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.

Design of photonic crystal fiber with elliptical air-holes to achieve simultaneous high birefringence and nonlinearity

A new type of V-shaped photonic crystal fiber with elliptical air-holes is proposed to realize simultaneous high bire- fringence and nonlinearity at a wavelength of 1.55 μm. The full vector finite element method was adopted to investigate its characteristics, including birefringence, nonlinearity, and dispersion. The PCF exhibited a very high birefringence of 2.89x10-2 and very high nonlinear coefficient of 102.69 W-1 .km 1. In particular, there were two zero-dispersion wave- lengths （ZDWs） in the visible （X： 640-720 nm and Y： 730-760 nm） and near-infrared regions （X： 1050-1606 nm and Y： 850-1500 nm）. The combination of high birefringence and nonlinearity allowed the PCF to maintain the polarization state and generate a broadband super continuum, with potential applications in nonlinear optics.

Nonlinearity Modulating Intensities and Spatial Structures of Central Pacific and Eastern Pacific El Nio Events

This paper compares data from linearized and nonlinear Zebiak-Cane model, as constrained by observed sea surface temperature anomaly （SSTA）, in simulating central Pacific （CP） and eastern Pacific （EP） E1 Nino. The difference between the temperature advections （determined by subtracting those of the linearized model from those of the nonlinear model）, referred to here as the nonlinearly induced temperature advection change （NTA）, is analyzed. The results demonstrate that the NTA records warming in the central equatorial Pacific during CP E1 Nino and makes fewer contributions to the structural distinctions of the CP E1 Nino, whereas it records warming in the eastern equatorial Pacific during EP E1 Nino, and thus significantly promotes EP E1 Nino during E1 Nino-type selection. The NTA for CP and EP E1 Nino varies in its amplitude, and is smaller in CP E1 Nino than it is in EP E1 Nino. These results demonstrate that CP E1 Nino are weakly modulated by small intensities of NTA, and may be controlled by weak nonlinearity; whereas, EP E1 Nino are significantly enhanced by large amplitudes of NTA, and are therefore likely to be modulated by relatively strong nonlinearity. These data could explain why CP E1 Nino are weaker than EP E1 Nino. Because the NTA for CP and EP E1 Nino differs in spatial structures and intensities, as well as their roles within different E1 Nino modes, the diversity of E1 Nino may be closely related to changes in the nonlinear characteristics of the tropical Pacific.

Bifurcation and chaos analysis for aeroelastic airfoil with freeplay structural nonlinearity in pitch

The dynamics character of a two degree-of-freedom aeroelastic airfoil with combined freeplay and cubic stiffness nonlinearities in pitch submitted to supersonic and hypersonic flow has been gaining significant attention. The Poincare mapping method and Floquet theory are adopted to analyse the limit cycle oscillation flutter and chaotic motion of this system. The result shows that the limit cycle oscillation flutter can be accurately predicted by the Floquet multiplier. The phase trajectories of both the pitch and plunge motion are obtained and the results show that the plunge motion is much more complex than the pitch motion. It is also proved that initial conditions have important influences on the dynamics character of the airfoil system. In a certain range of airspeed and with the same system parameters, the stable limit cycle oscillation, chaotic and multi-periodic motions can be detected under different initial conditions. The figure of the Poincare section also approves the previous conclusion.

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.

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR NONLINEAR PARABOLIC EQUATIONS WITH VARIABLE EXPONENT OF NONLINEARITY

The authors of this article study the existence and uniqueness of weak so- lutions of the initial-boundary value problem for ut = div（（｜u｜^δ ＋ d0）｜↓△｜^p（x,t）-2↓△u） ＋ f（x, t） （0 〈 δ 〈 2）. They apply the method of parabolic regularization and Galerkin＇s method to prove the existence of solutions to the mentioned problem and then prove the uniqueness of the weak solution by arguing by contradiction. The authors prove that the solution approaches 0 in L^2 （Ω） norm as t →∞.

