Implementation of nonlocal Bell-state measurement and quantum information transfer with weak Kerr nonlinearity

We propose a protocol to implement the nonlocal Bell-state measurement, which is nearly determinate with the help of weak cross-Kerr nonlinearities and quantum non-destructive photon number resolving detection. Based on the nonlocal Bell-state measurement, we implement the quantum information transfer from one place to another. The process is different from conventional teleportation but can be regarded as a novel form of teleportation without entangled channel and classic communication.

Negative Stiffness Mechanism on An Asymmetric Wave Energy Converter by Using A Weakly Nonlinear Potential Model

Salter's duck,an asymmetrical wave energy converter(WEC)device,showed high efficiency in extracting energy from 2D regular waves in the past;yet,challenges remain for fluctuating wave conditions.These can potentially be addressed by adopting a negative stiffness mechanism(NSM)in WEC devices to enhance system efficiency,even in highly nonlinear and steep 3D waves.A weakly nonlinear model was developed which incorporated a nonlinear restoring moment and NSM into the linear formulations and was applied to an asymmetric WEC using a time domain potential flow model.The model was initially validated by comparing it with published experimental and numerical computational fluid dynamics results.The current results were in good agreement with the published results.It was found that the energy extraction increased in the range of 6%to 17%during the evaluation of the effectiveness of the NSM in regular waves.Under irregular wave conditions,specifically at the design wave conditions for the selected test site,the energy extraction increased by 2.4%,with annual energy production increments of approximately 0.8MWh.The findings highlight the potential of NSM in enhancing the performance of asymmetric WEC devices,indicating more efficient energy extraction under various wave conditions.

Cauchy prior distribution-based AVO elastic parameter estimation via weakly nonlinear waveform inversion

Cauchy priori distribution-based Bayesian AVO reflectivity inversion may lead to sparse estimates that are sensitive to large reflectivities. For the inversion, the computation of the covariance matrix and regularized terms requires prior estimation of model parameters, which makes the iterative inversion weakly nonlinear. At the same time, the relations among the model parameters are assumed linear. Furthermore, the reflectivities, the results of the inversion, or the elastic parameters with cumulative error recovered by integrating reflectivities are not well suited for detecting hydrocarbons and fuids. In contrast, in Bayesian linear AVO inversion, the elastic parameters can be directly extracted from prestack seismic data without linear assumptions for the model parameters. Considering the advantages of the abovementioned methods, the Bayesian AVO reflectivity inversion process is modified and Cauchy distribution is explored as a prior probability distribution and the time-variant covariance is also considered. Finally, we propose a new method for the weakly nonlinear AVO waveform inversion. Furthermore, the linear assumptions are abandoned and elastic parameters, such as P-wave velocity, S-wave velocity, and density, can be directly recovered from seismic data especially for interfaces with large reflectivities. Numerical analysis demonstrates that all the elastic parameters can be estimated from prestack seismic data even when the signal-to-noise ratio of the seismic data is low.

A Modified Form of Mild-Slope Equation with Weakly Nonlinear Effect

Nonlinear effect is of importance to waves propagating from deep water to shallow water. The non-linearity of waves is widely discussed due to its high precision in application. But there are still some problems in dealing with the nonlinear waves in practice. In this paper, a modified form of mild-slope equation with weakly nonlinear effect is derived by use of the nonlinear dispersion relation and the steady mild-slope equation containing energy dissipation. The modified form of mild-slope equation is convenient to solve nonlinear effect of waves. The model is tested against the laboratory measurement for the case of a submerged elliptical shoal on a slope beach given by Berkhoff et al. The present numerical results are also compared with those obtained through linear wave theory. Better agreement is obtained as the modified mild-slope equation is employed. And the modified mild-slope equation can reasonably simulate the weakly nonlinear effect of wave propagation from deep water to coast.

ON PROBLEMS IN THE WEAKLY NONLINEAR THEORY OF HYDRODYNAMIC STABILITY AND ITS IMPROVEMENT

There are three main problems in the weakly nonlinear theory of hydrodynamic stability:(1)The ra- dius of convergence with respect to the perturbation parameter is too small and there is no concrete estimation for it.(2)The solution has a special structure, thus in general, it can not satisfy the initial condition posed by many practical problems.(3) When the linear part of its solution does not correspond to a neutral case. there are more than one way in determining the Landau constants, and practically no one knows which is the best way. In this paper, problems(1)and(2)are solved theoretically, and ways for its improvement have been proposed. By comparing the theoretical results with those obtained by numerical simulations, problem(3)has also been clari- fied.

