Nonlinear modes coupling of trapped spin-orbit coupled spin-1 Bose-Einstein condensates

We study analytically and numerically the nonlinear collective dynamics of quasi-one-dimensional spin-orbit coupled spin-1 Bose-Einstein condensates trapped in harmonic potential.The ground state of the system is determined by minimizing the Lagrange density,and the coupled equations of motions for the center-of-mass coordinate of the condensate and its width are derived.Then,two low energy excitation modes in breathing dynamics and dipole dynamics are obtained analytically,and the mechanism of exciting the anharmonic collective dynamics is revealed explicitly.The coupling among spin-orbit coupling,Raman coupling and spin-dependent interaction results in multiple external collective modes,which leads to the anharmonic collective dynamics.The cooperative effect of spin momentum locking and spin-dependent interaction results in coupling of dipolar and breathing dynamics,which strongly depends on spin-dependent interaction and behaves distinct characters in different phases.Interestingly,in the absence of spin-dependent interaction,the breathing dynamics is decoupled from spin dynamics and the breathing dynamics is harmonic.Our results provide theoretical evidence for deep understanding of the ground sate phase transition and the nonlinear collective dynamics of the system.

Application of complex nonlinear modes to determine dry whip motion in a rubbing rotor system

Dry whip motion is an instability of rubbing rotor system and may cause catastrophic failures of rotating machinery.Up to now,the related mechanisms of the dry whip is still not well understood.This paper aims to build the relationship between the complex nonlinear modes and the dry whip motion,and propose an effective method to predict the response characteristics and existence boundary of the dry whip through complex nonlinear modes.For the first time,the paper discusses how to use the complex nonlinear modes to predict the dry whip systematically,and as a consequence,the mechanism of the relationship between the complex nonlinear mode and the dry whip is revealed.The results show that the Backward Whirl(BW)mode motion of the rubbing rotor system dominates the response characteristics and the existence boundary of dry whip.The whirl amplitude and whirl frequency of dry whip are equal to the modal amplitude and modal frequency of the BW mode at the jump up point where the modal damping is equal to zero.The existence boundary corresponds to the critical rotation speed where the minimum of the modal damping of the BW mode motion is exactly equal to zero.Moreover,the proposed nonlinear modal method in this article is very effective for the prediction of dry whip of the more complicated practical rotor system,which has been verified by applying the predicted method into a rubbing rotor test rig.

SINGULAR ANALYSIS OF BIFURCATION OF NONLINEAR NORMAL MODES FOR A CLASS OF SYSTEMS WITH DUAL INTERNAL RESONANCES

The nonlinear normal modes (NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled. The bifurcation problem of the coupled NNM of system with 1 : 2 : 5 dual internal resonance is in two variables. The singular analysis of it is presented after separating the two variables by taking advantage of Maple algebra, and some new bifurcation patterns are found. Different from the NNMs of systems with single internal resonance, the number of the NNMs of systems with dual internal resonance may be more or less than the number of the degrees of freedom. At last, it is pointed out that bifurcation problems in two variables can be conveniently solved by separating variables as well as using coupling equations.

Bright and dark small amplitude nonlinear localized modes in a quantum one-dimensional Klein-Gordon chain

By means of the Glauber＇s coherent state method combined with multiple-scale method, this paper investigates the localized modes in a quantum one-dimensional Klein-Gordon chain and finds that the equation of motion of annihilation operator is reduced to the nonlinear Schroedinger equation. Interestingly, the model can support both bright and dark small amplitude travelling and non-travelling nonlinear localized modes in different parameter spaces.

Nonlinear excitation of a geodesic acoustic mode by reversed shear Alfvén eignemodes

The parametric decay process of a reversed shear Alfvén eigenmeode(RSAE)into a geodesic acoustic mode and a kinetic RSAE is investigated using nonlinear gyrokinetic theory.The excitation conditions mainly require the pump RSAE amplitude to exceed a certain threshold,which could be readily satisfied in burning plasmas operated in steady-state advanced scenario.This decay process can contribute to thermal plasma heating and confinement improvement.

SINGULAR CHARACTERISTICS OF NONLINEAR NORMAL MODES IN A TWO DEGREES OF FREEDOM ASYMMETRIC SYSTEMS WITH CUBIC NONLINEARITIES

Nonlinear normal modes in a two degrees of freedom asymmetric system with cubic nonlinearities as singularity occurs in the system are studied, based on the invariant space in nonlinear normal modes and perturbation technique. Emphasis is placed on singular characteristics as the linear coupling between subsystems degenerated. For nonresonances, it is analytically presented that a single-mode motion and localization of vibrations occur in the system, and the degree of localization relates not only to the coupling stiffness between oscillators, but also to the asymmetric parameter. The parametric threshold value of localization is analytically given. For 1 : 1 resonance, there exist bifurcations of normal modes with nonlinearly coupling stiffness and asymmetric parameter varying. The bifurcating set on the parameter and bifurcating curves of normal modes are obtained.

