A novel hyperchaos in the quantum Zakharov system for plasmas

The nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs) described by the one-dimensional quantum Zakharov equations (QZEs) is reinvestigated. A Galerkin type approximation is used to reduce the QZS to a simplified system (SS) of nonlinear ordinary differential equations which governs the temporal behaviors of the slowly varying envelope of the high-frequency electric field and the low frequency density fluctuation. This SS is then shown to establish the coexistence of novel hyperchaotic attractors, whose appearance is explained by means of the analysis of Lyapunov exponent spectra as well as the Kaplan-Yorke dimension. The system has an equilibrium point which depends parametrically on the nondimensional quantum parameter (H) proportional to quantum diffraction, the plasmon number (N) and the wave number of perturbation (α), and which can evolve into periodic, quasi-periodic, chaotic and hyperchaotic states in both semiclassical and quantum cases.     

Local discontinuous Galerkin methods for the generalized Zakharov system

In this paper we develop a local discontinuous Galerkin (LDG) method for the generalized Zakharov system. Two energy conservations of the LDG scheme are proved for the generalized Zakharov system. Numerical experiments for the Zakharov system are presented to illustrate the accuracy and capability of the methods, including accuracy tests, plane waves, soliton–soliton collisions of the standard and generalized Zakharov system and a two-dimensional problem.     

Some exact solutions of generalized Zakharov system

In this paper, we seek exact solutions of generalized Zakharov system. We use extended trial equation method to obtain exact solutions of this system. Consequently, we obtain some exact solutions including soliton solutions, rational, Jacobi elliptic and hyperbolic function solutions of this system by using extended trial equation method.     

A stable adaptive neural-network-based scheme for dynamical system control

A stable adaptive neural-network-based control scheme for dynamical systems is presented and a continuous recurrent neural network model of dynamical systems is constructed in this paper. A novel algorithm for updating weights in the neural network, which is not derived from the conventional back propagation algorithm, is also constructed. The proposed control law is obtained adaptively by a continuous recurrent neural network identifier, but not by a conventional neural network controller. In such a way, the stability in the sense of the Lyapunov stability can be guaranteed theoretically. The control error converges to a range near the zero point and remains within the domain throughout the course of the execution. Numerical experiments for a longitudinal vibration ultrasonic motor show that the proposed control scheme has good control performance.     

A conservative scheme for the relativistic Vlasov–Maxwell system

A new scheme for numerical integration of the 1D2V relativistic Vlasov–Maxwell system is proposed. Assuming that all particles in a cell of the phase space move with the same velocity as that of the particle located at the center of the cell at the beginning of each time step, we successfully integrate the system with no artificial loss of particles. Furthermore, splitting the equations into advection and interaction parts, the method conserves the sum of the kinetic energy of particles and the electromagnetic energy. Three test problems, the gyration of particles, the Weibel instability, and the wakefield acceleration, are solved by using our scheme. We confirm that our scheme can reproduce analytical results of the problems. Though we deal with the 1D2V relativistic Vlasov–Maxwell system, our method can be applied to the 2D3V and 3D3V cases.     

A conservative numerical scheme for solving an autonomous Hamiltonian system

A new numerical scheme is proposed for solving Hamilton’s equations that possesses the properties of symplecticity. Just as in all symplectic schemes known to date, in this scheme the conservation laws of momentum and angular momentum are satisfied exactly. A property that distinguishes this scheme from known schemes is proved: in the new scheme, the energy conservation law is satisfied for a system of linear oscillators. The new numerical scheme is implicit and has the third order of accuracy with respect to the integration step. An algorithm is presented by which the accuracy of the scheme can be increased up to the fifth and higher orders. Exact and numerical solutions to the two-body problem, calculated by known schemes and by the scheme proposed here, are compared.     

Zakharov方程的显式行波解

借助Mathematica软件，采用双函数法和吴文俊消元法，获得了等离子体物理中的重要方程组Zakharov方程的十组行波解，其中包括包络孤波解，孤子解. 关键词： Zakharov方程 孤子解     

Scattering for the Zakharov System in 3 Dimensions

We prove global existence and scattering for small localized solutions of the Cauchy problem for the Zakharov system in 3 space dimensions. The wave component is shown to decay pointwise at the optimal rate of t ^?1, whereas the Schrödinger component decays almost at a rate of t ^?7/6.     

