黏性介质中圆截面弹性细杆的平面振动

讨论圆截面弹性细杆在黏性介质中的平面振动. 基于Kirchhoff理论，以杆中心线的Frenet坐标系为参考系，建立其动力学方程，杆中心线为任意平面曲线时，其扭转振动与弯曲振动解耦. 讨论两端固定条件下任意形状杆的平面扭转振动，以及无扭转的轴向受压直杆和圆环杆的平面弯曲振动，导出其自由振动频率和阻尼系数. 证明空间域内压杆的Lyapunov稳定性和欧拉稳定性条件为时域内渐近稳定性的充分必要条件，或无阻尼压杆的稳定性必要条件. 圆环杆平衡恒满足渐近稳定性条件. 关键词： 弹性细杆 黏性介质 扭转振动 弯曲振动     

纵-扭复合振动模式指数型复合超声变幅杆的研究

本文对指数型纵－扭复合振动模式的复合超声变幅杆进行了理论及实验研究，该变幅杆由均匀截面直棒及指数型截面杆组成。文中推出了变幅杆中纵向振动及扭转振动的共振频率方程，通过发迹指数型变截面棒的截面变化规律，实现了同一变幅杆中纵向振动与扭转振动的同频共振。     

扭转超声振动系统中局部共振的研究

本文从扭转振动波动方程出发，推导出了具有类圆锥过渡段的复合阶梯型扭转变幅杆的频率方程解析表达式。从实验和理论上对该复合变幅杆的谐振频率随杆细端长度和直径的变化进行了测量和计算。通过对比，证明了复合振动系统中局部扭转共振现象的存在，并得到了其产生条件。     

影响弹簧扭转常数不确定度的因素分析

运用不确定度理论,推导了扭摆法测弹簧扭转常数的不确定度传递公式。通过应用塑料圆柱、金属圆筒和金属细杆三种不同形状的标准件来测量弹簧扭转常数,分析了影响测量弹簧扭转常数不确定度的几个因素,给出了减小实验误差的有效途径。     

圆截面弹性螺旋杆的稳定性与振动

基于Kirchhoff理论讨论圆截面弹性螺旋杆的动力学问题.以杆中心线的Frenet坐标系为参考系，建立用欧拉角描述的弹性杆动力学方程.讨论其在端部轴向力和扭矩作用下保持的无扭转螺旋线平衡状态.在静力学和动力学领域内讨论其平衡稳定性问题.还讨论了弹性杆平衡的Lyapunov稳定性和欧拉稳定性两种不同稳定性概念之间的区别和联系.在一次近似意义下证明了螺旋杆在空间域内的欧拉稳定性条件是时域内Lyapunov稳定性的必要条件.导出了解析形式螺旋杆三维弯曲振动的固有频率，为螺旋线倾角和受扰挠性线波数的函数. 关键词： 弹性螺旋杆 Kirchhoff动力学比拟 Lyapunov稳定性 欧拉稳定性     

SiC纳米杆的弛豫性能研究

采用Tersoff势对SiC驰豫性能进行了分子动力学模拟.模拟了SiC在驰豫过程中的动态平衡变化过程，研究了表面效应和小尺寸效应对原子位置，原子能量分布的影响.模拟结果表明，SiC纳米杆受表面效应和小尺寸效应的影响很大，在不加外载和约束的情况下，出现了不同于宏观SiC杆的弯扭屈伸现象，最终形成了带有一定扭转弯曲量、总能量达到最低的稳定状态. 关键词： SiC纳米杆 分子动力学 表面效应 小尺寸效应     

黏性流体中超细长弹性杆的动力学不稳定性

基于坐标基矢摄动的方法研究了黏性流体中超细长弹性杆动力学稳定性判据与失稳后的模态选择,推导出了黏性介质中超细长弹性杆Kirchoff动力学方程的一阶摄动表示,即线性的二阶偏微分方程组.以平面扭转DNA环为例,说明了以上结果的应用,得到了平面扭转DNA环的稳定性判据及其稳定的临界区域,讨论了其失稳后的模态选择及黏性阻力对其的影响.     

