A path integral approach to electronic friction of a nanometer-sized tip scanning a metal surface

In this work, we study the dissipation mechanism and frictional force of a nanometer-sized tip scanning a metal surface via a path integral approach. The metal, with internal degrees of freedom (c, c^†) and a tip with an internal degree of freedom (d, d^†) couple with one another by means of an exchanged potential, V. Having integrated out all internal degrees of freedom, we obtain the in-out amplitude. Moreover, we calculate the imaginary part of the in-out amplitude and the frictional force. We find the imaginary part of the in-out amplitude to be positive, and correlated to the sliding velocity in most cases. The frictional force is proportional to the sliding velocity for the case where v < 0.01. However, for cases where v > 0.01, the frictional force demonstrates nonlinear dependence on sliding velocity.     

THE NON-LINEAR DYNAMIC BEHAVIOR OF AN ELASTIC LINKAGE MECHANISM WITH CLEARANCES

In terms of Newton two-state model, by choosing two sets of generalized co-ordinates, this paper develops a unified dynamic model between the separation and collision process for the elastic linkage mechanism. This model incorporates the effects of rigidity and elasticity coupling and the angular velocity of crank is assumed to be variable in the operation. In addition, this paper provides a more simple and practical numerical solution method for convenient analysis. Through an example, the dynamic responses of the elastic linkage mechanism with clearances are analyzed, both the effects of elasticity and clearance on the dynamic behaviors of the mechanism are analyzed simultaneously and the non-linear behaviors caused by the clearance joints are analyzed by the dynamic model of rigid mechanism.     

Perturbation parameters associated with nonlinear responses of the head at small amplitudes

The head-neck system has multiple degrees of freedom in both its control and response characteristics, but is often modeled as a single joint mechanical system. In this study, we have attempted to quantify the perturbation parameters that would elicit nonlinear responses in a single degree-of-freedom neuromechanical system at small amplitudes and velocities of perturbation. Twelve healthy young adults seated on a linear sled randomly received anterior-posterior sinusoidal translations with +/-15 mm and +/-25 mm peak displacements at 0.81, 1.76, and 2.25 Hz. Head angular velocity and angular position data were examined using a nonlinear phase-plane analysis. Poincare sections of the phase plane were computed and Lyapunov exponents calculated to measure divergence (chaotic behavior) or convergence (stable behavior) of system dynamics. Variability of head angular position and velocity across the entire phase plot was compared to that of the Poincare sections to quantify spatial-temporal irregularity. Multiple equilibrium points and positive Lyapunov exponents revealed chaotic behavior at 0.81 Hz at both amplitudes whereas responses at 1.76 and 2.25 Hz exhibited periodic oscillations, clustered phase points, and negative Lyapunov exponents. However, intersubject variability increased at the lowest frequency and a few subjects presented chaotic behavior at all frequencies. An inverted pendulum with position and velocity threshold nonlinearity was adopted as a simplistic model of the head and neck. Simulations with the model resulted in features similar to those observed in the experimental data. Our principal finding was that increasing the perturbation amplitude had a stabilizing effect on the behavior across frequencies. Nonlinear behaviors observed at the lowest stimulus frequency might be attributed to fluctuations in control between the multiple sensory inputs. Although this study has not conclusively pointed toward any single mechanism as responsible for the responses observed, it has revealed clear directions for further investigation. To examine if changing the sensory modalities would elicit a significant change in the nonlinear behaviors observed here, further experiments that target a patient population with some sort of sensory deficit are warranted.     

On the non-synchronous rotation of binary systems

During the evolution of the binary system,many physical processes occur,which can influence the orbital angular velocity and the spin angular velocities of the two components,and influence the non-synchronous or synchronous rotation of the system.These processes include the transfer of masses and angular momentums between the component stars,the loss of mass and angular momentum via stellar winds,and the deformation of the structure of component stars.A study of these processes indicates that they are closely related to the combined effects of tide and rotation.This means,to study the synchronous or non-synchronous rotation of binary systems,one has to consider the contributions of different physical processes simultaneously,instead of the tidal effect alone.A way to know whether the rotation of a binary system is synchronous or non-synchronous is to calculate the orbital angular velocity and the spin angular velocities of the component stars.If all of these angular velocities are equal,the rotation of the system is synchronous.If not,the rotation of the system is non-synchronous.For this aim,a series of equations are developed to calculate the orbital and spin angular velocities.The evolutionary calculation of a binary system with masses of 10M⊙+6M⊙shows that the transfer of masses and angular momentums between the two components,and the deformation of the components structure in the semidetached or in the contact phase can change the rotation of the system from synchronous into non-synchronous rotation.     

