Theoretical and numerical calculations for the time-averaged acoustic force and torque acting on a rigid cylinder of arbitrary size in a low viscosity fluid

In this paper, theoretical calculations as well as numerical simulations are performed for the time-averaged acoustic force and torque on a rigid cylinder of arbitrary size in a fluid with low viscosity, i.e., the acoustic boundary layer is thin compared to the cylinder radius. An exact analytical solution and its approximation are proposed in the form of an infinite series including Bessel functions. These solutions can be evaluated easily by a mathematical software package such as mathematica and matlab. Three types of incident waves, plane traveling wave, plane standing wave, and dual orthogonal standing waves, are investigated in detail. It is found that for a small particle, the viscous effects for an incident standing wave may be neglected but those for an incident traveling wave are notable. A nonzero viscous torque is experienced by the rigid cylinder when subjected to dual orthogonal standing waves with a phase shift even when the cylinder is located at equilibrium positions without imposed acoustic forces. Furthermore, numerical simulations are carried out based on the FVM algorithm to verify the proposed theoretical formulas. The theoretical results and the numerical ones agree with each other very well in all the cases considered.     

Intracavity phase switching and phase-plane dynamics of a bistable optical device

Since the field inside an optical cavity is a complex quantity, analysis in the phase plane gives a deeper insight into its time evolution. This was emphasized by the findings of Hopf and Meystre. We have extended their numerical analysis to include the possibility of Ikeda instabilities, showing that parameters can be selected that avoid Ikeda instabilities but permit intracavity phase switching. Switching, both up and down, can always be accomplished by applying an external pulse which changes the cavity detuning for an appropriate number of round trips. Inclusion of diffraction effects in one transverse dimension does not prevent switching. Clear, preset, and flip-flop operations, analogous to electronic operations, can also be achieved by properly choosing the external control pulses.     

Distributions of switching times of single-domain particles using a time quantified Monte Carlo method

Using a time quantified Monte Carlo scheme we performed simulations of the switching time distribution of single mono-domain particles in the Stoner–Wohlfarth approximation. We considered uniaxial anisotropy and different conditions for the external applied field. The results obtained show the switching time distribution can be well described by two relaxation times, either when the applied field is parallel to the easy axis or for an oblique external field and a larger damping constant. We found that in the low barrier limit these relaxation times are in very good agreement with analytical results obtained from solutions of the Fokker–Planck equation related to this problem. When the damping is small and the applied field is oblique the shape of the distribution curves shows several peaks and resonance effects.     

Control of a unique active vibration isolator with a phase compensation technique and automatic on/off switching

This work examines the characteristics of a unique active vibration isolator and develops a control strategy for it. The proposed active vibration isolator is introduced and its dynamic model is presented. A characterization study is conducted to identify system parameters. It is shown that with a simple proportional feedback the closed-loop system has a very narrow stability margin due to the inherent dynamics of the actuator. To improve the stability of the closed-loop system and enhance the performance of vibration isolation, a phase compensator is incorporated in the control scheme. An optimization problem is formulated to determine the optimum controller parameters by minimizing the 2nd norm of the displacement transmissibility. Both absolute position feedback and relative position feedback are considered. In real time implementation, an automatic on/off switching strategy is devised to take full advantage of both the active isolator and passive isolator. The experimental results show that with the proposed control scheme, the isolator is capable of suppressing base excitations effectively.     

Nonlinear dynamics and synchronisation of pendula attached to a rotating hub

A model of a nonlinear system composed of a hub with attached two pendula rotating in a horizontal plane is studied in the paper. Each single pendulum, treated as a stiff and massless rod with a lumped mass, is connected to the hub by a flapping hinge. Nonlinear stiffness and viscous damping of the hinge is taken into consideration. The system is excited by an external torque generated by a DC motor which is considered as an ideal system with torque given by a harmonic function. For small oscillations the problem is linearised and then solved analytically. An influence of the structural parameters like mass of the hub and pendula length on natural end excited vibrations is presented. Large oscillations are studied by a continuation technique, directly from the original Ordinary Differential Equations of motion (ODE). The complete synchronisation, phase synchronisation, bifurcations and transition through resonances are analysed considering the influence of the mass of the hub. The existence of chaotic oscillations of the system and paths leading to chaos are demonstrated as well.     

Multiple modes of perpendicular magnetization switching scheme in single spin—orbit torque device

Spin—orbit torque (SOT) has been considered as one of the promising technologies for the next-generation magnetic random access memory (MRAM). So far, SOT has been widely utilized for inducing various modes of magnetization switching. However, it is a challenge that so many multiple modes of magnetization switching are integrated together. Here we propose a method of implementing both unipolar switching and bipolar switching of the perpendicular magnetization within a single SOT device. The mode of switching can be easily changed by tuning the amplitude of the applied current. We show that the field-like torque plays an important role in switching process. The field-like torque induces the precession of the magnetization in the case of unipolar switching, however, the field-like torque helps to generate an effective z-component torque in the case of bipolar switching. In addition, the influence of key parameters on the mode of switching is discussed, including the field-like torque strength, the bias field, and the current density. Our proposal can be used to design novel reconfigurable logic circuits in the near future.     

