Implementation of the Integrated Green’s Function Method for 3D Poisson’s Equation in a Large Aspect Ratio Computational Domain

The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, the integrated Green’s function method has been adopted to solve the 3D Poisson equation subject to open boundary conditions. In this paper, we report on the efficient implementation of this method, which can save more than a factor of 50 computing time compared with the direct brute force implementation and its improvement under certain extreme conditions.

二维线性化Navier-Stokes-Poisson方程解的逐点估计

本文研究了二维空间线性化的等熵可压缩Navier-Stokes-Poisson方程柯西问题.通过把方程组转变成关于单个函数的方程,求解出各个函数,得到方程组的格林函数.利用对格林函数的详细分析,获得了方程组解的逐点估计.结果显示方程组中电流密度以热核的速度衰减,动量密度衰减慢得多,且其L2范数不衰减.

广义结构Poisson括号与Casimir函数

证明了广义结构Poisson括号恒等于零的相关结果并得到验证,改进了广义Poisson括号的Casimir函数的结果,并得到了一个推论。

带投资和分红策略下复合Poisson-Geometric风险模型的研究

考虑投资和分红策略下,建立带有混合收费及索赔计数服从复合Poisson-Geometric过程的风险模型。运用全期望公式与积分变换公式,研究该模型红利付款现值期望函数满足的微积分方程和特定指数分布下满足的微分方程及解析解,通过数值模拟分析了固定保费率、初始资本、投资资产、索赔强度和红利边界对红利付款现值期望函数的影响,并分析其经济意义。

ON THE RUIN FUNCTIONS FOR A CORRELATED AGGREGATE CLAIMS MODEL WITH POISSON AND ERLANG RISK PROCESSES

This article considers a risk model as in Yuen et al. （2002）. Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is derived for the distribution of the surplus immediately before ruin, for the distribution of the surplus immediately after ruin and the joint distribution of the surplus immediately before and after ruin. The asymptotic property of these ruin functions is also investigated.

Study of Crustal Thickness and Poisson Ratio of Hebei and Its Adjacent Areas by Teleseismic Receiver Function

We collected waveforms of a teleseismic event which occurred from January 2007 to October 2011 from 174 broadband seismic stations deployed in Hebei and its adjacent areas. Using the H-k stacking method,the average thickness and Poisson's ratio of the crust are acquired. In order to obtain reliable receiver functions, the broadband seismograms of 488 teleseismic earthquakes occurring in the epicentral distance range from 30° to 90° with magnitudes larger than Mb6. 0 are collected. The results show that crustal thickness have conspicuous lateral heterogeneity and have good correlation to the regional geological tectonic features. Poisson ratio's value is equated with the global models estimates which fluctuate at about 0. 25. Crustal thickness has positive correlation to the topography and the Taihang Mountains form the transition zone of thick and thin crustal thickness. There is an obvious difference in crustal thickness beneath the north and south of the Shanxi earthquake zone and the Poisson ratio of Datong,Ningwu and Anze basins is greater than 0. 3. The crustal thickness beneath the Zhang-Bo( Zhangjiakou-Bohai Sea)earthquake zone decreases from west to north and its Poisson ratio shows conspicuous lateral heterogeneity. The thin crust and low Poisson ratio in the Huabei( North China)basin may correlate with the delamination of the North China craton.

Study of crustal thickness and poisson's ratio of the south of Erenhot area by teleseismic receiver function

The Xing’an Mongolian Orogenic Belt(XMOB) and the northern margin of North China Craton(NCC) have undergone multistage tectonic superimposition and the tectonic evolution is extremely complicated. We collect the teleseismic data of 44 temporary broadband seismic stations deployed in the XMOB and the northern margin of NCC to calculate the P wave receiver functions. The crustal thickness and average crustal ratio as well as the Poisson’s ratios beneath 33 stations are estimated using the H-κ stacking method. The results show:(1) the crustal thickness of the study area ranges from 38.7 to 42.7 km, with an average thickness of 41.2 km. There is a great difference in crustal thickness on both sides of Solonker suture zone. The characteristics of crustal thickness support the geodynamic model that the Paleo-Asian Ocean subducted and closed at the Solonker suture zone.(2) The Poisson’s ratios in the study area are low, ranging from 0.215 to 0.277, with an average value of 0.243, suggesting that the rock composition of the area is dominated by felsic-acid rocks.(3) There exists a negative correlation between the Poisson’s ratio and the crustal thickness. Combined with the lower values of Poisson’s ratio, we speculate that the delamination is the major mechanism in crustal extension and thinning in the study area.

Solution of the Poisson-Boltzmann Equation for a Cylindrical Particle with a Limited Length: Functional Theoretical Approach

With the help of the method of separation of variables and the Debye-Hüchel approximation, the Poisson-Boltzmann equation that describes the distribution of the potential in the electrical double layer of a cylindrical particle with a limited length has been firstly solved under a very low potential condition. Then with the help of the functional analysis theory this equation has been further analytically solved under general potential conditions and consequently, the corresponding surface charge densities have been obtained. Both the potential and the surface charge densities cointide with those results obtained from the Debye-Hüchel approximation when the very low potential of zeψ〈〈kT is introduced.