Sliding velocity dependence of adhesion in a nanometer-sized contact

The influence of sliding velocity on the adhesion force in a nanometer-sized contact was investigated with a novel atomic force microscope experimental setup that allows measuring adhesion forces while the probe is sliding at continuous and constant velocities. For hydrophobic surfaces, the adhesion forces (mainly van?der?Waals forces) remain constant, whereas for hydrophilic surfaces, adhesion forces (mainly capillary forces) decrease linearly with a logarithmic increase of the sliding velocity. The experimental data are well explained by a model based on a thermally activated growth process of a capillary meniscus.     

Nonlinear dynamics of a flexible mechanism with impact

The nonlinear dynamics of a slider-crank mechanism with a flexible rod is considered in this study. The flexible rod is modeled with lumped masses and periodically impacted by an external flexible sphere. The impact is modeled using a kinematic coefficient of restitution. Nonlinear dynamics tools are applied to analyze the simulated data captured from the connecting rod of the mechanism. The chaotic behavior of the system is analyzed. The stability of the motion is studied using the Lyapunov exponents. The dependence between the Lyapunov exponents and the corresponding angular velocity of the driver link of the mechanism is investigated.     

Experimental analysis of interface contact behavior using a novel image processing method

The spatial and temporal evolution of real contact area of contact interface with loads is a challenge. It is generally believed that there is a positive linear correlation between real contact area and normal load. However, with the development of measuring instruments and methods, some scholars have found that the growth rate of real contact area will slow down with the increase of normal load under certain conditions, such as large-scale interface contact with small roughness surface,which is called the nonlinear phenomenon of real contact area. At present, there is no unified conclusion on the explanation of this phenomenon. We set up an experimental apparatus based on the total reflection principle to verify this phenomenon and analyze its mechanism. An image processing method is proposed, which can be used to quantitative analysis micro contact behaviors on macro contact phenomenon. The weighted superposition method is used to identify micro contact spots, to calculate the real contact area, and the color superimposed image is used to identify micro contact behaviors.Based on this method, the spatiotemporal evolution mechanism of real contact area nonlinear phenomena is quantitatively analyzed. Furthermore, the influence of nonlinear phenomenon of real contact area on the whole loading and unloading process is analyzed experimentally. It is found that the effects of fluid between contact interface, normal load amplitude and initial contact state on contact behavior cannot be ignored in large-scale interface contact with small roughness surface.     

Time-domain observation of the spinmotive force in permalloy nanowires

The spinmotive force associated with a moving domain wall is observed directly in Permalloy nanowires using real time voltage measurements with proper subtraction of the electromotive force. Whereas the wall velocity exhibits nonlinear dependence on magnetic field, the generated voltage increases linearly with the field. We show that the sign of the voltage reverses when the wall propagation direction is altered. Numerical simulations explain quantitatively these features of spinmotive force and indicate that it scales with the field even in a field range where the wall motion is no longer associated with periodic angular rotation of the wall magnetization.     

(1+2)维各向同性介质中的旋转椭圆空间光孤子

从(1+2)维非局域非线性薛定谔方程出发, 通过坐标变换得到了旋转坐标系下的非局域非线性薛定谔方程. 假设响应函数为高斯型, 用虚时间法数值求解了旋转坐标系下的非局域非线性薛定谔方程的静态孤子解, 迭代出了不同非局域程度条件下的静态椭圆孤子数值解. 最后采用分步傅里叶算法, 以迭代的孤子解作为初始输入波形, 模拟了在不同的非局域程度条件下, (1+2)维椭圆空间光孤子的旋转传输特性. 强非局域时, 椭圆光孤子的长轴方向和短轴方向波形都是高斯型, 其他的非局域程度下, 不是高斯型. 由此表明：(1+2)维椭圆光孤子对非局域程度依赖性很强. 旋转角速度和功率均与非局域程度以及孤子的椭圆度有关.     

自驱动颗粒体系中的熵力

在许多纳米复合材料体系中熵力(entropy force)是普遍存在的,但由于熵力的存在会导致纳米颗粒的凝聚从而降低其许多性能,因此在大多数情况下熵力的存在对体系并无益处,所以研究如何减小熵力对体系的影响是非常重要的.不带角速度的自驱动粒子在熵力作用下会集聚在纳米颗粒(或者纳米棒)周围,这会对纳米颗粒(或者纳米棒)产生很大的相互作用力.对于纳米颗粒,在不带角速度的自驱动粒子体系中存在着非常大的排斥力.而对于纳米棒,由于纳米棒内外的不对称性,使得两个纳米棒之间会产生吸引-排斥转变,同时这个吸引-排斥转变与纳米棒之间的距离有关.当自驱动粒子加上一个自转角速度ω之后,熵力的作用就大大减弱,纳米颗粒不再集聚.研究结果有助于对非平衡态下纳米颗粒(或纳米棒)之间熵相互作用力的认识.     

