Selective Impact of Dispersion and Nonlinearity on Waves and Solitary Wave in a Strongly Nonlinear and Flattened Waveguide

The waveguide which is at the center of our concerns in this work is a strongly flattened waveguide, that is to say characterized by a strong dispersion and in addition is strongly nonlinear. As this type of waveguide contains multiple dispersion coefficients according to the degrees of spatial variation within it, our work in this article is to see how these dispersions and nonlinearities each influence the wave or the signal that can propagate in the waveguide. Since the partial differential equation which governs the dynamics of propagation in such transmission medium presents several dispersion and nonlinear coefficients, we check how they contribute to the choices of the solutions that we want them to verify this nonlinear partial differential equation. This effectively requires an adequate choice of the form of solution to be constructed. Thus, this article is based on three main pillars, namely: first of all, making a good choice of the solution function to be constructed, secondly, determining the exact solutions and, if necessary, remodeling the main equation such that it is possible;then check the impact of the dispersion and nonlinear coefficients on the solutions. Finally, the reliability of the solutions obtained is tested by a study of the propagation. Another very important aspect is the use of notions of probability to select the predominant solutions.

Combined influence of nonlinearity and dilation on slope stability evaluated by upper-bound limit analysis

The combined influence of nonlinearity and dilation on slope stability was evaluated using the upper-bound limit analysis theorem.The mechanism of slope collapse was analyzed by dividing it into arbitrary discrete soil blocks with the nonlinear Mohr–Coulomb failure criterion and nonassociated flow rule.The multipoint tangent(multi-tangent) technique was used to analyze the slope stability by linearizing the nonlinear failure criterion.A general expression for the slope safety factor was derived based on the virtual work principle and the strength reduction technique,and the global slope safety factor can be obtained by the optimization method of nonlinear sequential quadratic programming.The results show better agreement with previous research result when the nonlinear failure criterion reduces to a linear failure criterion or the non-associated flow rule reduces to an associated flow rule,which demonstrates the rationality of the presented method.Slope safety factors calculated by the multi-tangent inclined-slices technique were smaller than those obtained by the traditional single-tangent inclined-slices technique.The results show that the multi-tangent inclined-slices technique is a safe and effective method of slope stability limit analysis.The combined effect of nonlinearity and dilation on slope stability was analyzed,and the parameter analysis indicates that nonlinearity and dilation have significant influence on the result of slope stability analysis.

Periodic Modulation of Nonlinearity in a Two-Core Photonic Crystal Fiber: A Numerical Investigation

We present a numerical investigation of the propagation and the switching of ultra-short pulses (100 fs) in a two-core nonlinear coupler of photonic crystal fibers constructed with periodically modulated the non-linearity fiber (PMNL-PFC). Our simulations are taking into account different amplitude and frequency modulations of the PMNL-PFC. A coupler for coupling whose length is Lc = 1.8 cm, the transmission characteristics, the compression factor, the crosstalk (Xtalk) and extinction ratio (Xratio) levels of the first order solitons were studied for low to high pump energies considering 2Lc. By an analysis on the reference channel (channel 2), it is observed that at low modulation frequencies an increase occurs in the switching power increasing transmission efficiency. For high modulation frequencies, the transmitted energy efficiency loses. The switching pulses are stronger for low frequency and high amplitude modulation. The Xtalk is a function of the measurement made on the secondary channel (channel 1). It was observed that this unwanted high-frequency energy increases to lessen the measure of the amplitude modulation. In summary, we have demonstrated that introduction of a non-linearity profile takes the periodically modulated PMNL-PFC to strong variations at transmission efficiency, Xtalk, Xratio a function of frequency and modulation amplitude and the input power.

Multiple mixed state variable incremental integration for reconstructing extreme multistability in a novel memristive hyperchaotic jerk system with multiple cubic nonlinearity

Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability.Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting the incremental integration of the state variables into system parameters.However,this approach cannot solve memristive systems in the presence of nonlinear terms other than the memristor term.In addition,the converted state variables may suffer from a degree of divergence.To allow simpler mechanistic analysis and physical implementation of extreme multistability phenomena,this paper uses a multiple mixed state variable incremental integration(MMSVII)method,which successfully reconstructs a four-dimensional hyperchaotic jerk system with multiple cubic nonlinearities except for the memristor term in a three-dimensional model using a clever linear state variable mapping that eliminates the divergence of the state variables.Finally,the simulation circuit of the reduced-dimension system is constructed using Multisim simulation software and the simulation results are consistent with the MATLAB numerical simulation results.The results show that the method of MMSVII proposed in this paper is useful for analyzing extreme multistable systems with multiple higher-order nonlinear terms.

