Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation

For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.

Phase Relation of Harmonics in Nonlinear Focused Ultrasound

The phase relation of harmonics in high-intensity focused ultrasound is investigated numerically and experimen- tally. The nonlinear Westervelt equation is solved to model nonlinear focused sound field by using the finite difference time domain method. Experimental waveforms are measured by a robust needle hydrophone. Then the relative phase quantity is introduced and obtained by using the zero-phase filter. The results show that the nth harmonic relative phase quantity is approximately （n - 1） π/3 at geometric center and increases along the axial direction. Moreover, the relative phase quantity decreases with the increase of source amplitude. This phase relation gives an explanation of some nonlinear phenomena such as the discrepancy of positive and negative pressure.

Interference-Driven Designs of Nonlinear-Phase FIR Filter with Application in FBMC System

In the forthcoming 5G systems, new technologies, such as amorphous networks and non-orthogonal filter bank multicarriers(FBMC), provide an effective way to accommodate high-rate transmissions. Meanwhile, the prototype filter affects the adjacent channel interference, and therefore is important for FBMC systems. Besides, once the amorphous network is taken into account, the requirement for interference controlmust be much stricter. Accordingly, this paper focuses on the design of prototype filter with better ability of interference controlling, where we exploit the nonlinear phase FIR filter(NLPFF) instead of traditional linear phase FIR filter(LPFF) to achieve more optimization spaces under a small sacrifice of linear phase. In ourdesigns, both the amplitude and phase responsesare handled independently to approach the stopband performance enhancements, in while the nearly perfect reconstruction(NPR) conditionsare relaxed by pre-specified thresholds. Computer simulations confirm the effectiveness of the NLPFF designs, and demonstrate the advantages of the proposed NLPFF in FBMC applications.

Nonlinear effect of the structured light profilometry in the phase-shifting method and error correction

Digital structured light （SL） profilometry is increasingly used in three-dimensional （3D） measurement technology. However, the nonlinearity of the off-the-shelf projectors and cameras seriously reduces the measurement accuracy. In this paper, first, we review the nonlinear effects of the projector-camera system in the phase-shifting structured light depth measurement method. We show that high order harmonic wave components lead to phase error in the phase-shifting method. Then a practical method based on frequency domain filtering is proposed for nonlinear error reduction. By using this method, the nonlinear calibration of the SL system is not required. Moreover, both the nonlinear effects of the projector and the camera can be effectively reduced. The simulations and experiments have verified our nonlinear correction method.

A monolithic distributed phase shifter based on right-handed nonlinear transmission lines at 30 GHz

The epitaxial material, device structure, and corresponding equivalent large signal circuit model of GaAs planar Schottky varactor diode are successfully developed to design and fabricate a monolithic phase shifter, which is based on right-handed nonlinear transmission lines and consists of a coplanar waveguide transmission line and periodically distributed GaAs planar Schottky varactor diode. The distributed-Schottky transmission-line-type phase shifter at a bias voltage greater than 1.5 V presents a continuous 0°–360° differential phase shift over a frequency range from 0 to 33 GHz. It is demonstrated that the minimum insertion loss is about 0.5 dB and that the return loss is less than-10 dB over the frequency band of 0–33 GHz at a reverse bias voltage less than 4.5 V. These excellent characteristics, such as broad differential phase shift, low insertion loss, and return loss, indicate that the proposed phase shifter can entirely be integrated into a phased array radar circuit.

Berry phase in a generalized nonlinear two-level system

In this paper, we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field. Both the field nonlinearity and the atom-field coupling nonlinearity are considered. We find that the geometric phase depends on whether the index k is an odd number or an even number in the resonant case. In addition, we also find that the geometric phase may be easily observed when the field nonlinearity is not considered. The fractional statistical phenomenon appears in this system if the strong nonlinear atom-field coupling is considered. We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.

Nonlinear phase dynamics of ideal kink mode in the presence of shear flow

We investigate nonlinear phase dynamics of an ideal kink mode,induced by E×B flow.Here the phase is the cross phase(θ_(c))between perturbed stream function of velocity(f)and magnetic field(y),i.e.θ_(c)=θf−θψ.A dimensionless parameter,analogous to the R_(i)chardson number,R_(i)=16gkink w^(2)E^(2)(γkink:the normalized growth rate of the pure kink mode;wE:normalized E×B shearing rate)is defined to measure the competition between phase pinning by the current density and phase detuning by the flow shear.When R_(i)>1,θ_(c) is locked to a fixed value,corresponding to the conventional eigenmode solution.When R_(i).1,θ_(c) enters a phase slipping or oscillating state,corresponding to a nonmodal solution.The nonlinear phase dynamics method provides a more intuitive explanation of the complex dynamical behavior of the kink mode in the presence of E×B shear flow.