Nonlinear friction as a mechanism of directed motion

A simple model (ratchet model) of occurrence of directed motion under the action of a zero-mean fluctuating force is proposed. The motion arises when the symmetry in the velocity space is violated by nonlinear friction. The mechanism of the directed motion is discussed qualitatively. Existence conditions of the motion are derived. The efficiency of conversion of the fluctuating random force to the directed motion is estimated.     

Dynamics Modeling and Experimental Investigation of Gear Mechanism with Coupled Small Clearances

Internal gear mechanism is widely used in micro-nano satellites due to its compact structure and high precision transmission. However, the vibration coupling caused by the small clearance coupling is more obvious and cannot be ignored under low speed, light load and zero gravity conditions. Based on the geometric relationship between radial clearance and backlash, a coupled model between dynamic backlash and radial clearance of internal meshing gear is established. Based on the conformal contact theory, the radial collision force model of the gear shaft and shaft sleeve considering the small clearances is established. Additionally, a multi-clearance gear rotor system test device is built to measure the vibration acceleration of the internal gear rotor system by an acceleration sensor and transmitted to the industrial computer through a signal collector for data processing. Through the comparison of simulation and experiment, the accuracy of the gear dynamics model is verified. The analysis results show that, compared with the traditional model, the calculation results of the gear mechanism model considering the small clearance coupling is closer to the experimental data.     

利用传递熵对Lorenz系统和Walker环流信息传输方向的分析

基于传递熵方法, 分析Lorenz系统x, y, z三个分量之间的信息传输方向, 并应用温差与垂直速度的再分析资料对Walker环流进行分析. 研究结果表明: 1) 对于Lorenz系统而言, x与y分量之间, y是信息源, x是信息汇; y与z之间, y是信息源, z是信息汇; x与z分量之间的信息传递方向依赖于控制参数r; 且净信息传输的方向不随初值不同而改变; 2)在西太平洋地区, 温差对垂直速度的净信息输送占主导地位, 而赤道东太平洋地区则为垂直速度对温差的净信息输送占主导地位, 这与Walker环流物理机制是一致的, 且海陆热力差异对温差与垂直速度之间的信息输送影响较大; 3)冬季是温差与垂直速度之间的信息输送最强季节, 夏季和秋季次之, 春季最弱, 这可能是存在春季预报障碍的原因之一. 以上结果表明, 传递熵在气象领域有广阔的应用前景, 是测量动力学系统信息传递方向的一种有效方法和工具. 关键词： 传递熵 信息传输 Lorenz系统 Walker环流     

Moment excitation and the measurement of moment mobilities

Frequency response functions (FRF), such as mobilities, are widely used in the analysis of vibration and structure-borne sound and it is important that this FRF data can be measured accurately for all important degrees of freedom. In some cases three translational and three rotational components of both excitation and response may be of importance; i.e. three forces and moments, and three velocities and angular velocities. Of these, the measurement of angular velocity due to moment excitation is one of the most challenging. This paper describes a known approach, sometimes referred to as the central difference method, which can be used for this purpose. The central difference method is thought to be one of the most practicable methods for measuring moment mobilities because it avoids the need for a moment exciter; instead finite differences are used to approximate the moment mobility which is a spatial derivative of the more easily measured velocity to force mobility ratio. There does however remain some doubt regarding the accuracy of the central difference method because of the finite difference approximation made and the method's possible susceptibility to random and bias errors. To better understand the finite difference error, an error analysis using a Taylor series expansion and simulated experiments for plate and beam structures are provided. It is then argued that random and bias errors associated with the measurement chain should now, with modern instrumentation, be less of a problem. An experimental validation of the method using two approaches is used to test this hypothesis. It is concluded that the central difference method provides a good balance between measurement effort and data quality making it widely applicable.     

Ion drag as a mechanism of plasma dust structure rotation in a strata in a magnetic field

In experiments on complex plasmas, afixed strata region in which the levitation of dust structures is observed is investigated using the method of probing by calibrated dust particles of different sizes in an applied magnetic field under elevated pressures. The measured azimuthal velocity of the probing particles corresponds to the action of the ion drag force for 4 μm-size particles and to the entrainment by the rotating gas owing to the electron vortex flow inside the strata for 1 μm-size particles. Extrapolation to pressures and magnetic fields in which the rotation inversion of dust structures is observed in experiments shows that the ion drag is the dominating force causing rotation with a negative projection of the angular velocity onto the magnetic induction.     