Effect of Wave Nonlinearity on the Instantaneous Seabed Liquefaction

The nonlinear variation of wave is commonly seen in nearshore area,and the resulting seabed response and liquefaction are of high concern to coastal engineers.In this study,an analytical formula considering the nonlinear wave skewness and asymmetry is adopted to provide wave pressure on the seabed surface.The liquefaction depth attenuation coefficient and width growth coefficient are defined to quantitatively characterize the nonlinear effect of wave on seabed liquefaction.Based on the 2D full dynamic model of wave-induced seabed response,a detailed parametric study is carried out in order to evaluate the influence of the nonlinear variation of wave loadings on seabed liquefaction.Further,new empirical prediction formulas are proposed to fast predict the maximum liquefaction under nonlinear wave.Results indicate that(1)Due to the influence of wave nonlinearity,the vertical transmission of negative pore water pressure in the seabed is hindered,and therefore,the amplitude decreases significantly.(2)In general,with the increase of wave nonlinearity,the liquefaction depth of seabed decreases gradually.Especially under asymmetric and skewed wave loading,the attenuation of maximum seabed liquefaction depth is the most significant among all the nonlinear wave conditions.However,highly skewed wave can cause the liquefaction depth of seabed greater than that under linear wave.(3)The asymmetry of wave pressure leads to the increase of liquefaction width,whereas the influence of skewedness is not significant.(4)Compared with the nonlinear waveform,seabed liquefaction is more sensitive to the variation of nonlinear degree of wave loading.

Quasi-anti-parity–time-symmetric single-resonator micro-optical gyroscope with Kerr nonlinearity

Parity–time(PT) and quasi-anti-parity–time(quasi-APT) symmetric optical gyroscopes have been proposed recently which enhance Sagnac frequency splitting. However, the operation of gyroscopes at the exceptional point(EP) is challenging due to strict fabrication requirements and experimental uncertainties. We propose a new quasi-APT-symmetric micro-optical gyroscope which can be operated at the EP by easily shifting the Kerr nonlinearity. A single resonator is used as the core sensitive component of the quasi-APT-symmetric optical gyroscope to reduce the size, overcome the strict structural requirements and detect small rotation rates. Moreover, the proposed scheme also has an easy readout method for the frequency splitting. As a result, the device achieves a frequency splitting 10~5 times higher than that of a classical resonant optical gyroscope with the Earth's rotation. This proposal paves the way for a new and valuable method for the engineering of micro-optical gyroscopes.

Break Up of <i>N</i>-Soliton Bound State in a Gradient Refractive Index Waveguide with Nonlocal Nonlinearity

We study the propagation of N-soliton bound state in a triangular gradient refractive index waveguide with nonlocal nonlinearity. The study is based on the direct numerical solutions of the model and subsequent eigenvalues evolution of the corresponding Zakharov-Shabat spectral problem. In the waveguide with local nonlinearity, the velocity of a single soliton is found to be symmetric around zero and therefore the soliton oscillates periodically inside the waveguide. If the nonlocality is presence in the medium, the periodic motion of soliton is destroyed due to the soliton experiences additional positive acceleration induced by the nonlocality. In the waveguide with the same strength of nonlocality, a higher amplitude soliton experiences higher nonlocality effects, i.e. larger acceleration. Based on this soliton behavior we predict the break up of N-soliton bound state into their single-soliton constituents. We notice that the splitting process does not affect the amplitude of each soliton component.

More Compactification for Differential Systems

This article is a review and promotion of the study of solutions of differential equations in the “neighborhood of infinity” via a non traditional compactification. We define and compute critical points at infinity of polynomial autonomuos differential systems and develop an explicit formula for the leading asymptotic term of diverging solutions to critical points at infinity. Applications to problems of completeness and incompleteness (the existence and nonexistence respectively of global solutions) of dynamical systems are provided. In particular a quadratic competing species model and the Lorentz equations are being used as arenas where our technique is applied. The study is also relevant to the Painlevé property and to questions of integrability of dynamical systems.

Computation of Error in Estimation of Nonlinearity in ADC Using Histogram Technique

Computation of error in estimation of nonlinearity in ADC using histogram test are reported in this paper. Error determination in estimation of Differential Nonlinearity (DNL) and Integral Nonlinearity (INL) of an ADC is done by taking deviation of estimated value from actual value. Error in estimated INL and DNL is determined to check the usefulness of basic histogram test algorithm. Arbitrary error is introduced in ideal simulated ADC transfer characteristics and full scale simulated sine wave is applied to ADC for computation of error in estimation of transition levels and nonlinearity. Simulation results for 5 and 8 bit ADC are pre-sented which show effectiveness of the proposed method.