EXISTENCE OF THE MINIMAL POSITIVE SOLUTION OF SOME NONLINEAR ELLIPTIC SYSTEMS WHEN THE NONLINEARITY IS THE SUM OF A SUBLINEAR AND A SUPERLINEAR TERM

It is shown that there exists Λ>0 such that, for every λ∈(0,Λ), the semilinear elliptic system: - Δ u=λu｜u｜ q-1 +u｜u｜ p-1 -v inΩ, - Δ v=δu-γv in Ω, u=v=0 on Ω, where Ω∈R N(N≥2) is a bounded domain with smooth boundary and 0<q<1<p,has a minimal positive solution (u λ,v λ). Moreover: u λ and v λ are strictly increasing with respect to λ.

Slope stability analysis considering joined influences of nonlinearity and dilation

The soil masses of slopes were assumed to follow a nonlinear failure criterion and a nonassociated flow rule.The stability factors of slopes were calculated using vertical slice method based on limit analysis.The potential sliding mass was divided into a series of vertical slices as well as the traditional slice technique.Equating the external work rate to the internal energy dissipation,the optimum solutions to stability factors were determined by the nonlinear programming algorithm.From the numerical results,it is found that the present solutions agree well with previous results when the nonlinear criterion reduces to the linear criterion,and the nonassociated flow rule reduces to the associated flow rule.The stability factors decrease by 39.7%with nonlinear parameter varying from 1.0 to 3.0.Dilation and nonlinearity have significant effects on the slope stability factors.

A Boussinesq model with alleviated nonlinearity and dispersion

The classical Boussinesq equation is a weakly nonlinear and weakly dispersive equation, which has been widely applied to simulate wave propagation in off-coast shallow waters. A new form of the Boussinesq model for an uneven bottoms is derived in this paper. In the new model, nonlinearity is reduced without increasing the order of the highest derivative in the differential equations. Dispersion relationship of the model is improved to the order of Pade （2,2） by adjusting a parameter in the model based on the long wave approximation. Analysis of the linear dispersion, linear shoaling and nonlinearity of the present model shows that the performances in terms of nonlinearity, dispersion and shoaling of this model are improved. Numerical results obtained with the present model are in agreement with experimental data.

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.

Two-qubit and three-qubit controlled gates with cross-Kerr nonlinearity

Schemes for two-qubit and three-qubit controlled gates based on cross-Kerr nonlinearity are proposed in this paper.The probability of the success of these gates can be increased by quantum nondemolition detectors,which are used to judge which paths the signal photons pass through.These schemes are almost deterministic and require no ancilla photon.The advantages of these gates over the existing ones include less resource consumption and a higher probability of success,which make our schemes more feasible with current technology.

PREPARATION AND SECOND-ORDER OPTICAL NONLINEARITY OF NOVEL PHENOXYSILICON NETWORKS BY SOL-GEL PROCESS

Four phenoxysilicon networks for nonlinear optical (NLO) applications were designed and prepared by an extended sol-gel process without additional H2O and catalyst. All poled polymer network films possess high second-order nonlinear optical coefficients (d(33)) Of 10(-7)similar to 10(-8) esu. The investigation of NLO temporal stability at room temperature and elevated temperature (120 degreesC) indicated that these films exhibit high d(33) stability because the orientation of the chromophores are locked in the phenoxysilicon organic/inorganic networks.

A new beam element for analyzing geometrical and physical nonlinearity

Based on Timoshenko＇s beam theory and Vlasov＇s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange （UL） and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.

ASYMPTOTIC BEHAVIOR NEAR THE BOUNDARY OF A LARGE SOLUTION TO SEMILINEAR POISSON EQUATION WITH DOUBLE-POWER NONLINEARITY

We deal with a large solution to the semilinear Poisson equation with doublepower nonlinearityΔ^(u)=u^(p)+αu^(q)in a bounded smooth domain D■R^(n),where p>1,-1<q<p andα∈R.We obtain the asymptotic behavior of a solution u near the boundary OD up to the third or higher term.

