Inversion method of bubble size distribution based on acoustic nonlinear coefficient measurement

Measurements of bubble size distribution require the understanding of the acoustic characteristics of the medium.The bubbles show highly nonlinear properties under finite amplitude acoustic excitation,so the acoustic fields from bubble population are easily observed at the second harmonics as well as at the fundamental frequency,which shows that the nonlinear coefficient increases obviously.The inversion method of bubble size distribution based on nonlinear acoustic effects can peel off the influence of complex environment and obtain the size distribution coefficient information of bubbles more accurately.The previous nonlinear inversion methods of bubble size distribution are mostly based on the nonlinear scattering cross-section characteristics of bubbles.However,the stability of inversion is not high enough.In this paper,we introduce a new acoustic inversion method for bubble size distribution,which is based on the nonlinear coefficients of bubble medium.Compared with other inversion methods based on linear or nonlinear scattering cross section,the inversion method based on nonlinear coefficients of bubble medium proposed in this paper shows good robustness in both simulation and experiment.

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.

Nondegenerate solitons of the(2+1)-dimensional coupled nonlinear Schrodinger equations with variable coefficients in nonlinear optical fibers

We derive the multi-hump nondegenerate solitons for the(2+1)-dimensional coupled nonlinear Schrodinger equations with propagation distance dependent diffraction,nonlinearity and gain(loss)using the developing Hirota bilinear method,and analyze the dynamical behaviors of these nondegenerate solitons.The results show that the shapes of the nondegenerate solitons are controllable by selecting different wave numbers,varying diffraction and nonlinearity parameters.In addition,when all the variable coefficients are chosen to be constant,the solutions obtained in this study reduce to the shape-preserving nondegenerate solitons.Finally,it is found that the nondegenerate two-soliton solutions can be bounded to form a double-hump two-soliton molecule after making the velocity of one double-hump soliton resonate with that of the other one.

A novel three-ring-core few-mode fiber with large effective area and low nonlinear coefficient

A novel three-ring-core few-mode fiber with large effective area and low nonlinear coefficient is proposed in this paper. The fiber characteristics based on the full-vector finite element method(FEM) with perfect matched layer boundary conditions show that four supermodes with large effective area, low nonlinear coefficient and low differential mode group delay(DMGD) are achieved. With the increase of input wavelength, the effective areas of three-ring-core few-mode fiber are increased, and the nonlinear coefficients are decreased. The bending losses are increased with the increase of input wavelength, and are decreased with the increase of bending radius. Moreover, the proposed fiber performs a nonlinear coefficient and DMGD flattened profile at a large wavelength range.

ESTIMATE ACCURACY OF NONLINEAR COEFFICIENTS OF SQUEEZEFILM DAMPER USING STATE VARIABLE FILTER METHOD

The estimate model for a nonlinear system of squeeze film damper (SFD) is described.The method of state variable filter (SVF) is used to estimate the coefficients of SFD.The factors which are critical to the estimate accuracy are discussed

Nonlinear Refractive Index and Absorption Coefficient of Single-Shell Semiconductor Carbon Nanotube

The nonlinear refractive index and absorption coefficient of single\|shell semiconductor carbon nanotubes(CN s ) are calculated based on the two\|band approximation and Genkin\|Mednis approach. The results of nonlinear refractive index and absorption coefficient reach the order of 10 -8 and 10 -4 cm 2\5W -1 separately, which indicates that CN s have wonderful nonlinear optical properties. Taking into account the temperature effect and overlapping of σ and π orbits, the effect of relaxation term and chiral angle is discussed. The results show that the smaller the relaxation term, the larger the nonlinear absorption coefficient and refractive index. At the same time, CN s with different chiral angles have different results due to their different energy gap.