Adaptive Gain Tuning Rule for Nonlinear Sliding-mode Speed Control of Encoderless Three-phase Permanent Magnet Assisted Synchronous Motor

In this paper, an adaptive gain tuning rule is designed for the nonlinear sliding mode speed control(NSMSC) in order to enhance the dynamic performance and the robustness of the permanent magnet assisted synchronous reluctance motor(PMa-Syn RM) with considering the parameter uncertainties. A nonlinear sliding surface whose parameters are altering with time is designed at first. The proposed NSMSC can minimize the settling time without any overshoot via utilizing a low damping ratio at starting along with a high damping ratio as the output approaches the target set-point. In addition, it eliminates the problem of the singularity with the upper bound of an uncertain term that is hard to be measured practically as well as ensures a rapid convergence in finite time, through employing a simple adaptation law. Moreover, for enhancing the system efficiency throughout the constant torque region, the control system utilizes the maximum torque per ampere technique. The nonlinear sliding surface stability is assured via employing Lyapunov stability theory. Furthermore, a simple sliding mode estimator is employed for estimating the system uncertainties. The stability analysis and the experimental results indicate the effectiveness along with feasibility of the proposed speed estimation and the NSMSC approach for a 1.1-k W PMa-Syn RM under different speed references, electrical and mechanical parameters disparities, and load disturbance conditions.

Coupling of Cutoff Modes in a Chain of Nonlinear Metallic Nanorods

We study the coupling of cutoff modes in a chain of metallic nanorods embedded in a Kerr nonlinear optical medium with strong near-field interactions analytically. Based on a quasidiscreteness approach, we derive a system of two coupled nonlinear Schrbdinger equations governing the evolution of the envelopes of these modes. It is shown that this system supports a variety of subwavelength plasmonic lattice vector solitons of the bright- bright, bright-dark, dark-bright, and dark-dark type through a cross-phase modulation. It is also shown that the existence of different solitons depends strongly on the gap width scaled for the rod radius and the type of nonlinearity of the embedded medium.

Effect of Hyper-Resistivity on Nonlinear Tearing Modes

We analytically investigate nonlinear tearing modes with the anomalous electron viscosity or,as it is normally called,hyper-resistivity.In contrast to the flux average method used by previous work,we employ the standard singular perturbation technique and a quasilinear method to obtain the time evolution equation of tearing modes.The result that the magnetic flux grows with time in a scaling as t^（2/3）demonstrates that nonlinear tearing modes with the hyper-resistivity effect alone have a weaker dependence on time than that of the corresponding resistive case.

Adaptive Nonlinear Sliding Mode Control for DC Power Distribution in Commercial Buildings

The developing populace and industrialization power demand prompted the requirement for power generation from elective sources.The desire for this pursuit is solid due to the ever-present common assets of petroleum deri-vatives and their predominant ecological issues.It is generally acknowledged that sustainable power sources are one of the best answers for the energy emergency.Among these,Photovoltaic(PV)sources have many benefits to bestow a very promising future.If integrated into the existing power distribution infrastructure,the solar source will be more successful,requiring efficient Direct Current(DC)-Alternating Current(AC)conversion.This paper mainly aims to improve control-lers’performance between AC/DC Energy sources and the DC loads using the Adaptive Nonlinear Sliding Mode(ANSM)control method.The proposed ANSM method efficiently controls power quality issues,such as transient response,powerflow reliability and Total Harmonics Distortion(THD).The proposed con-troller is applied for both AC/DC and DC/DC converters and the performance of the proposed controller is validated through simulation checking the above para-meters.The simulation results confirm ANSM configuration is more reliable and efficient than the existing fuzzy and sliding mode control methods.

Transient Characteristics of a Nonlinear GaAs Photoconductive Semiconductor Switch

The transient resistance,voltage,and power of a nonlinear GaAs photoconductive semiconductor switch （PCSS） are presented by the finite difference formula to deal with the experiment data, based on the conversation of energy in the switch circuit. This method resolves the problem of directly measuring the transient characteristics of PCSS in nonlinear mode. The curve of transient voltage shows that the average electric field of PCSS in the lock-on period is always higher than the Gunn threshold,and increases monotonically. By comparing the transient power curves of the PCSS and the electrical source,it is demonstrated directly that the power shortage leads to the PCSS from the lock-on state into the selfturnoff state,so a controllable turnoff of the PCSS in lock-on by changing the distribution of the circuit power is predicted.

