Electron spin torque in atoms

The spin torque and zeta force, which govern spin dynamics, are studied by using monoatoms in their steady states. We find nonzero local spin torque in transition metal atoms, which is in balance with the counter torque, the zeta force. We show that d-orbital electrons have a crucial effect on these torques. Nonzero local chirality density in transition metal atoms is also found, though the electron mass has the effect to wash out nonzero chirality density. Distribution patterns of the chirality density are the same for Sc–Ni atoms, though the electron density distributions are different.     

Motor-driven bacterial flagella and buckling instabilities

Many types of bacteria swim by rotating a bundle of helical filaments also called flagella. Each filament is driven by a rotary motor and a very flexible hook transmits the motor torque to the filament. We model it by discretizing Kirchhoff’s elastic-rod theory and develop a coarse-grained approach for driving the helical filament by a motor torque. A rotating flagellum generates a thrust force, which pushes the cell body forward and which increases with the motor torque. We fix the rotating flagellum in space and show that it buckles under the thrust force at a critical motor torque. Buckling becomes visible as a supercritical Hopf bifurcation in the thrust force. A second buckling transition occurs at an even higher motor torque. We attach the flagellum to a spherical cell body and also observe the first buckling transition during locomotion. By changing the size of the cell body, we vary the necessary thrust force and thereby obtain a characteristic relation between the critical thrust force and motor torque. We present a elaborate analytical model for the buckling transition based on a helical rod which quantitatively reproduces the critical force-torque relation. Real values for motor torque, cell body size, and the geometry of the helical filament suggest that buckling should occur in single bacterial flagella. We also find that the orientation of pulling flagella along the driving torque is not stable and comment on the biological relevance for marine bacteria.     

Angular dependence of vertical force and torque when magnetic dipole moves vertically above flat high-temperature superconductor

The interaction between a permanent magnet (PM) assumed as a magnetic dipole and a flat high-temperature superconductor (HTS) is calculated by the advanced frozen-image model. When the dipole vertically moves above the semi-infinite HTS, the general analytical expression of vertical force and that of torque are obtained for an arbitrary angle between the magnetization direction of the PM and the c axis of the HTS. The variations of the force and torque are analyzed for angle and vertical movements in both zero-field cooling (ZFC) condition and field cooling (FC) condition. It is found that the maximum vertical repulsive or attractive force has the positive or negative cosine relation with the angle. However, the maximum torque has the positive or negative sine relation. From the viewpoint of the rotational equilibrium, the orientation of the magnetic dipole with zero angle is deemed to be an unstable equilibrium point in ZFC, but the same orientation is considered as a stable equilibrium point in FC. In addition, both of the variation cycles of the maximum force and torque with the angle are π.     

Bessel驻波对椭球形液滴的声辐射转矩

在实际的声操控中,由于声辐射力、表面张力和重力的共同作用,液滴往往呈现出椭球的形状,在螺旋声场中会受到力矩的作用而发生转动。从声波的散射理论出发,根据部分波展开法求解得到了椭球形液滴在Bessel驻波场中的声散射系数,并给出了其受到的声辐射转矩的解析式。在此基础上,对椭球形不可压缩液滴和椭球形可压缩液滴分别进行数值计算。仿真结果表明,不可压缩液滴的声辐射转矩与声束半锥角的关系更密切,而可压缩液滴则更依赖于特定的频率;提升Bessel驻波场的阶数有利于增强声辐射转矩的峰值,但在中低频处较难对可压缩液滴产生明显的力矩。该研究结果预期对利用螺旋声场进行液滴的操控具有理论指导作用。      

Optical Force Sensing with Cylindrical Microcontainers

Quantitative force sensing reveals essential information for the study of biological systems. Forces on molecules, cells, and tissues uncover functioning conditions and pathways. To analyze such forces, spherical particles are trapped and controlled inside an optical tweezers (OT) trap. Although these spherical particles are well‐established sensors in biophysics, elongated probes are envisioned for remote force sensing reducing heat damage caused by OT. There is thus a growing demand for force metrology with OT using complexly shaped objects, e.g., sac‐like organelles or rod‐like bacteria. Here, the employment of Zeolite‐L crystals as cylindrical force sensing probes inside a single optical trap is investigated. It is shown that cylindrical objects can be used as force probes since existing calibration assays can be performed with suitable corrections. Forces of active driving assays are compared with passive calibration methods. Finally, the investigations are extended to direct force measurements based on momentum calibration, in which the influence of rotation due to torque in a single optical trap is unveiled. Simulations reveal the relation between torque and the position of equilibrium in the trap. The results highlight the functionality of Zeolite‐L crystals as probes for force sensing, while opening perspectives for enhanced, accurate force metrology in biophotonics.     

