the natural Runge-Kutta (NRK) methods for the same class of nonlinear NDDEs, are given. In particular, it is shown that the (k, l)-algebraic stability of a RK method for ODEs implies the generalized asymptotic stability and the global stability of the induced NRK method. | Cheng-jian Zhang(Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, P. R. China) | 2002 | Journal of Computational Mathematics2002，20，6： | 18 |
| 7 | 关于二阶变系数线性微分方程求解法的研究显示文摘求二阶变系数线性微分方程的解,至今为止没有一种成规的方法.推导二阶变系数线性微分方程的一般解法.从特殊型和一般型的二阶变系数线性微分方程进行研究,从方程的自身特点出发,巧妙构造结构,利用降阶法把二阶变系数线性微分方程的求解问题转嫁为求一阶线性微分方程的解.只须构造结构系数函数即可解决二阶变系数线性微分方程通解或特解.利用构造结构的系数函数,再用降阶法可以求得二阶变系数线性微分方程通解或特解的一般方法. | 李高 常秀芳 | 2010 | 河北北方学院学报(自然科学版)2010，26，6： | 18 |
| 8 | Computational uncertainty principle in nonlinear ordinary differential equations (I)——Numerical results显示文摘In a majority of cases of long-time numerical integration for initial-value problems, roundoff error has received little attention. Using twenty-nine numerical methods, the influence of round-off error on numerical solutions is generally studied through a large number of numerical experiments. Here we find that there exists a strong dependence on machine precision (which is a new kind of dependence different from the sensitive dependence on initial conditions), maximally effective computation time (MECT) and optimal stepsize (OS) in solving nonlinear ordinary differential equations (ODEs) in finite machine precision. And an optimal searching method for evaluating MECT and OS under finite machine precision is presented. The relationships between MECT, OS, the order of numerical method and machine precision are found. Numerical results show that round-off error plays a significant role in the above phenomena. Moreover, we find two universal relations which are independent of the types of ODEs, initial | 李建平 曾庆存 丑纪范 | 2000 | Science China(Technological Sciences)2000，43，5： | 18 |
| 9 | Finite element formulation based on proper orthogonal decomposition for parabolic equations显示文摘A proper orthogonal decomposition (POD) method is applied to a usual finite element (FE) formulation for parabolic equations so that it is reduced into a POD FE formulation with lower dimensions and enough high accuracy. The errors between the reduced POD FE solution and the usual FE solution are analyzed. It is shown by numerical examples that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is also shown that this validates the feasibility and efficiency of POD method. | LUO ZhenDong CHEN Jing SUN Ping YANG XiaoZhong | 2009 | Science China Mathematics2009，52，3： | 16 |
| 10 | AN OSCILLATION CRITERIA FOR SECOND ORDERFUNCTIONAL EQUATIONS显示文摘This paper is concerned with the oscillation of second order linear functional equations of the form x(g(t)) P(t)x(t) + Q(t)x(g2(t)). where P,Q.g : [t0,∞ ] -R+ =[0, ∞] are given real valued functions such that g(t) t,limt-∞g(t) =∞. It is proved here that when 0 ≤m := lim inft-∞Q(t)P(g(t)) ≤1/4 all solutions of this equation oscillate if the condition is satisfied. It should be emphasized that the condition (*) can not be improved in some sense. | 申建华 IP. Stavroulakis | 2002 | Acta Mathematica Scientia2002，22，1： | 14 |
| 11 | FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH BROWNIAN MOTION AND POISSON PROCESS显示文摘Existence and uniqueness results of the solution to fully coupled forward-backward stochastic defferential equations with Brownian motion and Poisson process are obtained. Many stochastic Hamilton systems arising in stochastic optimal control systems with random jump and in mathemstical finance with security price discontinuously changing can be treated with these results. The continuity of the solution depending on parameters is also proved in this paper. | 吴臻 | 1999 | Acta Mathematicae Applicatae Sinica1999，15，4： | 14 |
| 12 | LAGUERRE PSEUDOSPECTRAL METHOD FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS显示文摘AbstractThe Laguerre Gauss-Radau interpolation is investigated. Some approximation results are obtained. As an example, the Laguerre pseudospectral scheme is constructed for the BBM equation. The stability and the convergence of proposed scheme are proved. The numerical results show the high accuracy of this approch. | Cheng-long Xu Ben-yu Guo | 2002 | Journal of Computational Mathematics2002，20，4： | 13 |
| 13 | Partial Regularity for Two Dimensional Landau-Lifshitz Equations | Chen Yunmei Ding Shijin Guo Doling Department of Mathematics, University of Florida, Gainesville, FL32611, U.S.A. Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing, 100088, China | 1998 | Acta Mathematica Sinica,English Series1998，14，3： | 12 |
