两层流体中二维非线性界面波的演化方程

给出两水平固壁间两层不可压缩理想流体中二维非线性界面波的演化方程，首先建立出这个演化方程，并由此方程在一定条件下得到二维非线性界面长波满足的近似方程，然后从理论上证明这个长波近似方程包含了以下两个描述一阶界面升高的著名的浅水孤立波方程；Korteweg-de Vries(KdV)方程和Kadomtsev-Petvishvili(KP)方程，所得特殊结果与前人的一致，表明所建立的二维非线性界面波演化方程正确且具有一般性。     

理想流体近似的讨论

针对大学物理中的理想流体模型进行了讨论, 从热力学方程和纳维 斯托克斯方程出发, 给出了理想 流体模型的近似过程, 澄清了理想流体模型的概念, 阐明了理想流体的运动过程是等熵过程. 通过对造成熵增( 耗 散)项的物理分析, 本文给出了理想流体近似可以视为冷流体近似的观点     

Spatially Homogeneous Bianchi Type V Cosmological Model in the Scale-Covariant Theory of Gravitation

We discuss spatially homogeneous and anisotropic Bianchi type-V spacetime filled with a perfect fluid in the framework of the seale-covariant theory of gravitation proposed by Canuto et al. By applying the law of variation for Hubble＇s parameter, exact solutions of the field equations are obtained, which correspond to the model of the universe having a big-bang type singularity at the initial time t = 0. The cosmological model, evolving from the initial singularity, expands with power-law expansion and gives essentially an empty space for a large time. The physical and dynamical properties of the model are also discussed.     

神奇的超流体

Science和Nature被誉为世界两大顶级杂志,主要报道当今自然科学研究最高水平的研究成果和进展.他们面向一般读者,属于综合性科学杂志,影响因子稳定在30左右.Science杂志1880年由爱迪生创办,1894年成为美国最大的科学团体"美国科学促进会"(AAAS)的出版物.全年共51期,为周刊,全球发行量超过150万份.英国的Nature杂志创办于1869年,曾发表达尔文、赫胥黎等大师的文章闻名于世.从2009年开始,《力学与实践》在《力学纵横》栏目发表朱克勤教授的系列科普文章,其特点是每篇文章的主题围绕Science和Nature的一篇论文展开,用通俗的语言介绍与力学研究相关的一些前沿问题,本期刊出"神奇的超流体".     

牛顿运动定律和机翼举力

将空气简化为理想流体，由牛顿运动定律推出气体做曲线运动时的切向伯努利方程和法向压强梯度表达式，并解释了机翼举力。     

A Plane-Symmetric Inhomogeneous Cosmological Model of Perfect Fluid Distribution with Electromagnetic Field I

A plane-symmetric inhomogeneous cosmological model of perfect fluid distribution with electro-magnetic field is obtained. F12 is the non-vanishing component of electromagnetic field tensor. To get a deterministic solution, we assume the free gravitational field is Petrov type-Ⅱ non-degenerate. Some physical and geometric properties of the model are also discussed.     

理想流体在粗细不均的水平管中绝热稳定流动不是等焓过程

说明理想流体沿粗细不均的水平管道作绝热稳定流动是变焓过程。     

引力塌缩系统的熵变

在共动坐标系下，对引力塌缩系统的熵变进行了研究，证明了理想流体系统的塌缩是等熵过程，有辐射热流的开放系统的塌缩是减熵过程．对非理想流体系统推出了熵变的一般公式，并应用到有辐射中微子的塌缩过程，其总熵是减少的．     

理想流体中定常自由涡环运动

本文研究理想均质不可压缩无界流体中的轴对称定常涡环运动。通过对柱坐标系下的定常Euler方程的高精度数值求解,给出了求涡核区有任意涡量分布情况下轴对称定常涡环解的方法,并就涡环的运动特性进行了讨论,其极限情况与已有的理论解完全一致。在此基础之上,还发展了一种柱坐标系下以傅氏级数为基函数作展开的高效谱方法,成功地解决了奇性(r=0)问题。     

Gauge principle and variational formulation for flows of an ideal fluid

A gauge principle is applied to mass flows of an ideal compressible fluid subject to Galilei transformation. A free-field Lagrangian defined at the outset is invariant with respeet to global SO(3) gauge transformations as well as Galilei transformations. The action principle leads to the equation of potential flows under constraint of a continuity equation. However, the irrotational flow is not invariant with respect to local SO(3) gauge transformations. According to the gauge principle, a gauge-covariant derivative is defined by introducing a new gauge field. Galilei invariance of the derivative requires the gauge field to coincide with the vorticity, i.e. the curl of the velocity field. A full gauge-covariant variational formulation is proposed on the basis of the Hamilton‘‘s principle and an assoicated Lagrangian. By means of an isentropic material variation taking into account individual particle motion, the Euler‘‘s equation of motion is derived for isentropic flows by using the covariant derivative. Noether‘‘s law associated with global SO(3) gauge invariance leads to the conservation of total angular momentum. In addition, the Lagrangian has a local symmetry of particle permutation which results in local conservation law equivalent to the vorticity equation.