红外光学系统系列化方案

分析了红外光学系统品种随意发展带来的问题,研究提出了专用组件系列化发展的技术途径。选择适合的系列化的数学方法,分析了红外光学系统的应用特性及系列化的条件,研究提出了红外光学系统系列化的方案和型谱架构。     

Blow-up results of viriel type for Zakharov equations

We consider the Zakharov equations in ^N (for N=2,N=3). We first establish a viriel identity for such equations and then prove a blow-up result for solutions with a negative energy.     

New Homoclinic and Heteroclinic Solutions for Zakharov System

A new type of homoclinic and heteroclinic solutions, i.e. homoclinic and heteroclinic breather solutions, for Zakharov system are obtained using extended homoclinic test and two-soliton methods, respectively. Moreover, the homoclinic and heteroclinic structure with local oscillation and mechanical feature different from homoclinic and heterocliunic solutions are investigated. Result shows complexity of dynamics for complex nonlinear evolution system. Moreover, the similarities and differences between homoclinic (heteroclinic) breather and homoclinic (heteroclinic) tube are exhibited. These results show that the diversity of the structures of homoclinic and heteroclinic solutions.     

New Homoclinic and Heteroclinic Solutions for Zakharov System

A new type of homoclinic and heteroclinic solutions, i.e. homoclinic and heteroclinic breather solutions, for Zakharov system are obtained using extended homoclinic test and two-soliton methods, respectively. Moreover, the homoclinic and heteroclinic structure with local oscillation and mechanical feature different from homoclinic and heterocliunic solutions are investigated. Result shows complexity of dynamics for complex nonlinear evolution system. Moreover, the similarities and differences between homoclinic (heteroclinic) breather and homoclinic (heteroclinic) tube are exhibited. These results show that the diversity of the structures of homoclinic and heteroclinic solutions.     

An efficient local time-stepping scheme for solution of nonlinear conservation laws

We develop an efficient local time-stepping algorithm for the method of lines approach to numerical solution of transient partial differential equations. The need for local time-stepping arises when adaptive mesh refinement results in a mesh containing cells of greatly different sizes. The global CFL number and, hence, the global time step, are defined by the smallest cell size. This can be inefficient as a few small cells may impose a restrictive time step on the whole mesh. A local time-stepping scheme allows us to use the local CFL number which reduces the total number of function evaluations. The algorithm is based on a second order Runge–Kutta time integration. Its important features are a small stencil and the second order accuracy in the L² and L^∞ norms.     

An adaptive multiresolution scheme with local time stepping for evolutionary PDEs

We present a fully adaptive numerical scheme for evolutionary PDEs in Cartesian geometry based on a second-order finite volume discretization. A multiresolution strategy allows local grid refinement while controlling the approximation error in space. For time discretization we use an explicit Runge–Kutta scheme of second-order with a scale-dependent time step. On the finest scale the size of the time step is imposed by the stability condition of the explicit scheme. On larger scales, the time step can be increased without violating the stability requirement of the explicit scheme. The implementation uses a dynamic tree data structure. Numerical validations for test problems in one space dimension demonstrate the efficiency and accuracy of the local time-stepping scheme with respect to both multiresolution scheme with global time stepping and finite volume scheme on a regular grid. Fully adaptive three-dimensional computations for reaction–diffusion equations illustrate the additional speed-up of the local time stepping for a thermo-diffusive flame instability.     

Optimal scheme for estimating a pure qubit state via local measurements

We present the optimal scheme for estimating a pure qubit state by means of local measurements on N identical copies. We give explicit examples for low N. For large N, we show that the fidelity saturates the collective measurement bound up to order 1/N. When the signal state lays on a meridian of the Bloch sphere, we show that this can be achieved without classical communication.     

