Dark optical solitons and conservation laws for parabolic and dual-power law nonlinearities in (2 + 1)-dimensions

This paper studies the dynamics of optical solitons with parabolic and dual-power law nonlinearities. The dark 1-soliton solution is first obtained by the ansatz method along with the necessary constraint conditions, for both of these nonlinearities. Subsequently, the invariance, conservation laws and double reductions of the governing nonlinear Schrödinger's equation are studied and the conserved densities are thus revealed.     

Optical soliton perturbation in a non-Kerr law media

This paper studies the optical soliton perturbation by the aid of soliton perturbation theory. The various perturbation terms, that arise in the study of optical solitons, are exhaustively studied in this paper. The adiabatic parameter dynamics of optical solitons are obtained in presence of these perturbation terms. The types of nonlinearities that are considered are Kerr law, power law, parabolic law as well as the dual-power law.     

Optical soliton perturbation in non-Kerr law media: Traveling wave solution

This paper analyses the dynamics of soliton propagation through optical fibers with non-Kerr law nonlinearities. The governing nonlinear Schrödinger equation is integrated in the presence of perturbation terms. The traveling wave hypothesis is used to carry out the integration. Domain restrictions on the soliton parameters are identified in the process. The five forms of nonlinearity that are studied are Kerr-law, power-law, parabolic-law, dual-power law and the log-law nonlinearity. Numerical simulations are presented for each of these nonlinear media.     

High nonlinearities in Langevin transducer: a comprehensive model

The design and simulation of power transducers are difficult since piezoelectric, dielectric and elastic properties of ferroelectric materials differ from linear behavior when driven at large levels. This paper is devoted to modeling of a resonant power transducer at a high level of dynamic mechanical stress. The power transducer is subjected to a sine electrical field E of varying frequency which was considered as the excitation of the transducer.The mechanical equation of the piezoelectric element is written using electrostriction. The dielectric part is written as a nonlinear function of an equivalent electric field including stress influence (scaling relationship between electric field and mechanical stress). Using various simulations, we show then that typical resonance nonlinearities are obtained, such as jump phenomenon of transducer speed amplitude and phase, resonance peak that become asymmetric, and diminution of mechanical quality factor. As a consequence, we state that those typical nonlinearities are only due to dielectric nonlinearities, in good correlation with typical ferroelectric behavior. Moreover, this demonstrates the usefulness of scaling relationships in ferroelectrics, which explain static depoling under stress and butterfly strain hysteresis loop. The same scaling law gives here several nonlinearities for resonant transducers as well.     

Optical solitons for non-Kerr law nonlinear Schrödinger equation with third and fourth order dispersions

In this paper, we obtain optical soliton solutions for non-Kerr law nonlinear Schrödinger equation (NLSE) with third order (3OD) and fourth order dispersions (4OD). We will use two integration schemes, namely sin-cosine method and Bernoulli’s equation approach with five laws of nonlinearities. Sine-cosine method is applicable to Kerr, power and anti-cubic laws, this method provides bright soliton solutions. The second method is applicable to parabolic and cubic quintic laws, this method generates dark soliton. The results may be used in discussing the propagation of optical solitons in highly dispersive media with Kerr, power, anti-cubic, parabolic and cubic quintic law nonlinearities.     

Optical soliton perturbation with spatio-temporal dispersion in parabolic and dual-power law media by semi-inverse variational principle

This paper studies the perturbed optical solitons with parabolic and dual-power law nonlinearities in presence of spatio-temporal dispersion. The semi-inverse variational principle is applied to extract an analytical 1-soliton solution to the governing equation. There are constraint conditions that naturally fall out for the existence of these solitons.     

Optical <Emphasis Type="Italic">Gaussons</Emphasis> and dark solitons in directional couplers with spatiotemporal dispersion

This paper study the dynamics of optical solitons for nonlinear directional couplers. This coupler system is considered with the group velocity dispersion and the cross-phase modulation of two components along with the spatiotemporal dispersion coefficients. The constraint conditions for the existence of optical Gaussons and dark solitons are listed under the log law and Kerr law nonlinearities, repectively. Additionally, a couple of other solutions known as singular periodic and combined dark-singular solitons, fall out as a by-product of this scheme. This scheme however fails to retrieve bright soliton solution.     

A novel adaptive finite-time controller for synchronizing chaotic gyros with nonlinear inputs

In this paper, the problem of the finite-time synchronization of two uncertain chaotic gyros is discussed. The parameters of both the master and the slave gyros are assumed to be unknown in advance. The effects of model uncertainties and input nonlinearities are also taken into account. An appropriate adaptation law is proposed to tackle the gyros' unknown parameters. Based on the adaptation law and the finite-time control technique, proper control laws are introduced to ensure that the trajectories of the slave gyro converge to the trajectories of the master gyro in a given finite time. Simulation results show the applicability and the efficiency of the proposed finite-time controller.     

