A NEW DIFFERENCE SCHEME WITH MULTI-TIME LEVELS

In view of making the best use of information coming from past observational data, a new difference scheme with multi-time levels (p>3) is suggested. Some mathematical characteristics of the scheme, which is called the retrospective scheme, are discussed. The numerical results of some examples show that the calculation accuracy of linear and nonlinear advection equations computed with the retrospective scheme is higher than that obtained via the leapfrog scheme. The scheme can be applied to many fields, such as meteorology, engineering physics, astronautics, environment and economy etc, where systematic observations are made normally.     

A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid

A conservative multi-tracer transport algorithm on the cubed-sphere based on the semi-Lagrangian approach (CSLAM) has been developed. The scheme relies on backward trajectories and the resulting upstream cells (polygons) are approximated with great-circle arcs. Biquadratic polynomial functions are used for approximating the density distribution in the cubed-sphere grid cells. The upstream surface integrals associated with the conservative semi-Lagrangian scheme are computed as line-integrals by employing the Gauss–Green theorem. The line-integrals are evaluated using a combination of exact integrals and high-order Gaussian quadrature. The upstream cell (trajectories) information and computation of weights of integrals can be reused for each additional tracer.The CSLAM scheme is extensively tested with various standard benchmark test cases of solid-body rotation and deformational flow in both Cartesian and spherical geometry, and the results are compared with those of other published schemes. The CSLAM scheme is accurate, robust, and moreover, the edges and vertices of the cubed-sphere (discontinuities) do not affect the overall accuracy of the scheme. The CSLAM scheme exhibits excellent convergence properties and has an option for enforcing monotonicity. The advantages of introducing cross-terms in the fully two-dimensional biquadratic density distribution functions are also examined in the context of Cartesian as well as the cubed-sphere grid which has six local sub-domains with discontinuous edges and corners.     

Optical encryption scheme for multiple color images using complete trinary tree structure

We propose an optical encryption scheme for multiple color images based on the complete trinary tree structure. In the proposed encryption scheme, the encryption modules (EMs) are taken as branch nodes, and the color components of plain images are input as leaf nodes. In each EM which consists of phase truncated Fresnel transforms and random amplitude-phase masks, three input images are subsequently encoded into a complex function and finally encrypted to a real-value image. The proposed encryption scheme can encrypt multiple color images into a real-value grayscale cipher image, and make different color images have different encryption and decryption paths. By the proposed encryption scheme, we can realize an authority management with high security among multiple users. In addition, the proposed scheme possesses the advantages such as high robustness against various attacks and high encryption efficiency. Moreover, as the number of plain color images increases, high quality of the decrypted color images can still be maintained. Extensive simulation results have shown the performance of the proposed scheme. The proposed scheme can also be directly extended to encrypt multiple gray images.     

无滤波高倍频光载毫米波生成技术

提出了一种无滤波的高倍频光载毫米波生成方案.该方案未使用相关的光/电滤波器就可16倍频的毫米波信号.整个系统采用三平行的马赫-曾德尔调制器结构和单个马赫-曾德尔调制器级联,通过调整系统的参数可以很好地抑制所有冗余光边带,只留下高质量的8阶光边带,无需任何光/电滤波器就能够得到16倍频的高质量毫米波信号.另外,详细分析了系统的工作原理,并通过仿真验证了调制深度、消光比、移相器偏移以及调制器偏压对系统的影响.研究结果表明将2 Gbit/s的非归零码型数据与10 GHz的射频信号混频后作为马赫-曾德尔调制器的驱动信号,系统经过50 km光纤传输后的链路功率代价为1.0 dB,具有良好的传输性能.该方案对于无滤波的高倍频毫米波生成有一定的参考价值.     

Q-S (lag or anticipated) synchronization backstepping scheme in a class of continuous-time hyperchaotic systems--a symbolic-numeric computation approach

First, a Q-S (lag or anticipated) synchronization of continuous-time dynamical systems is defined. Second, based on a backstepping design with one controller, a systematic, concrete, and automatic scheme is developed to investigate the Q-S (lag or anticipated) synchronization between the drive system and response system with a strict-feedback form. Two identical hyperchaotic Tamasevicius-Namajunas-Cenys(TNC) systems as well as the hyperchaotic TNC system and hyperchaotic Rossler system are chosen to illustrate the proposed scheme. Numerical simulations are used to verify the effectiveness of the proposed scheme. The scheme can also be extended to study Q-S (lag or anticipated) synchronization between other dynamical systems with strict-feedback forms. With the aid of symbolic-numeric computation, the scheme can be performed to yield automatically the scalar controller in computer.     

