Approximate traveling wave solution for shallow water wave equation

Reconstruction of Variational Iteration Method (RVIM) is used for computing the coupled Whitham-Broer-Kaup shallow water. Then RVIM solution is verified against exact one and is compared with powerful approximate solutions, the Homotopy Perturbation Method (HPM) and Homotopy Analysis Method (HAM). The existent error of the methods is computed and convergence of the RVIM solution has been presented. Results obtained expose effectiveness and capability of this method to solve the nonlinear systems in mechanics, analytically.     

智慧家庭App的设备控制页面动态呈现技术

对智慧家庭App进行设备控制的页面动态呈现技术进行了分析,提出了一种基于轻量级部件引擎的页面动态呈现技术,并结合实际案例进行了开发验证,对优化智慧家庭App设备控制的页面动态呈现技术进行了有益的探索。     

纳米尺寸自旋阀中电流驱动的自旋波发射

提出了在纳米赝自旋阀中的电流感应自旋传输矩的磁动力学描述,成功地解释了在磁纳米多层结构中的电流驱动微波发射和电流感应磁化翻转现象。自旋流极化由在电导匹配时的自旋流和化学势连续性边界条件决定。自旋矩的纵向和横向分量在自旋阀的电流驱动微波发射和电流感应磁化翻转现象中扮演了不同的角色:纵向自旋矩分量决定了电流感应磁化翻转(CIMS)效应,而横向自旋矩是自旋波发射(SWE)效应所不可缺少的。根据这一理论,由LLG方程自然得到自旋波发射的双模,分别为横向自旋矩引发的X和Y方向的振动,并引起磁多层电阻以频率2w或w(进动频率)随时间变化。磁场和自旋流共同决定了自旋波发射的频率和功率,这一理论预言了某种特殊的磁多层结构,如磁层相互垂直的结构,将具有大得多的微波发射效率,这一结论已经被实验所证实。     

Comparison of POD reduced order strategies for the nonlinear 2D shallow water equations

This paper introduces tensorial calculus techniques in the framework of POD to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree p. Such nonlinear terms have an online complexity of , where k is the dimension of POD basis and therefore is independent of full space dimension. However, it is efficient only for quadratic nonlinear terms because for higher nonlinearities, POD model proves to be less time consuming once the POD basis dimension k is increased. Numerical experiments are carried out with a two‐dimensional SWE test problem to compare the performance of tensorial POD, POD, and POD/discrete empirical interpolation method (DEIM). Numerical results show that tensorial POD decreases by 76× the computational cost of the online stage of POD model for configurations using more than 300,000 model variables. The tensorial POD SWE model was only 2 to 8× slower than the POD/DEIM SWE model but the implementation effort is considerably increased. Tensorial calculus was again employed to construct a new algorithm allowing POD/DEIM SWE model to compute its offline stage faster than POD and tensorial POD approaches. Copyright © 2014 John Wiley & Sons, Ltd.     

Constrained Hamilton variational principle for shallow water problems and Zu-class symplectic algorithm

In this paper, the shallow water problem is discussed. By treating the incompressible condition as the constraint, a constrained Hamilton variational principle is presented for the shallow water problem. Based on the constrained Hamilton variational principle, a shallow water equation based on displacement and pressure (SWE-DP) is developed. A hybrid numerical method combining the finite element method for spatial discretization and the Zu-class method for time integration is created for the SWEDP. The correctness of the proposed SWE-DP is verified by numerical comparisons with two existing shallow water equations (SWEs). The effectiveness of the hybrid numerical method proposed for the SWE-DP is also verified by numerical experiments. Moreover, the numerical experiments demonstrate that the Zu-class method shows excellent performance with respect to simulating the long time evolution of the shallow water.