MULTI-BUMP SOLUTIONS FOR NONLINEAR CHOQUARD EQUATION WITH POTENTIAL WELLS AND A GENERAL NONLINEARITY

In this article,we study the existence and asymptotic behavior of multi-bump solutions for nonlinear Choquard equation with a general nonlinearity-Δu+(λa(x)+1)u=(1/|x|α*F(u))f(u)in R^N,where N≥3,0<α<min{N,4},λis a positive parameter and the nonnegative potential function a(x)is continuous.Using variational methods,we prove that if the potential well int(a^-1(0))consists of k disjoint components,then there exist at least 2^k-1 multi-bump solutions.The asymptotic behavior of these solutions is also analyzed asλ→+∞.

Optical nonlinearity in measurement of urea and uric acid in blood

The Z-scan technique is a simple and effective tool for determining nonlinear optical properties of materials. This technique is utilized in meas-urement of urea and uric acid in blood. The nonlinear refractive index of urea and uric acid are found to vary linearly with concentration. Hence by calculating the nonlinear refractive index it is possible to measure their concentra-tion in the sample. The results of this method are found to be in good agreement with the conventional colorimetric method.

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.

Reliability analysis of circular concrete-filled steel tube with material and geometrical nonlinearity

Most of the previous research on concrete-filled steel tube is restricted to a deterministic approach. To gain clear insight into the random properties of circular concrete-filled steel tube, reliability analysis is carried out in the present study. To obtain the Structural nonlinear response and ultimate resistance capacity, material and geometrical nonlinear analysis of circular concrete-filled steel tube is performed with a three-dimensional degenerated beam ele- ment. Then we investigate the reliability of concrete-filled steel tube using the first-order reliability method combined with nonlinear finite element analysis. The influences of such parameters as material strength, slenderness, initial geo- metrical imperfection, etc. on the reliability of circular concrete-filled steel tube column are studied. It can be con- cluded that inevitable random fluctuation of those parameters has significant influence on structural reliability, and that stochastic or reliability methods can provide a more rational and subjective evaluation on the safety of CFT structures than a deterministic approach.

Critical embedment depth of a rigid retaining wall against overturning in unsaturated soils considering intermediate principal stress and strength nonlinearity

The overturning stability is vital for the retaining wall design of foundation pits, where the surrounding soils are usually unsaturated due to water draining. Moreover, the intermediate principal stress does affect the unsaturated soil strength; meanwhile, the relationship between the unsaturated soil strength and matric suction is nonlinear. This work is to present closed-form equations of critical embedment depth for a rigid retaining wall against overturning by means of moment equilibrium. Matric suction is considered to be distributed uniformly and linearly with depth. The unified shear strength formulation for unsaturated soils under the plane strain condition is adopted to characterize the intermediate principal stress effect, and strength nonlinearity is described by a hyperbolic model of suction angle. The result obtained is orderly series solutions rather than one specific answer; thus, it has wide theoretical significance and good applicability. The validity of this present work is demonstrated by comparing it with a lower bound solution. The traditional overturning designs for rigid retaining walls, in which the saturated soil mechanics neglecting matric suction or the unsaturated soil mechanics based on the Mohr-Coulomb criterion are employed, are special cases of the proposed result. Parametric studies about the intermediate principal stress, matric suction and its distributions along with two strength nonlinearity methods on a new defined critical buried coefficient are discussed.

Standing Waves for Quasilinear Schrödinger Equations with Indefinite Nonlinearity

In this article, we consider quasilinear Schrödinger equations of the form Such equations have been derived as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics. Unlike all known results in the literature, the nonlinearity is allowed to be indefinite. It is very interesting from physical and mathematical viewpoint. By mountain pass theorem and some special techniques, we prove the existence of solutions for the quasilinear Schrödinger equations with indefinite nonlinearity. This indefinite problem had never been considered so far. So our main results can be regarded as complementary work in the literature.