Exact solutions to the problem on the shape of an uncharged conducting liquid jet in a transverse electric field

Exact solutions are obtained for the problem of an equilibrium configuration of an uncharged cylindrical jet of a conducting liquid in a transverse electric field. The transverse cross section of the jet moving between two planar electrodes is deformed under the action of electrostatic forces (capillary forces play a stabilizing role). According to the solutions obtained, the initially circular cross section of the jet may be significantly (formally, unboundedly) stretched along the lines of forces of the field, and the boundaries of the jet asymptotically approach the electrodes.     

Viscous fluid streamlet flow down an inclined superhydrophobic surface

The problem of a steady flow of a viscous streamlet down an inclined plane superhydrophobic surface in a gravity field is investigated. A nonlinear partial differential equation for determining the unknown form of the streamlet cross section is derived. A class of nonuniform superhydrophobic surfaces, which are characterized by an effective slip tensor, for which the construction of self-similar solutions of the problem under consideration is possible, is found. The necessary conditions for the existence of self-similar solutions are found. The self-similar shapes of the wetting region and the streamlet cross section are found numerically for two examples of superhydrophobic surfaces. The results of the investigation can be used when experimentally determining the effective characteristics of superhydrophobic surfaces, namely, the components of the effective slip tensor.     

Experimental investigation of an air-magnetic-liquid resonator

Experimental results obtained by studying a vibratory system in which a magnetic liquid playing the role of a mass shuts off the cross section of a tube under the effect of a magnetic field and is spring-loaded by an air cavity and elasticity of ponderomotive type are discussed. An expression for the resonant frequency of vibrations is derived with allowance for both types of elasticity. The expression agrees well with the experimental data.     

Dipole-exchange spin wave spectrum in an anisotropic ferromagnetic waveguide with a rectangular cross section

A theory has been constructed that strictly describes the spectrum of dipole-exchange spin waves in an arbitrarily magnetized anisotropic ferrite waveguide with a rectangular cross section. The theory takes into account the spatial inhomogeneity of the internal magnetic field in the waveguide cross section. The influence of parameters of the ferrite waveguide on the distribution of the internal magnetic field in the waveguide cross section is analyzed. The dispersion characteristics of two waveguide types most widely used in practice are investigated. The dipole-exchange spin wave spectra calculated for a transversely magnetized waveguide are presented and the distributions of the dynamic magnetization in the waveguide cross section for several types of volume and localized spin-wave modes are constructed.     

Photodetachment of H- near an elastic surface in a magnetic field

This paper investigates the photodetachment of the negative hydrogen ion H near an elastic wall in a magnetic field.The magnetic field confines the perpendicular motion of the electron,which results in a real three-dimensional well for the detached electron.The analytical formulas for the cross section of the photodetachment in the threedimensional quantum well are derived based on both the quantum approach and closed-orbit theory.The magnetic field and the elastic surface lead to two completely different modulations to the cross section of the photodetachment.The oscillation amplitude depends on the strength of the magnetic field,the ion-wall distance and the photon polarization as well.Specially,for the circularly polarized photon-induced photodetachment,the cross sections display a suppressed(E E th) 1/2 threshold law with energy E in the vicinity above Landau energy E th,contrasting with the(E E th) 1/2 threshold law in the presence of only the magnetic field.The semiclassical calculation fits the quantum result quite well,although there are still small deviations.The difference is attributed to the failure of semiclassical mechanics.     

Inelastic neutron scattering from superconducting rings

For the first time the differential cross section for the inelastic magnetic neutron scattering by superconducting rings is derived taking account of the interaction of the neutron magnetic moment with the magnetic field generated by the superconducting current. Calculations of the scattering cross section are carried out for cold neutrons and thin film rings from type-II superconductors with the magnetic fields not exceeding the first critical field.     

