Connections Between the Riemann and the Lorentz Force Laws

It is known that for the magnetic force due to a closed circuit, the Weber force law can be identical to the Lorentz force law. In this investigation it is shown that for both the electric and the magnetic force of the quasi-static case, the Riemann force law can be identical to the Lorentz force law, while the former is based on a potential energy depending on a relative speed and is in accord with Newton's law of action and reaction.     

Force law in material media,hidden momentum and quantum phases

We address to the force law in classical electrodynamics of material media, paying attention on the force term due to time variation of hidden momentum of magnetic dipoles. We highlight that the emergence of this force component is required by the general theorem, deriving zero total momentum for any static configuration of charges/currents. At the same time, we disclose the impossibility to add this force term covariantly to the Lorentz force law in material media. We further show that the adoption of the Einstein–Laub force law does not resolve the issue, because for a small electric/magnetic dipole, the density of Einstein–Laub force integrates exactly to the same equation, like the Lorentz force with the inclusion of hidden momentum contribution. Thus, none of the available expressions for the force on a moving dipole is compatible with the relativistic transformation of force, and we support this statement with a number of particular examples. In this respect, we suggest applying the Lagrangian approach to the derivation of the force law in a magnetized/polarized medium. In the framework of this approach we obtain the novel expression for the force on a small electric/magnetic dipole, with the novel expression for its generalized momentum. The latter expression implies two novel quantum effects with non-topological phases, when an electric dipole is moving in an electric field, and when a magnetic dipole is moving in a magnetic field. These phases, in general, are not related to dynamical effects, because they are not equal to zero, when the classical force on a dipole is vanishing. The implications of the obtained results are discussed.     

Numerical calculations of the driving force on an Abrikosov vortex

The driving force on an Abrikosov vortex is calculated numerically from the London equation and involved energies for a vortex perpendicular to the screening current near the surface of a superconductor. Compared with previous analytical derivation of the total force, the partial magnetic, kinematic, and external forces are also obtained so that the nature of the driving force may be deeply discussed. It is shown that the force is neither a Lorentz force nor a Magnus force as often believed and that in order to get a correct result, the image effects and the work done by the applied field must be taken into account. A name of London force is suggested for the driving force. A deep understanding of the nature of the driving force on Abrikosov vortices may also be important in the study of vortex pinning and dynamics in type-II superconductors.     

驻波场中相位迟后的偶极力

计算了二能级原子在一个驻波场中的辐射压力，给出了在不对空间平均时的辐射压力的普遍表达式，指出辐射压力的零级项应应于受激压力，而一级项对应于偶极力，高队项则可忽略。文中详细地计算了各种不同情况下的偶极力和相位，指出对于不同速度，相位有不同的迟后，这样的结果将严重地影响原子在驻波场中的动力学，用光子再分配模型简单地对有力的相位随速度的变化作了解释。     

利用激光光梯度力消除气溶胶雾霾粒子的机理研究

针对气溶胶雾霾粒子在大气流中所受力的平衡体系(旋转升力平衡重力, 粒子与粒子之间依靠斥力形成稳定的网状的力平衡体系)的问题, 提出了用激光光梯度力破坏力平衡进而消除雾霾的新机理. 首先, 根据牛顿第二定理, 得到了粒子所受力的非线性方程组, 应用Runge-Kutta 法积分求解了雾霾颗粒在大气流中所受的主要力(空气曳引阻力、范德瓦耳斯斥力、旋转升力)的数值, 成功验证了西安市2013年12月17-25日、2014年2月20-26日两次雾霾检测试验结论: 在雾霾过程中, 粒径在0.5-0.835 μm径段的粒子数浓度增加最明显. 其次, 在雾霾粒子形成的均匀介质中, 计算了激光光梯度力的大小. 研究发现, 激光光梯度力的数量级恒大于雾霾颗粒所受主要力的数量级, 激光光梯度力完全可以破坏雾霾颗粒所受力的平衡体系. 因此, 用激光光梯度力消除雾霾是可行的, 这种新的解决雾霾的方法对人们的实际生活、环保及创建美丽的蓝天具有非常重要的意义.     