A High-Order WENO Finite Difference Scheme for the Equations of Ideal Magnetohydrodynamics

We present a high-order accurate weighted essentially non-oscillatory (WENO) finite difference scheme for solving the equations of ideal magnetohydrodynamics (MHD). This scheme is a direct extension of a WENO scheme, which has been successfully applied to hydrodynamic problems. The WENO scheme follows the same idea of an essentially non-oscillatory (ENO) scheme with an advantage of achieving higher-order accuracy with fewer computations. Both ENO and WENO can be easily applied to two and three spatial dimensions by evaluating the fluxes dimension-by-dimension. Details of the WENO scheme as well as the construction of a suitable eigen-system, which can properly decompose various families of MHD waves and handle the degenerate situations, are presented. Numerical results are shown to perform well for the one-dimensional Brio–Wu Riemann problems, the two-dimensional Kelvin–Helmholtz instability problems, and the two-dimensional Orszag–Tang MHD vortex system. They also demonstrate the importance of maintaining the divergence free condition for the magnetic field in achieving numerical stability. The tests also show the advantages of using the higher-order scheme. The new 5th-order WENO MHD code can attain an accuracy comparable with that of the second-order schemes with many fewer grid points.     

双色相干场高次谐波

通过数值求解一维含时薛定谔方程，研究了激光频率对谐波辐射的影响以及双色相干场（基频光与其二倍频光或三倍频光）作用于原子时的谐波辐射行为。结果表明，在其它条件相同时，用低频入射光可获得更高次谐波，但转换效率较低，高频入射光转换效率较高，但只能获得较低次谐波，基频光及其三倍频光同时作用于原子，谐波次数和转换效率都有所提高。基频光及其二倍频光同时作用于原子，不但谐波次数增多，转换效率提高，重要是的除了通     

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.     

Gas-kinetic scheme with discontinuous derivative for low speed flow computation

The present paper concerns the improvement of the gas-kinetic scheme (GKS) for low speed flow computation. In the modified GKS scheme, the flow distributions with discontinuous derivatives are used as an initial condition at the cell interface for the flux evaluation. This discontinuity is determined by considering both the flow characteristic and grid’s resolution. Compared with GKS method with a continuous slope for the flow variables at a cell interface, the new scheme is more robust and accurate. In the under resolved flow computation, the new scheme presents much less numerical oscillation. The extension of the current scheme to unstructured mesh is straightforward. To validate the method, both computations of 2D lid-driven cavity flow and 3D flow past a sphere are performed. The numerical results validate the current method.     

Scheme for Controlled Dense Coding via Cavity Decay

A scheme for controlled dense coding via cavity decay is proposed. In the scheme, two degenerate ground states of six-level atoms are used as the storage qubits and the leaky photons act as flying qubits. The system is robust against atomic spontaneous emissions and decoherence of cavity field. And the successful probability is nearly 1 with quantum nondemolition parity detectors and photon detectors, The scheme may be realized based on current technologies.     

A high-resolution,hybrid compact-WENO scheme with minimized dispersion and controllable dissipation

In this paper,a high-resolution,hybrid compact-WENO scheme is developed based on the minimized dispersion and controllable dissipation reconstruction technique.Firstly,a suffcient condition for a family of tri-diagonal compact schemes to have independent dispersion and dissipation is derived.Then,a specific 4th order compact scheme with low dispersion and adjustable dissipation is constructed and analyzed.Finally,the optimized compact scheme is blended with the WENO scheme to form the hybrid scheme.Moreover,the approximation dispersion relation approach is employed to optimize the spectral properties of the nonlinear scheme to yield the true wave propagation behavior of the finite difference scheme.Several test cases are carried out to verify the highresolution as well as the robust shock-capturing capabilities of the proposed scheme.     

Scheme for Controlled Dense Coding via Cavity Decay

A scheme for controlled dense coding via cavity decay is proposed. In the scheme, two degenerate ground states of six-level atoms are used as the storage qubits and the leaky photons act as flying qubits. The system is robust against atomic spontaneous emissions and decoherence of cavity field. And the successful probability is nearly 1 with quantum nondemolition parity detectors and photon detectors. The scheme may be realized based on current technologies.     

Evaluation of the applicability of a retrospective scheme based on comparison with several difference schemes

The evaluation of the applicability of a retrospective multi-time-level scheme (RT scheme) is carried out on the basis of comparison with the common leapfrog scheme (LF scheme) and its derivatives, and modified BOTT‘s positive-definite schemes used in atmospheric models. Two rational flow field tests confirm that at least the BOTT scheme tested may be applied, but apparently the best results are obtained by the RT scheme. The results of wavelet analysisshow that the RT scheme can better extract the useful information from the initial fields, i.e. to memorize many main initial characteristics, such as periods, thus offering a new approach to the short-term climate numerical prediction.     