Stochastic Oscillators with Quadratic Nonlinearity Using WHEP and HPM Methods

In this paper, quadratic nonlinear oscillators under stochastic excitation are considered. The Wiener-Hermite expansion with perturbation (WHEP) method and the homotopy perturbation method (HPM) are used and compared. Different approximation orders are considered and statistical moments are computed in the two methods. The two methods show efficiency in estimating the stochastic response of the nonlinear differential equations.

Effect of inertia nonlinearity on dynamic response of an asymmetric building equipped with tuned mass dampers

This study investigates the effect of nonlinear inertia on the dynamic response of an asymmetric building equipped with Tuned Mass Dampers(TMDs).In the field of structural engineering,many researchers have developed models to study the behavior of nonlinear TMDs,but the effect of nonlinear inertia has not received as much attention for asymmetric buildings.To consider nonlinear inertia,the equations of motion are derived in a local rotary coordinates system.The displacements and rotations of the modeled building and TMDs are defined by five-degree-of-freedom(5-DOFs).The equations of motion are derived by using the Lagrangian method.Also in the proposed nonlinear model,the equations of motion are different from a conventional linear model.In order to compare the response of the proposed nonlinear model and a conventional linear model,numerical examples are presented and the response of the modeled buildings are derived under harmonic and earthquake excitations.It is shown that if the nonlinear inertia is considered,the response of the modeled structures changes and the conventional linear approach cannot adequately model the dynamic behavior of the asymmetric buildings which are equipped with TMDs.

Polarization Jitters Caused by Fiber Nonlinearity in PM Optical Communication System

The phenomenon of polarization jitters caused by fiber nonlinearity is investigated. A general formula about the polarization jitter is concluded in polarization multiplexing (PM) system based on two orthogonal linear polarization states when the best polarization correction is used. A 100 Gb/s PM system based on NRZ code is investigated by simulation, and the Stocks parameter about polarization jitter and Poincare sphere diagrams are got for different power and phase difference of two orthogonal polarized light. The results show that the polarization jitters will be suppressed when the combined PM signal is the linear or circular polarization state.

Estimation of Longitudinal Tire Force Using Nonlinearity Observer

Tire forces are the major forces propelling the road vehicles. They significantly affect the dynamic behavior of the vehicles. Estimation of the tire forces is essential in vehicle dynamics and control. This paper presents an observer-based scheme for estimation of the longitudinal tire force of electric vehicles in real time.? The observer is based on a nonlinearity observer method. The pole-placement technique is used for determination of the observer gains. Simulation results demonstrate that the observer is able to estimate the tire force successfully. The experiments are implemented on a single-wheel electric vehicle test rig. The test rig comprises an electric motor driven wheel and a free-rolling drum simulating vehicle-on-road situations. Experimental results confirm the effectiveness of the present scheme.

Nonlinear wave propagation in acoustic metamaterials with bilinear nonlinearity

Nonlinear phononic crystals have attracted great interest because of their unique properties absent in linear phononic crystals.However,few researches have considered the bilinear nonlinearity as well as its consequences in acoustic metamaterials.Hence,we introduce bilinear nonlinearity into acoustic metamaterials,and investigate the propagation behaviors of the fundamental and the second harmonic waves in the nonlinear acoustic metamaterials by discretization method,revealing the influence of the system parameters.Furthermore,we investigate the influence of partially periodic nonlinear acoustic metamaterials on the second harmonic wave propagation,and the results suggest that pass-band and band-gap can be transformed into each other under certain conditions.Our findings could be beneficial to the band gap control in nonlinear acoustic metamaterials.

双管式挫屈束制(屈曲约束)支撑之耐震行为与应用

挫屈束制(屈曲约束)支撑一般是由十字型或一字型钢板构成之核心单元加上钢管混凝土构成之束制(约束)单元所组成。由于单核心断面之挫屈束制支撑在与构架接合时每一端需使用八片续接板及两套的螺栓,造成接合部分较长且易发生挫屈(屈曲),为了改善此种挫屈束制支撑与接合,相关研究已发展出以双T型核心配双钢管或双钢板核心配双钢管而组成之双钢管型挫屈束制支撑构件,并已成功地在台大完成一系列之试验,本研究进一步针对大尺寸之单层挫屈束制支撑构架进行试验。研究目的包括:(1)探讨支撑具不同核心长度比例构架之试验与解析行为;(2)研究挫屈束制支撑核心应变与楼层侧位移角之关系;(3)提供含挫屈束制支撑构架之分析与设计建议。由三组V型双钢板双钢管挫屈束制支撑构架之试验显示,支撑核心之极限应变可利用楼层的最大侧位移角需求,以简单的几何关系及支撑核心长度与工作点间长度之比值计算而得,试验结果亦显示,在构架产生最大侧位移角时支撑之核心拉应变会大于相邻支撑之核心压应变,显示两相邻支撑之轴拉力与轴压力在试体中有互相平衡之趋势,而不会发生最大轴压力显著大于最大轴拉力的现象。