The Electrodynamic 2-Body Problem and the Origin of Quantum Mechanics

We numerically solve the functional differential equations (FDEs) of 2-particle electrodynamics, using the full electrodynamic force obtained from the retarded Lienard–Wiechert potentials and the Lorentz force law. In contrast, the usual formulation uses only the Coulomb force (scalar potential), reducing the electrodynamic 2-body problem to a system of ordinary differential equations (ODEs). The ODE formulation is mathematically suspect since FDEs and ODEs are known to be incompatible; however, the Coulomb approximation to the full electrodynamic force has been believed to be adequate for physics. We can now test this long-standing belief by comparing the FDE solution with the ODE solution, in the historically interesting case of the classical hydrogen atom. The solutions differ. A key qualitative difference is that the full force involves a delay torque. Our existing code is inadequate to calculate the detailed interaction of the delay torque with radiative damping. However, a symbolic calculation provides conditions under which the delay torque approximately balances (3rd order) radiative damping. Thus, further investigations are required, and it was prematurely concluded that radiative damping makes the classical hydrogen atom unstable. Solutions of FDEs naturally exhibit an infinite spectrum of discrete frequencies. The conclusion is that (a) the Coulomb force is not a valid approximation to the full electrodynamic force, so that (b) the n-body interaction needs to be reformulated in various current contexts such as molecular dynamics.     

空间弹性细杆在扭矩作用下的屈曲

用有限元方法研究了三维弹性细杆在扭矩作用下的屈曲.利用自然坐标形式的细长空间曲杆的能量方程和2节点12个自由度的自然坐标形式的三维曲梁单元,采用特征值分析方法,研究分析了同时受有轴力和扭矩作用时的空间弹性细杆的屈曲问题.数值结果与存在的理论解极为吻合.具有一定曲率和挠率的空间细长曲杆,其临界扭矩值与扭矩的指向有着极其明显的关系.     

Radiation force and torque on a two-dimensional circular cross-section of a non-viscous eccentric layered compressible cylinder in acoustical standing waves

The purpose of this study is to develop an analytical formalism and derive series expansions for the time-averaged force and torque exerted on a compound coated compressible liquid-like cylinder,insonified by acoustic standing waves having an arbitrary angle of incidence in the polar(transverse)plane.The host medium of wave propagation and the eccentric liquid-like cylinder are non-viscous.Numerical computations illustrate the theoretical analysis with particular emphases on the eccentricity of the cylinder,the angle of incidence and the dimensionless size parameters of the inner and coating cylindrical fluid materials.The method to derive the acoustical scattering,and radiation force and torque components conjointly uses modal matching with the addition theorem,which adequately account for the multiple wave interaction effects between the layer and core fluid materials.The results demonstrate that longitudinal and lateral radiation force components arise.Moreover,an axial radiation torque component is quantified and computed for the non-absorptive compound cylinder,arising from geometrical asymmetry considerations as the eccentricity increases.The computational results reveal the emergence of neutral,positive,and negative radiation force and torque depending on the size parameter of the cylinder,the eccentricity,and the angle of incidence of the insonifying field.Moreover,based on the law of energy conservation applied to scattering,numerical verification is accomplished by computing the extinction/scattering energy efficiency.The results may find some related applications in fluid dynamics,particle trapping,mixing and manipulation using acoustical standing waves.     

