Nonlinear Coupled Interaction Research Articles

A novel M-shaped 2-DOF piezoelectric energy harvester with built-in outer-inner magnetic tri-stable oscillators for energy converting enhancement and applications

Tri-stable oscillators have been widely used to develop various nonlinear broadband energy harvesters. Focusing on further achieving high-performance piezoelectric energy harvester under broadband vibrations, a novel M-shaped 2-DOF piezoelectric energy harvester (M-PEH) with built-in outer-inner magnetic tri-stable oscillators is proposed, in which an inner magnetic tri-stable oscillator is built-in into a U-shaped outer magnetic tri-stable oscillator using its cut-out cantilever beam, assisted by the coupling interface to further enhance the dynamic responses. A complete physical model by considering the nonlinear coupling interaction between the outer-inner magnetic tri-stable oscillators is established to describe the dynamic performances under different system parameters. The theoretical model is well validated by experiments, which show that the proposed M-PEH has more compact size, wider operating frequency and higher power generation, offering an effective bandwidth of 20.1 Hz (5.1–25.2 Hz) at base excitation A = 5 m/s2, and achieving maximum output voltage 8.5 V and total peak power 26.7 μW. Compared to the original magnetic-coupling nonlinear tri-stable PEH, the effective bandwidth and total power have increased by 300 % and 662 % respectively, and the average power density is increased by 917 %. In addition, four main coupling interaction modes between the outer and inner built-in tri-stable oscillator are observed, in which the nonlinear synchronous coupling interaction is conducive to generating inter-well motion, leading to more mechanical energy being transferred from the outer tri-stable oscillator to the inner built-in tri-stable oscillator, thereby improving power generation capacity. Besides, the coupling interaction between these two tri-stable oscillators produces two close resonances which can be easily tuned to form a wide operating bandwidth. Practical applications prove that the proposed M-PEH has the ability to power low-powered electronic products, meeting the power supplying requirements of engineering community.

Dynamics coupling analysis between elastic supporting structure and TLD with and without slat screen

The slat screen (SS) has been widely used in tuned liquid damper (TLD) to increase damping and suppress structural vibration. This study proposes a linked-spring screen that has a movable screen elastically connected to the inner wall. Laboratory experiments of elastic supporting structure with TLD were first conducted on a hexapod table to obtain structural dynamics response under different conditions. Wavelet transform and wavelet-based bicoherence are used to analyze the nonlinear characteristics of sloshing waves. Meanwhile, a two-way coupling numerical model was validated to accurately predict the nonlinear coupling interaction between structure and TLD. Effects of the SS on reducing the structural vibration were numerically evaluated together with the interactions among elastic structure, TLD and SS. Finally, effects of spring stiffness on TLD with linked-spring screen were studied. Findings show that SS can not only enhance the internal dissipation by creating vortexes but also break waves through the perforation. Compared with conventional TLD, screen with Se = 0.75 and D/L = 0.15 can reduce the maximum displacement by 37.86 %. Besides, the linked-spring screen can further improve the damping performance because of the enhanced shear flow and turbulence intensity when it was moving. The optimal damping effect can be achieved for K = 500 N·m−1 where the further reduction ratio is 29.80 %.

Variable Time Headway Policy Based Platoon Control for Heterogeneous Connected Vehicles With External Disturbances

This article develops a new platoon control strategy for heterogeneous connected vehicles (CVs) subject to time delays and external disturbances. Specifically, based on the third-order vehicle model, a novel platoon controller is developed by embedding the variable time headway (VTH) spacing policy and the nonlinear motion coupling interactions between CVs. Simultaneously, an integral sliding mode (ISM) controller is developed to resist the disturbances. Then, the condition of asymptotic stability for the CV platoon and the upper bound of communication delay are deduced by using the Lyapunov theorem. Also, the string stability is proved by using the infinity-norm method. Finally, extensive simulations and co-simulations are provided to show the validity of the developed controller. Moreover, experiments with intelligent micro vehicles are conducted further to validate the practical feasibility of the developed controller.