NASA’s EM Drive Thrust from the Forces of the Quantum Vacuum of Spacetime

Building on the various manifestations of the forces latent in the quantum vacuum of spacetime such as Hawking’s radiation and Unruh temperature, we resolve a major paradox connected to an immensely important proposal by NASA scientists for constructing a practically fuelless spacecraft. In a nutshell, preliminary laboratory work shows that NASA’s electromagnetic drive project is viable and several experiments and measurements show it is real. Yet the proposal violates a fundamental principle of classical mechanics, namely Newton’s third law. The resolution of this paradox is quite straight forward in principle. It is simply the case that although the proposal seems to be based on classical mechanics and classical thinking it is only superficially so. Deep at the roots, the EM drive proposal of NASA is not classical physics but rather based on the vacuum forces of quantum cosmology and the theory of dark energy density of the universe. In fact the proposal is deeply linked to Hawking’s radiation and Unruh temperature, which is explained in some detail in the main body of the present short paper within the frame work of E-infinity Cantorian spacetime theory and D. Gross’ Heterotic superstring theory. In short the quintessence of our explanation is to regard the EM drive as a quasi electromagnetic cavity with an effective event horizon akin to that of a Hawking black hole emitting radiation causing ultimately the needed thrust to push the spacecraft forwards. In addition and by invoking fractal spacetime self similarity we show that a spacecraft will be subject to another cosmic thrust on the large scale of the entire cosmos.

变系数三阶周期边值问题的正解(英文)

研究了变系数非线性三阶周期边值问题的正解.非线性项可以关于空间变元奇异.利用适当的变换此问题被转换为一个Hammerstein积分方程,利用锥上的Guo-Krasno-selski不动点定理获得了1～2个正解的存在性.

Effects of thermo-magneto-electro nonlinearity characteristics on the stability of functionally graded piezoelectric beam

Due to the increasing interests in using functionally graded piezoelectric materials(FGPMs) in the design of advanced micro-electro-mechanical systems, it is important to understand the stability behaviors of the FGPM beams. In this study, considering the effects of geometrical nonlinearity, temperature, and electricity in the constitutive relations and the effect of the magnetic field on the FGPM beam, the Euler-Bernoulli beam model is adopted, and the nonlinear governing equation of motion is derived via Hamilton's principle. A perturbation method, which can decompose the deflection into static and dynamic components, is utilized to linearize the nonlinear governing equation. Then,a dynamic stability analysis is carried out, and the approximate analytical solutions for the nonlinear frequency and boundary frequencies of the unstable region are obtained.Numerical examples are performed to verify the present analysis. The effects of the static deflection, the static load factor, the temperature change, and the magnetic field flux on the stability behaviors of the FGPM beam are discussed. From the proposed analytical solutions and numerical results, one can easily and clearly find the effects of various controlled parameters, such as geometric and physical properties of the system, on the mechanical behaviors of structures, and the conclusions are very important and useful for the design of micro-devices.

Positive Solutions to the Nonhomogenous <i>p</i>-Laplacian Problem with Nonlinearity Asymptotic to <i>u^p</i>-1at Infinity in R<i>^N</i>

In this paper, we study the following problem {-Δpu+V(x)|u|p-2u=K(x)f(u)+h(x) in□ N, u∈W1,p(□ N), u>0 in □ N, (*) where 1<p<N,the potential V(x) is a positive bounded function, h∈Lp'(□ N), 1/p'+1/p=1, 1<p<N, h≥0, h≠0f(s) is nonlinearity asymptotical to sp-1at infinity, that is, f(s)~O(sp-1) as s→+∞. The aim of this paper is to discuss how to use the Mountain Pass theorem to show the existence of positive solutions of the present problem. Under appropriate assumptions on V, K, h and f, we prove that problem (*) has at least two positive solutions even if the nonlinearity f(s) does not satisfy the Ambrosetti-Rabinowitz type condition: 0≤F(u)≤∫uo f(s)ds≤1/p+θ f(u)u, u>0, θ>0.

Numerical Analyses Optical Solitons in Dual Core Couplers with Kerr Law Nonlinearity

In this paper, we present the results of numerical analysis of optical solitons in dual core couplers. We studied the optical couplers as an application for the non-linear Schr&ouml;dinger equation in the case of Kerr law for non-linear and clarify the exact solution in this case. Then we have provided a numerical study of the effect of changing the constants in the form of the three types of solitons: bright soliton and dark solitons and singular soliton.