Lax pair and vector semi-rational nonautonomous rogue waves for a coupled time-dependent coefficient fourth-order nonlinear Schrodinger system in an inhomogeneous optical fiber

Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-order nonlinear Schr?dinger system, which is discussed in this paper. For such a system, we work out the Lax pair, Darboux transformation, and corresponding vector semi-rational nonautonomous rogue wave solutions. When the group velocity dispersion(GVD) and fourth-order dispersion(FOD) coefficients are the constants, we exhibit the first-and second-order vector semirational rogue waves which are composed of the four-petalled rogue waves and eye-shaped breathers. Both the width of the rogue wave along the time axis and temporal separation between the adjacent peaks of the breather decrease with the GVD coefficient or FOD coefficient. With the GVD and FOD coefficients as the linear, cosine, and exponential functions, we respectively present the first-and second-order periodic vector semi-rational rogue waves, first-and second-order asymmetry vector semi-rational rogue waves, and interactions between the eye-shaped breathers and the composite rogue waves.

INITIAL-OBLIQUE DERIVATIVE PROBLEMS FOR NONLINEAR PARABOLIC SYSTEMS WITH MEASURABLE COEFFICIENTS

This paper deals with some initial-oblique derivative boundary value problems for nonlinear nondivergent parabolic systems of several second order equations with measurable coefficients in multiply connected domains. Firstly, a priori estimates of solutions for the initial-boundary value problems are given, and then by using the above estimates of solutions and the Leray-Schauder theorem, the existence and uniqueness of solutions for the problems are proved.

Design on a highly birefringent and nonlinear photonic crystal fiber in the C waveband

In this paper, a novel photonic crystal fiber （PCF） with high birefringence and nonlinearity is designed. The charac- teristics of birefringence, dispersion and nonlinearity are studied by using the full-vector finite element method （FVFEM）. The numerical results show that the phase birefringence and nonlinear coefficient of PCF can be up to 4.51× 10-3 and 32.8972 w-l.km-1 at 1.55 μm, respectively. The proposed PCF could be found to have important applications in the polarization-dependent nonlinear optics such as the pulse compress and reshaping in the C waveband.

Nonlinear optical characterization of phosphate glasses based on ZnO using the Z-scan technique

The nonlinear optical properties of a phosphate vitreous system [（ZnO）x-（MgO）30-x-（P2O5）70], where x=8, 10, 15, 18, and 20 mol% synthesized through the melt-quenching technique have been investigated by using the Z-scan technique. In the experiment, a continuous-wave laser with a wavelength of 405 nm was utilized to determine the sign and value of the nonlinear refractive （NLR） index and the absorption coefficient with closed and opened apertures of the Z-scan setup. The NLR index was found to increase with the ZnO concentration in the glass samples by an order of 10-10 cm2·W-1. The real and imaginary parts of the third-order nonlinear susceptibility were calculated by referring to the NLR index （n2） and absorption coefficient （β） of the samples. The value of the third-order nonlinear susceptibility was presented by nonlinear refractive or absorptive behavior of phosphate glasses for proper utilization in nonlinear optical devices. Based on the measurement, the positive sign of the NLR index shows a self-focusing phenomenon. The figures of merit for each sample were calculated to judge the potential of phosphate glasses for application in optical switching.

Effect of size and indium-composition on linear and nonlinear optical absorption of InGaN/GaN lens-shaped quantum dot

Based on the Schr ¨odinger equation for envelope function in the effective mass approximation, linear and nonlinear optical absorption coefficients in a multi-subband lens quantum dot are investigated. The effects of quantum dot size on the interband and intraband transitions energy are also analyzed. The finite element method is used to calculate the eigenvalues and eigenfunctions. Strain and In-mole-fraction effects are also studied, and the results reveal that with the decrease of the In-mole fraction, the amplitudes of linear and nonlinear absorption coefficients increase. The present computed results show that the absorption coefficients of transitions between the first excited states are stronger than those of the ground states. In addition, it has been found that the quantum dot size affects the amplitudes and peak positions of linear and nonlinear absorption coefficients while the incident optical intensity strongly affects the nonlinear absorption coefficients.