Nonlinear dynamics of a continuum Heisenberg spin chain with an anisotropy and an external magnetic field

By stereographically projecting the spin vector onto a complex plane in the equations of motion for a continuum Heisenberg spin chain with an anisotropy (an easy plane and an easy axis) and an external magnetic field, the effect of the magnetic field for integrability of the system is discussed. Then, introducing an auxiliary parameter, the Lax equations for Darboux matrices are generated recursively. By choosing the constants, the Jost solutions are satisfied the corresponding Lax equations. The exact soliton solutions are investigated, then the total magnetic momentum and its z-component are obtained. These results show that the solitary waves depend essentially on two velocities which describe a spin configuration deviating from a homogeneous magnetization. The depths and widths of solitary waves vary periodically with time. The center of an inhomogeneity moves with a constant velocity, while the shape of soliton also changes with another velocity and this shape is not symmetrical with respect to the center. The total magnetic momentum and its z-component vary with time.     

Magnetic bloch electron states and spin polarization in 2D superlattices without an inversion center with Rashba spin-orbit interaction in an electron gas

The quantum states of carriers in 2D doubly periodic n-type semiconducting superlattices without spatial inversion symmetry in an external magnetic field are calculated in the one-electron approximation. It is shown that the spin-orbit interaction and spin splitting in the magnetic field may lead to the occurrence of the photovoltaic effect in a 2D electron gas without an inversion center and to a nonzero spin magnetization of the electron gas in the plane perpendicular to the magnetic field.     

Resonance Compton scattering in an external magnetic field

The scattering of a photon by an electron in an external magnetic field under resonant conditions, when the photon energy is close to the splittings between the Landau levels, is investigated. Formulas are obtained for the cross section of the process taking account of the polarization of the electron. For external fields ～10¹² G the resonant Compton cross section is several orders of magnitude greater than the Thompson cross section, and the width of the resonance is tens of electron volts.     

光束截面的动量守恒及动量衍射发散度

在忽略了瞬逝波的条件下，证明真空中单色标量光场的光束截面的动量及其任一分量都与轴向坐标无关，为守恒量；文中还给出了动量衍射发散度的表达式。     

Kirchhoff方程的相对常值特解及其Lyapunov稳定性

对于超细长弹性杆静力学的Kirchhoff方程，用动力学的概念和方法研究其常值特解 和稳定性问题.计算了Kirchhoff方程相对固定坐标系、截面主轴坐标系以及中心线Frenet 坐标系的常值特解，进行了Kirchhoff动力学比拟，用一次近似理论分别讨论了它们的Lyapu nov稳定性，导出了若干稳定性判据，并在参数平面上绘出了稳定域. 关键词： 超细长弹性杆 Kirchhoff方程 常值特解 Lyapunov稳定性     

氢负离子在磁场和电介质表面附近光剥离的研究

利用闭合轨道理论, 研究了变化的磁场和不同电介质表面对氢负离子光剥离截面的影响, 并推导出了该体系下的光剥离截面公式. 结果发现, 氢负离子的光剥离截面不仅与磁场的强度有关, 而且还与电介质常数有关. 当氢负离子到电介质表面的距离和电介质常数一定时, 体系的光剥离截面中的振荡随磁场的变化而明显变化. 随着磁场强度的 增大, 体系的闭合轨道数目增多, 光剥离截面的振荡越来越复杂. 当氢负离子到电介质表面的距离和磁场强度一定时, 电介质常数的变化对光剥离截面的影响也很重要, 随着电介质常数的增大, 体系的闭合轨道数目增多, 光剥离截面的振荡也变得越来越复杂. 因此, 可以通过改变磁场强度和电解质常数来调整负离子的光剥离截面. 此结果 对于研究负离子体系在表面附近和外场中的光剥离问题具有一定的参考价值.     

Scattering by an array of parallel metallic carbon nanotubes

The scattering of electromagnetic wave by an array of parallel metallic single-walled carbon nanotubes is investigated based on the boundary-value method. Electronic excitations over each nanotube surface are modeled as an infinitesimally thin cylindrical layer of the free-electron gas. The scattering cross section of both transverse magnetic （TM） and transverse electric （TE） uniform plane waves by the system at normal incidences is obtained.     

