On the Klein–Gordon Equation in Higher Dimensions: Are Particle Masses Variable?

We consider ways to generalize the 4D Klein–Gordon equation of particle physics to higher dimensions. The most promising approach implies that the mass which appears in the 4D relation is a term in the source-free 5D relation. We check this explicitly for the case of exact solitonic and cosmological solutions of the Kaluza–Klein equations. In general, particle masses are variable; but are constant for the Schwarzschild and late-universe cases, in agreement with data from the solar system and astrophysics. Our results have significant implications for cosmology, and can easily be extended to 10D superstrings, 11D supergravity and higher dimensions.     

流体诱发水平悬臂输液管的内共振和模态转换(Ⅰ)

运用牛顿法导出水平悬臂刚性输液管的非线性动力学数学模型．为了对该模型进行理论分析,通过对各个相关实际物理量的量级定性分析,给出了模型中各个物理参数的量级．在此基础上,应用多尺度法首先得到输液管自由振动模态的特征函数,利用悬臂管的边界条件给出了特征值满足的特征方程, 发现管内流体速度可以诱发第一阶模态和第二阶模态3种形式的内共振分别是3∶1、2∶1和1∶1内共振, 从理论上解释了流速诱发水平悬臂输液管系统内共振的机理．由于3∶1内共振所对应的流速最小,因此这种形式的内共振是最先出现的,也是最重要的．     

Shock and traveling wave phenomena on an externally damped, non-linear string

We examine the propagation of shocks and traveling wave phenomena on a one-dimensional string that is executing finite-amplitude, transverse vibrations in a resisting medium. As part of our study, we develop an approach that allows us to describe, albeit approximately, the evolution and propagation of a shock front using analytical methods. In addition, exact traveling wave solutions, one of which involves the Lambert W-function, of the string's equation of motion are determined and analyzed. Lastly, a possible new form of the solution to the linearized problem is presented and extensions and other applications of the present work are briefly discussed.     

On the flow in a uniformly porous pipe

This article considers fully laminar flow of an incompressible viscous fluid in a uniformly porous pipe with suction and injection. An exact solution of the Navier–Stokes equations is given. The velocity filed can be expressed in a series form in terms of the modified Bessel function of the first kind of order n. The volume flux across a plane normal to the flow, the vorticity and the stress on the boundary are presented. The flow properties depend on the cross-Reynolds number, Ua/ν, where U is the suction velocity, a is the radius of the pipe and ν is the kinematic viscosity of the fluid. It is found that for large values of the cross-Reynolds number, the flow near the region of the suction shows a boundary layer character. In this region the velocity and the vorticity vary sharply. Outside the boundary layer, the velocity and the vorticity do not show an appreciable change.     

New method for geometric nonlinear analysis of large displacement drill strings

Introduction Drillstringsina3Dlargedisplacementwellboreareusuallyregardedas3Dcurved beamswithlargedisplacementandlargerotationbutwithsmallstrain,thus,therelationship betweenstressandstrainislinear.Thedeformationofdrillstringscanbecomposedoftwo parts:oneiscalledtheinitialdeformationcausedwhentheaxisofthedrillstringisdeformed fromitsstraightconfigurationtothepositioncoincidentwiththewellaxis,involvinglarge rotationsandwiththeimplicationoffiniterotationalproblem.Theotheristhedeformation fromthew…     

输流粘弹性曲管的稳定性分析

根据变质量弹性系统Hamilton原理,用变分法建立了输流粘弹性曲管的运动微分方程,并用归一化幂级数法导出了输流粘弹性曲管的复特征方程组．以两端固支Kelvin-Voigt模型粘弹性输流圆管为例,分析了无量纲延滞时间和质量比对输流管道无量纲复频率和无量纲流速之间的变化关系的影响．在无量纲延滞时间较大时,粘弹性输流圆管的特点是它的第1、2、3阶模态不再耦合,而是在第1、第2阶上先发散失稳,然后在1阶模态上再发生单一模态颤振．     

Analytic solutions of incompressible laminar flow in the inlet region of a pipe

The laminar analytic solutions of velocities and pressure in the central zone of the inlet region of pipe flow are given under the condition of uniform inflow, based on the Navier-Stokes equations of incompressible viscous flow.     

圆管入口段不可压缩层流流动的解析分析

从不可压缩粘性流体的Navier-Stokes方程出发,给出了在均匀来流条件下的圆管入口段层流流动中央区的速度分布及压力分布的解析解．     

Theoretical analysis of using airflow to purge residual water in an inclined pipe

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气流排除倾斜管道积水的理论分析

运用作者推导的动量积分关系式,分析了向有积水的斜置管道中分别吹入轴向气流和螺旋气流时积水的运动情况。结果表明:在大多数情况下,螺旋气流能除去斜置管道中积水;而轴向气流不能除去积水,一段时间后会出现逆流。这一结果与Horii和赵耀华等人在这个问题上所做的实验结果一致。此外,还讨论了不同的初始条件对排水情况的影响。