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边界
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Equations determining the velocity and density distributions within the mixing region of two incompressible gases with different densities are set up, their temperatures being assumed to be the same. For incompressible mixing the total number of gas molecules per unit volume is constant, although the density of the gaseous mixture varies from point to point due to diffusion of matter. As an illustration we consider the plane jet and steady motion. The boundary layer method of approximation can still be applied....

Equations determining the velocity and density distributions within the mixing region of two incompressible gases with different densities are set up, their temperatures being assumed to be the same. For incompressible mixing the total number of gas molecules per unit volume is constant, although the density of the gaseous mixture varies from point to point due to diffusion of matter. As an illustration we consider the plane jet and steady motion. The boundary layer method of approximation can still be applied. The boundary of the jet is shown to be the same as that for one fluid. The solution of the problem then depends upon the numerical value of the coefticient of viscosity of the mixture which is a function of the number of molecules of each constituent gas in the unit volume. The present method of investigation is applicable to the cylindrical and half jets and also to the case where the two gases are at different temperatures.

本文求出规定二不能压缩气体的分片合流运动时,速度与质量密度分布的微分方程式。假定两种气体的密度不同但温度则相等。不能压缩的定义是每单位体积中的两种气体分子数的和不变。本文只讨论一平面守恒注中所需要的微分方程式。粘滞流体运动中之边界近似法仍可应用。同样方法亦可用到守恒圆柱体注,半注及气体中温度不同诸问题。

In the recent years, the theory related to friction-lines has been independently developed both in Europe~[1] and here~[2-8], according the information~[1] reached the author in 1956. These investigations are based on the condition of least frictional resistance at a point.

塑压接触面之质点滑动线称“摩擦线”。滑动现象有两种基本类型,一为“长程滑动”,摩擦线为质点之长程连续轨迹,如抽拔,挤压,冲压等塑性过程中之滑动;一为“短程滑动”,质点仅在摩擦线上滑动一微小距离,如锻,轧,压力实验等过程中之滑动(小压缩时)。 过去对这两种滑动现象之规律未曾分别处理。本文将摩擦力接纯力学关系视为一切应力,即压应力p与摩擦应力τ,以边界平衡关系,相系于一应力函数F: τ=Fp, F=((l_1~2p_1~2+l_2~2p_2~2+l_3~2p_3~2)/(l_1~2p_1+l_2~2p_2+l_3~2p_3)~2)~(1/2) -1,p_1,p_2,p_3为内部主应力;l_1,l_2,l_3为p对p_1,p_2,p_3之夹角余弦。除视τ为p之函数τ=τ(p)外,对摩摩力之物理性质不作规定。 在此基础上,以住意质点滑动之最小摩阻功为基本条件分析滑向规律,一如任意质点滑动之最小摩阻力条件之于“陡线规律”。如此,则问题类于古典变分问题,变分方程引出两结论:在短程滑动中,滑向规律为已知之陡线规律;在长程滑动中为以下将提出之“等倾陡线规律”。并得到几个有关重要推论。

In this article the parametrically coupling of oscillations in a small ellipsoid of ferrite under the excitation of an uhf pumping of any spatial distribution is discussed. It is pointed out that the coupled oscillations may be induced through the two types of driving, field driving and magnetization driving. A special case of the former was recently discovered by Denton, who used a longitudinal pumping field uniform in space. A special example of the latter is found in Suhl's theoretical analysis and a number...

In this article the parametrically coupling of oscillations in a small ellipsoid of ferrite under the excitation of an uhf pumping of any spatial distribution is discussed. It is pointed out that the coupled oscillations may be induced through the two types of driving, field driving and magnetization driving. A special case of the former was recently discovered by Denton, who used a longitudinal pumping field uniform in space. A special example of the latter is found in Suhl's theoretical analysis and a number of experimental works after him. The pumping field transverse in direction and spatially uniform does not induce the coupled oscillations directly, but the rf magnetization of the Kittel precession excited by the pumping becomes the driving force of the oscillations. For each type of a uniform pumping we obtain from a set of differential equations the magnetostatic potential functions (the first order approximation) as linear combinations of Walker's functions. These solutions are different from those given by MOHOCOB. Making. use of the boundary conditions at the ferrire surface we find that for the Walker modes involved in the oscillations to be coupled, thtir indices must satisfy certain condi'ions. For the case of magnetostatic operations the dc magnetic field is tuned to a pair of the Walker modes, the potential functions may be reduced greatly. By studying the power drawn by the coupled oscillations from the pumping, we obtain the selection rules of a pair of magnetostatic modes excited by a pumping field of any given spatial distribution. We point out that for the determination of the amplitudes of the oscillations the equations derived from the conservation of energy and from the equality of the number of quanta emitted must be used. Finally, the threshold intensity of Denton's pumping field is derived using Suhl's method. We indicate that this method is based on a perturbation calculation.

在本文中我们系统地讨论了铁氧体小样品在超高频电源的激发下产生参量振璗的耦合关系,指出激发机构应分为磁场驱动和磁化驱动二类。前者的特例为Denton新近发现的,使用空间均匀的纵向注入场;后者的特例为Suhl最早所研究的,使用空间均匀的横向注入场所激发的一致进动的磁化向量为驱动力。从静磁势函数的耦合微分方程我们得到这二种特殊注入方式激发的静磁势函数的完全解(一次近似),表达为Walker函数的线性组合,在边界连续的要求下,这些势函数中的Walker模只在它们的指标之间适合一定的条件时才相互关联。当直流磁场调谐于一对Walker模时,耦合的静磁势简化为静磁操作的势函数。我们具体分析了静磁操作参量振璗从注入场吸取的功率,根据后者必须不为零才可能产生参量振璗,我们推导出空间均匀场激发一对静磁模的选择定则,恰与从边界连续推出的关联条件完全相同,并且进一步得到空间不均匀场激发一对静磁模的选择定则。我们指出,参量振璗的振幅的决定必须引用能量守恒和量子数相等的方程。最后我们采用Suhl的方法推算出空间均匀的纵向注入场的激发临阈强度,并且讨论了这一方法的近似性质。

 
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