SPLITTING OF THE SPECTRAL DOMAIN ELECTRICAL DYADIC GREEN’S FUNCTION IN CHIRAL MEDIA

A new method of formulating dyadic Green‘s functions in lossless , reciprocal and unbounded chiral medium was presented. Based on Helmholtz theorem and the nondivergence and irrotational splitting of dyadic Dirac delta-function was this method, the electrical vector dyadic Green‘s function equation was first decomposed into the nondivergence electrical vector dyadic Green‘s function equation and irrotational electrical vector dyadic Green‘s function equation, and then Fourier‘s transformation was used to derive the expressions of the non-divergence and irrotational component of the spectral domain electrical dyadic Green‘s function in chiral media. It can avoid having to use the wavefield decomposition method and dyadic Green‘s function eigenfunction expansion technique that this method is used to derive the dyadic Green‘s functions in chiral media.     

IMPULSIVE CONTROL FOR THE STABILIZATION AND SYNCHRONIZATION OF LUR＇ E SYSTEMS

An impulsive control scheme of the Lur‘e system and several theorems on stability of impulsive control systems was presented, these theorems were then used to find the conditions under which the Lur‘e system can be stabilized by using impulsive control with varying impulsive intervals. The parameters of Lur‘e system and impulsive control law are given, a theory of impulsive synchronization of two Lur‘e system is also presented. A numerical example is used to verify the theoretical result.     

The Bounds of the General M and J Sets and the Estimations for the Hausdorff's Dimension of the General J Set

The bounds of the general M and J sets were analytically offered. Some of the bounds were optimal in certain meaning. It not only solved the primary problem of the construction of fractal sets by escape time algorithm, and followed from the conclusion, but also offered two estimations of some special Julia set’s Hausdorff’s dimension by approximate linearization method. Foundation item: the National Natural Science Foundation of China (69974008). Biography: LIX Xiang-dong (1967-), Associate Professor, Doctor     

A CLASS OF ALTERNATING GROUP METHODOF BURGERS＇ EQUATION

Some new Saul‘ yev type asymmetric difference schemes for Burgers’ equation isgiven, by the use of the schemes, a kind of alternating group four points method for solvingnonlinear Burgers‘ equation is constructed here. The basic idea of the method is that thegrid points on the same time level is divided into a number of groups, the differenceequations of each group can be solved independently, hence the method with intrinsicparallelism can be used directly on parallel computer. The method is unconditionally stableby analysis of linearization procedure. The numerical experiments show that the method has good stability and accuracy.     

ASYMPTOTIC ANALYSIS OF MODE Ⅱ STATIONARY GROWTHCRACK ON ELASTIC-ELASTIC POWER LAWCREEPING BIMATERIAL INTERFACE

A mechanical model was established for mode Ⅱ interfacial crack static growingalong an elastic-elastic power law creeping bimaterial interface. For two kinds of boundaryconditions on crack faces, traction free and frictional contact, asymptotic solutions of thestress and strain near tip-crack were given. Results derived indicate that the stress andstrain have the same singularity, there is not the oscillatory singularity in the field; thecreep power-hardening index n and the ratio of Young‘s module notably influence the crack-tip field in region of elastic power law creeping material and n only influences distribution ofstresses and strains in region of elastic material. When n is bigger, the creepingdeformation is dominant and stress fields become steady, which does not change with n.Poisson‘s ratio does not affect the distributing of the crack-tip field.     

The high accuracy explicit difference scheme for solving parabolic equations 3-dimension

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STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM (Ⅰ)

Based on the mathematical model of a kind of complicated financial system, all possible things that the model shows in the operation of our country’s macro-financial system were analyzed, such as balance, stable periodic, fractal, Hopf-bifurcation, the relationship between parameters and Hopf-bifurcations,and chaotic motion etc. By the changes of parameters of all economic meanings, the conditions on which the complicated behaviors occur in such a financial system, and the influence of the adjustment of the macro-economic policies and adjustment of some parameter on the whole financial system behavior were analyzed. This study will deepen people’s understanding of the lever function of all kinds of financial policies.     

Waverider configurations derived from general conical flowfields

A method based on the computational fluid dynamics (CFD) is presented for a flexible waverider’s design. The generating bodies of this method could be any cones. In addition, either the leading edge or the profile of the scramjet’s inlet is used as the waverider’s definition curve, parameterized by the quadric function, the sigmoid function or the B-spline function. Furthermore, several numerical examples are carried out to validate the method and the relevant codes. The CFD results of the configurations show that all the designs are successful. Moreover, primary suggestions are proposed for practical design by comparing the geometrical and aerodynamic performances of the cone-derived waveriders at Mach 6. The project supported by the National Natural Science Foundation of China (10502053, 10372106 and 10402043), K. C. Wong Education Foundation of Hong Kong, the Key Laboratory of High Temperature Gas Dynamics of Chinese Academy of Sciences and the State Key Laboratory of Structural Analysis for Industrial Equipment of Dalian University of Technology.     