Modal analysis of a continuous gyroscopic second-order system with nonlinear constraints

A method for the modal analysis of continuous gyroscopic systems with nonlinear constraints is developed. This method assumes that the nonlinear constraint can be expressed as a piecewise linear force-deflection profile located at an arbitrary position within the domain. Using this assumption, the mode shapes and natural frequencies are first found for each state, then a mapping method based on the inner product of the mode shapes is developed to map the displacement of the system between the in-contact and out-of-contact states. To illustrate this method, a model for the vibration of a traveling string in contact with a piecewise-linear constraint is developed as an analog of the interaction between magnetic tape and a guide in data storage systems. Five design parameters of the guide are considered: flange clearance, flange stiffness, symmetry of the force-deflection profile in terms of flange stiffness and offset, and the guide's position along the length of the string. There are critical bifurcation thresholds, below which the system exhibits no chaotic behavior and is dominated by period one, symmetric behavior, and above which the system contains asymmetric, higher periodic motion with windows of chaotic behavior. These bifurcation thresholds are particularly pronounced for the transport speed, flange clearance, symmetry of the force deflection profile, and guide position. The stability of the system is sensitive to the system's velocity, and, compared to stationary systems, more mode shapes are needed to accurately model the dynamics of the system.     

The Force Acting on a Cylinder in a Ring Flow of a Viscous Fluid with a Small Eccentric Displacement

A system consisting of two circular cylinders one inside the other with parallel axes is considered. The outer cylinder of radius R₂ is fixed, and the inner cylinder of radius R₁ rotates with a sufficiently large angular velocity. The region between the cylinders is filled with an incompressible viscous fluid and, in the case of coaxial cylinders, Couette flow along circular trajectories arises. Upon an eccentric small displacement of the axis of the inner cylinder, the symmetry of the flow is disturbed and a force exerted on the inner cylinder by the fluid is created. Within the ideal fluid model, the force depends linearly on the transverse velocities and accelerations of the cylinder. In a viscous fluid, the force depends on the previous motion of the cylinder. It is expressed in terms of the velocity functional by analogy with the Basset force acting on a ball moving in a viscous fluid with a variable velocity.     

电压控制不连续导电模式DC-DC变换器的熵特性研究

结合DC-DC变换器非线性特性随反馈增益k变化的关系,以及熵能够反映序列总体统计特征的特点,提出一种基于熵估计DC-DC变换器非线性行为的新方法. 以一阶电压反馈不连续导电模式 DCM Buck和Boost变换器为例,详细分析了不同反馈增益k和初值x₀形成的数值序列及熵的分布情况. 研究结果表明：DC-DC变换器的熵由反馈增益k决定,与初值x₀无关,最终小于理论极大值log₂N （N为统计区间个数）;熵能够准确区分DC-DC变换器的倍周期分岔和混沌行为,从而得到一种新的可量化的DC-DC变换器非线性动力学行为指标;完善了该类变换器非线性动力学分析的理论和方法. 关键词： DC-DC变换器 熵 混沌 k')" href="#">反馈增益k     

Generalized formulation of the interactions between soft spheres

The goal of this paper is to identify the most general formulation that consistently links the different degrees of freedom in a contact between spherical soft particles. These contact laws have two parts: a set of “generalized contact velocities” that characterize the relative motion of the two particles, and a set of “generalized contact forces” that characterize the interparticle forces. One well known constraint on contact models is that the contact velocities must be objective. This requirement fixes the number of linearly independent contact velocities. We also present a previously unnoticed (in this context) constraint, namely, that the velocities and forces must be related in such a way that the stiffness matrix is symmetric. This constraint also places restrictions on the coupling between the contact forces. Within our generalized contact model, we discuss the expression for rolling velocity that need to be used in the calculation of rolling resistance, and the risk or producing perpetual mobile when other expressions of rolling velocity are using instead.     

工业中粉体颗粒的荷电机理及数值模拟方法

工业过程中粉体颗粒不可避免地会相互摩擦碰撞而荷电. 荷电颗粒的存在可能会危害正常的工业生产过程, 也可能对工业过程起促进作用. 因此, 荷电粉体颗粒及其特性受到了广泛的关注, 但目前对粉体颗粒的荷电机理依然缺乏透彻的了解, 尤其是在气固两相流动中的粉体颗粒荷电现象. 事实上, 工业中存在的粉体颗粒的运动都受到流体的影响, 是典型的气固两相流系统, 流体对粉体颗粒的作用使粉体颗粒接触的荷电现象变得更为复杂, 因此从两相流动的观点来研究粉体颗粒荷电的物理本质就显得越来越重要. 本文介绍了工业过程中的几种不同类型的粉体颗粒荷电行为, 回顾了颗粒的荷电机理与描述颗粒荷电的数学模型. 对于工业过程中颗粒的荷电现象及颗粒在多相流体中的动力学行为, 介绍了研究颗粒受流体影响时荷电特性的数值模拟方法. 本文旨在对粉体颗粒的荷电机理、应用以及研究方法进行梳理与探讨, 为正确认识工业过程中粉体颗粒的荷电现象并加以控制利用提供理论借鉴.