Estimating tail probabilities of heavy tailed distributions with asymptotically zero relative error

Efficient estimation of tail probabilities involving heavy tailed random variables is amongst the most challenging problems in Monte-Carlo simulation. In the last few years, applied probabilists have achieved considerable success in developing efficient algorithms for some such simple but fundamental tail probabilities. Usually, unbiased importance sampling estimators of such tail probabilities are developed and it is proved that these estimators are asymptotically efficient or even possess the desirable bounded relative error property. In this paper, as an illustration, we consider a simple tail probability involving geometric sums of heavy tailed random variables. This is useful in estimating the probability of large delays in M/G/1 queues. In this setting we develop an unbiased estimator whose relative error decreases to zero asymptotically. The key idea is to decompose the probability of interest into a known dominant component and an unknown small component. Simulation then focuses on estimating the latter ‘residual’ probability. Here we show that the existing conditioning methods or importance sampling methods are not effective in estimating the residual probability while an appropriate combination of the two estimates it with bounded relative error. As a further illustration of the proposed ideas, we apply them to develop an estimator for the probability of large delays in stochastic activity networks that has an asymptotically zero relative error.      

双对数模型对模型模拟误差的放缩问题探讨

对双对数模型lg Y=a0+a1lg X1+a2lg X2+…+anlg Xn与其对应的指数模型y=c0xa11xa22…xann的模拟相对误差的关系进行了探讨,指出双对数模型具有放大和缩小指数模型相对误差的特性.对二者的关系进行了理论推导和实例验证,并给出了二者的定量关系式.     

LES-DSMC方法研究超细颗粒气固两相流动过程

采用考虑颗粒脉动流动对气相湍流流动影响的大涡模拟(LES)研究气相湍流,采用直接模拟蒙特卡罗方法(DSMC)模拟颗粒间的碰撞。单颗粒运动满足牛顿第二定律,颗粒相和气相相间作用的双向耦合由牛顿第三定律确定,考虑超细颗粒间的van der Waals作用力。数值模拟垂直管内超细颗粒气固两相流动,对颗粒相速度、浓度以及团聚物流动过程进行分析。     

轴流式水轮机三维非定常湍流计算及压力脉动预测

水轮机的稳定性研究是目前工程上大型水轮机组流动分析的重要课题,本文以某水电站的大型轴流转桨式水轮机原型为基础建立计算模型,完成了从蜗壳进口到尾水管出口整个流道的非定常湍流计算,预测了固定导叶进口、转轮后、尾水管进口等多个位置的压力脉动,并利用FFT变换进行分析得到了压力脉动的频率和幅值,探讨了水轮机全流道内压力脉动产生和传播的原理．     

Memory management optimization problems for integrated circuit simulators

In hardware design, it is necessary to simulate the anticipated behavior of the integrated circuit before it is actually cast in silicon. As simulation procedures are long due to the great number of tests to be performed, optimization of the simulation code is of prime importance. This paper describes two mathematical models for the minimization of the memory access times for a cycle-based simulator.An integrated circuit being viewed as a directed acyclic graph, the problem consists in building a graph order on the vertices, compatible with the relation order induced by the graph, in order to minimize a cost function that represents the memory access time. For both proposed cost functions, we show that the corresponding problems are NP-complete. However, we show that the special cases where the graphs are in-trees or out-trees can be solved in polynomial time.     

钱塘江河口弯道潮流场的数值模拟

钱塘江河口潮流错综复杂．依靠零星的实测潮流资料无法全面描述其流场特征．本文采用Dcldt3D模型对钱塘江河口闻家堰至仓前河段的潮流场进行二维数值模拟．着重研究了河口弯道的流场特性．结果表明．河口弯道流场具有跟无潮河流弯道显著不同的特性．如弯道流速向下游递增；涨、落急主流线分歧；涨、落潮流对丁坝工程的响应不同．以及下游弯道水面横比降大于上游弯道．     

全息模拟再现像的三维重构

提出一种全息模拟再现像的三维重构方法，可以模拟再现得到三维再现像.计算机模拟再现许多幅在不同深度位置的二维光强分布；利用灰度级变化的聚焦度评价方法，通过寻找最大聚焦度值，确定再现三维像各像点的深度信息.实验证明,该方法能实现模拟再现像的三维重构，使数字全息术有希望成为一种全新的三维面形检测技术.再现像三维重构的实现可以更客观地对全息图进行像质评价，并验证计算机制全息术算法的正确性.     

采用光纤和YAP晶体的小型γ相机的蒙特卡罗模拟

基于波长位移光纤(WSF)耦合YAP晶体中的光子传输特性，用GEANT4软件包建立了一个蒙特卡罗模拟程序.对采用波长位移光纤耦合平板式YAP晶体的小型单管γ相机的性能进行了计算机模拟.采用波长位移光纤耦合光电倍增管光阴极面的读出方式，和晶体直接耦合光电倍增管光阴极面相比，在相同的晶体面积大小条件下，PSPMT光阴极面积可大大缩小，使费用降低.模拟结果表明：γ射线与晶体发生作用的地方所对应的光纤输出的平均光子数最少为15个，位置灵敏光电倍增管完全可以探测到.说明采用闪烁晶体－WSF－位置灵敏光电倍增管的读出方式是可行的；在用硅油耦合波长位移光纤和YAP晶体的情况下，获得的空间分辨率为1.28 mm(FWHM).模拟结果也说明了增加平均光子数对提高空间分辨率的重要性.     

各向同性湍流中颗粒引起湍流变动的直接模拟

本文通过直接数值模拟对均匀各向同性湍流中颗粒对湍流的变动作用进行了研究.颗粒相的体积分数很小而质量载荷足够大,以至于颗粒之间的相互作用可以忽略不计,而重点考虑颗粒与湍流间能量的交换。颗粒对湍流的反向作用使得湍动能的耗散率增强,以至于湍动能的衰减速率增大.湍动能的衰减速率随颗粒惯性的增大而增大。三维湍动能谱显示,颗粒对湍动能的影响在不同的尺度上是不均匀的。在低波数段,流体带动颗粒,而高波数段则相反.     

外加磁场微波等离子推力器内流场数值模拟

为了提高微波等离子推力器性能，改善等离子体对电磁波能量的吸收状况，提高核心区温度，提出外加磁场的方案，并对热等离子体进行了数值模拟.假设局域热平衡条件，采用Navier-Stokes，Maxwell和Saha方程，利用压力修正的半隐格式和时域有限差分求解方法，建立了径向磁镜场下推力器内等离子体流场的数值计算模型.数值模拟结果表明：外加磁场后的磁感应强度小于0.5 T时，推力器内热等离子体核心区最高温度随磁感应强度的增加而迅速提高.外加磁场后的磁感应强度大于0.5 T时，核心区最高温度随磁感应强度的增加而缓慢提高.磁感应强度为0.5 T时，热等离子体核心区最高温度与不加磁场相比提高了24%.外加磁场对等离子体流场速度分布影响不大. 关键词： 等离子体模拟 等离子体相互作用 等离子体流动