An overlooked electrostatic force that acts on a non-charged asymmetric conductor in a symmetric (parallel) electric field

Usually, when a material that has charge Q is placed in an electric field E, an electrostatic force F = QE acts on the material. This force does not act on a non-charged material. Nevertheless, when a non-charged material is placed in a convergent field, another electrostatic force acts. This force is called the gradient force. If the material is small and the shape is a sphere, the gradient force can be calculated by an approximate formula, but it cannot be calculated for other shapes. In this paper the gradient force that acts on a symmetric rod conductor in a convergent (asymmetric) field was simulated by an axis symmetry finite difference method.Under same simulation conditions without the next two points, the shape of the conductor and the form of the field were reversed. The shape of the conductor was changed into an asymmetric shape (e.g. bat shape), and the form of the field was changed into a symmetric (parallel) one. The electrostatic force that acts on the asymmetric conductor in the symmetric (parallel) field was simulated. It was found that approximately the same intensity force as in the first simulation also acts on this conductor. This force is thought to be an overlooked electrostatic force. I provisionally call it the asymmetric force in this paper.The asymmetric force with differently shaped conductors was simulated and it was found that the asymmetric force was maximized for a cup shaped conductor.Finally, the asymmetric force with the cup shaped conductor in normal and reversed parallel (symmetric) fields was simulated, and it was confirmed that the asymmetric force remains the same in both fields.     

气温和颗粒密度对声场中颗粒动力学影响的数值模拟

综合考虑黏性夹带力、Basset力、虚拟质量力和压力梯度力,建立颗粒在声场中的动力学模型,利用变步长四阶RungeKutta算法和二阶隐式Adams插值算法对颗粒的受力和运动进行数值模拟。将模拟和实验得到的颗粒运动特性进行对比,验证数值模拟的正确性。在此基础上,研究气温和颗粒密度对颗粒动力学的影响规律。结果表明,黏性夹带力对颗粒运动起主导作用;气温升高,压力梯度力与黏性夹带力之间的相位差减小,Basset力、虚拟质量力与黏性夹带力之间的相位差增大。研究还发现,气温较低时,颗粒密度对颗粒运动有重要影响,夹带系数随着密度的增加而迅速下降;气温较高时,颗粒密度对颗粒运动的影响较小,颗粒位移振幅和夹带系数相对低温时明显增加。      

Multifrequency radiation force of acoustic waves in fluids

In this article we introduce the concept of multifrequency radiation force produced by a polychromatic acoustic beam propagating in a fluid. This force is a generalization of dynamic radiation force due to a bichromatic wave. We analyse the force exerted on a rigid sphere by a plane wave with N frequency components. Our approach is based on solving the related scattering problem, taking into account the nonlinearity of the fluid. The radiation force is calculated by integrating the excess of pressure in the quasilinear approximation over the surface of the sphere. Results reveal that the spectrum of the multifrequency radiation force is composed of up to N(N−1)/2 distinct frequency components. In addition, the radiation force generated by plane progressive waves is predominantly caused by parametric amplification. This is a phenomenon due to the nonlinear nature of wave propagation in fluids.     

Laser-induced force for bubble-trapping in liquids

The laser-induced thermal force that traps a bubble in an absorbing liquid is studied theoretically and experimentally. The force origins from the thermal gradients of the surface tension induced by a laser beam over the bubble surface. It is shown that this force is proportional to the square of the bubble radius and to the thermal gradient of the surface tension. A simple experimental method based on comparison with the Archimedes' flotation force, is used for the measurement of this force. The experimental results, performed on ethanol solutions of iodine, confirm the theoretical predictions.     

Force between a magnetic tip and an inhomogeneous superconductor at zero field

The force exerted by a semi-infinite inhomogeneous superconductor with a planar interface to vacuum on a magnetic tip is studied theoretically in the absence of external magnetic fields. It is shown that the force has a contribution from inhomogeneities due to material defects with unique characteristics. Defects are taken into account in the London limit by allowing the mass parameter to vary spatially. The contribution from defects to the force is calculated analytically to first order in the deviation of the mass parameter from its constant value for the homogeneous superconductor, assuming that the tip is a point dipole perpendicular to the interface, and that it does not spontaneously create vortex matter. Random point defects and linear localized defects are considered phenomenologically. For each defect type the force dependence on the dipole position coordinates is obtained, and the force magnitudes are estimated numerically. The predictions for the dependence of the linear defect force on the dipole lateral position are found to agree qualitatively with experiment.     