Derivation of energy-based base shear force coefficient considering hysteretic behavior and P-delta effects

A modified energy-balance equation accounting for P-delta effects and hysteretic behavior of reinforced concrete members is derived. Reduced hysteretic properties of structural components due to combined stiffness and strength degradation and pinching effects, and hysteretic damping are taken into account in a simple manner by utilizing plastic energy and seismic input energy modification factors. Having a pre-selected yield mechanism, energy balance of structure in inelastic range is considered. P-delta effects are included in derived equation by adding the external work of gravity loads to the work of equivalent inertia forces and equating the total external work to the modified plastic energy. Earthquake energy input to multi degree of freedom（MDOF） system is approximated by using the modal energy-decomposition. Energybased base shear coefficients are verified by means of both pushover analysis and nonlinear time history（NLTH） analysis of several RC frames having different number of stories. NLTH analyses of frames are performed by using the time histories of ten scaled ground motions compatible with elastic design acceleration spectrum and fulfilling duration/amplitude related requirements of Turkish Seismic Design Code. The observed correlation between energy-based base shear force coefficients and the average base shear force coefficients of NLTH analyses provides a reasonable confidence in estimation of nonlinear base shear force capacity of frames by using the derived equation.

TESTING FOR VARYING DISPERSION IN DISCRETE EXPONENTIAL FAMILY NONLINEAR MODELS

It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.

Influence of Annealing Atmosphere on Varistor Property of TiO₂-Nb₂O₅-SrCO₃Ceramics

Varistor ceramics are typical electronic ceramics, which are widely used in circuits of overvoltage protection, high voltage stabilization and high energy surge absorption. TiO2 varistor ceramics has the advantages of low varistor voltage and good dielectric properties, but their low nonlinearity limited the application. The influence of annealing on the varistor properties of TiO2-Nb2O5-SrCO3 ceramics was investigated in this paper. TiO2-Nb2O5-SrCO3 varistor ceramics were prepared by the traditional method of ball grinding-forming-sintering and they were annealed in oxygen and nitrogen, respectively. The nonlinear coefficient α and the breakdown voltage EB of the samples were tested using the varistor dc parameter meter. The microstructure of samples was analyzed by XRD, SEM, STEM-EDAX and SAEDP. The results show that during annealing, Sr2+ ions with a larger radius obtain the kinetic energy and are segregated to grain boundaries, which increases the acceptor density of the grain boundaries and improves α. Annealing in an oxygen atmosphere, the enrichment of oxygen at grain boundaries is also helpful to increase the density of acceptor states and the height of the potential barrier, so as to further increase α. Meanwhile, annealing makes crystalline grains grow properly, which results in even grain size, reduces the porosity and increases the density of grains. So EB tends to reduce. As the doping concentration of Nb2O5 and SrCO3 is 0.15 mol%, respectively, and sintering temperature is 1300°C, TiO2-Nb2O5-SrCO3 varistor ceramics annealed in oxygen for 3 h at 750°C achieved the highest nonlinear coefficient α = 8.9 and the lowest breakdown voltage EB = 19.1 V·mm-1, which annealed in nitrogen achieved α = 8.4, EB = 20.6 V·mm-1, both superior to unannealed samples.

Numerical analysis of photonic crystal fiber with chalcogenide core tellurite cladding composite microstructure

Kinds of photonic crystal fibers with chalcogenide core tellurite cladding composite microstructure are proposed. The multi-core photonic crystal fiber can reach the higher nonlinearity coefficient and the larger effective mode area. The small single-core photonic crystal fiber has a very high nonlinearity coefficient. At the wavelength λ=0.8μm, the nonlinearity coefficient can reach 31.37053 W-1·m-1, at the wavelength λ=1.55μm, the nonlinearity coefficient is 11.19686W-1·m-1.