Global existence and blow-up phenomena of classical solutions for the system of compressible adiabatic flow through porous media

By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blowup phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘ small ‘ solution.     

RESEARCH OF REGULARITY OF THROWING MOVEMENT FOR SOLID PARTICLE ON THE SHAKER’S SCREEN

By means of Delta-function & unit step function to express the force of solid particle on plane inertial shaker’s screen, an mathematical model of the differential equation type was set up and solved. According to analysis of the solution, the relation is given between the throw period & displacement with the parameters of shaker design & solid particle. The method of numerical value calculation & analysis for the relation is given too.     

THE EXISTENCE OF PERIODIC SOLUTIONS FOR A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS AND THEIR APPLICATION

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THE CONSERVATION LAW OF NONHOLONOMIC SYSTEM OF SECOND-ORDER NON-CHETAVE’S TYPE IN EVENT SPACE

The conservation law of nonholonomic system of second-order non-Chataev’s type in event space is studied. The Jourdain’s principle in event space is presented. The invariant condition of the Jourdain’s principle under infinitesimal transformation is given by introducing Jourdain’s generators in event space. Then the conservation law of the system in event space is obtained under certain conditions. Finally a calculating example is given.     

Numerical simulation of blood flow and interstitial fluid pressure in solid tumor microcirculation based on tumor-induced angiogenesis

A coupled intravascular–transvascular–interstitial fluid flow model is developed to study the distributions of blood flow and interstitial fluid pressure in solid tumor microcirculation based on a tumor-induced microvascular network. This is generated from a 2D nine-point discrete mathematical model of tumor angiogenesis and contains two parent vessels. Blood flow through the microvascular network and interstitial fluid flow in tumor tissues are performed by the extended Poiseuille’s law and Darcy’s law, respectively, transvascular flow is described by Starling’s law; effects of the vascular permeability and the interstitial hydraulic conductivity are also considered. The simulation results predict the heterogeneous blood supply, interstitial hypertension and low convection on the inside of the tumor, which are consistent with physiological observed facts. These results may provide beneficial information for anti-angiogenesis treatment of tumor and further clinical research. The project supported by the National Natural Science Foundation of China (10372026).     

Numerical calculation for the coefficients of stokes harmonic waves of high order

This paper has reformulated the mathematical model and boundary conditions in the semi-physical plan (x,ψ)by using W.H.Hui’s method and suggested two new ways of numerical calculation for the coefficients of Stokes harmonic waves of high order. By transforming the perturbation parameter? into a new one we we rejind Cokelet’s results (1977) of phase speed and semi-waveheight expressions.     

Stability and vibration of a helical rod constrained by a cylinder

The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler’s angles as variables describing the attitude of the cross section. The existence conditions of helical equilibrium under constraint are discussed as a special configuration of the rod. The stability of the helical equilibrium is discussed in the realms of statics and dynamics, respectively. Necessary conditions for the stability of helical rod are derived in space domain and time domain, and the difference and relationship between Lyapunov’s and Euler’s stability concepts are discussed. The free frequency of flexural vibration of the helical rod with cylinder constraint is obtained in analytical form. The project supported by the National Natural Science Foundation of China (10472067). The English text was polished by Yunming Chen.     

Positive solutions to （n-1,1） m-point boundary value problems with dependence on the first order derivative

Using the extension of Krasnoselskii＇s fixed point theorem in a cone, we prove the existence of at least one positive solution to the nonlinear nth order m-point boundary value problem with dependence on the first order derivative. The associated Green＇s function for the nth order m-point boundary value problem is given, and growth conditions are imposed on the nonlinear term f which ensures the existence of at least one positive solution. A simple example is presented to illustrate applications of the obtained results.     

A version of Hill＇s lemma for Cosserat continuum

On the basis of Hill＇s lemma for classical Cauchy continuum, a version of Hill＇s lemma for micro-macro homogenization modeling of heterogeneous Cosserat continuum is presented in the flame of average-field theory. The admissible boundary conditions required to prescribe on the representative volume element for the modeling are extracted and discussed to ensure the satisfaction of Hill-Mandel energy condition and the first-order average field theory.