光栅卡卷尺测长技术

本文在光栅卡尺技术和力矩电机技术的基础上，把卡尺量程扩大到２０ｍ作成卡卷尺。利用力矩电机作为卡卷尺的卷紧机构和利用力矩电机作为保证光栅编码器标尺光栅平直度的施力元件，在此基础上，发展了光栅卡卷尺测长技术。基于莫尔条纹技术的光栅卡尺测长技术与其它现有长度测量技术相比成本较低、性能可靠，其测量精度可达０．０５ｍｍ甚至更高。为克服实际应用中卡卷尺的平直度对测量精度的影响，在系统设计中使力矩电机工作在堵转状态作为保证光栅卡卷尺标尺光栅平直的施力元件，并设计了线性调节的力距电机电源。对系统的检测表明，在２０ｍ测程内测量精度为０．１ｍｍ。     

Analysis of the magnetic field, force, and torque for two-dimensional Halbach cylinders

The Halbach cylinder is a construction of permanent magnets used in applications such as nuclear magnetic resonance apparatus, accelerator magnets and magnetic cooling devices. In this paper the analytical expression for the magnetic vector potential, magnetic flux density and magnetic field for a two dimensional Halbach cylinder are derived. The remanent flux density of a Halbach magnet is characterized by the integer p. For a number of applications the force and torque between two concentric Halbach cylinders are important. These quantities are calculated and the force is shown to be zero except for the case where p for the inner magnet is one minus p for the outer magnet. Also the force is shown never to be balancing. The torque is shown to be zero unless the inner magnet p is equal to minus the outer magnet p. Thus there can never be a force and a torque in the same system.     

Shape transition and propulsive force of an elastic rod rotating in a viscous fluid

The deformation of an elastic rod rotating in a viscous fluid is considered, with applications related to flagellar motility. The rod is tilted relative to the rotation axis, and experiments and theory are used to study the shape transition when driven either at constant torque or at constant speed. At low applied torque, the rod bends gently and generates small propulsive force. At a critical torque, the rotation speed increases abruptly, and the rod forms a helical shape with increased propulsive force. We find good agreement between theory and experiment. A simple physical model is presented to capture and explain the essential behavior.     

Large magnetic anisotropy in single crystal us

It is shown for ferromagnetic US that an extremely large anisotropy restrains magnetic moments to 〈111〉 easy axes, resulting in a near cos θ angular dependence of the magnetization away from the 〈111〉 axes. This is further confirmed by torque measurements, which in addition show large hysteresis effects upon rotation through the hard axes. It is illustrated through torque and magnetization measurements that a near stable domain configuration can be established by field rotation through decreasing angular amplitude around a hard 〈001〉 direction. The anisotropy constant K₁(T) is estimated by computing the small angle through which the magnetization deviates from the 〈111〉 axes when a field is applied along the [001] direction.     

Biased quasiballistic spin torque magnetization reversal

We explore the ultrafast limit of spin torque magnetization reversal time. Spin torque precession during a spin torque current pulse and free magnetization ringing after the pulse is detected by time-resolved magnetotransport. Adapting the duration of the pulse to the precession period allows coherent control of the final orientation of the magnetization. In the presence of a hard axis bias field, we find optimum quasiballistic spin torque magnetization reversal by a single precessional turn directly from the initial to the reversed equilibrium state.     

Spin force and torque in non-relativistic Dirac oscillator on a sphere

The spin force operator on a non-relativistic Dirac oscillator (in the non-relativistic limit the Dirac oscillator is a spin one-half 3D harmonic oscillator with strong spin–orbit interaction) is derived using the Heisenberg equations of motion and is seen to be formally similar to the force by the electromagnetic field on a moving charged particle. When confined to a sphere of radius R, it is shown that the Hamiltonian of this non-relativistic oscillator can be expressed as a mere kinetic energy operator with an anomalous part. As a result, the power by the spin force and torque operators in this case are seen to vanish. The spin force operator on the sphere is calculated explicitly and its torque is shown to be equal to the rate of change of the kinetic orbital angular momentum operator, again with an anomalous part. This, along with the conservation of the total angular momentum, suggests that the spin force exerts a spin-dependent torque on the kinetic orbital angular momentum operator in order to conserve total angular momentum. The presence of an anomalous spin part in the kinetic orbital angular momentum operator gives rise to an oscillatory behavior similar to the Zitterbewegung. It is suggested that the underlying physics that gives rise to the spin force and the Zitterbewegung is one and the same in NRDO and in systems that manifest spin Hall effect.     

