刚体滚动摩擦力的方向及实验证明

在一个物体相对于沿着另外一个物体滚动或者有滚动趋势时,滚动的物体与接触面之间存在摩擦力．如果物体在滚动的过程中有滑动,称为有滑滚动;如果滚动过程中没有滑动,称为无滑滚动,或纯滚动．     

圆柱体的滚动摩擦系数的测量研究

从圆柱体在斜面上的基本受力分析入手,推导圆柱体沿斜面运动过程中的发生滚动的临界角及滚动摩擦系数的关系式。并通过简单的实验装置测定了铁质圆柱体与玻璃的滚动摩擦系数和静摩擦系数分别约为0.0921和0.121。理论与实验结果基本符合,表明该实验方法对于测定静摩擦系数和滚动摩擦系数的有效性,也为力学基本问题的研究提供了方法。     

同向相对运动的叠放体摩擦力做功问题

解决同向相对运动的叠放体摩擦力做功问题,关键是挖掘出两相对运动物体的摩擦力和位移变化临界条件.本文通过对两种不同运动情况的摩擦力做功问题进行分析和比较,分解教学难点,以达到教学目标.     

关于动滑轮中摩擦力的讨论

在直线运动中，静摩擦力和滑动摩擦力的作用及做功问题，已有明确结论．这些结论是：一对静摩擦力做功之和为零，所以有（一对）静摩擦力存在不会引起机械能的改变；一对滑动摩擦力做功之和一定不为零，所以有（一对）滑动摩擦力存在一定伴随着机械能转化为热（内能）的过程，     

圆滚线运动的等时性

当一圆轮沿一直线做纯滚动时，轮缘上任一点在空间的运动轨迹就是圆滚线，或称旋轮线．在经典力学中这是一条既有趣又有用的曲线．借助于它来讨论圆轮沿直线做纯滚动时轮缘上任一点的速度和加速度就不需要考虑两个运动的叠加．有趣的是质点沿圆滚线运动具有等时性，     

球体作非纯滚动时所受的滑动摩擦力及运动分析

本文从分析一个物理实验出发，论述球体作非纯滚动的有关问题．指出判断球体作非纯滚动所受的滑动摩擦力的方向的方法，提出该摩擦力作功的计算公式应为Ｗ＝Ｆｒ·∫ｖｐｄｔ．在此基础上，进一步明确功的定义，并阐述求解球体作非纯滚动问题的一般方法。     

谈摩托车在转弯中的倾斜

高速行驶的摩托车为什么只有倾斜车身，才能转弯呢?下面讨论这个问题．摩托车转弯时需要向心力F而其大小为mx^2／R．弯越急、车速越快，所需向心力就越大．向心力主要是地面对车轮的静摩擦力(如图1)．其方向指向圆弧的圆心，且与车的运动方向垂直，其作用点是路面与车轮的接触点．作用点随车轮的滚动而不断地变化．只要摩托车转弯所需的向心力不超过路面对车轮的最大静摩擦力，车就不会冲出赛道并横向滑倒．     

对滑动摩擦力做功问题的分析

计算滑动摩擦力做功的问题在中学和大学物理教学中经常出现,在一些物理书刊上也经常出现.这里,先讲一下计算滑动摩擦力做功的传统方法及其存在的问题,然后谈对这个问题的看法.     

力做功的求解方法

一个变力做功的问题,求解方法一般不只一种,但大部分运用动能定理、功能原理等方法求解,本文通过一道例题探讨变力做功的另一种解法.     

圆轮在固定面纯滚动时加速度瞬心的轨迹分析

推导了圆轮在固定面上纯滚动时其上任意点的加速度计算公式,数值分析了圆轮在固定面纯滚动时加速度瞬心轨迹的分布规律,可加深理解圆轮纯滚动时的运动规律,为平面运动图形上点的加速度分析提供了另一种有效方法.     

