Application of the Conditional Nonlinear Local Lyapunov Exponent to Second-Kind Predictability

In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The effectiveness of this algorithm is validated and compared with the nonlinear local Lyapunov exponent(NLLE)and signal-to-noise ratio methods using a coupled Lorenz model.The results show that the CNLLE method is able to capture the slow error growth constrained by external forcings,therefore,it can quantify the predictability limit induced by the external forcings.On this basis,a preliminary attempt was made to apply this method to measure the influence of ENSO on the predictability limit for both atmospheric and oceanic variable fields.The spatial distribution of the predictability limit induced by ENSO is similar to that arising from the initial conditions calculated by the NLLE method.This similarity supports ENSO as the major predictable signal for weather and climate prediction.In addition,a ratio of predictability limit(RPL)calculated by the CNLLE method to that calculated by the NLLE method was proposed.The RPL larger than 1 indicates that the external forcings can significantly benefit the long-term predictability limit.For instance,ENSO can effectively extend the predictability limit arising from the initial conditions of sea surface temperature over the tropical Indian Ocean by approximately four months,as well as the predictability limit of sea level pressure over the eastern and western Pacific Ocean.Moreover,the impact of ENSO on the geopotential height predictability limit is primarily confined to the troposphere.

Atlantic blocking events in a simplified nonlinear baroclinic model for local finite-amplitude wave activity

为研究北大西洋阻高的形成机制,本文在局部有限振幅波活动(LWA)框架下进行了一系列数值实验.采用的数值模型能显式地描绘出两种重要的大气内部动力过程,即非线性纬向位涡通量和Rossby波包传播.模拟结果显示,这两种动力学过程均是形成大西洋阻高的重要机理.具体地,非线性纬向位涡通量和Rossby波包传播,分别是大西洋阻高南部和北部LWA形成的主导因子.因此,本研究综合了前人关于大西洋阻高的研究成果,为其形成机理提供了新的认识.

Nonlinear characteristic investigation of magnetorheological damper-rotor system with local nonlinearity

Magnetorheological(MR)dampers show superior performance in reducing rotor vibration,but their high nonlinearity will cause nonsynchronous response,resulting in fatigue and instability of rotors.Herein,we are devoted to the investigation of the nonlinear characteristics of MR damper mounted on a flexible rotor.First,Reynolds equations with bilinear constitutive equations of MR fluid are employed to derive nonlinear oil film forces.Then,the Finite Element(FE)model of rotor system is developed,where the local nonlinear support forces produced by MR damper and its coupling effects with the rotor are considered.A hybrid numerical method is proposed to solve the nonlinear FE motion equations of the MR damper-rotor system.To validate the proposed model,a rotor test bench with two dual-coil MR dampers is constructed,upon which experimental studies on the dynamic characteristics of MR damper-rotor system are carried out.The effects of different system parameters,including rotational speed,excitation current and amount of unbalance,on nonlinear dynamic behaviors of MR damper-rotor system are evaluated.The results show that the system may appear chaos,jumping,and other complex nonlinear phenomena,and the level of the nonlinearity can be effectively alleviated by applying suitable excitation current and oil supply pressure.

Sparse Kernel Locality Preserving Projection and Its Application in Nonlinear Process Fault Detection

Locality preserving projection (LPP) is a newly emerging fault detection method which can discover local manifold structure of a data set to be analyzed, but its linear assumption may lead to monitoring performance degradation for complicated nonlinear industrial processes. In this paper, an improved LPP method, referred to as sparse kernel locality preserving projection (SKLPP) is proposed for nonlinear process fault detection. Based on the LPP model, kernel trick is applied to construct nonlinear kernel model. Furthermore, for reducing the computational complexity of kernel model, feature samples selection technique is adopted to make the kernel LPP model sparse. Lastly, two monitoring statistics of SKLPP model are built to detect process faults. Simulations on a continuous stirred tank reactor (CSTR) system show that SKLPP is more effective than LPP in terms of fault detection performance.

Determining the Spectrum of the Nonlinear Local Lyapunov Exponents in a Multidimensional Chaotic System

For an n-dimensional chaotic system, we extend the definition of the nonlinear local Lyapunov exponent （NLLE） from one- to n-dimensional spectra, and present a method for computing the NLLE spectrum. The method is tested on three chaotic systems with different complexity. The results indicate that the NLLE spectrum realistically characterizes the growth rates of initial error vectors along different directions from the linear to nonlinear phases of error growth. This represents an improvement over the traditional Lyapunov exponent spectrum, which only characterizes the error growth rates during the linear phase of error growth. In addition, because the NLLE spectrum can effectively separate the slowly and rapidly growing perturbations, it is shown to be more suitable for estimating the predictability of chaotic systems, as compared to the traditional Lyapunov exponent spectrum.