Determination of the 2D amplitude-phase structure of an optical field and the transfer function in the case of a convolution-like effect of a medium

A solution of the phase problem in optics as applied to the simultaneous detection and analysis of the phase-amplitude structure of image-forming or image-transmitting 2D optical fields and the phase-amplitude structure of probed media or objects, transfer or instrumental functions of signal-transmitting media, or field-or image-forming systems is considered. The effect of media or objects is described by the operation of convolution. The essence of the method applied is the introduction of two additional modulators, which in some way perform the function of visualizing the phase information. Optical schemes of two types are considered. In both cases, the first additional modulation precedes the action of a medium or an object. The second additional modulation takes place either in the plane immediately behind the probed medium (first type of scheme) or in the plane of spatial frequencies formed by the optical system (second type of scheme). In the first variant, the plane of detection is that of the spatial frequencies; in the second variant, it is the plane of the image formation. The resulting intensity distributions yield a solution to the problem.     

Acoustic wave scattering from a composed shell reinforced by a single rib: characteristics of peripheral waves

The steady-state axisymmetrical problem of a plane acoustic wave scattering from a composed shell is considered. The shell has a cylindrical part and two hemispherical endcaps. The rib is a ring of rectangular cross-section that divides the shell into two equal parts. The motion of the shell and the rib is described by the equations of elasticity theory, and the liquid is described by the Helmholtz equation. The solution is obtained numerically by a coupled finite element/boundary element model. Two peripheral waves are generated in the shell: the membrane S0 wave and the bending type water-borne A wave. The form function, acoustic spectrogram and dispersion curves of the phase velocities are presented, and the effect of the rib on the peripheral waves is discussed.     

Joule heating and spin-transfer torque investigated on the atomic scale using a spin-polarized scanning tunneling microscope

The influence of a high spin-polarized tunnel current onto the switching behavior of a superparamagnetic nanoisland on a nonmagnetic substrate is investigated by means of spin-polarized scanning tunneling microscopy. A detailed lifetime analysis allows for a quantification of the effective temperature rise of the nanoisland and the modification of the activation energy barrier for magnetization reversal, thereby using the nanoisland as a local thermometer and spin-transfer torque analyzer. Both the Joule heating and spin-transfer torque are found to scale linearly with the tunnel current. The results are compared to experiments performed on lithographically fabricated magneto-tunnel junctions, revealing a very high spin-transfer torque switching efficiency in our experiments.     

NON-LINEAR DYNAMICS AND CONTROL OF CHAOS FOR A TACHOMETER

The dynamic behaviors of a rotational tachometer with vibrating support are studied in the paper. Both analytical and computational results are used to obtain the characteristics of the system. The Lyapunov direct method is applied to obtain the conditions of stability of the equilibrium position of the system. The center manifold theorem determines the conditions of stability for the system in a critical case. By applying various numerical analyses such as phase plane, Poincaré map and power spectrum analysis, a variety of periodic solutions and phenomena of the chaotic motion are observed. The effects of the changes of parameters in the system can be found in the bifurcation diagrams and parametric diagrams. By using Lyapunov exponents and Lyapunov dimensions, the periodic and chaotic behaviors are verified. Finally, various methods, such as the addition of a constant torque, the addition of a periodic torque, delayed feedback control, adaptive control, Bang-Bang control, optimal control and the addition of a periodic impulse are used to control chaos effectively.     

Coupling between switching regulation and torque generation in bacterial flagellar motor

The bacterial flagellar motor plays a crucial role in both bacterial locomotion and chemotaxis. Recent experiments reveal that the switching dynamics of the motor depend on the rotation speed of the motor, and thus the motor torque, nonmonotonically. Here we present a unified mathematical model which treats motor torque generation based on experimental torque-speed curves and the torque-dependent switching based on the conformational spread model. The model successfully reproduces the observed switching rate as a function of the rotation speed, and provides a generic physical explanation independent of most details. A stator affects the switching dynamics through two mechanisms: accelerating the conformational flipping rate of individual rotor-switching units, which contributes most when the stator works at a high torque and thus a low speed; and influencing a larger number of rotor-switching units within unit time, whose contribution is the greatest when the motor rotates at a high speed. Consequently, the switching rate shows a maximum at intermediate speed, where the above two mechanisms find an optimal output. The load-switching relation may serve as a mechanism for sensing the physical environment, similar to the chemotaxis mechanism for sensing the chemical environment. It may also coordinate the switch dynamics of motors within the same cell.     

On the electromagnetic energy density and energy transfer rate in a medium with dispersion due to conduction

The simplest dispersion relation determined by dissipation due to conduction is considered; the electromagnetic energy density in a plane monochromatic wave and its (phase and group) velocity are determined, as well as the energy and momentum transfer rates. It is shown that the energy density at low frequencies in this case has the form of the electrostatic density, in which the permittivity is replaced by its real part, and the energy transfer rate in a plane electromagnetic wave is equal to the phase velocity. The group velocity may exceed the speed of light.     