Nonlinear phase error analysis of equivalent thickness in a white-light spectral interferometer

A white light spectral interferometry based on a Linnik type system was established to accurately measure the thin film thickness through transparent medium.In practical work,the equivalent thickness of a beam splitter and the mismatch of the objective lens introduce nonlinear phase errors.Adding a transparent medium also increases the equivalent thickness.The simulation results showthat the equivalent thickness has a significant effect on thin film thickness measurements.Therefore,it is necessary to perform wavelength correction to provide a constant equivalent thickness for beamsplitters.In the experiments,some pieces of cover glasses as the transparent medium were added to the measured beam and then a standard thin film thickness of 1052.2±0.9 nm was tested through the transparent medium.The results demonstrate that our system has a nanometer-level accuracy for thin film thickness measurement through transparent medium with optical path compensation.

Phased Array Beam Fields of Nonlinear Rayleigh Surface Waves

This study concerns calculation of phased array beam fields of the nonlinear Rayleigh surface waves based on the integral solutions for a nonparaxial wave equation. Since the parabolic approximation model for describing the nonlinear Rayleigh waves has certain limitations in modeling the sound beam fields of phased arrays, a more general model equation and integral forms of quasilinear solutions are introduced. Some features of steered and focused beam fields radiated from a linear phased array of the second harmonic Rayleigh wave are presented.

Nonlinear Kinetic Theory and Pulse Interactions in Phase Transition

The kinetics of nucleation of phase transition is a phenomenal theory.Some new technologies of preparation of nanomaterials,for example,by shock wave and by electropulsing,are pulse interactions.Based on the known nonlinear theories of phase transition,the nonlinear kinetics of phase transition is discussed,and a soliton-like model is proposed. This mathematical method can not only explain the basic characteristics of pulse interactions and suddenness of phase transition, and possesses a consistency of mechanism for nucleation and growth.

Nonlinear Phase Noise Estimate Based on Electronic Orthogonal Coherent for 112 Gb/s PDM-4QAM System

In this paper, we proposed a novel method of joint phase noise estimate (JPNE) for PDM-M-QAM (M = 4, 16, 32, 64, …) transmission systems, and established the theoretical model to illustrate the operation mechanism. The simulation of laser phase noise and fiber nonlinearity compensation based on the proposed JPNE method had also been demonstrated. For 112 Gb/s PDM-4QAM transmission system, the simulation results had showed that the optimum launch power increased from -4 dBm to at least 0 dBm compared with the condition of no phase noise compensation in reach of all simulation distances.

Orientation-enhanced nonlinear optical properties and phase-conjugate reflective system of a novel Azobenzene doped polymer film

This paper reports that the nonlinear refractive index of a novel organic optical storage film doped azodiphenylamine polymer is measured by using the Z-scan technique. The nonlinear refractive index up to 3.7× 10^-6 cm^2/W induced by thermo-optical effect is obtained. It indicates that the sample has excellent optical non- linear properties. The physical mechanism of the great nonlinear optical effect is analysed and the optical conjugate characteristic is also discussed with degenerate four-wave-mixing. The phase conjugate wave diffracted from the formative refractive index grating in the sample is acquired and its equivalent reflectivity reaches about 22%. On this basis, the reflective wave phase-conjugated mirror system was designed, and the image aberration experienced in propagation in the storage experiment is corrected by using the system.

Influence of Laser Phase Noise on Nonlinear Optical Fiber Transmission System

he influence of laser linewidth on optical fiber transmission systems has been investigated. The maximum transmission distances at different linewidths are first calculated in linear systems with various bit rates. Then it is found that SPM can significantly enhance the PMAM noise which severely deteriorates the performance of system with high optical power and large dispersion. In this case, the laser linewidth and optical power must be well controlled.

MATHEMATICAL MODEL OF TWO-PHASE FLUID NONLINEAR FLOW IN LOW-PERMEABILITY POROUS MEDIA WITH APPLICATIONS

A mathematical model of two-phase fluid nonlinear flow in the direction of normal of ellipse through low-permeability porous media was established according to a nonlinear flow law expressed in a continuous function with three parameters, a mass conservation law and a concept of turbulent ellipses. A solution to the model was obtained by using a finite difference method and an extrapolation method. Formulas of calculating development index not only before but also after water breaks through an oil well in the condition of two-phase fluid nonlinear flow in the media were derived. An example was discussed. Water saturation distribution was presented. The moving law of drainage front was found. Laws of change of pressure difference with time were recognized. Results show that there is much difference of water saturation distribution between nonlinear flow and linear flow; that drainage front by water moves faster, water breaks through sooner and the index gets worse because of the nonlinear flow; and that dimensionless pressure difference gets larger at the same dimensionless time and difficulty of oil development becomes bigger by the nonlinear flow. Thus, it is necessary that influence of nonlinear flow on development indexes of the oil fields be taken into account. The results provide water-flooding development of the oilfields with scientific basis.