Ion larmour radius effect on rf ponderomotive forces and induced poloidal flow in tokamak plasmas

Analytical approximations are used to clarify the effect of Larmour radius on rf ponderomotive forces and on poloidal flows induced by them in tokamak plasmas. The electromagnetic force is expressed as a sum of a gradient part and of a wave momentum transfer force, which is proportional to wave dissipation. The first part, called the gradient electromagnetic stress force, is combined with fluid dynamic (Reynolds) stress force, and gyroviscosity is included into viscosity force to model finite ion Larmour radius effects in the momentum response to the rf fields in plasmas. The expressions for the relative magnitude of different forces for kinetic Alfven waves and fast waves are derived.     

非球形效应对强声场中次Bjerknes力的影响

考虑了非球形气泡在声场中的形状振动,推导了非球形气泡和球形气泡之间的次Bjerknes力方程,数值模拟了声场中非球形气泡和球形气泡之间的次Bjerknes力和两个球形气泡之间的次Bjerknes力,并对非球形气泡和球形气泡之间的次Bjerknes力的影响因素进行了分析讨论.研究结果表明:当驱动声压振幅大于非球形气泡的Black阈值且又能使得非球形气泡稳定振动时,在第一个声驱动周期内,非球形气泡和球形气泡之间的次Bjerknes力和两个球形气泡的次Bjerknes力方向差异较大,在大小上是两个球形气泡次Bjerkens力的数倍,且有着更长的作用距离.非球形气泡和球形气泡之间的次Bjerknes力取决于非球形气泡的形状模态、两个气泡初始半径的比值、驱动声压振幅、气泡间距和两个气泡的相对位置.     

Effect of polarization force on the Jeans instability of self-gravitating dusty plasma

The effect of polarization force acting on massive charged dust grains is investigated analytically on the Jeans instability of self-gravitating dusty plasma. The gravitational force acting on the massive negatively charged interstellar dust grains are considered in presence of both electrical and polarization forces. The basic equations of the problem are formulated and a general dispersion relation is obtained using plane wave approximation in low frequency wave mode. The effect of polarization force in the dispersion relation of the problem, condition of the Jeans instability and expression of the critical Jeans wave number is examined. The unstable growing modes due to self-gravitational force are studied in the situation when polarization force on the dust grain exceeds over the electrical force in magnitude. It is observed that the polarization force increases the growth rate of the system.     

路堤倾角变化对高速列车侧风运行气动特性影响

采用计算流体力学方法,探讨路堤倾角变化对高速列车侧风运行气动特性影响.结果表明:随着路堤倾角增大,头车侧向力系数先增加后减小,而中间车侧向力系数则持续减小.尾车上的侧向力系数先是略微减小,当路堤倾角达到47.5°时,侧向力系数随倾角增加而增加.作用在中间车上的负升力随着路堤倾角增加而增加.尾车的升力系数对路堤倾角变化非常敏感,变化幅度较大.路堤倾角变化时高速列车绕流流场变化,从而导致列车受到的气动力发生变化.     

Finite-temperature Casimir effect in piston geometry and its classical limit

We consider the Casimir force acting on a d-dimensional rectangular piston due to a massless scalar field with periodic, Dirichlet and Neumann boundary conditions and an electromagnetic field with perfect electric-conductor and perfect magnetic-conductor boundary conditions. The Casimir energy in a rectangular cavity is derived using the cut-off method. It is shown that the divergent part of the Casimir energy does not contribute to the Casimir force acting on the piston, thus renders an unambiguously defined Casimir force acting on the piston. At any temperature, it is found that the Casimir force acting on the piston increases from −∞ to 0 when the separation a between the piston and the opposite wall increases from 0 to ∞. This implies that the Casimir force is always an attractive force pulling the piston towards the closer wall, and the magnitude of the force gets larger as the separation a gets smaller. Explicit exact expressions for the Casimir force for small and large plate separations and for low and high temperatures are computed. The limits of the Casimir force acting on the piston when some pairs of transversal plates are large are also derived. An interesting result regarding the influence of temperature is that in contrast to the conventional result that the leading term of the Casimir force acting on a wall of a rectangular cavity at high temperature is the Stefan–Boltzmann (or black-body radiation) term which is of order T ^d+1, it is found that the contributions of this term from the two regions separating the piston cancel with each other in the case of piston. The high-temperature leading-order term of the Casimir force acting on the piston is of order T, which shows that the Casimir force has a nontrivial classical ℏ→0 limit. Explicit formulas for the classical limit are computed.     