Helical waves of an elastic cylindrical shell

Properties of helical waves of a cylindrical shell described by Kirchhoff-Love equations are considered. The problem is reduced to the case of the propagation of plane waves in an equivalent plate. On the basis of the corresponding dispersion equation and its solution, a conclusion is made about the anisotropy of the shell properties. Dispersion curves are plotted for different angles of propagation of helical waves with respect to the shell axis. Displacements of the shell along and across the direction of wave propagation are calculated.     

The sensitivity of surface guided modes to the bond quality between a concrete block and a composite plate

Ultrasonic modes guided along the surface of a concrete block covered by a composite plate are investigated. First of all, the propagation phenomenon is studied by predicting the dispersion curves for various modes supposed to exist in this structure. Then, focus is made on a specific mode expected to be sensitive to the quality of the bond between the concrete and the composite, according to its through-thickness displacement field. Its dispersion curve is re-plotted for various states of this bond, which is modelled as a thin layer with varying properties. Limit cases corresponding to total disbond and perfect bond are considered. Experiments are then made on two composite-concrete assemblies for these two extreme cases using a contact PZT transmitter and an air-coupled receiver system. The phase velocities are in good agreement with the predicted dispersion curves, thus showing the potential of the ultrasonic guided mode to control the quality of bonds in such structures.     

基于电机辅助的纯电动汽车模式切换控制策略

为了提高纯电动汽车动力系统的工作效率,提出了一种基于电机辅助的纯电动汽车模式切换控制策略。首先,在传统纯电动汽车结构基础上配置一个小功率电机,得到一种双电机型纯电动汽车;其次,在双电机型纯电动汽车各驱动和各再生制动模式下,对其动力系统进行动力学分析和能量平衡分析,得出了系统在各模式下的工作效率模型;然后,以使动力系统工作效率最大为原则,制定了模式切换控制策略,确定了车辆的目标运行模式和两电机的目标转矩;最后,在Advisor仿真平台CYC_NEDC循环工况下,对该模式切换控制策略进行仿真,结果表明,与传统纯电动汽车相比,该控制策略使动力系统的工作效率提高了约6%。     

Field-induced magnetoelastic instabilities in antiferromagnetic molecular wheels

The magnetic torque of the antiferromagnetic molecular wheel CsFe8 was studied down to 50 mK and up to 28 T. Below about 0.5 K phase transitions were observed at the field-induced level crossings (LCs). Intermolecular magnetic interactions are very weak excluding field-induced magnetic ordering. A magnetoelastic coupling was considered. A generic model shows that the wheel structure is unconditionally unstable at the LCs, and the predicted torque curves explain the essential features of the data well.     

铁磁/重金属双层薄膜结构中磁性状态的稳定性分析

本文在理论上研究了铁磁/重金属双层薄膜结构中自旋霍尔效应自旋矩驱动的磁动力学. 通过线性稳定性分析, 获得了以电流和磁场为控制参数的磁性状态相图. 发现通过调节电流密度和外磁场, 可以获得不同的磁性状态, 例如: 平面内的进动态、平面内的稳定态以及双稳态. 当外磁场的方向在一定的范围时, 通过调节电流密度可以实现磁矩的翻转和进动. 同时, 通过数值求解微分方程, 给出了这些磁性状态磁矩的演化轨迹.     

Measurement of the amplitude and phase structures of an optical field and the transfer function for describing the effect of a medium in the form of a modulating function

The phase problem in optics is solved as applied to the detection and analysis of the amplitude and phase structures of two-dimensional optical fields forming or transmitting an image and the amplitude and phase structures of the transfer or instrumental functions of either the media containing optical inhomogeneities or the systems forming fields and involving instrumental distortions. The effect of the medium is characterized by a modulating function and described by a multiplication operation. Two variants of the optical scheme are considered. In each variant, the spatial-frequency spectrum is formed by the first optical system and the first spatial modulation is introduced in the spatial-frequency plane. The second optical system is arranged in the same plane. This system images the field under investigation into the plane located at the exit of the transmitting medium. In the first variant of the optical scheme, the second spatial modulation is introduced in the same plane. The third optical system forms a spatial-frequency spectrum in the detection plane. In the second variant of the scheme, an image of the plane positioned at the exit of the probing medium is formed in the detection plane by the third optical system. The second spatial modulation is introduced in the spatial-frequency plane of the third optical system. In both variants, four independent two-dimensional intensity distributions that make it possible to solve the problem posed are detected at the exit.     

Intertwined Hamiltonians in two-dimensional curved spaces

The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincaré half plane (AdS₂), de Sitter plane (dS₂), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle.     

Division of a Set of Segments into Nonintersecting Parts on a Discrete Plane

The problem of dividing segments into nonintersecting parts on a discrete plane is considered. An algorithm for solving this problem and methods of its further improvement are suggested. The complexity of the algorithm is analyzed.