STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,

MODE Ⅰ AND MODE Ⅱ CRACK TIP ASYMPTOTIC FIELDS WITH STRAIN GRADIENT EFFECTS

The strain gradient effect becomes significant when the size of frac- ture process zone around a crack tip is comparable to the intrinsic material length l, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dom- inant strain field is irrotational. For mode Ⅰ plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist si- multaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode Ⅱ plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode Ⅱ plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode Ⅰ and mode Ⅱ, because the present theory is based only on the rotational gradi- ent of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient.

Higher order asymptotic fields for mode Ⅰ crack in functionally gradient material

Higher order stress fields for a mode Ⅰ crack perpendicular to the direction of property variation in a functionally gradient material(FGM), which has an exponential variation of elastic modulus along the gradient direction, were obtained through an asymptotic analysis. The Poisson’s ratio of the FGMs was assumed to be constant throughout the analysis. The first five terms in the asymptotic expansions of crack tip stress fields were derived to bring out the influence of nonhomogeneity on the structure of the stress field explicitly. The analysis reveals that only the higher order terms in the expansion are influenced by the material nonhomogeneity. Moreover, it can be seen from expressions of higher order stress fields that at least three terms must be considered in the case of FGMs in order to explicitly account for the nonhomogeneity effects on the structure of crack tip stress fields.

AN INVESTIGATION ON ASYMPTOTIC NEAR-TIP FIELDS OF DYNAMIC CRACK IN AN ELASTIC-PERFECTLY PLASTIC COMPRESSIBLE MATERIAL

The stress and deformation fields near the tip of a mode-I dynamic crack steadily propagating in an elastic-perfectly plastic compressible material are considered under plane strain conditions. Within the framework of infinitesimal displacement gradient theory, the material is characterized by the Von Mises yield criterion and the associated J(2) flow theory of plasticity. Through rigorous mathematical analysis, this paper eliminates the possibilities of elastic unloading and continuous asymptotic fields with singular deformation, and then constructs a fully continuous and bounded asymptotic stress and strain field. It is found that in this solution there exists a parameter phi(0) which cannot be determined by asymptotic analysis but may characterize the effect of the far field. Lastly the variations of continuous stresses, velocities and strains around the crack tip are given numerically for different values of phi(0).

The Rate of Asymptotic Normality of Frequency Polygon Density Estimation for Spatial Random Fields

This paper is to investigate the convergence rate of asymptotic normality of frequency polygon estimation for density function under mixing random fields, which include strongly mixing condition and some weaker mixing conditions. A Berry-Esseen bound of frequency polygon is established and the convergence rates of asymptotic normality are derived. In particularly, for the optimal bin width , it is showed that the convergence rate of asymptotic normality reaches to ?when mixing coefficient tends to zero exponentially fast.

压电材料切口奇异物理场计算

采用切口尖端奇性特征分析与有限元法相结合的思路,计算压电材料切口尖端的力学和电学奇异物理场.首先基于奇性渐近展开技巧,推演压电材料切口的奇性特征方程,引入插值矩阵法求解,获得切口尖端奇性渐近展开式的奇性指数、特征角函数及其导数.再根据有限元法的位移和电势计算结果较应力和电位移高一阶精度的特点,利用稀疏有限元网格,计算出切口附近的位移和电势,代入切口尖端物理场渐近展开式,求出幅值系数.根据计算出的幅值系数、奇性指数、特征角函数及其导数,重构出切口尖端附近的奇异应力场和电位移场,继而计算出切口的应力强度因子和电位移强度因子.本文提出半解析方法,基于有限元稀疏网格计算结果,利用较小的计算量,获得较高精度的奇异物理场.该方法无须对有限元法的插值函数进行改造,适合嵌入商业有限元软件,直接用于工程压电材料结构安全分析.

带散射体的电力系统多级传输线高频耦合模型

高频电磁场会与架空输电线路产生耦合,一旦高频电磁场的波长小于传输线的高度,经典传输线理论就不再适用。传统的全波数值算法虽然可以解决这一问题,但求解效率不高,需要消耗大量的时间与计算资源。此外,电力系统输电线路往往有多个垂直端,线路布局复杂,而以往针对电力系统传输线的高效求解研究都是只有左右两个垂直端的较为简单的模型,与实际电力系统传输线的结构不符,没有考虑中间带有垂直端的情况。为了解决这些问题,文中提出一种理论有效的方法来解决有损耗地面上方带有散射体的电力系统多级传输线的高频电磁场耦合问题。采用计算效率高的渐近法,并在渐近法中引入散射体的概念,以考虑更复杂的电路结构。最后通过数值算例验证了该方法的准确性和有效性。