弹性压扭直杆的Greenhill公式对精确模型的推广

将圆截面Kirchhoff弹性压扭直杆的Greenhill公式推广到精确模型.基于平面截面假定,在弯扭的基础上增加了拉压和剪切变形,将弹性杆的位形表达为截面的弧坐标历程.由弹性杆精确模型的平衡微分方程,得到了两端受力螺旋作用时对应于直线平衡状态的特解,导出了线性化扰动方程及其通解,再根据两端为铰支时的边界条件以及积分常数存在非零解的条件导出弹性直杆精确模型的Greenhill公式.结果表明,由力螺旋表示的稳定域为一对称的封闭区域,拉压和剪切对稳定性的影响取决于拉压柔度与剪切柔度之差、抗弯刚度和杆长这三个因素.     

Scattering from an anisotropic cylindrical dielectric shell

The electromagnetic scattering from an anisotropic cylindrical dielectric shell is formulated by using the wave functions for anisotropic media and the boundary-value method. The cylindrical shell is assumed to be infinite in length, and it is illuminated by a plane wave or a cylindrical wave from a line source. The problem is two-dimensional and the solutions to both types of polarization (TE and TM) are presented. Numerical results for the effects of various geometrical and electrical parameters on the bistatic radar cross section are presented.     

求任意形状截面无限长直载流螺线管磁场的一种方法

在电磁学中,无限长直载流螺线管的磁场是一个基本与核心的问题,为了得到这一系统的磁场,通常的做法是：先就圆截面情况计算,然后把截面为任意形状无限长直螺线管看成是由无数大大小小的圆截面螺线管叠加而成,由此得到螺线管内的磁场均匀而管外磁场为零的一般结论.这里给出了一种推导截面为任意形状无限长直螺线管内外磁场的直接方法.先计算螺线管表面一窄条的磁场,再算总磁场.这种方法物理图像清楚,数学过程简单,可以在教学中加以应用.     

Backward Compton scattering and QED with noncommutative plane in the strong uniform magnetic field

In the strong uniform magnetic field, the noncommutative plane (NCP) caused by the lowest Landau level (LLL) effect, and QED with NCP (QED-NCP) are studied. Being similar to the condensed matter theory of quantum Hall effect, an effective filling factor f(B) is introduced to characterize the possibility that the electrons stay on the LLL. The analytic and numerical results of the differential cross section for the process of backward Compton scattering in accelerator with unpolarized or polarized initial photons are calculated. The existing data of BL38B2 in Spring-8 have been analyzed roughly and compared with the numerical predictions primitively. We propose a precise measurement of the differential cross sections of backward Compton scattering in a strong     

Dark soliton interaction of spinor Bose-Einstein condensates in an optical lattice

We study the magnetic soliton dynamics of spinor Bose-Einstein condensates in an optical lattice which results in an effective Hamiltonian of anisotropic pseudospin chain. An equation of nonlinear Schrödinger type is derived and exact magnetic soliton solutions are obtained analytically by means of Hirota method. Our results show that the critical external field is needed for creating the magnetic soliton in spinor Bose-Einstein condensates. The soliton size, velocity and shape frequency can be controlled in practical experiment by adjusting the magnetic field. Moreover, the elastic collision of two solitons is investigated in detail.     

Backward Compton scattering and QED with noncommutative plane in the strong uniform magnetic field

In the strong uniform magnetic field,the noncommutative plane(NCP) caused by the lowest Landau level (LLL) effect,and QED with NCP (QED-NCP) are studied.Being similar to the condensed matter theory of quantum Hall effect,an effective filling factor f(B) is introduced to characterize the possibility that the electrons stay on the LLL.The analytic and numerical results of the differential cross section for the process of backward Compton scattering in accelerator with unpolarized or polarized initial photons are calculated.The existing data of BL38B2 in Spring-8 have been analyzed roughly and compared with the numerical predictions primitively.We propose a precise measurement of the differential cross sections of backward Compton scattering in a strong perpendicular magnetic field.which may reveal the effects of NCP.