Theoretical solution of second-harmonic generation in periodically poled lithium niobate and chirped periodically poled lithium niobate thin film via quasi-phase-matching

We present an effective nonlinear coupled mode coefficient model to evaluate and analyze the second harmonic generation (SHG) process under the quasi-phase-matching (QPM) scheme in periodically poled lithium niobate (PPLN) thin film. The theoretical model derives directly from the nonlinear coupled mode equations and simplifies the QPM process in PPLN thin film. The simulated results agree excellently with the rigorous numerical calculations in a variety of situations. We also propose using the chirped PPLN (CPPLN) thin film to achieve the SHG of ultrashort laser pulse and develop a broadband nonlinear coupled mode theory to evaluate this complex nonlinear coupling interaction process. All the frequency components in fundamental wave (FW) and second harmonic wave (SHW) have been considered in the theory, and the spectral evolution of FW and SHW can be obtained by solving a series of nonlinear coupled mode equations. CPPLN thin film supports broadband up-conversion in telecommunications bands and can generate broadband entangled photons in infrared region, which shows great potential in optical communication and quantum optics. The developed theories provide an efficient tool to design and optimize the PPLN and CPPLN thin film for various applications based on nonlinear frequency conversion and help to achieve high-efficiency on-chip SHG of the ultrashort laser pulse.

Terahertz-induced cascaded interactions between spectra offset by large frequencies.

We explore the dynamics of a system where input spectra in the optical domain with very disparate center frequencies are strongly coupled via highly phase-matched, cascaded second-order nonlinear processes driven by terahertz radiation. The only requirement is that one of the input spectra contain sufficient bandwidth to generate the phase-matched terahertz-frequency driver. The frequency separation between the input spectra (or pump and seed spectra) can be more than ten times larger than the phase-matched terahertz frequency. This is in contrast to our previous work on cascaded parametric amplification, where the frequency separation between the pump and seed is required to be equal to the phase-matched terahertz frequency. A practical application of such a system where the cascading of a narrowband pump line centered at 1064 nm induced by a group of weaker seed lines centered about 1030 nm and separated by the phase-matched terahertz frequency is introduced. This approach is predicted to generate terahertz radiation with percent-level conversion efficiencies and millijoule-level pulse energies in cryogenically-cooled periodically poled lithium niobate. A model that solves for the nonlinear coupled interaction of terahertz and optical waves is employed. The calculations account for second and third-order nonlinearities, dispersion in the optical and terahertz domains as well as terahertz absorption. Ramifications of pulse formats on laser-induced damage are estimated by tracking the generated free-electron density. Strategies to mitigate laser-induced damage are outlined.

A semi-active control method for decreasing longitudinal torsional vibration of vehicle engine system: Theory and experiments

Due to diverse working conditions, the vehicle engine system may generate complicated nonlinear whole-body vibration with wide frequency band. Since conventional vibration control methods are usually designed in terms of the external excitations and implemented based on the linear models, their performance is difficult to improve. In this study, a new semi-active vibration absorption method that is both independent of external excitations and capable of dealing with nonlinear vibration problem is put forward to decrease the longitudinal torsional vibration of the vehicle engine system. It sufficiently utilizes nonlinear coupling and modal interaction to transfer and dissipate vibration energy, rather than relies on linear neutralization. A novel vibration absorber scheme with controllable frequency and controllable damping is proposed, which can be readily implemented by the control algorithms. Numerical simulations and virtual prototyping simulations have verified the correctness of theoretical research. Experimental investigations have been carried out to successfully examine the effectiveness and the feasibility of the proposed method.

A multiphase model for exploring tumor cell migration driven by autologous chemotaxis

