JORDAN CANONICAL FORMS OF MATRICES OVER QUATERNION FIELD

ＪＯＲＤＡＮＣＡＮＯＮＩＣＡＬＦＯＲＭＳＯＦＭＡＴＲＩＣＥＳＯＶＥＲＱＵＡＴＥＲＮＩＯＮＦＩＥＬＤ￥ＣｈｅｎＬｏｎｇｘｕａｎ（陈龙玄）ＨｏｕＲｅｎｍｉｎ（侯仁民）ＷａｎｇＬｉａｎｇｔａｏ（王亮涛）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｙａ...     

Gram determinant solutions to nonlocal integrable discrete nonlinear Schrödinger equations via the pair reduction

In this paper, Gram determinant solutions of local and nonlocal integrable discrete nonlinear Schrödinger (IDNLS) equations are studied via the pair reduction. A generalized IDNLS equation is firstly introduced which possesses the single Casorati determinant solution. Two kinds of Gram determinant solutions are presented from Casorati determinant ones due to the gauge freedom. The different pair constraint conditions for wave numbers are imposed and then solutions of local and nonlocal IDNLS equations are derived in terms of Gram determinant.     

ORTHOGONAL POLYNOMIALS AND DETERMINANT FORMULAS OF FUNCTION-VALUED PADE-TYPE APPROXIMATION USING FOR SOLUTION OF INTEGRAL EQUATIONS

To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Pade-type approximation is denned. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Pade-type approximation are explicitly given.     

Orthogonal polynomials and determinant formulas of function-valued Padé-type approximation using for solution of integral equations

To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given. Project supported by the National Natural Science Foundation of China (No.10271074)     

Partial roll-up of a viscoelastic Kármán street

The instantaneous velocity field of a circular cylinder wake is built using a PIV technique when a small amount of viscoelastic liquid is introduced through the cylinder. It is shown that the viscoelastic fluid slows down the vorticity concentration and produces a street of partially rolled-up vortices. The underlying mechanism appears very analogous to that of a surface tension in the Kelvin–Helmholtz instability. The partial roll-up is studied in terms of the Weiss determinant. This quantity is a local measurement of the spatial separation between the strain and vorticity. In the viscoelastic wake, the Weiss determinant reaches much lower values than in the Newtonian wake. This result shows that the elasticity prevents the clear separation between vorticity and strain during the roll-up process. Since the Weiss determinant is directly related to the pressure field, it suggests that elasticity can drastically modify the pressure levels even when vorticity and strain levels are unaffected.     

Change of Sign of the Corrector’s Determinant for Homogenization in Three-Dimensional Conductivity

In this paper we study the positivity of the determinant of the local electric field in a conducting composite. We know by [1] that the positivity holds true in two dimensions for any periodic structure. Using a different approach from [11] we prove that is also the case for a laminate microstructure in any dimension. However, and this is the main result of the paper, we provide an example of a two-phase three-dimensional periodic composite for which the determinant changes sign.     

The effect of virtual mass on the basic equations for unsteady one-dimensional heterogeneous flows

A separated two-component flow model is presented which includes virtual mass forces coupling the momentum equations of the two components. It is shown that for physically realistic situations four real roots of the characteristics determinant can exist. These are associated with the acoustic propagation velocities and the fiow velocities of the constitutive phases. Direct analytical solution of the full characteristic determinant is difficult. However, for low Mach number flows an acoustic propagation velocity is obtained which falls between the well-known true separated and homogeneous wave speeds, and compares favorably with experimental data for glass/water and air/water mixtures.     

On the derivation of the constitutive equation of the simple fluid from that of a simple material

It is shown, by the use of the symmetry group of a fluid, that the stress in an elastic fluid depends on the current value of the deformation gradient through the absolute value of the determinant of the deformation gradient, whereas in a simple fluid it depends on this value of the determinant and the history of the relative deformation gradient and nothing else. This derivation is then used to show some of the errors in the criticisms made about the work of Noll. Additionally, a lacuna in Noll's derivation is removed to overcome the only valid criticism made about this theory of simple fluids.     

An evolutionary search technique to determine natural frequencies and mode shapes of composite Timoshenko beams

Natural frequencies and mode shapes of composite Timoshenko beams are determined by a diversity guided evolutionary algorithm (DGEA) with different boundary conditions. After applying boundary conditions, frequency equation is obtained in determinant form. Then, natural frequencies and consequently mode shapes are obtained using DGEA where the absolute value of determinant is the subject of optimization. Advantages of employing DGEA are: first, all natural frequencies are produced in a simple run, second, its simplicity for implementation and third, the procedure is not computationally prohibitive. Results clearly show the applicability of the proposed method for obtaining natural frequencies and mode shapes.     

Die numerische Bestimmung stabiler Gleichgewichtslagen von Vielkörper-Satellitensystemen

Übersicht Für Satelliten, die aus vielen gelenkig gekoppelten starren Körpern oder Gyrostaten bestehen, lassen sich die Gleichgewichtslagen auf Kreisbahnen im Gravitationsfeld nur in speziellen Fällen analytisch bestimmen. In der vorliegenden Arbeit wird ein numerisches Verfahren geschildert, das stabile Gleichgewichtslagen für beliebig aufgebaute Systeme bestimmt. Dabei werden eine einfache analytische Formulierung für Dämpfungsmomente in den Kugelgelenken eines Vielkörper-Satelliten sowie das Energieintegral der Bewegungsgleichungen bei kreisförmiger Umlaufbahn angegeben. Die Eigenfrequenzen kleiner Schwingungen um die Gleichgewichtslage erweisen sich als Doppelwurzeln einer reellen Frequenzdeterminante.

