Analysis of a Class of Symmetric Equilibrium Configurations for a Territorial Model

<正>Motivated by an animal territoriality model,we consider a centroidal Voronoi tessellation algorithm from a dynamical systems perspective.In doing so,we discuss the stability of an aligned equilibrium configuration for a rectangular domain that exhibits interesting symmetry properties.We also demonstrate the procedure for performing a center manifold reduction on the system to extract a set of coordinates which capture the long term dynamics when the system is close to a bifurcation.Bifurcations of the system restricted to the center manifold are then classified and compared to numerical results.Although we analyze a specific set-up,these methods can in principle be applied to any bifurcation point of any equilibrium for any domain.     

冲击载荷作用下裂纹动态响应的数值模拟

对垂直、剪切以及斜向等各种冲击载荷作用下裂纹的动态响应进行了数值模拟,得到了一系列随时间变化的动态应力场以及应变场图;根据其定义,计算出了相应的动态应力强度因子,进而分析了斜向载荷作用下裂纹起裂情况,并对最优断裂问题进行了阐述。     

45钢柱壳膨胀断裂的应变率效应

采用前照明高速分幅照相技术拍摄到在爆轰加载下45钢柱壳表面裂纹生成、扩展及产物泄漏过程的清晰图像,较准确地测量了膨胀断裂的时间与应变。 45钢柱壳在炸药爆轰加载下,断裂应变随应变率的增加而增加,当应变率达到一定值,断裂应变随应变率的增加而降低,出现了动态断裂中的塑性峰现象。     

具源项的奇异扩散方程解的存在性及渐近性

讨论了一类具源项的奇异扩散方程的第二初边值问题,证明了经典解的存在性以及时间充分大时解的渐近性质.     

具奇性系数p-Laplace方程解的熄灭性质

主要利用Hardy不等式及Soblev嵌入定理讨论了具奇性系数的P-Laplace方程解的熄灭性质.     

Asymptotic behavior of positive solutions of semilinear elliptic equations in ℝ n , II

In this paper, we will analyze further to obtain a finer asymptotic behavior of positive solutions of semilinear elliptic equations in R^n by employing the Li＇s method of energy function.     

On the limitations of classical benchmark functions for evaluating robustness of evolutionary algorithms

Although evolutionary algorithms (EAs) have some operators which let them explore the whole search domain, still they get trapped in local minima when multimodality of the objective function is increased. To improve the performance of EAs, many optimization techniques or operators have been introduced in recent years. However, it seems that these modified versions exploit some special properties of the classical multimodal benchmark functions, some of which have been noted in previous research and solutions to eliminate them have been proposed.In this article, we show that quite symmetric behavior of the available multimodal test functions is another example of these special properties which can be exploited by some EAs such as covariance matrix adaptation evolution strategy (CMA-ES). This method, based on its invariance properties and good optimization results for available unimodal and multimodal benchmark functions, is considered as a robust and efficient method. However, as far as black box optimization problems are considered, no special trend in the behavior of the objective function can be assumed; consequently this symmetry limits the generalization of optimization results from available multimodal benchmark functions to real world problems. To improve the performance of CMA-ES, the Elite search sub-algorithm is introduced and implemented in the basic algorithm. Importance and effect of this modification is illustrated experimentally by dissolving some test problems in the end.     

Oscillation criteria for second order nonlinear neutral differential equations

By refining the standard integral averaging technique, we obtain new oscillation criteria for a class of second order nonlinear neutral differential equations of the form

(r(t)(x(t)+p(t)x(t-τ))^′)^′+q(t)f(x(t),x(σ(t)))=0.     

Asymptotic behavior of the periodic wave solution for the (3+1)-dimensional Kadomtsev-Petviashvili equation

In this paper, the one- and two-periodic wave solutions for the (3+1)-dimensional Kadomtsev-Petviashvili equation are presented by means of the Hirota’s bilinear method and the Riemann theta function. The rigorous proofs on asymptotic behaviors of these two solutions are given that soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure.     

Reconstruction of cracks of different types from far‐field measurements

In this paper, we deal with the acoustic inverse scattering problem for reconstructing cracks of possibly different types from the far‐field map. The scattering problem models the diffraction of waves by thin two‐sided cylindrical screens. The cracks are characterized by their shapes, the type of boundary conditions and the boundary coefficients (surface impedance). We give explicit formulas of the indicator function of the probe method, which can be used to reconstruct the shape of the cracks, distinguish their types of boundary conditions, the two faces of each of them and reconstruct the possible material coefficients on them by using the far‐field map. To test the validity of these formulas, we present some numerical implementations for a single crack, which show the efficiency of the proposed method for suitably distributed surface impedances. The difficulties for numerically recovering the properties of the crack in the concave side as well as near the tips are presented and some explanations are given. Copyright © 2009 John Wiley & Sons, Ltd.