Trees at an Interface

A lattice tree at an interface between two solvents of different quality is examined as a model of a branched polymer at an interface. Existence of the free energy is shown, and the existence of critical lines in its phase diagram is proven. In particular, there is a line of first order transitions separating a positive phase from a negative phase (the tree being predominantly on either side of the interface in these phases), and a curve of localization–delocalization transitions which separate the delocalized positive and negative phases from a phase where the tree is localized at the interface. This model is generalized to a branched copolymer which is examined in a certain averaged quenched ensemble. Existence of a thermodynamic limit is shown for this model, and it is also shown that the model is self-averaging. Lastly, a model of branched polymers interacting with one another through a membrane is considered. The existence of a limiting free energy is shown, and it is demonstrated that if the interaction is strong enough, then the two branched polymers will adsorb on one another.     

Design of a Reflective Aspherical Surface of a Compact Beam-Shaping Device

A compact beam-shaping device with a reflective aspherical surface is proposed. The device converts a circular symmetric Gaussian beam from a laser into a uniform distribution on a target plane. The device consists of a laser, a reflective aspherical surface formed on the base plane inclined by 45° against the optical axis, and a spacer. The surface is designed for an optical device used as a transmitter of indoor wireless optical communication, which is one of the promising applications. The designed surface is obtained by approximation using polynomial. Beam shaping of a simulated surface and a uniform intensity distribution on the target plane is obtained. The intensity distribution generated by the surface is numerically simulated and evaluated if the surface is misaligned. It is clarified that the generated distribution is tolerable for the misalignment.     

Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel

Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a “backward flow” is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.     

Relativity of quantum states in entanglement swapping

The entanglement swapping protocol is analyzed in a relativistic setting, where shortly after the entanglement swapping is performed, a Bell test is performed. For an observer in the laboratory frame, a Bell violation is observed between the qubits with the swapped entanglement. In a moving frame, the order of the measurements is reversed, and a Bell violation is observed even though the particles are not entangled, directly or indirectly, or at any point in time. Although the measurement results are identical, the wavefunctions for the two frames are starkly different — one is entangled and the other is not. Furthermore, for boosts in a perpendicular direction, in the presence of decoherence, we show that the maximum Bell violation can occur across non-simultaneous points in time. This is a signature of entanglement that is spread across both space and time, showing both non-local and non-simultaneous aspects of entanglement.     

The shape gradient of the least-squares objective functional in optimal shape design problems of radiative heat transfer

Optimal shape design problems of steady-state radiative heat transfer are considered. The optimal shape design problem (in the three-dimensional space) is formulated as an inverse one, i.e., in the form of an operator equation of the first kind with respect to a surface to be optimized. The operator equation is reduced to a minimization problem via a least-squares objective functional. The minimization problem has to be solved numerically. Gradient minimization methods need the gradient of a functional to be minimized. In this paper the shape gradient of the least-squares objective functional is derived with the help of the shape sensitivity analysis and adjoint problem method. In practice a surface to be optimized may be (or, most likely, is to be) given in a parametric form by a finite number of parameters. In this case the objective functional is, in fact, a function in a finite-dimensional space and the shape gradient becomes an ordinary gradient. The gradient of the objective functional, in the case that the surface to be optimized is given in a finite-parametric form, is derived from the shape gradient. A particular case, that a surface to be optimized is a “two-dimensional” polyhedral one, is considered. The technique, developed in the paper, is applied to a synthetic problem of designing a “two-dimensional” radiant enclosure.     

Open Systems Viewed Through Their Conservative Extensions

A typical linear open system is often defined as a component of a larger conservative one. For instance, a dielectric medium, defined by its frequency dependent electric permittivity and magnetic permeability is a part of a conservative system which includes the matter with all its atomic complexity. A finite slab of a lattice array of coupled oscillators modelling a solid is another example. Assuming that such an open system is all one wants to observe, we ask how big a part of the original conservative system (possibly very complex) is relevant to the observations, or, in other words, how big a part of it is coupled to the open system? We study here the structure of the system coupling and its coupled and decoupled components, showing, in particular, that it is only the systemrsquo;s unique minimal extension that is relevant to its dynamics, and this extension often is tiny part of the original conservative system. We also give a scenario explaining why certain degrees of freedom of a solid do not contribute to its specific heat.     