Propagation of optical vortex solitons due to the Gouy phase in strongly nonlocal nonlinear media

In this paper, we present a study on the propagation of the symmetrical optical vortices formed by two collinear Laguerre-Gauss solitons in strongly nonlocal nonlinear media. The optical vortices, which move along the beam axis as the light propagates, result in a rotation of the beam＇s transverse profile. This physical reason of the rotation is the Gouy phase acquired by the component beams.

Theoretical Computation of Nonlinear System Equations of Heavier Pellets Movements for Two Phase Flow

This paper presents nonlinear ordinary differential equations (ODES) of the heavier pellets movement for two phase flow, which actually represent a system of equations. The usual methods of solution such as Runge -Kutta method and it's datum results are discussed. This paper solves ODES of general form using variable mesh-length, linearizing the nonlinear terms by finite analysis method, fuilding an iteration sequence, and amending the nonlinear terms by iteration . The conditions of convergent operation of iteration solution is checked. The movement orbit and velocity of the pellets are calculated. Analysis of research results and it's application examples are illustrated.

Cross-phase modulation instability in optical fibres with exponential saturable nonlinearity and high-order dispersion

Utilizing the linear-stability analysis, this paper analytically investigates and calculates the condition and gain spectra of cross-phase modulation instability in optical fibres in the ease of exponential saturable nonlinearity and high-order dispersion. The results show that, the modulation instability characteristics here are similar to those of conventional saturable nonlinearity and Kerr nonlinearity. That is to say, when the fourth-order dispersion has the same sign as that of the second-order one, a new gain spectral region called the second one which is far away from the zero point may appear. The existence of the exponential saturable nonlinearity will make the spectral width as well as the peak gain of every spectral region increase with the input powers before decrease. Namely, for every spectral regime, this may lead to a unique value of peak gain and spectral width for two different input powers. In comparison with the case of conventional saturable nonlinearity, however, when the other parameters are the same, the variations of the spectral width and the peak gain with the input powers will be faster in case of exponential saturable nonlinearity.

Optical nonlinearity measurement of 4-(N-methyl,N-hydroxyethl)amino,4'-nitroazobenzene using a transmittance technique with a phase object(T-PO) with top-hat beams at 600-nm wavelength

The transmittance technique with a phase object（T-PO）,for measuring optical nonlinear coefficients is proposed with a top-hat beam.The sensitivity of the T-PO with a top-hat beam is a factor of 4 greater than that with a Gaussian beam.The validity of this method is verified by measuring the nonlinearity of a well-characterized liquid,CS 2 at 532-nm wavelength.The ease of use of this method has been proved by measuring a new compound 4-（N-methyl,N-hydroxyethyl）amino,4＇-nitroazobenzene（ANAB） at 600-nm wavelength,indicating that this method can be extended to the measurement of optical nonlinearities in a wide-band spectrum.

稠油油藏体相流体非线性渗流理论模型

根据稠油油藏体相流体渗流特点,建立基于稠油吸附边界层和屈服特性影响下的稠油体相流体非线性渗流理论模型及启动压力梯度理论公式,并利用岩心渗流与启动压力梯度试验结果对理论模型计算结果进行验证。结果表明:理论计算结果与试验结果拟合较好,启动压力梯度理论公式计算结果平均偏差为7.77%,稠油油藏体相流体非线性渗流理论模型计算结果平均偏差为7.50%,均在可接受偏差范围内,并且该模型针对不同流变类型的流体渗流都具有较好的普适性。

Terahertz Wave Generation via Nonlinear Parametric Process from <i>ε</i>-GaSe Single Crystals Grown by Liquid Phase Solution Method

Terahertz (THz)-wave generation has been conducted based on difference frequency mixing (DFM) process with phonon-polariton excitation of ε-GaSe single crystals implemented with liquid-phase solution growth using the temperature difference method under controlled vapour pressure for the first time. The type-eoo phase matching condition for the DFM process at around 10 THz is satisfied by changing the incident angle into the crystal. The maximum conversion efficiency in the present DFG process is about 10-6?J-1?using a 0.1-mm-thick GaSe single crystal with the only ε- phase polytype, which can be greater than that of the commercially available Bridgman grown GaSe crystal including both ε- and γ-phase polytypes.