高功率微波天线电磁仿真方法研究进展

高功率微波(high-power microwave,HPM)天线作为HPM系统与外界交互能量的通道,其对HPM系统的性能具有重要的影响。设计HPM天线时,受制于有限的测量手段和高昂的实验成本,难以通过实验方法对HPM天线性能进行分析。相较于实验方法,高效精确的电磁仿真方法是分析HPM天线性能最有效、最经济的研究手段。目前,HPM天线主流电磁仿真方法包括:全波仿真方法、高频渐近方法以及混合方法。本文对近年来HPM天线电磁仿真方法的新进展进行了介绍,总结了各种电磁仿真方法的优缺点,可为HPM天线性能仿真方法的选取提供思路。

The asymptotic field of mode Ⅰ quasi-static crack growth on the interface between a rigid and a pressure-sensitive material

A mechanical model of the quasi-static interface of a mode I crack between a rigid and a pressure-sensitive viscoelastic material was established to investigate the mechanical characteristic of ship-building engineering hi-materials. In the stable growth stage, stress and strain have the same singularity, ie （σ, ε） ∝ r^-1/（n-1）. The variable-separable asymptotic solutions of stress and strain at the crack tip were obtained by adopting Airy＇s stress function and the numerical results of stress and strain in the crack-tip field were obtained by the shooting method. The results showed that the near-tip fields are mainly governed by the power-hardening exponent n and the Poisson ratio v of the pressure-sensitive material. The fracture criterion of mode I quasi-static crack growth in pressure-sensitive materials, according to the asymptotic analyses of the crack-tip field, can be viewed from the perspective of strain.

HIGHER-ORDER ANALYSIS OF NEAR-TIP FIELDS AROUND AN INTERFACIAL CRACK BETWEEN TWO DISSIMILAR POWER LAW HARDENING MATERIALS

By means of an asymptotic expansion method of a regular series, an exact higher-order analysis has been carried out for the near-tip fields of an in- terfacial crack between two different elastic-plastic materials. The condition of plane strain is invoked. Two group of solutions have been obtained for the crack surface conditions: (1) traction free and (2) frictionless contact, respectively. It is found that along the interface ahead of crack tip the stress fields are co-order continuous while the displacement fields are cross-order continuous. The zone of dominance of the asymptotic solutions has been estimated.

Asymptotic solutions for the asymmetric flow in a channel with porous retractable walls under a transverse magnetic field

The self-similarity solutions of the Navier-Stokes equations are constructed for an incompressible laminar flow through a uniformly porous channel with retractable walls under a transverse magnetic field. The flow is driven by the expanding or contracting walls with different permeability. The velocities of the asymmetric flow at the upper and lower walls are different in not only the magnitude but also the direction. The asymptotic solutions are well constructed with the method of boundary layer correction in two cases with large Reynolds numbers, i.e., both walls of the channel are with suction, and one of the walls is with injection while the other one is with suction. For small Reynolds number cases, the double perturbation method is used to construct the asymptotic solution. All the asymptotic results are finally verified by numerical results.

HIGHER ORDER ASYMPTOTIC SOLUTION OF MODE Ⅰ CRACK GROWTH IN ELASTIC-PERFECTLY PLASTIC MEDIA

A higher order asymptotic solution of near-tip field is studied for plane-atrain Mode-Ⅰ quasi-static steady crack growth in the incompressible (v=1/2) elastic perfectly-plastic media.The results show that the near-tip stress and strain are fully continuous,and the strain possesses In (A/r) singularity at the crack tip.The expressions of the stress,strain and velocity in each region are also given.

POWER LAW NONLINEAR VISCOELASTIC CRACK-TIP FIELDS

The aim of this paper is to derive the power law type nonlinear viscoelastic crack-tip fields.For the requirement of later derivation,the HRR singular fields and the high-order asymp- totic fields are first examined.That they are essentially the isotropic,incompressible,power law type nonlinear elastic crack-tip fields is illustrated.After a concise review of the elasticity recov- ery correspondence principle for solving the nonlinear viscoelastic problems,the correspondence principle for solving the crack problems of power law type nonlinear viscoelastic materials under the first type boundary condition is proposed.The solution of the crack-tip stress,strain fields for the power law type nonlinear viscoelastic materials,especially for the modified polypropylene, is obtained.

THE NEAR TIP FIELDS AND TEMPERATURE DISTRIBUTION AROUND A CRACK IN A BODY OF HARDENING MATERIAL CONTAINING SMALL DAMAGE

In this paper, the following conclusions are reached: The influence of damage on the stress and strain feilds can be neglected in an asymptotic sense for the solutions of damage field in a plastic solid containing small damage. The formulation of the problem is simplified with an uncoupled approach. Based on experimental results of plastic damage, most of the damage in the material are con- sidered as small damage with the critacal damage variable ω_c<<1. Using this approach, closed form ex- pressions of the near tip damage fields for mode Ⅲ, mode I and the temperature distribution induced by plastic dissipation in a hardening material containing damage are deduced. We point out that the temperature distribution in the process zone is strongly dependent on the damage of materials even for the small damage case. The results of the predicted value of the temperature rise near the tip region ignoring the damage effect is appreciably higher than the observed data. The main reason of this discrepancy is the presence of damage dissipation and the fact that its influence on the calculation of plas- tic dissipation have not been appropriately taken account of. The calculation is improved by taking in- to account the damage effect on the temperature rise, then the T_(max) value is in better accord with the experimental value.

