A dual‐weighted trust‐region adaptive POD 4‐D Var applied to a finite‐volume shallow water equations model on the sphere

In this paper we study solutions of an inverse problem for a global shallow water model controlling its initial conditions specified from the 40‐yr ECMWF Re‐analysis (ERA‐40) data sets, in the presence of full or incomplete observations being assimilated in a time interval (window of assimilation) with or without background error covariance terms. As an extension of the work by Chen et al. (Int. J. Numer. Meth. Fluids 2009), we attempt to obtain a reduced order model of the above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4D‐Var for a finite volume global shallow water equation model based on the Lin–Rood flux‐form semi‐Lagrangian semi‐implicit time integration scheme. Different approaches of POD implementation for the reduced inverse problem are compared, including a dual‐weighted method for snapshot selection coupled with a trust‐region POD adaptivity approach. Numerical results with various observational densities and background error covariance operator are also presented. The POD 4‐D Var model results combined with the trust‐region adaptivity exhibit similarity in terms of various error metrics to the full 4D Var results, but are obtained using a significantly lesser number of minimization iterations and require lesser CPU time. Based on our previous and current work, we conclude that POD 4‐D Var certainly warrants further studies, with promising potential of its extension to operational 3‐D numerical weather prediction models. Copyright © 2011 John Wiley & Sons, Ltd.     

A self-adaptive trust region method for the extended linear complementarity problems

By using some NCP functions, we reformulate the extended linear complementarity problem as a nonsmooth equation. Then we propose a self-adaptive trust region algorithm for solving this nonsmooth equation. The novelty of this method is that the trust region radius is controlled by the objective function value which can be adjusted automatically according to the algorithm. The global convergence is obtained under mild conditions and the local superlinear convergence rate is also established under strict complementarity conditions. This work is supported by National Natural Science Foundation of China (No. 10671126) and Shanghai Leading Academic Discipline Project (S30501).     

中国西北地区沙尘暴的发生规律研究

借助MATLAB软件,根据中国西北地区六个省份1981～2005年沙尘暴发生天数、月平均风速、大风发生天数、月平均气温、月降水量、月平均相对湿度的统计数据,研究中国西北地区沙尘暴的区域分布和时间分布规律及其与气象因子的关系.方差分析结果表明:西北地区沙尘暴危害程度省份差异不显著,不同观测站所在地沙尘暴危害程度的差异显著,不同月份沙尘暴危害程度的差异也显著;聚类分析结果表明:拐子湖等站点所在地受沙尘暴危害最严重,各年4月份受沙尘暴危害最严重,北京地区8月份几乎不发生沙尘暴;相关分析结果表明:西北地区沙尘暴的气候影响因子为月平均风速、月大风发生天数和月相对湿度.由回归分析得到,沙尘暴每月发生天数y随月份t的变化规律为正态分布.研究结果可供有关部门参考.     

Modelling and control of flexible joint robot based on Takagi–Sugeno fuzzy approach and its stability analysis via sum of squares

This article proposes a Takagi–Sugeno (T-S) fuzzy model of single-link rotary flexible joint robot. The proposed control method is based on parallel distributed control. The parameters of T-S controller are improved by distributed population genetic algorithm (GA) with chaos GA. Using Hermite–Biehler theorem in distributed population, GA is made to have a fast convergence. Dividing search space into several sub-spaces causes a better response, and chaos disturbance helps the whole algorithm to reach a best answer. The stability of the controller is analysed via the sum of squares programming, and finally, it is implemented on the plant.     

假设检验中p值的灵活运用

给出假设检验中p值的定义以及双边检验p值与单边检验p值的关系,介绍了利用p值将三种检验同时进行的方法及意义,最后给出应用实例.     

Correlation between supercooled liquid region and crystallization behavior with alloy composition of La-Al-Cu metallic glasses

Bulk metallic glasses (BMGs) with large supercooled liquid region are promising materials for superplastic forming. In this paper, we demonstrate a microstructure-based strategy to pinpoint the composition with the largest supercooled liquid region in La 86 x Al 14 Cu x (x=16 at%-20 at%) metallic glass system. By monitoring the changes in crystallization behavior of the glassy alloys with composition to search for the alloys exhibiting eutectic crystallization, the glassy alloys with the largest supercooled...     

A technique for flow-enhanced magnetic resonance angiography of the lower extremities

A two-dimensional, flow-enhanced gradient echo pulse sequence for nuclear magnetic resonance angiography is described. It employs interleaved, presaturated slices to acquire data efficiently on imagers which favor interleaved acquisition over sequential acquisition for multislice imaging. It is useful on any imager when the effective TR is extended to enhance the sensitivity to slow flow. The technique was applied to the region from aortic bifurcation to the iliac bifurcations of three normal volunteers. The right and left common iliac arteries and veins, the separation of the external and internal iliac arteries, and secondary branches were clearly depicted.     

Trust region affine scaling algorithms for linearly constrained convex and concave programs

We study a trust region affine scaling algorithm for solving the linearly constrained convex or concave programming problem. Under primal nondegeneracy assumption, we prove that every accumulation point of the sequence generated by the algorithm satisfies the first order necessary condition for optimality of the problem. For a special class of convex or concave functions satisfying a certain invariance condition on their Hessians, it is shown that the sequences of iterates and objective function values generated by the algorithm convergeR-linearly andQ-linearly, respectively. Moreover, under primal nondegeneracy and for this class of objective functions, it is shown that the limit point of the sequence of iterates satisfies the first and second order necessary conditions for optimality of the problem. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.The work of these authors was based on research supported by the National Science Foundation under grant INT-9600343 and the Office of Naval Research under grants N00014-93-1-0234 and N00014-94-1-0340.