It has been demonstrated that interstitial fluid (IF) flow can play a crucial role in tumor cell progression. In the seminal works by Swartz and collaborators (Fleury et al., 2006; Shields et al., 2007) it was discovered that due to this flow, chemokine ligands secreted by tumor cells selectively tend to bind to receptors (CCR7) on the downstream side of the cells that in turn stimulate cells to migrate in the direction of the flow. This migration process was denoted as autologous chemotaxis. Previous mathematical modeling of autologous chemotaxis apparently has been restricted to single-phase considerations. The purpose of this work is to explore how a multiphase approach can be used where the fluid and cancer cells are treated as two separate phases with their own momentum balance equations. A mathematical model is derived that sheds light on essential nonlinear coupling mechanisms and interactions that are involved. The role played by fluid-ECM (friction type of term) and cell-ECM interaction forces (adhesion forces) are demonstrated. In particular, a fluid generated stress term in the mathematical expression for the cell velocity is highlighted. This term reflects how the flowing fluid will try to push the cancer cells in the downstream direction whose effect must be counterbalanced by the cancer cells by creating a sufficiently strong cell-ECM resistance force. Moreover, in order to represent the autologous chemotaxis migration mechanism we include (i) a component to represent stagnant ECM concentration (collagen); (ii) a chemical component representing chemokine that can convect with the fluid; and (iii) a third chemical component to represent protease secreted by the cancer cells which is able to release ECM-bound chemokine through proteolytic activity. The resulting model allows us to demonstrate how the autologous chemotaxis transport mechanism is governed by formation of chemokine concentration gradients that are asymmetric and skewed in the flow direction. We test the model behavior for a flow system with an external imposed pressure gradient which is comparable with the laboratory experiments by Swartz and collaborators. Sensitivity to changes in circumstances like blocking of the CCR7 receptor needed for autologous chemotaxis and elimination of the pressure driven IF flow (i.e., no flow) are explored and discussed. We also illustrate the model behavior in an envisioned tumor setting where increased IF flow is produced from leaky blood vessels that sit on the inside of the tumor. An increased fluid flow towards the region on the outside of the tumor is then generated where it is adsorbed by lymphatic vessels and gives rise to a characteristic elevated IF pressure profile that decreases at the tumor periphery. In turn, this results in an autologous chemotactic driven migration of cancer cells at the rim of the tumor. The simulation illustrates how the autologous chemotactic cell migration mechanism discovered by Swartz and collaborators possibly can be used as a means for metastasis by generating aggressive cell migration towards lymphatic vessels.

Nonlinear Dynamics Modeling and Analysis of Underwater Mud-Penetrator Steering System

Adopting underwater mud-penetrator to thread the steel wire is one of the important steps in the current wreck salvage process, which is safer and more efficient than threading with manpower by the diver. This paper first establishes the kinematics model of the underwater mud-penetrator in the inertial coordinate system and discussed the drill steering mechanism and force characteristics under the nonlinear coupling interaction between drill bit, drill pipe, and seabed geology. Based on the Newton–Eulerian method, the nonlinear dynamic model of mud-penetrator is established, and the influence of guiding angle, geological features, and propelling force on steering process is analyzed through simulation. The simulation results show that the steering process of underwater mud-penetrator is the compound movement of the drill bit translation and deflection. The reduction of the guiding angle and the increase of the propulsive force can effectively improve the guiding ability of the non-excavation drill bit. As the guiding angle decreases pi/12–pi/15, the deflection angle of the drill bit is increased by 2°–3°, and as propulsion increases 500 N, the deflection angle of the drill bit is increased by 3°. The area of the guiding plate also has a great influence on the guiding ability of the drill bit, and the deflection angle is inversely proportional to the area of the drill guiding plate. The deflection angle is more sensitive to soft geological changes. The simulation results are of great significance help to understand the process of drilling guidance process for wrecking and salvaging, and it can help to improve the threading success rate and salvage efficiency.

Theory of terahertz generation by optical rectification using tilted-pulse-fronts.

A model for terahertz (THz) generation by optical rectification using tilted-pulse-fronts is developed. It simultaneously accounts for in two spatial dimensions (2-D) (i) the spatio-temporal variations of the optical pump pulse imparted by the tilted-pulse-front setup, (ii) the nonlinear coupled interaction of THz and optical radiation, (iii) self-phase modulation and (iv) stimulated Raman scattering. The model is validated by quantitative agreement with experiments and analytic calculations. We show that the optical pump beam is significantly broadened in the transverse-momentum (kx) domain as a consequence of its spectral broadening due to THz generation. In the presence of this large frequency and transverse-momentum (or angular) spread, group velocity dispersion causes a spatio-temporal break-up of the optical pump pulse which inhibits further THz generation. The implications of these effects on energy scaling and optimization of optical-to-THz conversion efficiency are discussed. This suggests the use of optical pump pulses with elliptical beam profiles for large optical pump energies. Furthermore, it is seen that optimization of the setup is highly dependent on optical pump conditions. Trade-offs in optimizing the optical-to-THz conversion efficiency on the spatial and spectral properties of THz radiation are discussed to guide the development of such sources.