啁啾匹配OPCPA方案用于消除超短激光脉冲的预脉冲

采用了一种利用啁啾匹配光参量啁啾脉冲放大（OPCPA）技术来消除泵浦脉冲时间窗口内的预脉冲的方法,并对该方法展开了数值模拟研究。分析了泵浦光脉冲形状、预脉冲提前时间等因素对预脉冲消除效果以及信噪比提升情况的影响。通过与传统的非共线OPCPA方案对比,发现啁啾匹配OPCPA方案可以消除掉离主脉冲更近的预脉冲,且它对预脉冲的消除效果受泵浦光脉冲形状的影响较小。     

Nonlinear image encryption using a fully phase nonzero-order joint transform correlator in the Gyrator domain

A novel nonlinear image encryption scheme based on a fully phase nonzero-order joint transform correlator architecture (JTC) in the Gyrator domain (GD) is proposed. In this encryption scheme, the two non-overlapping data distributions of the input plane of the JTC are fully encoded in phase and this input plane is transformed using the Gyrator transform (GT); the intensity distribution captured in the GD represents a new definition of the joint Gyrator power distribution (JGPD). The JGPD is modified by two nonlinear operations with the purpose of retrieving the encrypted image, with enhancement of the decrypted signal quality and improvement of the overall security. There are three keys used in the encryption scheme, two random phase masks and the rotation angle of the GT, which are all necessary for a proper decryption. Decryption is highly sensitivity to changes of the rotation angle of the GT as well as to little changes in other parameters or keys. The proposed encryption scheme in the GD still preserves the shift-invariance properties originated in the JTC-based encryption in the Fourier domain. The proposed encryption scheme is more resistant to brute force attacks, chosen-plaintext attacks, known-plaintext attacks, and ciphertext-only attacks, as they have been introduced in the cryptanalysis of the JTC-based encryption system. Numerical results are presented and discussed in order to verify and analyze the feasibility and validity of the novel encryption–decryption scheme.     

A mass,energy, vorticity,and potential enstrophy conserving lateral boundary scheme for the shallow water equations using piecewise linear boundary approximations

A numerical scheme for treating fluid–land boundaries in inviscid shallow water flows is derived that approximates boundary profiles with piecewise linear segments (shaved cells) while conserving the domain-summed mass, energy, vorticity, and potential enstrophy. The new scheme is a generalization of a previous scheme that also conserves these quantities but uses stairsteps to approximate boundary profiles. Numerical simulations are carried out demonstrating the conservation properties and accuracy of the piecewise linear boundary scheme (the PLS) for inviscid flows and comparing its performance with that of the stairstep scheme (the STS). It is found that while both schemes conserve all four domain-summed quantities, the PLS generates depth and velocity fields that are one-half to one order more accurate than those generated by the STS, and it generates vorticity and potential vorticity fields that are at least as accurate as those generated by the STS and often more accurate. The higher accuracy of the PLS is due to its ability to generate smoother flow fields near boundaries of arbitrary shape.     

Generation of Vibrational Entangled Coherent States of Two Trapped Ions

We propose a scheme for the generation of entangled coherent states for the center-of-mass and relative vibrational modes of two trapped ions. In the scheme the ions are simultaneously illuminated by a single standing-wave laser tuned to the carrier. The scheme allows the production of an entangled coherent states with a considerably high speed as long as a laser field of sufficiently high intensity is available.     

Generation of Vibrational Entangled Coherent States of Two Trapped Ions

We propose a scheme for the generation of entangled coherent states for the center-of-mass and relative vibrational modes of two trapped ions. In the scheme the ions are simultaneously illuminated by a single standing-wave laser tuned to the carrier. The scheme allows the production of an entangled coherent states with a considerably high speed as long as a laser field of sufficiently high intensity is available.     

Improving consensus and synchronizability of networks of coupled systems via adding links

The problem of improving the consensus and synchronizability for weighted networks of dynamic systems via adding links among them is investigated in this paper. A weighted network entropy is introduced to measure the homogeneity of the weighted networks. The relationship between the homogeneity and the consensus and synchronizability is analyzed. A solution scheme is proposed to improve the consensus and synchronizability of the weighted networks through maximizing their homogeneity via adding as few links as possible. Weighted networks created from the Barrat model are tested by using the proposed scheme, and two commonly used link-adding approaches are selected to compare with this scheme. Computer simulation results show that the proposed link-adding scheme can enhance the consensus and the synchronizability of the weighted networks effectively and efficiently.     

黏性激波管的有限体积WENO格式数值模拟

本文采用OpenFOAM软件下实现的一种可实现任意阶数,可应用于非结构网格的有限体积WENO格式对黏性激波管问题进行模拟。模拟中对流项离散采用3阶精度、4阶精度该类WENO格式,网格形式采用结构网格和三角形非结构网格。结果表明,采用该类格式,三角形非结构网格的算精度、效率优于结构网格,3阶精度格式计算效率优于4阶精度。该工作表明OpenFOAM下采用3阶精度该类格式及非结构网格对叶轮机械内部流动等复杂流场的模拟更具优势与应用潜力.