| 14 | A PSEUDOSPECTRAL METHOD FOR VORTICITY EQUATIONS ON SPHERICAL SURFACE显示文摘The pseudospectral method for solving vorticity equations on spherical surface is discussed. An interpolation procedure, which is different from the usual onesl is proposed. Based on such an interpolation, the pseudospectral scheme is constructed. Its generalized stability and convergence are analyzed rigorously. The theoretical analysis and computational skills can also be applied to other nonlinear partial differential equations defined on spherical surface. | 曹卫明 郭本瑜 | 1997 | Acta Mathematicae Applicatae Sinica1997，13，2： | 11 |
| 15 | NumericalmodelforsolvingBousiinesq-typeequations:comparisonandvalidation显示文摘NumericalmodelforsolvingBousiinesq-typeequations:comparisonandvalidationZouShiliandXuBenhe(ReceivedMay20,1997;acceptedAugust1... | Zou Shili and Xu Benhe (Received May 20, 1997 accepted August 13, 1997) | 1998 | Acta Oceanologica Sinica1998，17，3： | 11 |
| 16 | Variational principles and governing equations in nano-dielectrics with the flexoelectric effect显示文摘The flexoelectric effect is very strong and coupled with large strain gradients for nanoscale dielectrics. At the nanoscale, the electrostatic force cannot be ignored. In this paper, we have established the electric enthalpy variational principle for nanosized dielectrics with the strain gradient and the polarization gradient effect, as well as the effect of the electrostatic force. The complete governing equations, which include the effect of the electrostatic force, are derived from this variational principle, and based on the principle the generalized electrostatic stress is obtained, the generalized electrostatic stress contains the Maxwell stress corresponding to the polarization and strain, and stress related to the polarization gradient and strain gradient. This work provides the basis for the analysis and computations for the electromechanical problems in nanosized dielectric materials. | HU ShuLing & SHEN ShengPing* MOE Key Laboratory for Strength and Vibration, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China | 2010 | Science China(Physics,Mechanics & Astronomy)2010，53，8： | 11 |
| 17 | THE OPCM STRAIN GAUGES FOR STRAIN AND STRESS MEASUREMENT OF ORTHOTROPIC MATERIAL STRUCTURES显示文摘The orthotropic mechanical sensor of piezoelectric composite material made from piezoelectricceramic and resin materials and their sensing mechanism are presented.The sensing equations of the ad-hered-and embedded-type sensing units are deduced,which are used to detect the stresses in orthotropicmaterial structures.The surface strain of the orthogonal plate is measured under the action of the planar stressfield,and the error is analyzed. | Luo Ying Tao Baoqi | 2000 | Acta Mechanica Solida Sinica2000，13，4： | 11 |
| 18 | OSCILLATION AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF DELAY DIFFERENTIAL EQUATIONS WITH IMPULSES显示文摘OSCILLATIONANDASYMPTOTICBEHAVIOROFSOLUTIONSOFDELAYDIFFERENTIALEQUATIONSWITHIMPULSESShenJianhua(申建华)&WangZhicheng(王志成)(HunanUn... | 申建华 王志成 | 1994 | Annals of Differential Equations1994，10，1： | 10 |
| 19 | EXISTENCE OF NON-TRIVIAL SOLUTION FOR SUPERLINEAR SYSTEM OF INTEGRAL EQUATIONS AND ITS APPLICATIONS显示文摘1.IntroductionTherearealotofresultsaboutHammersteinintegralequations(see[1]),butsupen-linearproblemsaredifficult;thereareonlyafewresultsaboutit.In[2,3]theauthorsstudysuperliniearintegralequations;in[4]theauthorsstudysystemofsuperlinearintegralequatio... | 张志涛 | 1999 | Acta Mathematicae Applicatae Sinica1999，15，2： | 10 |
| 20 | Numerical simulation of aerodynamic interaction for a tilt rotor aircraft in helicopter mode显示文摘A rotor CFD solver is developed for simulating the aerodynamic interaction phenomenon among rotor, wing and fuselage of a tilt rotor aircraft in its helicopter mode. The unsteady Navier–Stokes equations are discretized in inertial frame and embedded grid system is adopted for describing the relative motion among blades and nacelle/wing/fuselage. A combination of multi-layer embedded grid and ‘‘extended hole fringe' technique is complemented in original grid system to tackle grid assembly difficulties arising from the narrow space among different aerodynamic components, and to improve the interpolation precision by decreasing the cell volume discrepancy among different grid blocks. An overall donor cell searching and automatic hole cutting technique is used for grid assembly, and the solution processes are speeded up by introduction of Open MP parallel method. Based on this solver, flow fields and aerodynamics of a tilt rotor aircraft in hover are simulated with several rotor collective angles, and the corresponding states of an isolated rotor and rotor/wing/fuselage model are also computed to obtain reference solution.Aerodynamic interference influences among the rotor and wing/fuselage/nacelle are analyzed,and some meaningful conclusions are drawn. | Ye Liang Zhang Ying Yang Shuo Zhu Xinglin Dong Jun | 2016 | Chinese Journal of Aeronautics2016，29，4： | 10 |
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