一类含脉冲的随机区间细胞神经网络模型的周期解和稳定性

讨论了一类含脉冲的S-分布时滞随机区间细胞神经网络的周期解和指数稳定性问题。利用随机分析的知识、不等式技巧和Poincaré压缩映像理论,研究了系统周期解的存在性和稳定性,得到了S-分布时滞随机细胞神经网络周期解的存在性和全局p阶指数稳定性的新代数判据,同时对周期解的指数收敛率进行了估计,最后通过例子说明了结果的实用性和有效性。     

具有任意阶非线性薛定谔方程的新行波解

对具有任意阶非线性薛定谔方程的行波解进行了研究。给出具有任意阶非线性薛定谔方程的精确解。利用行波变换和辅助函数法把具有任意阶非线性薛定谔方程最终转化为一个非线性常微分方程的解,通过对这个微分方程的研究可以得到具有任意阶非线性薛定谔方程的行波解。具有任意阶非线性薛定谔方程存在的孤立波解、三角孤立波解、扭孤立波解、Jacobi椭圆函数解。得到了具有任意阶非线性薛定谔方程新的Jacobi椭圆函数解。     

高频GPS动态监测地表形变的试验与研究

设计了位移形变模拟试验场并进行位移形变模拟试验,利用Bernese 5.0软件的单历元单点定位功能,处理并分析了位移模拟形变试验获取的1 Hz GPS数据.并以2008年5月12日汶川地震为例,获取了震中附近3个GPS站(成都、简阳和郫县)震前的短临位移过程及震后短时间的动态时变序列,结果显示各站的形变结果在时间上具有很好的一致性.利用动态时序的地震波到时和震中距离估计地震波地壳平均速度为3.17 km/s.     

花岗伟晶岩结构结晶动力学的研究进展

在地质流体演化方面,花岗伟晶岩位于花岗岩与热液石英脉的过渡位置,对其结构的实验研究对理解火成岩结构具有重要意义。长期以来,花岗伟晶岩被认为是花岗岩浆平衡结晶、缓慢冷却的结果,但近年来的一系列结晶动力学计算和实验发现伟晶岩在过冷却状态下快速生长,其结构主要受到结晶动力学参数的制约,F、B、P等助熔剂和H2O是影响这些参数的主要因素,富助溶剂的硅酸盐水溶液可作为伟晶岩的结晶介质。但由于快速淬火式实验设备的弊端,这些实验只能由淬火后的实验产物估算各类结晶动力学参数,只能以易淬火成玻璃的含水硅酸盐熔体作为结晶介质,只能静态地研究某一过冷却度下的结晶动力学状态。近年来,最新式热液金刚石压腔已经定型,可以模拟包括富助溶剂硅酸盐水溶液在内的各类伟晶岩结晶介质,能够在控制冷却速率的同时原位观测和微束分析晶体生长的动态特征,是模拟伟晶岩结构的理想工具,具有广阔的应用前景。     

The rectilinear three-body problem

The rectilinear equal-mass and unequal-mass three-body problems are considered. The first part of the paper is a review that covers the following items: regularization of the equations of motion, integrable cases, triple collisions and their vicinities, escapes, periodic orbits and their stability, chaos and regularity of motions. The second part contains the results of our numerical simulations in this problem. A classification of orbits in correspondence with the following evolution scenarios is suggested: ejections, escapes, conditional escapes (long ejections), periodic orbits, quasi-stable long-lived systems in the vicinity of stable periodic orbits, and triple collisions. Homothetic solutions ending by triple collisions and their dependence on initial parameters are found. We study how the ejection length changes in response to the variation of the triple approach parameters. Regions of initial conditions are outlined in which escapes occur after a definite number of triple approaches or a definite time. In the vicinity of a stable Schubart periodic orbit, we reveal a region of initial parameters that corresponds to trajectories with finite motions. The regular and chaotic structure of the manifold of orbits is mostly defined by this periodic orbit. We have studied the phase space structure via Poincaré sections. Using these sections and symbolic dynamics, we study the fine structure of the region of initial conditions, in particular the chaotic scattering region.     