纳米接触过程中黏着规律的变化

本文应用大规模分子动力学方法, 模拟了两种具有不同粗糙形貌的、刚性球形探头与弹性平面基体之间的纳米尺度接触, 计算了探头与基体之间的拉离力和黏着功, 研究了接触过程中界面黏着力随载荷的变化规律, 分析了接触界面原子的法向应力分布. 研究发现, 原子级光滑接触的黏着力随着载荷的增大而线性增大, 而原子级粗糙接触的黏着力-载荷曲线分为以不同斜率增长的两个阶段. 相比于原子级光滑探头, 原子级粗糙探头与基体之间具有较小的拉离力和黏着功, 却在接触过程中形成了较大的黏着力. 因此, 拉离力和黏着功不能表征出纳米接触过程中原子吸引作用对界面法向力的贡献大小.     

Calculation of the electric potential and Lorentz force acting on a locally ionized region in a magnetohydrodynamic flow placed in a nonuniform magnetic field

An analytical solution to electrodynamic equations for the electric potential in a locally ionized magnetohydrodynamic (MHD) flow in the nonuniform magnetic field produced by a straight-line conductor is found. Analytical formulas are obtained to evaluate the volume density of the Lorentz force and the integral Lorentz force acting on the locally ionized region of the MHD flow. It is shown that the MHD action on the locally ionized flow in the nonuniform magnetic field can be used to control the elevating force as well as the ratio of the elevating force to the drag force.     

载荷对壁虎刚毛束的摩擦各向异性特性影响的实验研究

用离体壁虎刚毛阵列在自制微黏附摩擦测试台上对预加载荷对刚毛摩擦与黏着的各向异性特性的影响进行了实验研究.实验结果表明,在逆壁虎刚毛自然弯曲方向卷出实现脱附时, 刚毛所受摩擦力与法向力成正比,摩擦系数为0.6;沿顺刚毛自然弯曲方向卷入实现黏附时, 随预载荷增加摩擦力增加,法向力由黏附力变为斥力.在同等预载荷下,卷入方向的摩擦力是卷出方向的2倍以上. 本文提出了摩擦各向异性特征参数,对壁虎刚毛的黏着与摩擦各向异性进行了定量表征, 这种特性是由刚毛的弯曲及多等级结构决定的. 关键词： 壁虎刚毛 黏着 摩擦 各向异性     

Casimir-Polder力对左手材料板附近的原子的动力学作用

本文研究了初始处于激发态的两能级原子在左手材料附近运动时Casimir-Polder力对原子动力学的影响. 左手材料有两个的作用: 一是在距离界面波长区域内提供了较强的Casimir-Polder共振力, 二是在这一范围原子的自发辐射受到抑制, 延长了作用时间. 这两种效应使得依靠原子自发辐射这一过程中的Casimir-Polder力能对原子的运动学产生影响, 并将一定初速度的原子排斥远离界面. 由于原子偶极矩的取向会影响Casimir-Polder力的性质, 因此对于某些初始条件(初速度和初始位置), 不同偶极矩取向的原子有不同的运动学结果, 会被吸引到界面或反射出去, 从而对具有不同偶极矩方向的原子进行筛选. 当然由于Casimir-Polder力很小, 能够反射的初速度也很小, 但是已经可以反抗极低温的热涨落, 我们的理论预估值约为15 μupK. 如果和其他约束手段同时作用, 便能对原子的动力学产生更为有利的控制.     

Atoms near magnetodielectric bodies: van der Waals energy and the Casimir-Polder force

Based on macroscopic QED in linear, causal media, a consistent theory for the Casimir-Polder force acting on an atom positioned near dispersing and absorbing magnetodielectric bodies is presented. The perturbative result for the van der Waals energy is shown to exhibit interesting new features in the presence of magnetodielectric bodies. To go beyond perturbation theory, we start with the center-of-mass equation of motion and derive a dynamical expression for the Casimir-Polder force acting on an atom prepared in an arbitrary electronic state. For a nondriven atom in the weak coupling regime, the force as a function of time is shown to be a superposition of force components that are related to the electronic density matrix elements at a chosen time. These force components depend on the position-dependent polarizability of the atom, which correctly accounts for the body-induced level shifts and broadenings.