相对论磁化运动等离子体的介电张量

 定义了相对论磁化运动等离子体(MMP)的物理模型。利用微扰理论导出了系统的介电张量，研究发现，MMP具有完全不同于静态磁化等离子体介电张量的形式。对电磁波沿轴向传播的情况进行了数值模拟计算，结果表明，系统的共振频率随等离子体密度的增加而非线性增加，在相同的条件下，右旋波的共振频率高于左旋波的共振频率。对于传播的右旋电磁波，增加纵向磁场，共振频率提高，而对于左旋电磁波，增加纵向磁场，共振频率降低。     

A New Algorithm for the Segre Classification of the Trace-Free Ricci Tensor

A new algorithm, based on the introduction of new spinor quantities, for the Segre classification of the trace-free Ricci tensor is presented. It is capable of automatically distinguishing between the two Segre types [1,1(11)] and [(1,1)11] where all other known algorithms fail to do so.     

A lower bound for the invariants of the configuration tensor for some well-known differential models

A method is given to determine lower bounds for the invariants of a configuration tensor in 3D flows. For some well-known differential models these lower bounds are given. Except for the Giesekus and the FENE-P model, the lower bounds are the values in equilibrium.     

Bounded factorization property for Fréchet spaces

An operator T ∈ L(E, F) factors over G if T = RS for some S ∈ L(E, G) and R ∈ L(G, F); the set of such operators is denoted by L^G(E, F). A triple (E, G, F) satisfies bounded factorization property (shortly, (E, G, F) ∈ ???) if L^G(E, F) ? LB(E, F), where LB(E, F) is the set of all bounded linear operators from E to F. The relationship (E, G, F) ∈ ??? is characterized in the spirit of Vogt's characterisation of the relationship L(E, F) = LB(E, F) [23]. For triples of K?othe spaces the property ??? is characterized in terms of their K?othe matrices. As an application we prove that in certain cases the relations L(E, G₁) = LB(E, G₁) and L(G₂, F) = LB(G₂, F) imply (E, G, F) ∈ ??? where G is a tensor product of G₁ and G₂.     

A strip yield model solution for an internally cracked piezoelectric strip

An analysis of the crack closure and fatigue crack growth rate have been carried out for an infinitely long poled piezoelectric ceramic strip weakened by a straight hair line internal crack. The ceramic under consideration is assumed to be mechanically more brittle. The crack faces are perpendicular to the poled direction of the strip. The crack faces open in Mode-I deformation on account of in-plane tension applied to the edges of the strip together with either an in-plane electric displacement prescribed on edges of the strip or a uniform constant electric field prescribed on its edges. As a result, a yield zone is formed ahead of each tip of the crack. The yield zones developed are then arrested by applying a normal, cohesive, linearly varying yield point-stress to their rims. For each case, the Fourier transform method is used to find a solution. The resulting integral equations are solved numerically. Expressions are derived for the crack opening displacement and the crack growth rate. The variations in these quantities are plotted in relation to the affecting parameters, viz., the strip thickness, the yield zone length, the electric displacement, and material constants. A case study is presented graphically for PZT-4, PZT-5H, and BaTiO₃ ceramics. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 5, pp. 647–664, September–October, 2008.     

方形爆炸抛撒装置结构优化

为了研究方形抛撒装置壳体破坏规律及燃料分散特性,开展了抛撒装置外场实验并利用LS-DYNA仿真软件进行了数值模拟,模拟结果与实验结果相吻合。进一步分析装置倒圆角及刻槽深度对壳体破裂效果及燃料分散速度的影响规律,结果表明:倒圆角与增加刻槽深度有利于减小壳体棱边处应力集中的影响,圆角半径增至10 mm或刻槽深度增至1.2 mm时,棱边处不再破裂;同一装置壳体边部和中部位置采用不同深度的刻槽可有效减少壳体破裂不均现象。当边缘处刻槽深度为1.2 mm、中间刻槽为1.6 mm时,壳体均匀破裂;当棱边处倒10 mm圆角,边部刻槽深度为0.8 mm,中部刻槽为1.2 mm时,抛撒装置既能满足壳体均匀开裂,又可提高壳体强度,同时可将燃料分散平均速度差值降低22%,从而有效提高燃料抛撒效率。     

Weak localization corrections to the anomalous Hall effect

We calculate localization corrections to the anomalous Hall conductivity in the framework of side-jump and skew scattering mechanisms. In contrast to the ordinary Hall effect, there exists a nonvanishing localization correction to the anomalous Hall resistivity. The correction to the anomalous Hall conductivity vanishes in case of side-jump mechanism, but is nonzero for the skew scattering.     

Quantitative Inheritance Properties for Simultaneous Approximation by Tensor Product Operators

Our results describe how quantitative properties of univariate operators are inherited by the tensor product of their parametric extensions. This includes statements concerning simultaneous approximation. The estimates are in terms of partial and total moduli of smoothness of higher order. Applications are given for cubic interpolatory splines and Bernstein operators. Further applications are possible.     

拟常曲率流形上的二阶平行张量

本文证明了如下结果：（1）在一个拟常曲率流形M上，[0,2]型平行张量是度量张量的常数倍。（2）在拟常曲率流形M上，不存在非零平行2－形式。除非对应于M的生成元的Ricci主曲率等于零。     

有序分子体系的三阶和四阶非线性光谱学的实验可观测量和宏观感应率及微观极化率张量元

对于线性和非线性光谱，有序的分子体系(如分子界面和分子膜)的取向分析可以通过对形式非常简单的广义取向泛函．对于二阶非线性光谱学，即光学二次谐波和和频振动光谱，这一简化描述对于理解分子界面和膜的光谱和取向的细节很有助益．为了将这一简化描述应用于更高阶的相干非线性光谱学，对于具有旋转对称性的界面或膜的三阶和四阶非线性光谱学的实验可观测量和宏观感应率及微观极化率张量元进行了计算并得到了具体表达式．这些通用的表达式将有助于典型的三、四阶非线性光谱学，即光学三次谐波、简并的相干反斯托克斯拉曼光谱、光学四次谐波和简并