Comparison of Nonlinear Local Lyapunov Vectors with Bred Vectors, Random Perturbations and Ensemble Transform Kalman Filter Strategies in a Barotropic Model

The breeding method has been widely used to generate ensemble perturbations in ensemble forecasting due to its simple concept and low computational cost. This method produces the fastest growing perturbation modes to catch the growing components in analysis errors. However, the bred vectors （BVs） are evolved on the same dynamical flow, which may increase the dependence of perturbations. In contrast, the nonlinear local Lyapunov vector （NLLV） scheme generates flow-dependent perturbations as in the breeding method, but regularly conducts the Gram-Schmidt reorthonormalization processes on the perturbations. The resulting NLLVs span the fast-growing perturbation subspace efficiently, and thus may grasp more com- ponents in analysis errors than the BVs. In this paper, the NLLVs are employed to generate initial ensemble perturbations in a barotropic quasi-geostrophic model. The performances of the ensemble forecasts of the NLLV method are systematically compared to those of the random pertur- bation （RP） technique, and the BV method, as well as its improved version--the ensemble transform Kalman filter （ETKF） method. The results demonstrate that the RP technique has the worst performance in ensemble forecasts, which indicates the importance of a flow-dependent initialization scheme. The ensemble perturbation subspaces of the NLLV and ETKF methods are preliminarily shown to catch similar components of analysis errors, which exceed that of the BVs. However, the NLLV scheme demonstrates slightly higher ensemble forecast skill than the ETKF scheme. In addition, the NLLV scheme involves a significantly simpler algorithm and less computation time than the ETKF method, and both demonstrate better ensemble forecast skill than the BV scheme.

Bright and dark small amplitude nonlinear localized modes in a quantum one-dimensional Klein-Gordon chain

By means of the Glauber＇s coherent state method combined with multiple-scale method, this paper investigates the localized modes in a quantum one-dimensional Klein-Gordon chain and finds that the equation of motion of annihilation operator is reduced to the nonlinear Schroedinger equation. Interestingly, the model can support both bright and dark small amplitude travelling and non-travelling nonlinear localized modes in different parameter spaces.

Quantitative Comparison of Predictabilities of Warm and Cold Events Using the Backward Nonlinear Local Lyapunov Exponent Method

The backward nonlinear local Lyapunov exponent method(BNLLE)is applied to quantify the predictability of warm and cold events in the Lorenz model.Results show that the maximum prediction lead times of warm and cold events present obvious layered structures in phase space.The maximum prediction lead times of each warm(cold)event on individual circles concentric with the distribution of warm(cold)regime events are roughly the same,whereas the maximum prediction lead time of events on other circles are different.Statistical results show that warm events are more predictable than cold events.

Localized waves in three-component coupled nonlinear Schrdinger equation

We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.

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.

LoLocalized Spatial Soliton Excitations in(2+1)-Dimensional Nonlinear Schrdinger Equation with Variable Nonlinearity and an External Potential

We report on the localized spatial soliton excitations in the multidimensional nonlinear Schrodinger equation with radially variable nonlinearity coefficient and an external potential. By using Hirota＇s binary differential operators, we determine a variety of external potentials and nonlinearity coefficients that can support nonlinear localized solutions of different but desired forms. For some specific external potentials and nonlinearity coefficients, we discuss features of the corresponding （2＋1）-dimensional multisolitonic solutions, including ring solitons, lump solitons, and soliton clusters.

Quantifying local predictability of the Lorenz system using the nonlinear local Lyapunov exponent

The nonlinear local Lyapunov exponent（NLLE） can be used as a quantification of the local predictability limit of chaotic systems. In this study, the phase-spatial structure of the local predictability limit over the Lorenz-63 system is investigated. It is found that the inner and outer rims of each regime of the attractor have a high probability of a longer than average local predictability limit, while the center part is the opposite. However, the distribution of the local predictability limit is nonuniformly organized, with adjacent points sometimes showing quite distinct error growth.The source of local predictability is linked to the local dynamics, which is related to the region in the phase space and the duration on the current regime.