Limitations to THz generation by optical rectification using tilted pulse fronts

Terahertz (THz) generation by optical rectification (OR) using tilted-pulse-fronts is studied. A one-dimensional (1-D) model which simultaneously accounts for (i) the nonlinear coupled interaction of the THz and optical radiation, (ii) angular and material dispersion, (iii) absorption, iv) self-phase modulation and (v) stimulated Raman scattering is presented. We numerically show that the large experimentally observed cascaded frequency down-shift and spectral broadening (cascading effects) of the optical pump pulse is a direct consequence of THz generation. In the presence of this large spectral broadening, the large angular dispersion associated with tilted-pulse-fronts which is ~15-times larger than material dispersion, accentuates phase mismatch and degrades THz generation. Consequently, this cascading effect in conjunction with angular dispersion is shown to be the strongest limitation to THz generation in lithium niobate for pumping at 1 µm. It is seen that the exclusion of these cascading effects in modeling OR, leads to a significant overestimation of the optical-to-THz conversion efficiency. The results are verified with calculations based on a 2-D spatial model. The simulation results are supported by experiments.

Research on Horizontal Displacement and Torsion Coupling Effect of Structure-Soil System

In this paper, the vibration equation of the structure-soil nonlinear interaction system was qualitatively analyzed by using the modern dynamic theory. Based on the multilinear kinematic hardening mode, the nonlinear finite element method was applied for the solution of the horizontal and torsional stiffness between the foundation and soil interaction system. And a mechanical model of the structure-soil nonlinear interaction system was established. The Lagrange energy method is used to build the coupling vibration equation of the structural horizontal displacement and torsion. The Primary resonance of the structure-soil nonlinear interaction system was studied by using the multiple scales method. By analyzing the nonlinear coupling interaction between different structures and soil, the coupling effect of structure system was revealed by appearing energy transfer from high order horizontal vibration to low order torsional vibration, and also the vibration characteristics and the behavior of energy transfer were obtained.

Entanglement and quantum teleportation in a nonlinear spin channel

The ground state and thermal entanglement of a two-qubit spin system in the presence of the nonlinear coupling interaction is investigated. It is found that the nonlinear coupling interaction can excite and enhance the entanglement both for ferromagnetic chain and anti-ferromagnetic ones even at the higher temperature. The entanglement teleportation via the quantum channel constructed by this system is also discussed, and the influence of the nonlinear coupling interaction on the fidelity of the teleportation is studied. The results show that both the entanglement of the output state and the fidelity can be increased by inducing a proper nonlinear coupling interaction.

A theoretical study of nonlinear magnetoelectric effect in magnetostrictive–piezoelectric trilayer

A novel nonlinear theoretical model is established for magnetoelectric (ME) effect in trilayer of magnetostrictive and piezoelectric phases, in which the nonlinear magnetic-mechanical coupling behavior for the magnetostrictive phase is firstly taken into account. In this theoretical model, the interface coupling parameter k is used for characterizing actual bonding conditions at the interface. The coupled magnetic-mechanical-electric effect involving linear and nonlinear coupling interactions in the ME laminated composites is numerically simulated using this nonlinear model. The numerical results predict giant ME effect for Terfenol-D based ME laminated composites. The quantitative dependences of the giant ME effect on the applied magnetic field, the piezoelectric property of piezoelectric phase, the volume fraction of magnetostrictive phase and the interface coupling parameter k are discussed in details. All of these dependences indicate that the nonlinear theoretical model established in this article can accurately capture nonlinear magnetic-mechanical-electric coupling behavior for Terfenol-D based ME laminated composites. The giant ME effect predicted for the Terfenol-D/PMN-FT/Terfenol-D composites is in excellent agreement with recent experimental data available. It confirms the validity and reliability of the obtained nonlinear theoretical model, and demonstrates the significance and necessity of considering the nonlinear magnetic-mechanical coupling behavior of Terfenol-D. (C) 2010 Elsevier Ltd. All rights reserved.