推广的一类Lie代数及其相关的一族可积系统

对已知的Lie代数An-1作直接推广得到一类新的Lie代数gl(n,C).为应用方便，本文只考虑Lie代数gl(3,C)情形.构造了gl(3,C)的一个子代数，通过对阶数的规定，得到了一类新的loop代数.作为其应用，设计了一个新的等谱问题，得到了一个新的Lax对.利用屠格式获得了一族新的可积系统，具有双Hamilton结构,且是Liouville可积系.作为该方程族的约化情形，得到了新的耦合广义Schrdinger方程. 关键词： Lie代数 可积系 Hamilton结构     

Secure Physical Layer Network Coding versus Secure Network Coding

When a network has relay nodes, there is a risk that a part of the information is leaked to an untrusted relay. Secure network coding (secure NC) is known as a method to resolve this problem, which enables the secrecy of the message when the message is transmitted over a noiseless network and a part of the edges or a part of the intermediate (untrusted) nodes are eavesdropped. If the channels on the network are noisy, the error correction is applied to noisy channels before the application of secure NC on an upper layer. In contrast, secure physical layer network coding (secure PLNC) is a method to securely transmit a message by a combination of coding operation on nodes when the network is composed of set of noisy channels. Since secure NC is a protocol on an upper layer, secure PLNC can be considered as a cross-layer protocol. In this paper, we compare secure PLNC with a simple combination of secure NC and error correction over several typical network models studied in secure NC.     

含单排线缺陷锯齿型石墨烯纳米带的电磁性质

基于密度泛函理论的第一性原理方法,研究了含单排线缺陷锯齿型石墨烯纳米带(ZGNR)的电磁性质,主要计算了该缺陷处于不同位置时的能带结构、透射谱、自旋极化电荷密度、总能以及布洛赫态.研究表明,含单排线缺陷的ZGNR和无缺陷的ZGNR在非磁性态和铁磁态下都为金属.虽然都为金属,但其呈金属性的成因有差异.在反铁磁态下,单排线缺陷越靠近ZGNR的边缘,对ZGNR电磁性质的影响越明显,缺陷由ZGNR对称轴线向边缘移动过程中,含单排线缺陷的ZGNR有一个半导体-半金属-金属的相变过程.虽然线缺陷靠近中线的ZGNR为半导体,但由于缺陷引入新的能带,导致含单排线缺陷的ZGNR的带隙小于无缺陷ZGNR的带隙.单排线缺陷紧邻边界时,含缺陷ZGNR最稳定;单排线缺陷位于次近邻边界位置时,含缺陷ZGNR最不稳定.在反铁磁态下,对单排线缺陷位于对称轴线的ZGNR施加适当的横向电场,可以实现半导体到半金属的转变.这些研究结果对于发展基于石墨烯的纳米电子器件有重要的意义.     

高功率宽调谐范围掺Yb3+光子晶体光纤激光器

采用闪耀光栅作为色散元件,构建了前向、后向输出两种结构的可调谐掺Yb3 光子晶体光纤激光器,并对其输出特性进行了分析研究.在抽运功率5.75W时,前向输出结构实现了1050.6～1110.2 nm的连续调谐输出,光谱线宽约0.1 nm,边模抑制比大于44 dB.在调谐激光波长为1085 nm时,得到最高输出功率677 mW.结构改进的后向输出结构的可调谐输出结构在抽运功率4.43 W,调谐波长1075 nm,实现了2.21 W的功率输出,斜率效率为73%;调谐范围50.9 nm(1042.1～1093 nm),光谱线宽小于0.08 nm,边模抑制比大于50 dB.两种结构的可调谐激光器输出均为线偏振光,偏振度大于89.5%.