Vaidya—Schwarzschild—de Sitter时空中时间尺度变换的纯规范势

同稳态时空一样，动态Ｖａｉｄｙａ－Ｓｃｈｗａｒｚｓｃｈｉｌｄ－ｄｅ Ｓｉｔｔｅｒ时空中的Ｈａｗｋｉｎｇ效应可看作时间尺度变换下的补偿效应，补偿场纯规范势的一个分量表征黑洞温度，另一个表征黑洞温度变化率。     

Maxwell流体在震荡的矩形输送管道中的流动

分析了不可压缩Maxwell流体在震荡矩形截面管道中的非稳定流动问题.利用Fourier变换和Laplace变换作为数学工具,提出了问题的解,该解可以看成稳态解和暂态解之和.大倍数时,暂态消失,解可以表示为稳态解.在极限情况的案例中给出了Newton流体的解.当震荡频率不存在时,得到了Maxwell流体在震荡矩形截面管道中流动问题的解.最后,以图形形式给出不同参数时,矩形管道正弦震荡达到稳态所需要的时间.同时,分别描绘了x和y变化时的速度曲线.     

胶体有效粘滞系数的理论研究

胶体是自然界和工业应用中的常见对象。胶体领域的一个中心理论问题是如何根据胶体系统的微结构来确定胶体的流变性质。由于处理多粒子系统边值问题的困难,现有的胶体理论都局限于低颗粒浓度。该文中发展了变换场方法,用该方法可以计算含胶体颗粒的不可压缩粘滞流体的有效粘滞系数,颗粒可以是固体也可以是流体。在低颗粒浓度,该理论预测与爱因斯坦关于悬浮体的公式以及Taylor关于乳浊液的公式完全吻合。在高颗粒浓度,该文的结果与Nunan和Keller的结果相一致,其方法可以用于预测非球形颗粒悬浮体的有效粘滞系数。     

自对偶杨-Mills场的正则约化——Ernst引力方程

从SDYM场的正则形式出发,在稳态、轴对称情况下进行了正则约化,得到了Ernst方程的正则形式,从而将Ernst讨论的稳态、轴对称引力纳入正则SDYM范畴.     

Artin空间中SU(3)规范场的几何解析

研究4维Artin空间中SU(3)规范场的线性化问题.首先对Yang-Mills方程的推导进行了讨论,给出了恰当的Yang-Mills方程的概念,其具有明确的几何意义.其次,构造了一类线性微分变换,称之为Artin空间SU(3)规范场的示性变换.示性变换是应用数学机械化方法确定的.经由示性变换,将非线性的恰当的Yang-Mills方程变为一组线性方程,实现了SU(3)规范场的场方程的线性化.从而证明了,对于恰当的Yang-Mills方程,SU(3)规范场包括8个独立的规范场.     

Yang-Mills规范场的存在性、可解性(一)

应用数学机械化方法研究欧氏空间中$SU(2)$ Yang-Mills规范场的存在性问题.首先对YM--方程的结构进行了讨论,说明YM--方程由它的奇部份和偶部份联立组成.对于YM--方程构造了一类线性微分变换,称之为$SU(2)$规范场的示性变换.经示性变换,将非线性的YM--方程的奇部份变为一组Laplace方程,实现了$SU(2)$规范场方程的线性化.从而证明了$SU(2)$规范场存在3个独立的Yang-Mills规范场.     

SU(3)规范场的恰当形式(欧空间)

应用数学机械化方法讨论SU(3)规范场的规范化问题.首先提出一种具有明确几何意义的Yang-Mills方程,称其为恰当的Yang-Mills方程.然后构造了一类线性微分变换,称之为SU(3)规范场的示性变换,它具体给出联络和截面之间的微分关系.经由示性变换,将非线性的恰当的YM-方程变为一组线性Laplace方程,即实现了规范场YM-方程的线性化.从而证明了SU(3)规范场包括8个独立的Yang-Mills规范场.     