A nonlinear bottom-following controller for underactuated autonomous underwater vehicles

The bottom-following problem for underactuated autonomous underwater vehicles （AUV） was addressed by a new type of nonlinear decoupling control law. The vertical bottom-following error and pitch angle error are stabilized by means of the stem plane, and the thruster is left to stabilize the longitudinal bottom-following error and forward speed. In order to better meet the need of engineering applications, working characteristics of the actuators were sufficiently considered to design the proposed controller. Different from the traditional method, the methodology used to solve the problem is generated by AUV model without a reference orientation, and it deals explicitly with vehicle dynamics and the geometric characteristics of the desired tracking bottom curve. The estimation of systemic uncertainties and disturbances and the pitch velocity PE （persistent excitation） conditions are not required. The stability analysis is given by Lyapunov theorem. Simulation results of a full nonlinear hydrodynamic AUV model are provided to validate the effectiveness and robustness of the proposed controller.

Nonlinear Derivative and Integral Sliding Control for Tracked Vehicle Steering with Hydrostatic Drive

In the steering process of tracked vehicle with hydrostatic drive,the motion and resistance states of the vehicle are always of uncertain and nonlinear characteristics,and these states may undergoe large-scale changes.Therefore,it is significant to enhance the steering stability of tracked vehicle with hydrostatic drive to meet the need of future battlefield.In this paper,a sliding mode control algorithm is proposed and applied to achieve desired yaw rates.The speed controller and the yaw rate controller are designed through the kinematics and dynamics analysis.In addition,the nonlinear derivative and integral sliding mode control algorithm is designed,which is supposed to efficiently reduce the integration saturation and the disturbances from the unsmooth road surfaces through a conditional integrator approach.Moreover,it improves the response speed of the system and reduces the chattering by the derivative controller.The hydrostatic tracked vehicle module is modeled with a multi-body dynamic software RecurDyn and the steering control strategy module is modeled by MATLAB/Simulink.The co-simulation results of the whole model show that the control strategy can improve the vehicle steering response speed and also ensure a smooth control output with small chattering and strong robustness.

Decoupled nonsingular terminal sliding mode control for affine nonlinear systems

A decoupled nonsingular terminal sliding mode control（DNTSMC） approach is proposed to address the tracking control problem of affine nonlinear systems.A nonsingular terminal sliding mode control（NTSMC） method is presented,in which the nonsingular terminal sliding surface is defined as a special nonsingular terminal function and the convergence time of the system states can be specified.The affine nonlinear system is firstly decoupled into linear subsystems via feedback linearization.Then,a nonsingular terminal sliding surface is defined and the NTSMC method is applied to each subsystem separately to ensure the finite time convergence of the closed-loop system.The verification example is given to demonstrate the effectiveness and robustness of the proposed approach.The proposed approach exhibits a considerable advantage in terms of faster tracking error convergence and less chattering compared with the conventional sliding mode control（CSMC）.

Realization of nonreciprocal acoustic energy transfer using an asymmetric strong nonlinear vibroacoustic system

In this paper,an asymmetric vibroacoustic system that can passively realize nonreciprocal transmission of acoustic energy is reported.This experimental system consists of a waveguide,a strongly nonlinear membrane,and three acoustic cavities with different sizes.The theoretical modeling of the system is verified by experiments,and parametric analysis is also carried out.These intensive studies reveal the nonreciprocal transmission of acoustic energy in this prototype system.Under forward excitation,internal resonance between the two nonlinear normal modes of the vibroacoustic system occurs,and acoustic energy is irreversibly transferred from the waveguide to the nonlinear membrane.However,under backward excitation,there is no internal resonance in the system.Energy spectra and wavelet analysis are used to highlight the mechanism of nonreciprocal transfer of acoustic energy.Consequently,nearly unidirectional(preferential)transmission of acoustic energy transfer is shown by this system.The nonreciprocal acoustic energy transfer method illustrated in this paper provides a new way to design the odd acoustic element.

Selective enhancement of oblique waves caused by finite amplitude second mode in supersonic boundary layer

Nonlinear interactions of the two-dimensional （2D） second mode with oblique modes are studied numerically in a Mach 6.0 fiat-plate boundary layer, focusing on its selective enhancement effect on amplification of different oblique waves. Evolution of oblique modes with various frequencies and spanwise wavenumbers in the presence of 2D second mode is simulated successively, using a modified parabolized stability equation （PSE） method, which is able to simulate interaction of two modes with different frequen- cies efficiently. Numerical results show that oblique modes in a broad band of frequencies and spanwise wavenumbers can be enhanced by the finite amplitude 2D second mode instability wave. The enhancement effect is accomplished by interaction of the 2D second mode, the oblique mode, and a forced mode with difference frequency. Two types of oblique modes are found to be more amplified, i.e., oblique modes with frequency close to that of the 2D second mode and low-frequency first mode oblique waves. Each of them may correspond to one type of transition routes found in transition experiments. The spanwise wavenumber of the oblique wave preferred by the nonlinear interaction is also determined by numerical simulations.