Thermodynamic Consistency and Thermomechanical Dynamics (TMD) for Nonequilibrium Irreversible Mechanism of Heat Engines

The irreversible mechanism of heat engines is studied in terms of thermodynamic consistency and thermomechanical dynamics (TMD) which is proposed for a method to study nonequilibrium irreversible thermodynamic systems. As an example, a water drinking bird (DB) known as one of the heat engines is specifically examined. The DB system suffices a rigorous experimental device for the theory of nonequilibrium irreversible thermodynamics. The DB nonlinear equation of motion proves explicitly that nonlinear differential equations with time-dependent coefficients must be classified as independent equations different from those of constant coefficients. The solutions of nonlinear differential equations with time-dependent coefficients can express emergent phenomena: nonequilibrium irreversible states. The couplings among mechanics, thermodynamics and time-evolution to nonequilibrium irreversible state are defined when the internal energy, thermodynamic work, temperature and entropy are integrated as a spontaneous thermodynamic process in the DB system. The physical meanings of the time-dependent entropy, T(t)dS(t), , internal energy, dƐ(t), and thermodynamic work, dW(t), are defined by the progress of time-dependent Gibbs relation to thermodynamic equilibrium. The thermomechanical dynamics (TMD) approach constitutes a method for the nonequilibrium irreversible thermodynamics and transport processes.

Affirming nonlinear optical coefficient constancy from z-scan measurement

Goodness of fit is demonstrated for theoretical calculation of z-scan data based on beams propagating in the nonlinear medium and the Fresnel–Kirchhoff diffraction integral in experiments with high nonlinear refraction and absorption. The constancy of nonlinear optical parameters is achieved regardless of sample thickness and laser intensity, which clarifies the physical significance of optical parameters. We have obtained γ = 2.0 × 10-19 m2/W and β = 5.0 × 10-13 m/W for carbon disulfide excited by a pulsed laser at 800 nm with pulse duration of 35 fs,which are independent of sample thickness and laser intensity. Affirming constancy of the extracted parameters to the incident light intensity may become a practice to verify the goodness of the z-scan experiment.

NN-based Output Tracking for More General Stochastic Nonlinear Systems with Unknown Control Coefficients

This paper considers the output tracking problem for more general classes of stochastic nonlinear systems with unknown control coefficients and driven by noise of unknown covariance. By utilizing the radial basis function neural network approximation method and backstepping technique, we successfully construct a controller to guarantee the solution process to be bounded in probability.The tracking error signal is 4th-moment semi-globally uniformly ultimately bounded（SGUUB） and can be regulated into a small neighborhood of the origin in probability. A simulation example is given to demonstrate the effectiveness of the control scheme.

Third-order nonlinear phenomenon generated on the inner surface of bulk lithium niobate crystals with magnesium doping

When two synchronized laser beams illuminate the inner surface of bulk lithium niobate crystals with magnesium doping(5%/mol MgO:LiNbO_(3))under the condition of total reflection,semi-degenerate four-wave mixing(FWM)is generated.On this basis,a more sophisticated frequency conversion process on the interface of nonlinear crystal has been researched.The generation mechanism of FWM is associated with the fundamental waves reflected on the inner surface of the nonlinear crystal.Analysis of the phase-matching mechanism confirms that the FWM is radiated by the third-order nonlinear polarized waves,which are stimulated by the third-order nonlinear susceptibility coefficient of the nonlinear crystal.Theoretically calculated and experimentally measured corresponding data have been presented in this article.These results are expected to provide new inspiration for further experimental and theoretical research on frequency conversion in nonlinear crystals.

Effect of sintering temperature on microstructure and nonlinear electrical characteristics of ZnO varistor

The nonlinear properties of ZBMCCS-based varistors,which are composed of ZnO-Bi_(2)O_(3)-MnO_(2)-Cr_(2)O_(3)-Sb_(2)O_(3)-Co_(3)O_(4) and SiO_(2) are studied inrelation to sintering temperature,in the range of 1280–1350℃.The samples are investigated for grain morphology by using scanning electron microscope(SEM).These samples were examined by using X-ray diffraction patterns(XRD)and DC electrical measurements.X-ray diffraction analysis of the samples show the presence of ZnO,Zn_(2)SiO_(4) willemite phase and Co_(2.33)Sb_(0.67)O_(4) spinel phases.The average grain size of ZnO increased as the sintering temperature increased from 2.57 to 6.84
m.In the examined temperature range,the breakdown field decreased from 2992 to 127 V/cm with the increase of sintering temperature.This system gives a relatively high nonlinearity coefficientα=33.61(at a sintering temperature of 1280℃)with a low leakage current of 0.21 mA/cm^(2).