Partial compensation of Kerr nonlinearities by optical phase conjugation in optical fiber transmission systems without power symmetry

We investigate the suppression of Kerr nonlinearities by optical phase conjugation (OPC) in a fiber transmission system without power symmetry by including all the manifestations of the Kerr nonlinearities. We found that OPC cannot completely compensate for all Kerr nonlinearities in absence of power symmetry, and some nonlinearities may become even worse if one of the nonlinearities is fully compensated. Therefore, it is necessary to optimize the compensation system to eliminate the most dominating nonlinearity. Simulation results are presented to demonstrate the interplay of various kinds of nonlinearities. The need of proper design for transmission systems to suppress the dominating nonlinear effect is shown when all manifestations of Kerr nonlinearity are not compensated simultaneously.     

Modelling of nonlinear crack–wave interactions for damage detection based on ultrasound—A review

The past decades have been marked by a significant increase in research interest in nonlinearities in micro-cracked and cracked solids. As a result, a number of different nonlinear acoustic methods have been developed for damage detection. A general consensus is that – under favourable conditions – nonlinear effects exhibited by cracks are stronger than crack-induced linear phenomena. However, there is still limited understanding of physical mechanisms related to various nonlinearities. This problem remains essential for implementation of nonlinear acoustics for damage-detection applications. This paper reviews modelling approaches used for nonlinear crack–wave interactions. Various models of classical and nonclassical crack-induced elastic, thermo-elastic and dissipative nonlinearities have been discussed.     

Adaptive synchronization of uncertain chaotic systems via switching mechanism

This paper deals with the problem of synchronization for a class of uncertain chaotic systems.The uncertainties under consideration are assumed to be Lipschitz-like nonlinearity in tracking error,with unknown growth rate.A logic-based switching mechanism is presented for tracking a smooth orbit that can be a limit cycle or a chaotic orbit of another system.Based on the Lyapunov approach,the adaptation law is determined to tune the controller gain vector online according to the possible nonlinearities.To demonstrate the efficiency of the proposed scheme,the well-known chaotic system namely Chua’s circuit is considered as an illustrative example.     

Traveling Fronts in a Reactive Boussinesq System: Bounds and Stability

This paper considers a simplified model of active combustion in a fluid flow, with the reaction influencing the flow. The model consists of a reaction-diffusion-advection equation coupled with an incompressible Navier-Stokes system under the Boussinesq approximation in an infinite vertical strip. We prove that for certain ignition nonlinearities, including all that are C², and for any domain width, planar traveling front solutions are nonlinearly and exponentially stable within certain weighted H² spaces, provided that the Rayleigh number ρ is small enough. The same result holds for bistable nonlinearities in unweighted H² spaces. We also obtain uniform bounds on the Nusselt number, the bulk burning rate, and the average maximum vertical velocity for chemistries that include bistable and ignition nonlinearities.     

Numerical modeling of high-power ultrasonic systems: current status and future trends

Numerical models of high power ultrasonic systems are usually based on finite element or boundary element methods. The basic physical models are linear and rely upon the theory of elasticity, the constitutive law of piezoelectricity and the theory of linear acoustics. They are only valid at low drive level. Some recent developments include nonlinearities of the transduction mechanism and of the propagation medium. In this paper, standard and advanced numerical models are discussed and illustrated by several application examples of high power ultrasonics.     

Chaos: Possible underpinnings for quantum mechanics?

Alternative, parallel explanations for a number of counter-intuitive concepts connected with the foundations of quantum mechanics can be constructed in terms of nonlinear dynamics. These include ideas as diverse as the statistical exponential decay law and spontaneous symmetry breaking to decoherence itself and the inference from violations of Bell’s inequality that local reality is ruled out in hidden variable extensions of quantum mechanics. Such alternative explanations must not be taken as demonstrations of nonlinear underpinnings for quantum mechanics, but they do raise the possibility of their existence. In this article I delve a bit into ideas connected with the exponential decay law and with Bell’s inequality as demonstrations. Then an investigation of the Klein-Gordon equation shows that it should not come as a complete surprise that quantum mechanics just might contain fundamental nonlinearities.     