Spin textures in condensates with large dipole moments

We have solved numerically the ground states of a Bose-Einstein condensate in the presence of dipolar interparticle forces using a semiclassical approach. Our motivation is to model, in particular, the spontaneous spin textures emerging in quantum gases with large dipole moments, such as $^{52}\mathrm{Cr}$ or $\mathrm{Dy}$ condensates, or ultracold gases consisting of polar molecules. For a pancake-shaped harmonic (optical) potential, we present the ground-state phase diagram spanned by the strength of the nonlinear coupling and dipolar interactions. In an elongated harmonic potential, we observe a helical spin texture. The textures calculated according to the semiclassical model in the absence of external polarizing fields are predominantly analogous to previously reported results for a ferromagnetic $F=1$ spinor Bose-Einstein condensate, suggesting that the spin textures arising from the dipolar forces are largely independent of the value of the quantum number $F$ or the origin of the dipolar interactions.

Neuromuscular Plasticity and Rehabilitation of the Ocular Near Response

The near response is composed of cross-coupled interactions between convergence and other distance-related oculomotor responses including accommodation, vertical vergence, and cyclovergence. The cross-coupling interactions are analogous to the body postural reflexes that maintain balance. Near-response couplings guide involuntary motor responses during voluntary shifts of distance and direction of gaze without feedback from defocus or retinal-image disparity. They optimize the disparity stimulus for stereoscopic depth perception and can be modified by optically induced sensory demands placed on binocular vision. In natural viewing conditions, the near response is determined by passive orbital mechanics and active-adaptable tonic components. For example, the normal coupling of vertical vergence with convergence in tertiary gaze is partly a byproduct of passive orbital mechanics. Both, adapted changes of vertical vergence in response to anisophoria, produced by unequal ocular magnification (aniseikonia), and adapted changes in the orientation of Listing's plane in response to torsional disparities can be achieved by a combination of passive orbital mechanics and neural adjustments for the control of the vertical vergence and cyclovergence. Adaptive adjustments are coupled with gaze direction, convergence angle, and head tilt. Several adaptation studies suggest that it is possible to achieve non-linear changes in the coupling of both vertical vergence and cyclovergence with gaze direction. This coupling can be achieved with changes in neural control signals of ocular elevator muscles that are cross-coupled with both convergence and direction of tertiary gaze. These linear and non-linear coupling interactions can be adapted to compensate for (1) anisophoria induced by spectacle corrections for anisometropia, (2) accommodative esotropia, (3) convergence excess and insufficiency, and (4) non-concomitant deviations with ocular torticollis associated with trochlear palsy. The adaptable near-response couplings form the basis of an area of orthoptics that optimizes visual performance by facilitating our natural ability to calibrate neural pathways underlying binocular postural reflexes.

Towards anomalous diffusion with nonlinear interactions for Hamiltonian chaotic systems

A macroscopic transport equation has been derived from the underlying microscopic dynamics and a general fluctuation-dissipation relation is proposed for a microscopic system composed of the collective degrees of freedom coupled to finite intrinsic ones through a weak interaction. With the aid of numerical simulation, it is shown that there is substantial difference in correlation function and hence a difference in the statistical process between linear and nonlinear coupling interaction. It turned out that the statistical relaxation in the finite system has an anomalous diffusion and the fluctuation effects have finite correlation time.

Random responses of a two-degree-of-freedom structure with strongly nonlinear coupling and parametric interaction

This paper investigates the random responses of a TDOF structure with strongly nonlinear coupling and parametric vibration. With the nonlinear coupling of inertia in the equations of motion of the system being removed by successive elimination, the non-Gaussian moment equation method (NGM) is applied and 69 moment equations are integrated with central cumulative truncation technique. The stochastic central difference-cum-statistical linearization method(SCD-SL) and the digital simulation method(DSM) are also used. A comparison of results by different methods are given and the SCD-SL method is the most efficient method.