扭转角测量系统中焦距误差分析

针对莫尔条纹测量扭转变形方案，分析了双光栅在光学系统存在焦距误差时对扭转角测量精度的影响。通过在传统的莫尔条纹测量扭转角理论公式的基础上引入焦距对于光栅像的缩放效应，推导出含有焦距因子的扭转角测量模型。由模型可知,随着光学系统焦距差异的增大，对应的扭转角也会随之发生较大变化。特别当光栅夹角在小角度范围（1°～3°）内变化时尤为明显，最终影响到扭转变形的测量精度。在设计的实验中，利用2个已知焦距的光学系统，通过采集莫尔条纹图像进行扭转角精度分析，验证了该文提出的理论。     

强阻尼非线性热弹耦合杆系统的全局吸引子

本文主要以算子半群理论为依据,证明了一类强阻尼非线性热弹耦合杆方程组在初边值条件下,全局吸引子的存在性,并且对吸引子维数做了估计. 关键词： 热弹耦合杆系统 强阻尼 非线性 全局吸引子     

矩形扭转压电换能器的研制

本文从压电和机械振动等基本理论出发，首次较系统地建立了矩形扭转压电换能器的理论，推导出频率方程，并通过实验进行了验证。     

Effect of the dependence of the specular reflectance on the angle of incidence of electrons on the impedance

We obtain the solution to the problem of the skin effect in a metal with specular-diffusion boundary conditions for arbitrary values of the anomaly parameter in the form of the Neumann series. For this purpose, we develop a method based on the idea of representation of not only the boundary condition imposed on the field (as is conventionally done), but also the boundary condition imposed on the distribution function, in the form of a source. The specular reflectance is an arbitrary function of the angle of incidence of electrons on the metal surface.     

Violations of the Pauli principle and the interior of the sun

The consequences of a violation of the Pauli principle for the physics of the solar interior are explored. It is found that a bound state of two protons becomes possible. This leads to an increase in the rate of hydrogen burning in the sun. Because a very large cross section for this reaction is in clear contradiction with the theory of stellar structure when compared with observations of solar luminosity, radius and mechanical oscillations, stringent limits on a violation of the Pauli principle in the two nucleon system can be given. However, a very small violation of the Pauli principle in the two nucléon system might solve the longstanding solar neutrino problem.     

Singularity index of the electromagnetic field on the edge in the presence of the Veselago medium

The singularity index of the electromagnetic field on the edge of wedge structures of two types (with and without ideally conducting sides) is investigated in the presence of a sector of a medium with negative permittivity and permeability (the Veselago medium). Restrictions on the material and geometrical parameters at which the condition on the edge is violated are determined. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 56–58, August, 2006.     

On the effect of spontaneous polarization on the height of the Schottky barrier at the metal-ferroelectric contact

A comparison of the available concepts on the effect of spontaneous polarization on the height of the Schottky barrier at the metal-ferroelectric contact with the corresponding experimental data has been used as a basis for setting up an alternative model of this phenomenon, which draws on the dependence of the electron work function of a ferroelectric on the magnitude and orientation of the spontaneous polarization vector.     

Investigation of the morphology of the van der Waals surface of the InSe single crystal

The morphology of the (0001) van der Waals surfaces of the layered single crystal In_1.03Se_0.97, which were prepared using different techniques, has been investigated by scanning probe microscopy methods. It has been assumed that the van der Waals surface prepared with the use of an adhesive tape oxidizes in air due to the chemisorption of acid agents on dangling bonds of the metal and selenium. An analysis of the current-voltage characteristics of the tunneling current has shown that the composition of natural oxides represents a mixture of phases of the In₂O₃ oxide and wide-band-gap selenium oxides. In the InSe surface prepared by cleavage with subsequent exposure in air for approximately 2 min, the scanning with a tunneling microscope has revealed a surface ordering in the form of a corrugation of a complex profile with a fine structure. The last fact reflects the charge density redistribution after the chemisorption of gas molecules from air on this surface and its relaxation to the state with a minimum energy. Atoms of the basal plane are observed on the InSe(0001) van der Waals surface prepared by cleavage in an oxygen-free medium. The surface corrugation is absent. Point defects cause a disturbance of the periodic potential of the single crystal, which extends over a distance equal to four lattice spacings and appears as a shadowing. A technique has been proposed for producing In₂O₃ oxide nanostructures on the surface of the single crystal of the layered semiconductor InSe with the use of an atomic-force microscope probe as a nanoindenter. The ability of the probe to operate in gaseous and liquid media significantly extends the capabilities of the method.     