Analytical solutions for the steady-state seepage field in a finite seabed with a lined tunnel

Abstract

Analytical solutions for the steady-state seepage field in a finite seabed under homogeneous and isotropic conditions with a drained circular lined tunnel are developed. A numerical model is established using the COMSOL Multiphysics software to verify the solutions presented in this study, and strong agreement is found. A parameter analysis considering the seabed thickness, coefficient of permeability, tunnel burial depth and lining thickness is presented. The results indicate that the error induced by ignoring the thickness of the seabed cannot be neglected when the tunnel is close to the bottom of the seabed.     

圆弧状凹陷地形在平面SH波入射下的动力响应：高频解答

利用波函数的Fourier-Bessel级数展开法和外域型Graf加法公式,推导了圆弧状凹陷地形对平面SH波二维散射问题的解析解。与现有其他解析解不同的是,该解析解的获得无须求解线性方程组,从而避免了高频波入射下方程组系数矩阵可能出现的病态问题。因此,既使在入射波频率很高的情况下,该解析解也能够收敛。利用该解,在一个非常宽的频带范围内讨论了凹陷地形的几何形状对地面运动的影响。     

Fast and accurate earthquake location within complex medium using a hybrid globallocal inversion approach

A novel hybrid approach for earthquake location is proposed which uses a combined coarse global search and fine local inversion with a minimum search routine, plus an examination of the root mean squares (RMS) error distribution. The method exploits the advantages of network ray tracing and robust formulation of the Fréchet derivatives to simultaneously update all possible initial source parameters around most local minima (including the global minimum) in the solution space, and finally to determine the likely global solution. Several synthetic examples involving a 3-D complex velocity model and a challenging source-receiver layout are used to demonstrate the capability of the newly-developed method. This new global-local hybrid solution technique not only incorporates the significant benefits of our recently published hypocenter determination procedure for multiple earthquake parameters, but also offers the attractive features of global optimal searching in the RMS travel time error distribution. Unlike the traditional global search method, for example, the Monte Carlo approach, where millions of tests have to be done to find the final global solution, the new method only conducts a matrix inversion type local search but does it multiple times simultaneously throughout the model volume to seek a global solution. The search is aided by inspection of the RMS error distribution. Benchmark tests against two popular approaches, the direct grid search method and the oct-tree important sampling method, indicate that the hybrid global-local inversion yields comparable location accuracy and is not sensitive to modest level of noise data, but more importantly it offers two-order of magnitude speed-up in computational effort. Such an improvement, combined with high accuracy, make it a promising hypocenter determination scheme in earthquake early warning, tsunami early warning, rapid hazard assessment and emergency response after strong earthquake occurrence.     

基于Levy-Mises本构关系及D-P屈服准则的轴对称圆巷理想弹塑性解

如何判断巷道开挖后在无支护反力条件下的围岩弹塑性变形及围岩应力重新分布的力学行为一直是人们研究的重点问题。卡斯特纳方程(Kastner equation)的求解存在以下不足和缺陷：(1) 对支护反力的力学处理存在缺陷,不具有工程实际意义;(2) 塑性区应力求解,没有使用到假设的理想弹塑性材料的塑性本构关系;(3) 塑性区应力求解,没有考虑沿巷道轴向方向的应力的影响。基于增量型本构关系即Levy-Mises关系及D-P屈服准则,对轴对称圆巷进行了理想弹塑性条件的求解。公式计算结果与卡斯特纳方程计算结果和数值模拟计算结果分别进行了对比分析。由于该求解弥补了卡斯特纳方程求解中忽略的3个问题,因此,其结果更具有理论意义和实践价值。     

条形埋置基础固结分析计算图表

基于比奥固结理论,用有限元方法研究了有限饱和土层中条形埋置基础的固结沉降特性。仔细分析了影响固结度的3个参数：基础埋深与土层厚度的比值;土层厚度与基础宽度的比值;土骨架的泊松比。根据分析结果,提出了归一化无量纲时间,并给出了计算条形埋置基础固结度的计算图表。这些图表为基础设计提供了便捷准确的计算方法。运用文中图表计算固结度的最大误差不超过3 %。