增强的串级非线性

介绍了χ⁽²⁾串级非线性.讨论了串级光克尔非线性和串级光折变非线性的增强机制,并指出二阶和三阶非线性的相互转化,为光学非线性工程设计提供了可行性 关键词： 串级非线性 光克尔效应 光折变效应     

Linearization methods of laser interferometers for pico/nano positioning stages

Presented work introduces methods for improving linearity of a heterodyne laser interferometer system. The heterodyne configuration exhibits high potential in demanding applications, like pico/nano positioning. Those applications require superior accuracy, more difficult to obtain in a homodyne configuration of the laser interferometer. The homodyne setup is more susceptible to external light, variation of DC offset and higher noises, especially the 1/f noise. Those issues are filtered out in the heterodyne configuration. The main disadvantage of heterodyne setup are higher measurement nonlinearities. In this paper there are first introduced sources of nonlinearities and their impact on the overall accuracy. According to those findings there are proposed techniques to eliminate error caused by parasite beams, i.e. nonlinearities. Presented method is based on digital signal processing and is reliable and easy to use. In the shown approach the nonlinearities correction is completely automatic. Such system is applicable for X/Y positioning stages. Presented configuration of the laser interferometer is able to track the displacement with 100 pm resolution up to 7 m/s of translation velocity. The resolution can be improved to 10 pm by limitation of maximal velocity. In the paper there is confirmed that errors caused by nonlinearities are in range of ±0.6 nm. Achieved accuracy is comparable to capacitance gauges with presented laser interferometer having much better dynamic range.     

Exact Solutions of the Two-Dimensional Cubic-Quintic Nonlinear Schrdinger Equation with Spatially Modulated Nonlinearities

Applying the similarity transformation,we construct the exact vortex solutions for topological charge S ≥ 1 and the approximate fundamental soliton solutions for S = 0 of the two-dimensional cubic-quintic nonlinear Schrdinger equation with spatially modulated nonlinearities and harmonic potential.The linear stability analysis and numerical simulation are used to exam the stability of these solutions.In different profiles of cubic-quintic nonlinearities,some stable solutions for S ≥ 0 and the lowest radial quantum number n = 1 are found.However,the solutions for n ≥ 2 are all unstable.     

平衡衔铁受话器的非线性特性与失真仿真模型

平衡衔铁受话器(BAR)具有尺寸小、电声转换效率高和灵敏度高等特点。在大振幅振动时, BAR存在显著的非线性,并导致较严重的失真。利用磁路的集总参数模型(LPM)深入研究BAR的非线性,确立可表征其非线性特性的4个非线性参数,采用迭代计算方法研究平衡衔铁磁阻对非线性特性的重要影响。基于所提出的网格移动和旋转等效的有限元模型(FEM),考虑平衡衔铁磁阻的非线性,准确仿真计算得到非线性参数,再将它们代入到非线性LPM模型中,最终建立FEM与LPM相结合的失真仿真模型。实验结果表明,该失真仿真模型可比较准确地预测BAR在不同加载电压时的总谐波失真以及二次和三次谐波失真。     

A multi-input multi-output adaptive feed-forward controller for vibration alleviation on a large blended wing body airliner

Turbulent atmosphere, gusts, and manoeuvres significantly excite aircraft rigid body motions and structural vibrations, which leads to reduced ride comfort and increased structural loads. In particular BWB (Blended Wing Body) aircraft configurations, while promising a significant fuel efficiency improvement compared to wing-tube configurations, exhibit severe sensitivity to gusts. In general, a flexible aircraft represents a lightly damped structure involving a large variety of uncertainties due to fuel mass variations during flight, control system nonlinearities, aerodynamic nonlinearities, and structural nonlinearities, to name just a few. Especially at the beginning of flight testing of a newly developed aircraft type, plant models generally require a lot of verification and adjustment based on obtained flight test data, before they can be used reliably for control law design. Adaptive control already is a well-established method for many active noise and vibration control problems, and thus is proposed here for application to the problem of gust load alleviation. However, safety requirements are significantly higher for gust load alleviation systems than for most noise and vibration control systems. This paper proposes a MIMO (Multi-Input Multi-Output) adaptive feed-forward controller for the alleviation of turbulence-induced rigid body motions and structural vibrations on aircraft. The major contribution to the research field of active noise and vibration control is the presentation of a detailed stability analysis of the MIMO adaptive algorithm in order to support potential certification of this method for a safety-critical application. Finally, the proposed MIMO adaptive feed-forward vibration controller is applied to a longitudinal flight dynamics model of a large flexible BWB airliner in order to verify the derived vibration controller on a challenging control problem.     

Experimental investigation of the thermo-optical nonlinearity of solutions of synthesized rare-earth complexes

The large nonlinearities of the solutions of a new type of rare-earth complexes R_E(TTA)₄:HP, synthesized by ourselves, are experimentally demonstrated. The critical powers for the self-trapping of a laser beam in the solutions were measured. The dependence of the self-trapping critical powers on the absorptivity of the solutions and the type of solute complexes was found. The analysis for the experimental results shows that the effects of self-focusing and self-trapping of light in the solutions are not due to the change of molecular local density but the thermo-optical nonlinearities of the dissolved molecules themselves.