一种鲁棒性强的OFDM 水声通信系统*

为了在不同衰落水声信道下实现正交频分复用水声通信,该文提出了一种鲁棒性强的正交频分复用水声通信方案,方案包括编码调制、信道估计和多普勒估计等内容。为了使该系统更稳健,整个信道编码分为两个步骤。首先,循环冗余校验编码器和里德-所罗门编码器用于编码整个数据包,然后循环冗余校验编码器和Turbo 编码器用于编码每个数据帧,其中比特交织编码调制技术用来对抗信道的时变特性。为了得到水声信道估计,使用线性最小均方误差估计器来处理导频数据得到信道估计值。多普勒估计包括帧的多普勒估计和符号的多普勒估计。实验结果表明该系统在不同的衰落信道下都能实现正确的跟踪和译码,系统的鲁棒性能优越。此外,该系统算法计算简单,易于实现,具有良好的工程应用价值。     

A local refinement purely meshless scheme for time fractional nonlinear Schrodinger equation in irregular geometry region

A local refinement hybrid scheme(LRCSPH-FDM)is proposed to solve the two-dimensional(2D)time fractional nonlinear Schrodinger equation(TF-NLSE)in regularly or irregularly shaped domains,and extends the scheme to predict the quantum mechanical properties governed by the time fractional Gross-Pitaevskii equation(TF-GPE)with the rotating Bose-Einstein condensate.It is the first application of the purely meshless method to the TF-NLSE to the author’s knowledge.The proposed LRCSPH-FDM(which is based on a local refinement corrected SPH method combined with FDM)is derived by using the finite difference scheme(FDM)to discretize the Caputo TF term,followed by using a corrected smoothed particle hydrodynamics(CSPH)scheme continuously without using the kernel derivative to approximate the spatial derivatives.Meanwhile,the local refinement technique is adopted to reduce the numerical error.In numerical simulations,the complex irregular geometry is considered to show the flexibility of the purely meshless particle method and its advantages over the grid-based method.The numerical convergence rate and merits of the proposed LRCSPH-FDM are illustrated by solving several 1D/2D(where 1D stands for one-dimensional)analytical TF-NLSEs in a rectangular region(with regular or irregular particle distribution)or in a region with irregular geometry.The proposed method is then used to predict the complex nonlinear dynamic characters of 2D TF-NLSE/TF-GPE in a complex irregular domain,and the results from the posed method are compared with those from the FDM.All the numerical results show that the present method has a good accuracy and flexible application capacity for the TF-NLSE/GPE in regions of a complex shape.     

A gradient-augmented level set method with an optimally local,coherent advection scheme

The level set approach represents surfaces implicitly, and advects them by evolving a level set function, which is numerically defined on an Eulerian grid. Here we present an approach that augments the level set function values by gradient information, and evolves both quantities in a fully coupled fashion. This maintains the coherence between function values and derivatives, while exploiting the extra information carried by the derivatives. The method is of comparable quality to WENO schemes, but with optimally local stencils (performing updates in time by using information from only a single adjacent grid cell). In addition, structures smaller than the grid size can be located and tracked, and the extra derivative information can be employed to obtain simple and accurate approximations to the curvature. We analyze the accuracy and the stability of the new scheme, and perform benchmark tests.     

A general method to obtain vibrational symmetry adapted bases in a local scheme

A general approach to obtain symmetry adapted bases from a local set of states is presented. The approach is based on the identification of the invariant subspaces which, when projected by means of the eigenfunction method developed by Chen (1989, Group Representation Theory for Physicists Singapore, World Scientific), allow the generation of a symmetry adapted basis. The symmetrized functions so obtained are further taken as a basis to diagonalize simultaneously a set of normal number operators, which provides a set of normal states expanded in terms of the symmetry adapted local basis. In this approach the normal number operators are generated implicitly from the one quantum space through a tensorial formalism. Although the normal operators are defined in a harmonic basis, the locality of the basis allows the approach to be extended to anharmonic functions. This approach has the additional advantage of allowing the elimination of the spurious states, a common problem in a local coordinate representation. An important advantage of this symmetrization method is that it allows generation of a code to analyse any molecular system with a minimum set of input data.