---

Summary Equilibrium positions for a satellite consisting of many interconnected rigid bodies or gyrostats moving in a circular orbit about a center of gravity can be determined analytically only in special cases. In this publication a numerical method is described that allows to calculate stable equilibrium positions for systems of arbitrary complexity. For this purpose a simple analytical formulation is developed for the treatment of damping moments in the spherical joints of a many-body satellite. The energy integral is given for the equations of motion in a circular orbit. The eigenfrequencies of small oscillations about the equilibrium position are shown to be double roots of a real frequency determinant.

     

Hopf分岔的代数判据及其在车辆动力学中的应用

利用Hurwitz行列式,给出平衡点失稳而发生Hopf分岔的代数判定准则和计算方法,这一方法将Hopf分岔点的求解转化为一个非线性方程的求解问题,从而克服了以前方法在计算Hopf分岔点时,对于参数的每一次变化通过求特征根并判定特征根的实部是否为零的庞大工作量。应用这一方法,我们进行了非线性车辆系统蛇行运动稳定性的研究,得到了轮对系统发生蛇行运动的临界速度的解析表达式。     

Evans Functions,Jost Functions,and Fredholm Determinants

The principal results of this paper consist of an intrinsic definition of the Evans function in terms of newly introduced generalized matrix-valued Jost solutions for general first-order matrix-valued differential equations on the real line, and a proof of the fact that the Evans function, a finite-dimensional determinant by construction, coincides with a modified Fredholm determinant associated with a Birman–Schwinger-type integral operator up to an explicitly computable nonvanishing factor.     

Pore-Structure-Based Determination of Unsaturated Hygric Properties of Porous Materials

Transport in Porous Media - A reliable and practical method of hygric property characterisation is a major determinant in properly analysing hygric performance of built constructions. The current...     

An individualized simulation model based on continuous,independent, ground force measurements after intramedullary stabilization of a tibia fracture

Archive of Applied Mechanics - The interfragmentary movement (IFM) is a key determinant for the fracture healing process. Different simulation models allow the prediction of the IFM in the fracture...     

On the Ubiquity of Fracture in Nonlinear Elasticity

This paper points out a subtle and little known consequence of assuming rank-one convexity for an isotropic hyperelastic material [e.g., of assuming a common ordering of principal stretches and principal stresses and hence the Baker–Ericksen inequalities]. What is shown is that rank-one convexity necessarily privilages those affine deformations which are dilatations: – the stored-energy associated with a dilatation is smaller than the stored energy associated with any other affine deformation possessing the same determinant. Also pointed out are fracture related consequences of this property that arise when the stored-energy function assigns to the dilatation of determinant δ > 0 a value A(δ∈) which is not an everywhere convex function of (0,∞). This revised version was published online in August 2006 with corrections to the Cover Date.     

捷联惯导姿态算法若干问题的研究

研究了捷联系统姿态更新的等效旋动矢量算法，并以锥运动为条件，对等效旋动矢量算法进行了优化。此外还对四元数、旋动矢量及其优化算法进行了仿真比较。仿真结果表明：等效转动矢量算法的精度明显优于四元数算法，且等效转动矢量的采样频率越高，姿态更新算法的精度就越高。     

COMPUTATION FORMULAS OF GENERALIZED INVERSE PADE APPROXIMANTS USING FOR SOLUTION OF INTEGRAL EQUATIONS

For the generalized inverse function-valued Padé approximants, its mtact computation formulas are given. The explicit determinantal formulas for the denominator scalar polynomials and the numerator function-valued polynomials are first established. A useful existence condition is given by means of determinant form.     

Effect of inlet volute wrap angle on the flow field and performance of double inlet gas cyclones

In response to the divergent understanding of double inlet cyclone performance in the literature, the effect of inlet volute wrap angle on the performance and flow field of double inlet cyclone separator was studied by Computational Fluid Dynamic (CFD) method. The results showed that the inlet volute wrap angle can affect the comparison results of the single and double inlet gas cyclones with the same total inlet cross-sectional area and velocity. 0° and 90° volute double inlet improved the efficiency mainly by separating particles below 10 μm, while 180° volute double inlet had no separation advantage for any particles, so the symmetrical double inlet does not always improve the efficiency, and the appropriate inlet volute wrap angle should be selected according to the actual situation, otherwise, the expected performance requirements of the symmetrical double inlet cyclone cannot be achieved. Compared with the flow field, it is found that the inlet volute wrap angle changed the tangential velocity of the symmetrical double inlet cyclone separator, thus changing the performance.     

Wave propagation in double helical rods

The propagation of waves in helical rods has been studied extensively. However, studying the wave propagation in double helical rods have received less attention although this can be useful in multiple fields of science and engineering. Obtaining an analytical model for a double helical rod is challenging since the curvature and tortuosity are not constant. Thus, resolving the wave behaviour analytically is nearly impossible. In this paper, wave propagation in a double helical rod will be studied using the wave and finite element method which is a technique that can be used to model homogeneous and periodic one and two dimensional structures based on the periodic structure theory. For modelling a double helical rod, the finite element model of a single turn is processed using Bloch waves. The dispersion curves and wavemodes are obtained and the similarities and differences of waves in helical and double helical rods are highlighted.     

Hydrodynamic stability of boundary layers with mass transfer

The stability of boundary layers involving mass transfer described by a two-parameter family of Fockner-Scane (F-S) solutions is analyzed. An effective method of solving the boundary problem is proposed for the F-S equation. A determinant method is proposed for solving the stability equation. The critical values of the stability characteristics are found over a wide range of gradient and mass-transfer parameters.