微极性流体在上下正交移动的渗透平行圆盘间的流动

分析了上下正交运动的两平行圆盘间的非稳态的不可压缩的二维微极性流体的流动．应用von Krmn类型的一个相似变换,偏微分方程组(PDEs)被转化成一组耦合的非线性常微分方程(ODEs)．应用同伦分析方法,得到方程的解析解,并且详细讨论了不同的物理参数,像膨胀率,渗透Reynolds数等,对流体的速度场的影响．     

SU(2)规范场的恰当形式(欧空间)

应用数学机械化方法研究欧氏空间中SU(2)规范场的正规化问题.首先对Yang-Mills方程的表述进行了讨论,给出了一种具有物理和几何意义的YM-方程,称其为恰当的(exact)YM-方程.对于这种恰当的YM-方程,构造了一类线性微分变换,称之为SU(2)规范场的示性变换.经由示性变换,将非线性的恰当的YM-方程变为一组Laplace方程,实现了SU(2)规范场方程的线性化,即场方程的正规化.从而证明了SU(2)规范场存在3个独立的Yang-Mills规范场.     

带Neumann边界条件的相场方程解的渐近性态

利用Simon-Lojasiewicz型不等式,获得了带Neumann边界条件的相场方程解的渐近性态.本文所考虑的稳态问题含有非局部项.     

The stress system in a suspension of drops in an electric field

Summary In this paper an expression for the particle stress tensor of a suspension of drops in an electric field is given. It shows that the particle stress tensor of a suspension of drops in an electric field depends on the intensity of the applied electric field, dielectric constants, viscosity coefficients and conductivity coefficients of liquids inside and outside the drop. It also denotes that a suspension of drops in an electric field must be taken into account as a non-Newtonian fluid.

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Résumé Dans le présent travail on donne une expression pour le tenseur des tensions des particules d'une suspension de gouttes de liquide dans un champ électrique. Elle montre que le tenseur des tensions des particules d'une suspension de gouttes de liquide dans un champ électrique dépend de l'intensité du champ électrique appliqué, des constantes diélectriques, des coefficients des viscosités et des coefficients des conductivités des liquides à l'intérieur et à l'extérieur de la goutte. Elle montre que la suspension des gouttes de liquide dans un champ électrique doit être considérée comme un fluide non newtonien.

     

Flow-induced anisotropic viscosity in short fiber reinforced polymers

The commonly used flow models for fiber reinforced polymers often neglect the flow induced mechanical anisotropy of the suspension. With an increasing fiber volume fraction, this plays, however, an important role. There are some models which count on this effect, they are, however, phenomenological and require a fitted model parameter. In this paper, a micromechanically based constitutive law is proposed which considers the flow induced anisotropic viscosity of the fiber suspension. The introduced viscosity tensor can handle arbitrary anisotropy of the fluid-fiber mixture depending on the actual fiber orientation distribution. A homogenization method for unidirectional structures in contribution with orientation averaging is used to determine the effective viscosity tensor. The motion of rigid ellipsoidal fibers induced by the flow of the matrix material is described by Jeffery's equation. A numerical implementation of the introduced model is applied to representative flow modes. The calculated stress values are analyzed in transient and stationary flow cases. They show a less pronounced anisotropic viscous behaviour in every investigated case compared to the results obtained by the use of the Dinh-Armstrong constitutive law. The reason for the qualitative difference is that the presented model depends on the complete orientation information, while the other one is linear in the fourth-order fiber orientation tensor. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On conformal Killing symmetric tensor fields on Riemannian manifolds

A vector field on Riemannian manifold is called conformal Killing if it generates oneparameter group of conformal transformation. The class of conformal Killing symmetric tensor fields of an arbitrary rank is a natural generalization of the class of conformal Killing vector fields, and appears in different geometric and physical problems. In this paper, we prove that a trace-free conformal Killing tensor field is identically zero if it vanishes on some hypersurface. This statement is a basis of the theorem on decomposition of a symmetric tensor field on a compact manifold with boundary to a sum of three fields of special types. We also establish triviality of the space of trace-free conformal Killing tensor fields on some closed manifolds.     