Weakly Nonlinear Rayleigh–Taylor Instability in Cylindrically Convergent Geometry

The Rayleigh–Taylor instability（RTI） in cylindrical geometry is investigated analytically through a second-order weakly nonlinear（WN） theory considering the Bell–Plesset（BP） effect. The governing equations for the combined perturbation growth are derived. The WN solutions for an exponentially convergent cylinder are obtained. It is found that the BP and RTI growths are strongly coupled, which results in the bubble-spike asymmetric structure in the WN stage. The large Atwood number leads to the large deformation of the convergent interface. The amplitude of the spike grows faster than that of the bubble especially for large mode number m and large Atwood number A. The averaged interface radius is small for large mode number perturbation due to the mode-coupling effect.

Periodic Solutions of Porous Medium Equations with Weakly Nonlinear Sources

In this paper, we show the existence of the time periodic solutions to the porous medium equations of the formut= Δ (|u| m-1 u)+B(x,t,u)+f(x,t) in Ω×Rwith the Dirichlet boundary value condition, where m>1, Ω is a bounded domain in R N with smooth boundary Ω , the continuous function f and the Hlder continuous function B(x,t,u) are periodic in t with period ω and the nonlinear sources are assumed to be weaker, i.e., B(x,t,u) u≤b 0|u| α+1 with constants b 0≥0 and 0≤α<m.

ON THE RESONANT GENERATION OF WEAKLY NONLINEAR STOKES WAVES IN REGIONS WITH FAST VARYING TOPOGRAPHY AND FREE SURFACE CURRENT

The effect of nonlinearity on the free surface wave resonated by an incident flow over rippled beds, which consist of fast varying topography superimposed on an otherwise slowly varying mean depth, is studied using a WKBJ-type perturbation approach. Synchronous, superharmonic and in particular subharmonic resonance were selectively excited over the fast varying topography with corresponding wavelengths. For a steady current the dynamical system is autonomous and the possible nonlinear steady states and their stability were investigated. When the current has a small oscillatory component the dynamical system becomes non-autonomous, chaos is now possible.

Parabolic Approximation of the Weakly Nonlinear Mild Slope Equation with Bottom Friction

This paper presents a refined parabolic approximation model of the mild slope equation to simulate the combination of water wave refraction and diffraction in the large coastal region. The bottom friction and weakly nonlinear term are included in the model. The difference equation is established with the Crank-Nicolson scheme. The numerical test shows that some numerical prediction results will be inaccurate in complicated topography without considering weak nonlinearity; the bottom friction will make wave height damping and it can not be neglected for calculation of wave field in large areas.

Weak Nonlinear Matter Waves in a Trapped Spin-1 Condensates

The dynamics of the weak non//near matter sofitary waves in a spin-1 condensates with harmonic external potential are investigated analytically by a perturbation method. It is shown that, in the small amplitude limit, the dynamics of the solitary waves are governed by a variable-coetficient Korteweg-de Vries （KdV） equation. The reduction to the （KdV） equation may be useful to understand the dynamics of nonlinear matter waves in spinor BECs. The analytical expressions for the evolution of soliton show that the small-amplitude vector solitons of the mixed types perform harmonic oscillations in the presence of the trap. Furthermore, the emitted radiation profiles and the soliton oscillation frequency are also obtained.

THE RE-EXAMINATION OF THE WEAKLY NONLINEAR THEORY OF HYDRODYNAMIC STABILITY

The weakly nonlinear theory has been widely applied in the problem of hydrodynamic stability and also in other fields. However, although its application has been successful for some problems, yet, for other problems, the results obtainedhre not satisfactory, especially for problems like transition or the evolution of the vortex in the free shear flow, for which the goal of the theoretical investigation is not seeking for a steady state, but predicting an evolutional process. In this paper, we shall examine the reason for the unsuccessfulness and suggest ways for its amendment.