含临界非局部项的Schrodinger-Poisson系统解的存在性

本文研究一类含临界非局部项和在无穷远处消失位势的Schrodinger-Poisson系统的非平凡解的存在性问题,利用变分方法获得了至少存在一个非平凡解的结果。

一种改进能量函数的显微图像拼接算法

针对传统最佳缝合线算法难以有效消除显微图像拼接后的拼接缝问题,提出一种基于最佳缝合线的图像融合优化算法。首先,利用ORB(oriented FAST and rotated BRIEF)算法对待拼接图像进行特征提取并定位重叠区域;其次,设计改进能量函数,结合动态规划技术,在重叠区域内有效搜索出最佳缝合线,基于这条缝合线,进一步采用改进融合方法有效融合两幅图像;最后,利用泊松融合方法消除重叠区域与非重叠区域之间存在的拼接缝,得到最终图像。实验结果显示,该方法将最佳缝合线两侧像素的相似度提高了5%左右,降低了能量损失,有效消除了拼接缝,提高了图像质量。

具有消失位势的Schrödinger-Poisson系统的可解性

利用山路引理、Hölder不等式、嵌入不等式和估值等,研究了一类含临界非局部项且位势在无穷远处消失的Schrödinger-Poisson系统的非平凡解的存在性.首先利用嵌入不等式证明了泛函具有紧性,然后利用截断函数对泛函进行了估值,最后用变分方法证明了该系统至少有一个非平凡解.所得结果丰富了椭圆型方程解的相关理论.

Constitutive Model for Rubberlike Materials

The isotropic continuum stored energy (CSE) functional, fully combined with the Poisson function, has been applied to constitutively model compressible as well as incompressible rubberlike materials. The isotropic CSE constitutive model fits uniaxial tension test and predicts unfitted pure shear and equibiaxial tension tests of incompressible S4035A thermoplastic elastomer (TPE). Furthermore, the isotropic CSE model along with the Poisson function fits uniaxial tension test along with the kinematic relation test and predicts unfitted pure shear and equibiaxial tension tests along with the corresponding kinematic relation tests of a compressible synthetic rubber. The detailed procedures for uniquely identifying constitutive parameters are emphasized, the experimental characterization results are discussed, and the principles for constitutive models are summarized and augmented.

有关流形上Poisson结构的几点讨论

讨论了微分同胚对Poisson流形上Poisson结构的保持 ,得到了微分同胚所诱导的Poisson括号的一些性质 ,最后 。

角色动画中基于隐式曲面的皮肤变形方法

提出了一种角色动画中基于隐式曲面的皮肤变形方法,主要面向具有骨骼层次以及相关蒙皮权重的动画模型,利用隐式曲面来驱动皮肤变形.首先,采用埃尔米特径向基函数和泊松圆盘采样对给定骨骼绑定的网格部分进行重建,把角色模型的体积近似当作一组局部的三维标量场,并保留原有的网格属性;其次,构造场函数,通过场函数纠正几何蒙皮技术的结果;最后,结合两种组合算子,使用隐式方法在人体模型上形成合理可信的皮肤变形效果.本方法不会产生糖纸扭曲和关节膨胀的问题,并且可以生成皮肤接触效果和肌肉凸起.由于该方法是后处理,因此非常适合标准动画制作流程.

利用Poisson积分推导Hotine函数及Hotine公式应用问题

给出一种直接利用改进的Poisson积分确定Hotine函数的推导 ,其中不包括函数的零阶和一阶项。讨论了Hotine公式在陆地和海洋局部重力场逼近中的应用问题。

纤维丛上的Poisson结构

在文[1]的基础上,将纤维丛理论与广义Hamilton系统理论相结合,得到了Poisson丛,进而讨论了Poisson丛的一些性质。

采用Poisson方程生成曲线网格时源项P、Q选择的研究

采用 Poisson方程进行曲线网格生成时 ,如何确定合适的调节因子 P、Q函数是网格生成技术中的一个重要的研究内容。本文提出一种新的构造 P、Q函数的方法 ,该方法直接利用边界网格节点的分布信息来控制区域内部网格节点的分布 ,生成的正交曲线网格令人满意。该方法可应用于河道、湖泊等一类复杂边界的二维流速场的数值模拟中。

基于航空重力梯度数据重建高分辨率局部重力场的径向基函数方法

基于径向基函数技术,研究了利用航空重力梯度数据重建局部重力场模型的方法,建立了泊松小波径向基函数和航空重力梯度张量之间的解析关系.以频率域变换和等效源方法为例讨论了不同梯度分量转换方法对重力场建模的影响,分析了基函数埋深深度对建模的影响.以澳大利亚珀斯Kauring试验场为例,采用实测航空重力梯度垂直分量构建了高分辨率重力场模型.结果表明,局部地形扰动对建模的影响较大,即使在平原或丘陵区域,也要考虑其影响.此外,不同梯度分量转换方法对于区域重力异常恢复的影响较小.再者,基函数埋深深度对建模影响较大;相比于采用重力数据建模而言,基于航空重力梯度数据求解时,基函数的适宜埋深深度更浅.联合航空重力梯度数据求解能显著提高重力场模型在高频和甚高频波段的分辨率和精度.与实测航空重力数据对比表明,利用航空重力梯度数据可构建分辨率约为0.15 km、精度优于1 mGal的重力场模型.

多元Poisson分布及其性质

首先给出了多元Poisson分布的一种定义,然后从研究其特征函数入手,讨论了多元Poisson分布的边缘分布、条件分布以及数字特征等一系列性质.最后给出了多元Poisson分布与多项分布以及多元正态分布之间的关系.

带Poisson跳和Markovian转换的随机时滞泛函微分方程数值解的收敛性（英文）

为了近一步研究带Poisson跳和Markovian转换的随机时滞泛函微分方程数值解的收敛性问题,文中给出带Poisson跳和Markovian转换的随机时滞泛函微分方程Euler数值解迭代格式.在弱条件下,利用Laypunov泛函方法和随机分析理论证明了数值解依概率收敛于方程的解.所得结果覆盖了许多非线性时滞微分方程已经存在的某些理论,而且实验说明此结论比以往的结论更容易验证.