A regularity criterion for 2D MHD flows with horizontal dissipation and horizontal magnetic diffusion

This paper concerns the conditional global regularity of incompressible MHD equations with horizontal dissipation and horizontal magnetic diffusion in two dimension. When only horizontal dissipation and horizontal magnetic diffusion are present, there is no control on the vertical derivatives of velocity field and magnetic field, which is the main difficulty to establish the global regularity. In this paper, we establish a global regularity criterion in terms of one entry of the velocity gradient tensor or one entry of the magnetic field gradient tensor, which extends the recent work (Fan and Ozawa, 2014).     

S—R分解定理的唯一性,存在性和客观性

对于连续体的一切物理可能的变形场，其变形梯度张量F可被分解为一个对称张量S和一个正交张量R的直和，这便是S-R分解定理．本文通过矩阵方法和张量方法证明了S-R分解定理的唯一性、存在性和客观性．     

Finsler spaces with recurrent pseudocurvature tensor

Sinha [2] has defined pseudocurvature tensor field in ann-dimensional Finsler spaceF _n. In the present paper we have studied some recurrent properties of pseudocurvature tensor.     

Correspondences of ribbon categories

Much of algebra and representation theory can be formulated in the general framework of tensor categories. The aim of this paper is to further develop this theory for braided tensor categories. Several results are established that do not have a substantial counterpart for symmetric tensor categories. In particular, we exhibit various equivalences involving categories of modules over algebras in ribbon categories. Finally, we establish a correspondence of ribbon categories that can be applied to, and is in fact motivated by, the coset construction in conformal quantum field theory.     

The 1/N Expansion of Multi-Orientable Random Tensor Models

Multi-orientable group field theory (GFT) was introduced in Tanasa (J Phys A 45:165401, 2012), as a quantum field theoretical simplification of GFT, which retains a larger class of tensor graphs than the colored one. In this paper we define the associated multi-orientable identically independent distributed multi-orientable tensor model and we derive its 1/N expansion. In order to obtain this result, a partial classification of general tensor graphs is performed and the combinatorial notion of jacket is extended to the m.o. graphs. We prove that the leading sector is given, as in the case of colored models, by the so-called melon graphs.     

Symmetric Hermitian decomposability criterion,decomposition, and its applications

The Hermitian tensor is an extension of Hermitian matrices and plays an important role in quantum information research. It is known that every symmetric tensor has a symmetric CP-decomposition. However, symmetric Hermitian tensor is not the case. In this paper, we obtain a necessary and sufficient condition for symmetric Hermitian decomposability of symmetric Hermitian tensors. When a symmetric Hermitian decomposable tensor space is regarded as a linear space over the real number field, we also obtain its dimension formula and basis. Moreover, if the tensor is symmetric Hermitian decomposable, then the symmetric Hermitian decomposition can be obtained by using the symmetric Hermitian basis. In the application of quantum information, the symmetric Hermitian decomposability condition can be used to determine the symmetry separability of symmetric quantum mixed states.     

Cylindrical wave solutions of the field equations representing zero-rest-mass scalar fields and those of lichnerowicz's « total radiation » in a generalized Einstein-Rosen space-time

Summary Lichnerowicz (1960), by using a property of the Riemann tensor, has given the field equations, R_ij=ϱw_iw_j, w_iwⁱ=0, ϱ being a scalar and has termed them as representing a state of ? total radiation ?. Recently Rao (1970) derived these field equations under a geometrical relation which as stated by him imposes on the Rieman tensor a severe restriction, and he obtained a class of exact solutions of the above field equations corresponding to the cylindrically symmetric space-time with two degrees of freedom. The present authors, in this paper, have obtained exact wave solutions of the field equations representing zero-rest-mass scalar field in the generalized Einstein-Rosen space-time, and it has been shown that by a suitable choice of the scalar field, the field equations considered by Lichnerowicz and Rao can be deduced without imposing any condition on the geometrical nature of the Riemann tensor. Finally a method is given by which most general solutions of these field equations, can be generated from those of the empty space field equations. It is further shown that the solutions of Rao (1960) are only a special case of those found in this paper. Entrata in Redazione il 15 settembre 1976.