SPH粒子初始化均布方法及其均布质量评价

光滑粒子流体动力学(SPH)是一种拉格朗日型无网格粒子法,粒子均布程度是影响SPH分析精度和稳定性的重要因素.本文基于射线法提出了一种在异形多边形区域内均布SPH粒子的方法,先在多边形的最小外包矩形范围内均布粒子,再通过射线法和辅助筛选条件保留区域内的粒子;通过生成粒子的Voronoi多边形计算其变异系数值(Cv),作为SPH粒子均布质量的评价标准,其值越小,粒子均布质量越高.为验证该方法提高分析精度的有效性,基于爆轰侵彻的经典实验,建立由经典三角形和四边形均布粒子法构建的模型甲、模型乙和本文模型丙,用LS-DYNA中的SPH模块进行仿真分析.研究表明,模型丙的Cv分别比模型甲和模型乙低4.88%和5.22%;模型甲、乙和丙射流头部速度分别为5 960、5 900和6 060 m/s,较经典实验的6 100 m/s分别相差2.3%、3.3%和0.7%,相对于模型甲和模型乙,模型丙计算精度提高了1.6%和2.6%.因此,本文方法可快速有效地均匀布置SPH粒子,提高分析精度.     

Modeling rock fragmentation by coupling Voronoi diagram and discretized virtual internal bond

The rock fragmentation involves the inter-block and the intra-block fracture. A simulation method for rock fragmentation is developed by coupling Voronoi diagram (VD) and discretized virtual internal bond (DVIB). The DVIB is a lattice model that consists of bonds. The VD is used to generate the potential block structure in the DVIB mesh. Each potential block may contain any number of bond cells. To characterize the inter-block fracture, a hyperelastic bond potential is employed for the bond cells that are cut by the VD edges. While to characterize the intra-block fracture, an elastobrittle bond potential is adopted for the bonds in a block. By this method, both the inter-block and intra-block fracture can be well simulated. The simulation results suggest that this method is a simple and efficient approach to rock fragmentation simulation with block smash.     

基于BP神经网络的小样本星图识别方法

为解决星敏感器的星图识别算法高实时性和鲁棒性,采用了BP神经网络;根据飞行轨迹精简了导航星及对应的模式,即一个视场中的一幅星图对应一个惟一的导航模式。采用二维Voronoi图计算向平面上最大空圆,构造了完备的圆视场集合;经过反复比较,选择以恒星为顶点能构造包含视场中所有星的凸多边形的导航模式,以其角距和顶角作为识别向量,具有平移和旋转不变性,并以该模式为BP神经网络的训练样本。仿真试验表明：该方法的识别成功率达100%,识别时间小于20ms。     

Cooperative Sensing and Distributed Control of a Diffusion Process Using Centroidal Voronoi Tessellations

<正>This paper considers how to use a group of robots to sense and control a diffusion process.The diffusion process is modeled by a partial differential equation (PDE),which is a both spatially and temporally variant system.The robots can serve as mobile sensors,actuators,or both.Centroidal Voronoi Tessellations based coverage control algorithm is proposed for the cooperative sensing task.For the diffusion control problem,this paper considers spraying control via a group of networked mobile robots equipped with chemical neutralizers,known as smart mobile sprayers or actuators,in a domain of interest having static mesh sensor network for concentration sensing.This paper also introduces the information sharing and consensus strategy when using centroidal Voronoi tessellations algorithm to control a diffusion process.The information is shared not only on where to spray but also on how much to spray among the mobile actuators.Benefits from using CVT and information consensus seeking for sensing and control of a diffusion process are demonstrated in simulation results.     

Location of a semi-obnoxious facility with elliptic maximin and network minisum objectives

This paper considers the problem of locating a single semi-obnoxious facility on a general network, so as to minimize the total transportation cost between the new facility and the demand points (minisum), and at the same time to minimize the undesirable effects of the new facility by maximizing its distance from the closest population center (maximin). The two objectives employ different distance metrics to reflect reality. Since vehicles move on the transportation network, the shortest path distance is suitable for the minisum objective. For the maximin objective, however, the elliptic distance metric is used to reflect the impact of wind in the distribution of pollution. An efficient algorithm is developed to find the nondominated set of the bi-objective model and is implemented on a numerical example. A simulation experiment is provided to find the average computational complexity of the algorithm.     

A new lower bound on the surface area of a Voronoi polyhedron

Summary We prove that the mininum surface area of a Voronoi cell in a unit ball packing in <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>{\mathbb E}^3$ is at least $16.1977$. This result provides further support for the Strong Dodecahedral Conjecture according to which the minimum surface area of a Voronoi cell in a $3$-dimensional unit ball packing is at least as large as the surface area of a regular dodecahedron of inradius $1$, which is about $16.6508\ldots\,$.     

On the Asymptotic Uniformity of the Quantization Error for Moran Measures on ℝ 1

Let E be a Moran set on ℝ1 associated with a bounded closed interval J and two sequences     

Farthest-polygon Voronoi diagrams

Given a family of k disjoint connected polygonal sites in general position and of total complexity n, we consider the farthest-site Voronoi diagram of these sites, where the distance to a site is the distance to a closest point on it. We show that the complexity of this diagram is O(n), and give an O(nlog³n) time algorithm to compute it. We also prove a number of structural properties of this diagram. In particular, a Voronoi region may consist of k−1 connected components, but if one component is bounded, then it is equal to the entire region.     

Higher moments of certain <Emphasis Type="Italic">L</Emphasis>-functions on the critical line

We study the sixth-power moments of certain L-functions belonging to a sub-class of the Selberg’s class on the critical line and, using this, we conclude an upper bound for the fourth-power moments of certain L-functions related to GL ₃ on the critical line. This is an analogue of the upper bound for the twelfth-power moment of the Riemann zeta-function on the critical line. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 341–380, July–September, 2007.     

A nearest neighbor sweep circle algorithm for computing discrete Voronoi tessellations

An algorithm for computing discrete, 2-dimensional, Euclidean Voronoi tessellations is presented. The algorithm combines a limiting sweep circle approach with a nearest neighbor cellular approach. It reduces the computational cost of the naïve approach while at the same time giving the Euclidean Voronoi tessellations that simple nearest neighbor algorithms are unable to produce. The algorithm is shown, through analytical methods, to produce good approximations to corresponding continuous Voronoi tessellations depending on the definition of neighbor used in the nearest neighbor step and the mesh size. The quality of different types of neighbor definitions are discussed as well as the computational cost. The algorithm is general enough to be easily extended to higher dimensions and nonuniform meshes. The analysis lays the groundwork for the computation of discrete centroidal Voronoi tessellations where some kind of numerical integration is required.