Crack tip higher order stress fields for functionally graded materials with generalized form of gradation

A generalized form of material gradation applicable to a more broad range of functionally graded materials(FGMs) was presented.With the material model,analytical expressions of crack tip higher order stress fields in a series form for opening mode and shear mode cracks under quasi-static loading were developed through the approach of asymptotic analysis.Then,a numerical experiment was conducted to verify the accuracy of the developed expressions for representing crack tip stress fields and their validity in full field data analysis by using them to extract the stress intensity factors from the results of a finite element analysis by local collocation and then comparing the estimations with the existing solution.The expressions show that nonhomogeneity parameters are embedded in the angular functions associated with higher terms in a recursive manner and at least the first three terms in the expansions must be considered to explicitly account for material nonhomogeneity effects on crack tip stress fields in the case of FGMs.The numerical experiment further confirms that the addition of the nonhomogeneity specific terms in the expressions not only improves estimates of stress intensity factor,but also gives consistent estimates as the distance away from the crack tip increases.Hence,the analytical expressions are suitable for the representation of crack tip stress fields and the analysis of full field data.

Asymptotic Behavior of Soliton Solutions with a Double Spectral Parameter for Principal Chiral Field

The soliton solutions with a double spectral parameter for the principal chiral field are derived by Darboux transformation. The asymptotic behavior of the solutions as time tends to infinity is obtained and the speeds of the peaks in the asymptotic solutions are not constants.

复杂多场景下机械臂避障运动规划方法研究

为提高工业机械臂在狭窄通道、多障碍物等复杂多场景下避障运动规划的成功率和效率,建立了基于圆柱体和球体包围盒机械臂与障碍物之间的碰撞检测模型,并提出了一种基于启发式概率融合人工势场法的改进型RRT^(*)算法(P-artificial potential field-RRT^(*),PAPF-RRT^(*))。采样上引入概率目标偏向与随机采样点优选策略,对采样点进行位置优选约束,增强采样导向性和质量;为改变传统新节点扩展方向和特殊环境下局部最优问题,融合人工势场法的目标引力与障碍物斥力和自适应步长,使算法在APF产生的合力范围下实时引导新节点扩展方向和步长大小,降低过度的探索和碰撞区域扩展;对冗余节点进行删除,并采用三次B样条插值优化,提高机械臂轨迹的柔顺性。仿真结果表明,所提算法较传统RRT^(*)算法在平均路径搜索时间上降低了56.75%,路径长度缩短了17.74%。导入机械臂模型后可视化仿真结果证明,所提算法可使机械臂成功避障且快速平稳运行到目标点。

ALMOST SURELY TIME-SPACE INTERMITTENCY FOR THE PARABOLIC ANDERSON MODEL WITH A LOG-CORRELATED GAUSSIAN FIELD

In this paper, we consider the continuous parabolic Anderson model with a logcorrelated Gaussian field, and obtain the precise quenched long-time asymptotics and spatial asymptotics. To overcome the difficulties arising from the log-correlated Gaussian field in the proof of the lower bound of the spatial asymptotics, we first establish the relation between quenched long-time asymptotics and spatial asymptotics, and then get the lower bound of the spatial asymptotics through the lower bound of the quenched long-time asymptotics.

渐近边界条件在轴对称无界高压静电场计算中的应用

将渐近边界条件技术引入到有限元数值计算方法中，计算了具有轴对称特性的两种典型高压电极无界静电场问题。结果表明：采用渐近边界条件后，计算结果具有较高的精度，可以尽可能地缩小人工边界的设置范围；该技术保留了有限元法的显著优点—系数矩阵的高度稀疏性和对称性；对于长宽比值较大的窄形电极问题，如采用人工边界为矩形的渐近边界条件，将会使计算效率显著提高。

刚性一粘弹性材料界面Ⅱ型裂纹准静态扩展的渐近解

在准静态扩展条件下 ,研究了刚性—粘性材料界面Ⅱ型裂纹尖端场的分布问题 .通过量级分析得出在粘性、弹性变形同时占主导地位时 ,应力、应变具有相同的奇异性量级 .推导了问题的控制方程、界面连接条件 ,求得了裂纹尖端应力场的渐近解 ,讨论了材料参数对场分布的影响 .由于在非稳态扩展中稳态场是占主导地位的 。