THE APPLICATION OF NONLINEAR GAUGE MATHOD TO THE ANALYSIS OF LOCAL FINITE DEFORMATION IN THE NECKING OF CYLINDRICAL BAR

Localized deformation and instability is the focal point of research in mechanics. The most typical problem is the plastic analysis of cylindrical bar neckingand shear band under uniaxial tension. Traditional elasto-plastic mechanics of infinitesimal deformation can not solve this problem successfully. In this paper, on the basis of S(strain) -R(rotation) decomposition theorem, the authors obtain the localstrain distribution and progressive state of axial symmetric finite deformation of cylindrical bar under uniaxial tension adopting nonlinear gauge approximate method and computer modelling technique.

NONLINEAR APPROXIMATION OF A VARIATION OF L^1 UNDER THE LOCAL HAAR CONDITION

In this paper, we discuss the nonlinear approximation of a variation of L1 under the local Haar condition. Theorems on characterizations (including alternations), unicity and strong unicity of the nonlinear approximation are obtained, the associated linear problem equivalent to the nonlinear approximation are given.

基于改进差分进化算法的水下恒定电流元定位方法随电极数量的变化

针对水下非合作军事目标的远程被动电场定位需求,提出利用非规则布放的测量电极获得水下电位数据,并采用边界变异自适应差分进化算法可以实现对半无限大海水中恒定电流元的准确定位。从半无限大海域中恒定电流元所产生的标量电位表达式出发,通过建立目标函数,将电流元的定位问题转化为目标函数最小值优化问题;然后引入参数自适应策略和边界变异处理机制,以解决基本差分进化算法存在的易陷入局部最优解、收敛性差、抗噪能力弱等问题。仿真分析和实验室定位结果表明:所提出的边界变异自适应差分进化算法在解决水下恒定电流元定位问题时,具有不依赖初值、搜索范围大、抗噪性能好等优点,具有较强的实用性。

On Local Existence and Blow-Up of Solutions for Nonlinear Wave Equations of Higher-Order Kirchhoff Type with Strong Dissipation

In this paper, we study on the initial-boundary value problem for nonlinear wave equations of higher-order Kirchhoff type with Strong Dissipation: . At first, we prove the existence and uniqueness of the local solution by the Banach contraction mapping principle. Then, by “Concavity” method we establish three blow-up results for certain solutions in the case 1): , in the case 2): and in the case 3): . At last, we consider that the estimation of the upper bounds of the blow-up time is given for deferent initial energy.

Localized waves of the coupled cubic–quintic nonlinear Schrdinger equations in nonlinear optics

We investigate some novel localized waves on the plane wave background in the coupled cubic-quintic nonlinear Schrdinger （CCQNLS） equations through the generalized Darboux transformation （DT）. A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higher-order localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed：（i） the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions; （ii） hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons; （iii） hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α. These results further uncover some striking dynamic structures in the CCQNLS system.

具有对数源项的粘弹性Petrovsky方程解的局部适定性及高能爆破现象

本文侧重研究具有对数源项的粘弹性Petrovsky方程初边值问题解的爆破性质。结合Faedo-Galerkin逼近技巧和压缩映射原理,证明问题解的局部适定性。同时,利用反证技巧及凹性引理给出了高能解的爆破现象。

基于Global/Local法的螺栓连接结构静强度渐进破坏

为了研究螺栓连接结构静强度渐进破坏特点,应用Global/Local有限元分析技术,分两级建立了螺栓连接结构有限元模型,并对其进行了带EWK断裂子程序的材料/几何非线性有限元分析。结果表明:螺栓连接结构的断裂部位位于螺栓孔边缘,当加载到最大载荷的42%时开始出现破坏单元,在加载到最大载荷的48%之前裂纹扩展是一个稳态的过程,之后便迅速扩展直至整体结构失效。Global/Local分析技术提高了整个过程的分析效率。

基于分布式传感器的地下浅层震源定位

针对无线传感器网络中的(TDOA)节点无源定位中的非线性优化问题,提出一种基于双种群粒子群(DIR-WOA)的鲸鱼优化的TDOA定位算法;在标准鲸鱼算法的基础上,引入混沌模型,改进粒子种群生成方式,利用主辅粒子群进行相互制约,有效解决粒子易陷入局部最优的问题,迅速得到全局最优解;仿真结果表明,改进算法相较于标准鲸鱼算法,增强了粒子搜索范围,算法收敛时间减少了0.568 8 s,定位误差减小到0.029 m。