ParametricVibration Analysis of Pipes Conveying Fluid by Nonlinear Normal Modes and a Numerical Iterative Approach

Nonlinear normal modes and a numerical iterative approach are applied to study the parametric vibrations of pipes conveying pulsating fluid as an example of gyroscopic continua.The nonlinear non-autonomous governing equations are transformed into a set of pseudo-autonomous ones by employing the harmonic balance method.The nonlinear normal modes are constructed by the invariant manifold method on the state space and a numerical iterative approach is adopted to obtain numerical solutions,in which two types of initial conditions for the modal coefficients are employed.The results show that both initial conditions can lead to fast convergence.The frequency-amplitude responses with some modal motions in phase space are obtained by the present iterative method.Quadrature phase difference and traveling waves are found in the time-domain complex modal analysis.

Nonlinear modal electromechanical coupling factor for piezoelectric structures containing nonlinearities

Within the linear framework,the Modal Electromechanical Coupling Factor(MEMCF)is an important indicator to quantify the dynamic conversion of mechanical energy and electrical energy of piezoelectric structures.It is also an important tool to guide the piezoelectric damping design of linear structures.Advanced aircraft often fly in maneuvers,and the variable working conditions induce drastic changes in the load level on structures.Geometric and contact nonlinearities of thin-walled structures and joint structures are often activated.To achieve a good vibration reduction effect covering all working conditions,one cannot directly use linear electromechanical coupling theory to instruct the piezoelectric damping design for nonlinear structures.Therefore,this paper defines the Nonlinear Modal Electromechanical Coupling Factor(NMEMCF)and proposes the corresponding numerical method for the first time to quantitatively evaluate the electromechanical coupling capability of nonlinear piezoelectric structures.Three candidate definitions of the NMEMCF are given,including two frequency definitions and one energy definition.The energy definition is the most promising one.It is not only applicable to both conservative and dissipative nonlinear structures but also compatible with the linear MEMCF.In addition,based on the energy formula,the NMEMCF can be obtained by only performing one nonlinear modal analysis in the open-circuit state.The analytical findings and the numerical tool are validated against two piezoelectric structures with different types of nonlinearities.A strong correlation among the NMEMCF,geometric parameters,and energy dissipation is observed.The results confirm that the proposed NMEMCF captures the physics of the electromechanical coupling phenomenon associated with nonlinear piezoelectric structures and can be used as an essential design indicator of piezoelectric damping,especially for variable working conditions.

Asymmetric nonlinear-mode-conversion in an optical waveguide with PT symmetry

Asymmetric mode transformation in waveguide is of great significance for on-chip integrated devices with one-way effect,while it is challenging to achieve asymmetric nonlinear-mode-conversion(NMC)due to the limitations imposed by phase-matching.In this work,we theoretically proposed a new scheme for realizing asymmetric NMC by combining frequencydoubling process and periodic PT symmetric modulation in an optical waveguide.By engineering the one-way momentum from PT symmetric modulation,we have demonstrated the unidirectional conversion from pump to second harmonic with desired guided modes.Our findings offer new opportunities for manipulating nonlinear optical fields with PT symmetry,which could further boost more exploration on on-chip nonlinear devices assisted by non-Hermitian optics.

Self-adjustment of a nonlinear lasing mode to a pumped area in a two-dimensional microcavity [Invited]

We numerically performed wave dynamical simulations based on the Maxwell–Bloch(MB) model for a quadrupole-deformed microcavity laser with spatially selective pumping. We demonstrate the appearance of an asymmetric lasing mode whose spatial pattern violates both the x-and y-axes mirror symmetries of the cavity.Dynamical simulations revealed that a lasing mode consisting of a clockwise or counterclockwise rotating-wave component is a stable stationary solution of the MB model. From the results of a passive-cavity mode analysis, we interpret these asymmetric rotating-wave lasing modes by the locking of four nearly degenerate passive-cavity modes. For comparison, we carried out simulations for a uniform pumping case and found a different locking rule for the nearly degenerate modes. Our results demonstrate a nonlinear dynamical mechanism for theformation of a lasing mode that adjusts its pattern to a pumped area.