Spectral methods for pantograph-type differential and integral equations with multiple delays

We analyze the convergence properties of the spectral method when used to approximate smooth solutions of delay differential or integral equations with two or more vanishing delays. It is shown that for the pantograph-type functional equations the spectral methods yield the familiar exponential order of convergence. Various numerical examples are used to illustrate these results.      

并行化光滑分子动力学方法及其与分子动力学的耦合

提出光滑分子动力学方法(SMD)的并行化计算方法,编制光滑分子动力学以及光滑分子动力学-分子动力学(SMD-MD)耦合的并行程序,并分析铜纳米单晶的单向拉伸和带裂纹板的拉伸问题.光滑分子动力学在分子动力学基础上引入背景网格,在背景网格点上求解运动方程,由此将控制MD临界时间步长的因素化为背景网格单元尺寸,扩大可用的时间积分步长,缩短总计算时间.通过单晶拉伸和带裂纹板拉伸等较大规模问题的计算,验证方法的正确性.与传统分子动力学相比,SMD和SMD-MD耦合方法可以节约计算时间.     

不均匀不稳定磁场下高分辨液体核磁共振新技术的研究进展

高分辨核磁共振（Nuclear Magnetic Resonance,NMR）谱的获得通常需要高度稳定且均匀的强静磁场. 阻抗磁体或阻抗－超导混合磁体可获得比超导磁体高得多的磁场, 但它们的磁场的稳定性与均匀性比较差;另一方面, 在活体定域波谱研究中,样品内部组分的磁化率差异,运动或生理活动等作用将不可避免地导致磁场的不均匀不稳定,并且这些不稳定不均匀性无法通过锁场匀场等传统的方法消除. 基于分子间零量子相干的方法、空间编码单扫描快速方法、反卷积技术等日渐成为在不均匀不稳定磁场下获取高分辨率的NMR谱的研究热点.     

Adaptive co-evolution of strategies and network leading to optimal cooperation level in spatial prisoner’s dilemma game

We study evolutionary prisoner's dilemma game on adaptive networks where a population of players co-evolves with their interaction networks. During the co-evolution process, interacted players with opposite strategies either rewire the link between them with probability $p$ or update their strategies with probability $1-p$ depending on their payoffs. Numerical simulation shows that the final network is either split into some disconnected communities whose players share the same strategy within each community or forms a single connected network in which all nodes are in the same strategy. Interestingly, the density of cooperators in the final state can be maximised in an intermediate range of $p$ via the competition between time scale of the network dynamics and that of the node dynamics. Finally, the mean-field analysis helps to understand the results of numerical simulation. Our results may provide some insight into understanding the emergence of cooperation in the real situation where the individuals' behaviour and their relationship adaptively co-evolve.     

Model for cascading failures with adaptive defense in complex networks

<正>This paper investigates cascading failures in networks by considering interplay between the flow dynamic and the network topology,where the fluxes exchanged between a pair of nodes can be adaptively adjusted depending on the changes of the shortest path lengths between them.The simulations on both an artificially created scale-free network and the real network structure of the power grid reveal that the adaptive adjustment of the fluxes can drastically enhance the robustness of complex networks against cascading failures.Particularly,there exists an optimal region where the propagation of the cascade is significantly suppressed and the fluxes supported by the network are maximal. With this understanding,a costless strategy of defense for preventing cascade breakdown is proposed.It is shown to be more effective for suppressing the propagation of the cascade than the recent proposed strategy of defense based on the intentional removal of nodes.     

High precision Zernike modal gray map reconstruction for liquid crystal corrector

This paper proposes a new Zernike modal gray map reconstruction algorithm used in the nematic liquid crystal adaptive optics system. Firstly, the new modal algorithm is described. Secondly, a single loop correction experiment was conducted, and it showed that the modal method has a higher precision in gray map reconstruction than the widely used slope method. Finally, the contrast close-loop correction experiment was conducted to correct static aberration in the laboratory. The experimental results showed that the average peak to valley (PV) and root mean square (RMS) of the wavefront corrected by mode method were reduced from 2.501\lambda (\lambda =633~nm) and 0.610\lambda to 0.0334\lambda and 0.00845\lambda , respectively. The corrected PV and RMS were much smaller than those of 0.173\lambda and 0.048\lambda by slope method. The Strehl ratio and modulation transfer function of the system corrected by mode method were much closer to diffraction limit than with slope method. These results indicate that the mode method can take good advantage of the large number of pixels of the liquid crystal corrector to realize high correction precision.     

机载制导武器导航系统嵌入式软件结构设计

输入的及时获取及系统的及时输出是导航系统正常工作的基础和核心。在分析机载制导武器导航系统软件结构的基础上,对包含传递对准和组合导航在内的导航软件,进行了多进程、进程优先级以及进程间通信机制的分析和设计。基于对导航系统用卡尔曼滤波器内数据交换的分析,指出在多进程之间存在对多个核心数据的共同存取,采用进程同步机制实现了核心数据协同,给出了核心进程的流程图,完成了一个基于多任务实时操作系统的机载制导武器导航系统软件框架,并在某型机载制导武器导航系统中得到成功应用。     

自适应Kalman滤波在SINS初始对准中的应用

为了提高捷联惯导系统的对准精度和收敛速度,提出了一种基于Sage-Husa自适应滤波算法的初始对准方法。针对方位小失准角的情况,推导出精对准误差模型和自适应Kalman滤波方程。常规Kalman滤波算法,在噪声统计特性已知的情况下,使用比较方便;多数情况下,噪声统计特性是处于未知状态,从而引入自适应Kalman滤波算法。它利用观测到的数据自动进行噪声统计特性的在线估计和修正,使系统达到最佳的滤波效果。通过仿真验证,该自适应滤波算法有效地提高了收敛速度和对准精度。     

求解变分型积分方程的一种新型数值方法——有限变分法

将作者提出的多虚拟裂纹扩展法(MVCE法)拓展为求解变分型积分方程问题的一种新型数值方法——有限变分法(FVM)。它的基本思想是,给定有限个(N个)局部变分模式,将所求解的未知量用适当的方法离散化,针对这N个局部变分模式列出N个方程,求解N个未知系数,从而求得未知量。单一未知变量FVM的最终方程组的系数矩阵通常是一个对称的窄带矩阵,对角元是大数,有很好的数值计算性能。用FVM求解了三维I型裂纹前缘的应力强度因子(SIF)分布。利用基于FVM的通用权函数法计算程序,可以高精度和高效率地求解表面力、体积力和温度载荷共同作用情况下三维裂纹前缘SIF的分布及其时间历程。FVM可以被推广到更广泛的领域,是一个求解变分型积分方程问题的普遍适用的新型数值方法。     

一种新的运动自适应去隔行算法

提出基于棱边方向检测的运动自适应去隔行算法,该算法能充分利用图像序列的时间和空间上的相关信息,采用新颖的相邻场运动检测方法区分视频序列中的运动和静止部分.对于运动部分,使用改进的基于棱边方向的边沿自适应插值算法;对于静止部分,采用三点中值滤波插值算法.仿真实验表明：算法无论在画面视觉效果还是视频图像信噪比,均达到良好了效果.