GLOBAL EXISTENCE FOR THE NONHOMOGENEOUS QUASILINEAR WAVE EQUATION WITH A LOCALIZED WEAKLY NONLINEAR DISSIPATION IN EXTERIOR DOMAINS

It is proved that the global existence for the nonhomogeneous quasilinear wave equation with a localized weakly nonlinear dissipation in exterior domains.

Slowly moving matter-wave gap soliton propagation in weak random nonlinear potential

We systematically investigate the motion of slowly moving matter wave gap solitons in a nonlinear potential, produced by the weak random spatial variation of the atomic scattering length. With the weak randomness, we construct an effective-particle theory to study the motion of gap solitons. Based on the effective-particle theory, the effect of the randomness on gap solitons is obtained, and the motion of gap solitons is finally solved. Moreover, the analytic results for the general behaviours of gap soliton motion, such as the ensemble-average speed and the reflection probability depending on the weak randomness are obtained. We find that with the increase of the random strength the ensemble-average speed of gap solitons decreases slowly where the reduction is proportional to the variance of the weak randomness, and the reflection probability becomes larger. The theoretical results are in good agreement with the numerical simulations based on the Cross-Pitaevskii equation.

REGULARITY OF H^1 ∩L^(n((γ-1)/(2-γ))) WEAK SOLUTIONS FOR NONLINEAR ELLIPTIC SYSTEMS

Let us consider the following elliptic systems of second order-D_α(A_i~α(x, u, Du))=B_4(x, u, Du), i=1, …, N, x∈Q(?)R^n, n≥3 (1) and supposeⅰ) |A_i~α(x, u, Du)|≤L(1+|Du|);ⅱ) (1+|p|)^(-1)A_i~α(x, u, p)are H(?)lder-continuous functions with some exponent δ on (?)×R^N uniformly with respect to p, i.e.ⅲ) A_i~α(x, u, p) are differentiable function in p with bounded and continuous derivativesⅳ)ⅴ) for all u∈H_(loc)~1(Ω, R^N)∩L^(n(γ-1)/(2-γ))(Ω, R^N), B(x, u, Du)is ineasurable and |B(x, u, p)|≤a(|p|~γ+|u|~τ)+b(x), where 1+2/n<γ<2, τ≤max((n+2)/(n-2), (γ-1)/(2-γ)-ε), (?)ε>0, b(x)∈L2n/(n+2), n^2/(n+2)+e(Ω), (?)ε>0.Remarks. Only bounded open set Q will be considered in this paper; for all p≥1, λ≥0, which is clled a Morrey Space.Let assumptions ⅰ)-ⅳ) hold, Giaquinta and Modica have proved the regularity of both the H^1 weak solutions of (1) under controllable growth condition |B|≤α(|p|~γ+|u|^((n+2)/(n-2))+b, 0<γ≤1+2/n and the H^1∩L~∞ weak solutions of (1) under natural growth condition |B|≤α|p|~2+b with a smallness condition 2aM<λ(|u|≤M), which implys that the H^1∩L~∞ weak solutions have the same regularty in the case of 1+2/n<γ<2. In the case of γ=2, many counterexamples (see [2] showed that u must be in H^1L~∞, while in the case of 1+2/n<γ<2, we consider the H^1∩L^n(γ-1)/(2-γ) weak solutions of (1), weaken the instability conditions upon them (from L~∞ to L^n(γ-1)/(2-γ) and obtain the same regularity results. Finally we show that the exponent n(γ-1)/(2-γ) can not be docreased anymore for the sake of the regularity results.Delinition 1. We call u∈H^1∩L^n(γ-1)/(2-γ)(Q, R^N) be a weak solution of (1), providod that where We use the convention that repeated indices are summed. i, j go from 1 to N ann α, β from 1 to n.

Beta Distribution of Surface Elevation of Random Waves

A probability density function (PDF) is derived of beta distribution with both lambda (3) skewness) and lambda (4) (kurtosis) as parameters for weakly nonlinear wave surface elevation by use of a method recently proposed by Srokosz. This PDF not only has a simpler form than the well-known Gram-Charlier Series PDF derived by Longuet-Higgins, but also overcomes an obvious shortcoming of the latter that when the series is unsuitably truncated, the resulting PDF is locally negative. To test the derived beta PDF, laboratorial experiments of wind waves are conducted. The experimental data indi cate that the theoretical requirements of the parameters in the beta PDF are fulfilled. The experimental results show that the present PDF is in better agreement with the measured data than the beta PDF only including parameter lambda (3), and also than the Gram-Charlier Series PDF truncated up to the term of H-6.