Constraining the topology of the universe

The first year data from the Wilkinson Microwave Anisotropy Probe are used to place stringent constraints on the topology of the Universe. We search for pairs of circles on the sky with similar temperature patterns along each circle. We restrict the search to back-to-back circle pairs, and to nearly back-to-back circle pairs, as this covers the majority of the topologies that one might hope to detect in a nearly flat universe. We do not find any matched circles with radius greater than 25 degrees. For a wide class of models, the nondetection rules out the possibility that we live in a universe with topology scale smaller than 24 Gpc.     

On the description of quadratic and cubic optical effects of propagation of femtosecond pulses within the framework of the model of the saturable potential

It is shown that, for describing the simultaneous manifestation of nonlinear effects of different orders (quadratic, cubic, etc.) in propagation of high-intensity femtosecond pulses, it is sufficient to use the saturable potential of the restoring force. With the use of computer simulation, it is demonstrated that the spectrum of the response of a medium calculated on the basis of the Duffing equation with quadratic and cubic nonlinearity is in qualitative agreement with the spectrum calculated on the basis of the equation with a saturable restoring force. The dependence of the frequency corresponding to the maximum spectral radiance on the duration of the interacting pulse is discussed. It is noted that, for ultrashort pulses, even in the case of their propagation in a linear medium, the response can occur at the natural frequency rather than at the frequency of the propagating pulse.     

Application of the Modified Method of Discrete Sources and the Method of Pattern Equations to the Solution of the Problem of Wave Diffraction on a Body with a Rough Boundary

Optics and Spectroscopy - A two-dimensional diffraction problem on a cylindrical body with a rough boundary has been considered. In this paper, two aspects of the diffraction problem on a body with...     

Determination of the mass spectrum of the bound state in the framework of the relativistic hamiltonian approach

We propose one a variant of calculation of the energy spectrum of bound state systems with relativistic corrections. In the framework of quantum field theory, an expression that takes into account relativistic corrections to the mass of the bound state with a known nonrelativistic pair interaction potential is proposed on the basis of calculating the asymptotic behavior of correlation functions of the corresponding field currents with the necessary quantum numbers. Excluding the time variables allows one to determine nonperturbative corrections to the interaction potential. The following results have been obtained in the framework of this approach. The nonperturbative corrections arising due to the relativistic nature of a system to the interaction Hamiltonian are determined. The dependence of the constituent mass of bound-state forming particles on the free state mass and on the orbital and radial quantum numbers is analytically derived. The energy level shift of muonic hydrogen taking into account relativistic corrections is calculated. The energy spectrum of a wide class of potentials that describe the Coulomb bound state is analytically derived with relativistic corrections. The mass spectrum of the glueballs and the constituent masses of the gluons are analytically calculated taking into account spin-orbit, spin—spin, and tensor interactions. Our numerical results have shown very good agreement with the lattice data. Taking into account nonperturbative and nonlocality characters of interactions, the mass spectrum of the mesons consisting of light-light and light-heavy quarks with orbital and radial excitations is determined. Our results show that good agreement with the experimental data for the slope and the intercept of the Regge trajectory can be obtained only taking into account the nonperturbative and the nonlocal characters of interactions. The dependences of the constituent masses of constituent particles on the masses of a free state are certain. When quarks are light, then the difference between current and valent masses of quarks is greater than valent masses of quarks, and when quarks are heavy, then the difference between these masses is insignificant. One of the alternative variants of taking nonlocality into account has been suggested for the definition of properties of hadrons at large distances. The dependence of the constituent masses of constituent particles on the radius of confinement is determined.     

The determination of the refractive index and the thickness of thin films of aluminium oxide on aluminium by the polarimetric method

Formulas for the reflection of light from glass (i. e. a dielectric) coated with a thin non-metallic film are generalized for the case of the reflection of light from a metal coated with a thin non-metallic film, e. g. a film of aluminium oxide on aluminium. It is shown how the refractive index and the thickness of the aluminium oxide film on an aluminium mirror can be determined by measurements in polarized light. In conclusion the results of Drude's classical theory of thin non-metallic films on metallic mirrors are compared with the results obtained by the author on the basis of the interference of light in thin films.