A numerical approach based on the meshless collocation method in elastodynamics

In this paper, a collocation technique with the modified equilibrium on line method （ELM） for imposition of Neumann （natural） boundary conditions is presented for solving the two-dimensional problems of linear elastic body vibrations. In the modified ELM, equilibrium over the lines on the natural boundary is satisfied as Neumann boundary condition equations. In other words, the natural boundary conditions are satisfied naturally by using the weak formulation. The performance of the modified version of the ELM is studied for collocation methods based on two different ways to construct meshless shape functions： moving least squares approximation and radial basis point interpolation. Numerical examples of two-dimensional free and forced vibration analyses show that by using the modified ELM, more stable and accurate results would be obtained in comparison with the direct collocation method.     

Markov chain-based analysis of a modified Cooper-Frieze model

From the perspective of probability, the stability of a modified Cooper- Frieze model is studied in the present paper. Based on the concept and technique of the first-passage probability in the Markov theory, we provide a rigorous proof for the exis- tence of the steady-state degree distribution, and derive the explicit formula analytically. Moreover, we perform extensive numerical simulations of the model, including the degree distribution and the clustering.     

基于神经网络技术的乘波体优化设计

乘波体是高超声速飞行器的主要组成部分,也是飞行器产生升力的主要部分. 针对基 于计算流体动力学(CFD)分析的乘波体优化设计问题,引入人工神经元网络响应面方法. 选 取一定数量的乘波体外形,进行气动性能分析后,利用乘波体的外形控制参数和气动参数做 为训练样本对乘波体进行训练. 利用这些训练样本对人工神经网络进行训练. 在优化计算中 以充分训练的神经网络替代CFD分析,发展了一种基于神经网络技术的乘波体优化设计方法. 利用该方法在马赫数6、雷诺数7\times 10^6条件下,分别对乘波体进行了最大升阻比的单目标和综 合考虑升阻比、容积及表面积的多目标优化. 计算结果表明,采用神经网络响应面技术可在 保证计算稳定性的条件下有效提高计算效率.     

Nets with Hexagonal Cell Structure

We establish a continuum theory of inextensible nets with hexagonal cell structure. Some qualitative properties of the equilibrium problem and possible singularities are discussed.      

等p路径十砂土本构关系的归一化特性及数值建模方法

用神经网络对土体进行建模能反映应力路径相关性、反映土的剪胀剪缩以及反映体应力、剪应力对体应变、剪应变的交互影响,因而成为一种比较理想的建模方式.能否在样本有限的情况下获得精度比较高的本构模型正是主要的研究目的.通过研究中密砂在等p路径下的三轴试验曲线,发现其应力-应变关系曲线在常规应力范围内具有归一化特性.选择合适的归一化指标对砂土三轴试验数据进行归一化,以归一化的试验数据为训练样本进行神经网络训练,得到了比较理想的砂土的神经网络本构模型.本构模型仿真值与试验值符合较好,表明所给出的建模方法是合理的.提出的建模方法可以在所有试验数据的基础上自动实现概率寻优,能有效降低噪声信号的干扰、减小试验数据的分散造成的影响.     

Design of state estimator for uncertain neural networks via the integral-inequality method

The issue of state estimation is studied for a class of neural networks with norm-bounded parameter uncertainties and time-varying delay. Some new linear matrix inequality (LMI) representations of delay-dependent stability criteria are presented for the existence of the desired estimator for all admissible parametric uncertainties. The proposed method is based on the S-procedure and an extended integral inequality which can be deduced from the well-known Leibniz–Newton formula and Moon’s inequality. The results extend some models reported in the literature and improve conservativeness of those in the case that the derivative of the time-varying delay is assumed to be less than one. Two numerical examples are given to show the effectiveness and superiority of the results.     

Modified DM Models for Aging Networks Based on Neighborhood Connectivity

Two modified Dorogovtsev-Mendes （DM） models of aging networks based on the dynamics of connecting nearest-neighbors are introduced. One edge of the new site is connected to the old site with probability - kt^-α as in the DM＇s model, where the degree and age of the old site are k and t, respectively. We consider two cases, i.e. the other edges of the new site attaching to the nearest-neighbors of the old site with uniform and degree connectivity probability, respectively. The network structure changes with an increase of aging exponent α It is found that the networks can produce scale-free degree distributions with small-world properties. And the different connectivity probabilities lead to the different properties of the networks.     

Synchronization in delayed map lattices with scale-free interactions

In this paper, we study synchronization of delayed map lattices with scale-free interactions. By numerical simulations and theoretical analysis, we find that time delays influence the network synchronization but the heterogeneity seems to have little effect on network synchronization, yet no synchronization happens with the homogeneously topological structures.     

Adaptive local routing strategy on a scale-free network

Due to the heterogeneity of the structure on a scale-free network, making the betweennesses of all nodes become homogeneous by reassigning the weights of nodes or edges is very difficult. In order to take advantage of the important effect of high degree nodes on the shortest path communication and preferentially deliver packets by them to increase the probability to destination, an adaptive local routing strategy on a scale-free network is proposed, in which the node adjusts the forwarding probability with the dynamical traffic load (packet queue length) and the degree distribution of neighbouring nodes. The critical queue length of a node is set to be proportional to its degree, and the node with high degree has a larger critical queue length to store and forward more packets. When the queue length of a high degree node is shorter than its critical queue length, it has a higher probability to forward packets. After higher degree nodes are saturated (whose queue lengths are longer than their critical queue lengths), more packets will be delivered by the lower degree nodes around them. The adaptive local routing strategy increases the probability of a packet finding its destination quickly, and improves the transmission capacity on the scale-free network by reducing routing hops. The simulation results show that the transmission capacity of the adaptive local routing strategy is larger than that of three previous local routing strategies.     

应用荧光光谱和径向基函数神经网络定量检测三聚氰胺

实验发现三聚氰胺溶液在紫外光激发下产生较强荧光,测得其荧光峰在310～600 nm之间,荧光峰值波长为420 nm左右,荧光相对强度与三聚氰胺溶液浓度呈现复杂的非线性关系。提出了采用径向基函数神经网络结合荧光光谱对三聚氰胺溶液浓度进行测定的方法。对每个样本选取30个发射波长值所对应的荧光强度作为网络数据,训练、建立了径向基函数神经网络。应用训练好的径向基函数神经网络,对5种三聚氰胺溶液的浓度进行预测,结果相对误差分别为0.93%,0.09%,0.31%,1.55%,4.61%。该方法能快捷、准确地测定三聚氰胺在溶液中的含量,为三聚氰胺检测及食品安全监管提供了一种新方法。