Prediction of separation flows around a 6:1 prolate spheroid using RANS/LES hybrid approaches

This paper presents hybrid Reynolds-averaged Navier-Stokes （RANS） and large-eddy-simulation （LES） methods for the separated flows at high angles of attack around a 6：1 prolate spheroid. The RANS/LES hybrid meth- ods studied in this work include the detached eddy simulation （DES） based on Spalart-Allmaras （S-A）, Menter＇s k-ω shear-stress-transport （SST） and k-o9 with weakly nonlinear eddy viscosity formulation （Wilcox-Durbin＋, WD＋） models and the zonalANS/LES methods based on the SST and WD＋ models. The switch from RANS near the wall to LES in the core flow region is smooth through the implementation of a flow-dependent blending function for the zonal hybrid method. All the hybrid methods are designed to have a RANS mode for the attached flows and have a LES behavior for the separated flows. The main objective of this paper is to apply the hybrid methods for the high Reynolds number separated flows around prolate spheroid at high-incidences. A fourth-order central scheme with fourth-order artificial viscosity is applied for spatial differencing. The fully implicit lower-upper symmetric-Gauss-Seidel with pseudo time sub-iteration is taken as the temporal differentiation. Comparisons with available measurements are carried out for pressure distribution, skin friction, and profiles of velocity, etc. Reasonable agreement with the experiments, accounting for the effect on grids and fundamental turbulence models, is obtained for the separation flows.

Throughflow and g-jitter effects on binary fluid saturated porous medium

A non-autonomous complex Ginzburg-Landau equation （CGLE） for the finite amplitude of convection is derived, and a method is presented here to determine the amplitude of this convection with a weakly nonlinear thermal instability for an oscillatory mode under throughflow and gravity modulation. Only infinitesimal disturbances are considered. The disturbances in velocity, temperature, and solutal fields are treated by a perturbation expansion in powers of the amplitude of the applied gravity field. Throughfiow can stabilize or destabilize the system for stress free and isothermal boundary conditions. The Nusselt and Sherwood numbers are obtained numerically to present the results of heat and mass transfer. It is found that throughfiow and gravity modulation can be used alternately to heat and mass transfer. Further, oscillatory flow, rather than stationary flow, enhances heat and mass transfer.

Surface Tension Effect on Harmonics of Rayleigh-Taylor Instability

Using the method of the parameter expansion up to the third order, explicitly investigates surface tension effect on harmonics at weakly nonlinear stage in Rayleigh-Taylor instability （RTI） for arbitrary Atwood numbers and compares the results with those of classical RTI within the framework of the third-order weakly nonlinear theory. It is found that surface tension strongly reduces the linear growth rate of time, resulting in mild growth of the amplitude of the fundamental mode, and changes amplitudes of the second and third har- monics, as is expressed as a tension factor coupling in amplitudes of the harmonics. On the one hand, surface tension can either decrease or increase the space amplitude; on the other hand, surface tension can also change their phases for some conditions which are explicitly determined.

Coupling between velocity and interface perturbations in cylindrical Rayleigh–Taylor instability

Rayleigh–Taylor instability(RTI)in cylindrical geometry initiated by velocity and interface perturbations is investigated analytically through a third-order weakly nonlinear(WN)model.When the initial velocity perturbation is comparable to the interface perturbation,the coupling between them plays a significant role.The difference between the RTI growth initiated only by a velocity perturbation and that only by an interface perturbation in the WN stage is negligibly small.The effects of the mode number on the first three harmonics are discussed respectively.The low-mode number perturbation leads to large amplitudes of RTI growth.The Atwood number and initial perturbation dependencies of the nonlinear saturation amplitude of the fundamental mode are analyzed clearly.When the mode number of the perturbation is large enough,the WN results in planar geometry are recovered.

Allowable Generalized Quantum Gates Using Nonlinear Quantum Optics

In this paper, we give an efficient physical realization of a double-slit duality quantum gate. Weak cross- Kerr nonlinearity is exploited here. The probability of success can reach 1/2. Asymmetrical slit duality control gate also can be constructed conveniently. The special quantum control gate could be realized easily in optical system by our current experimental technology.