共轴载流正三角形线圈间的相互作用

从计算回路的磁通量出发,应用虚位移原理,通过Mathematica数学软件,数值计算得到了共轴正三角形载流线圈间的相互作用力和力矩与线圈距离以及交错角度的关系曲线.     

Torque on an ideal plasma

Ripples in the confining field may exert a torque on a rotating plasma. Time reversal symmetry implies that this torque should vanish for an ideal plasma. However, even in an apparently ideal plasma, singularities can give rise to a nonzero torque. This torque is evaluated for a simple configuration. Although the primary force is magnetic, an essential contribution arises from other nonlinear terms in the equations of motion. The net force is confined to the singular layer, in the direction of the ripple wave vector and related to the energy absorbed in the layer.     

A semiflexible polymer ring acting as a nano-propeller

The dynamics of a rotating elastic nano-ring driven in a viscous fluid by an externally applied torque about a specific axis is studied using elasto-hydrodynamic simulations. We show that a helical deformation of the ring filament is excited, and that this leads to directed propulsion which is independent of the direction of rotation. It is found that the propulsive force and efficiency initially increase as the torque is increased, and then decrease discontinuously at a buckling transition at a critical torque. This unique propulsive behavior at the shape transition arises due to its specific geometry, i.e., circularity of an elastic filament. The implications of the behavior for artificial microscopic devices are discussed.     

近距离牛顿反平方定律实验检验进展

为了统一描述自然界的四种基本相互作用,科学家提出了很多理论模型,其中很多理论认为牛顿反平方定律在近距离下会发生偏离,或存在其他的非牛顿引力作用,而理论的正确与否需要高精度的实验检验.国际上很多研究组在不同间距下采用不同的技术对反平方定律进行了高精度的实验检验,本文重点介绍华中科技大学引力中心采用密度调制法分别在亚毫米与微米范围进行的实验研究进展.在亚毫米范围采用精密扭秤技术,在对牛顿引力进行双补偿、抑制电磁干扰后,结合零实验与非零实验结果,在作用程为70—300μm区间对Yukawa形式的破缺给出国际上精度最高的限制.在微米范围采用悬臂梁作为弱力传感器,通过测量金球和密度调制吸引质量间水平力的变化来检验非牛顿引力是否存在,实验结果不需进行Casimir力和静电力背景扣除,是此间距下不依赖于Casimir力和静电力理论计算模型的两个结果之一.     

Forces between charged surfaces in a solvent primitive model electrolyte

Grand canonical Monte Carlo (GCMC) simulations have been performed to investigate the components of the force between parallel charged surfaces in an electrolyte. The solvent primitive model (SPM) was used to investigate the effect of neutral hard sphere solvent particles on the force between the surfaces. The effects of particle size, wall charge density, charge valency of the electrolyte, and the exclusion of neutral hard sphere are discussed. When solvent particles are considered, the total force between the charged surfaces is always repulsive, even for divalent counterions. This is different from the earlier conclusion reached with a restricted primitive model electrolyte. The repulsive force decreases in going from monovalent counterions to divalent counterions.     

Estimation of clamping force in high-tension bolts through ultrasonic velocity measurement

The estimation of clamping force has been regarded as the main issue in the maintenance of high-tension bolts. This paper proposes a method which uses the dependency of ultrasonic velocity on stress based on the nonlinear elastic effect. The variation of ultrasonic velocity in the range of actual stress acting in the bolt is very small so that the precise measurement of ultrasonic velocity is needed. In this paper, we adopt a method to measure ultrasonic velocity, where the TOF (time of flight) of a tone-burst ultrasonic wave is precisely measured by using the phase detection technique. In order to verify the usefulness of the proposed method, two kinds of experiments are carried out. The first one measures ultrasonic velocity when the bolt is stressed by the tension tester, and from this, the exact axial force acting in the bolt can be determined. The results show good agreement with the expected linear relationship between ultrasonic velocity and axial stress. The second experiment measures ultrasonic velocity when the bolt is stressed by the torque wrench. The results show that ultrasonic velocity decreased as the torque increased, which is identical to the theoretically expected tendency. From these results, it can be said that the proposed method is adequate in evaluating clamping force in high-tension bolts.