The gravitational potential of a homogeneous polyhedron or don't cut corners

A polyhedron can model irregularly shaped objects such as asteroids, comet nuclei, and small planetary satellites. With minor effort, such a model can incorporate important surface features such as large craters. Here we develop closed-form expressions for the exterior gravitational potential and acceleration components due to a constant-density polyhedron. An equipotential surface of Phobos is illustrated.     

Mineralogy and crystal structure determination of Mg-fillowite

Accurate crystal structure determination of complex phosphate Mg-fillowite.—Na₂Ca(Mn₄Mg₂Fe)₇[PO₄]₆ has been finished. Mg-fillowite occurs in muscovite-pegmatite in the Altay area, Xinjiang, China. It is of the trigonal lattice, with space group R-3, unit cell a=1.5143(3)nm, c=4.3191(2) nm, V=8.5736 nm³, Z = 18. The R-factor of the determination accuracy is R (I<2 σ(I)) = 0.0776. The cationic polyhedra consist of two kinds of structural units: compound column and screw column. In three-dimensional space, they are linked with each other through corner sharing or edge sharing to build the entire structure. There are 45 atoms in an asymmetric unit and 720 atoms in a unit cell. In terms of types and connection manners of the coordination polyhedra, the degree of complicity is rarely seen in all mineral crystal structures. Study of such a structure is significant for the classification of phosphate and the building rule of coordination polyhedra in a complex crystal structure.     

Volcanic ash and tsunami record of the Minoan Late Bronze Age Eruption (Santorini) in a distal setting,southwestern Turkey

We present the volcanic ash and tsunami record of the Minoan Late Bronze Age Eruption of Santorini (LBAES) in a distal setting in southwestern Turkey. In one of the drilled cores at the Letoon Hellenic antique site on Eşençay Delta, we encountered a 4 cm thick tephra deposit underlain by 46 cm thick tsunami-deposited sand (tsunamite), and an organic-rich layer that we ¹⁴C dated to 3295 ± 30 bp or 1633 bc. The relationship between Santorini distal volcanic ash and underlying tsunamite is described and interpreted. LBAES occurred in four main phases: (1) plinian; (2) phreatomagmatic; (3) phreatomagmatic with mudflows; and (4) ignimbritic flows and co-ignimbrite tephra falls. In this study, we aim to understand which eruptive phases generate distal ash during the Minoan eruptive sequence by examining the 3D surface morphology of ash formed by different fragmentation processes. To that end, we used numerous statistical multivariates, 3D fractal dimension of roughness, and a new textural parameter of surface area-3D/plotted area-2D to characterise the eruption dynamics. Based on ash surface morphologies and the calculated statistical parameters, we propose that that distal ash is represented by a single layer composed of well-mixed (coarse to fine) magmatic and phreatomagmatic ash.     

区域多维发展综合测度方法及应用

借鉴国内外区域发展研究从单要素、单指标走向多要素、多指标综合测度的学术思路,从收入、消费、教育、人口城镇化、交通及生活设施等6个维度选择了12个指标,建立了多面体法区域多维发展综合测度方法及模型,改建了适用于区域多维发展综合测度的多边形法和向量和法定量模型,并与已得到广泛应用的加权求和法一起按县级、地级和省级单元对中国的区域多维发展状况进行了综合测度实证研究。结果表明：不同维度单项指标值和区域多维发展指数在全国各县级单元之间存在着显著差异;区域多维发展指数在空间分布上呈现出东部沿海高、中部及北方沿边地区中等、西南及西部沿边地区低的基本格局,高和较高类型区主要分布在东部沿海、中西部城市以及能矿资源开发地区,低和较低类型区基本上与国家新认定的集中连片贫困区的分布一致;按县级、地级和省级不同尺度单元,借助SPSS和EXCEL软件对4种方法测算结果的相关性分析表明,多面体法、多边形法、向量和法、加权求和法在实际应用中具有等效性,选用任何一种方法都能达到区域多维发展综合测度和评价的目的。     

REVIEWS OF GEOGRAPHIC SOFTWARE

Geographic Software Reviewed in this article: RUNMOD . Colin Prowse and Sima Yazdani . STATE DATA SYSTEM. Dave Garson . PC-DRAW DOCUMAP . Carl Youngman . SITE EVALUATION AND LOCATION SYSTEM (SELS) . Douglas Love and Jerome Deichert .     

冰脊形成过程的离散元模拟及影响因素分析

冰脊对极地船舶及海洋工程结构的冰载荷设计及冰区安全运行具有重要的影响,其几何形态是重要的考虑因素。为研究冰脊的几何形态,本文基于Voronoi切割算法构造扩展多面体海冰单元,并使其相互冻结形成平整冰;采用离散单元法模拟海冰在相对运动时挤压形成冰脊的动力过程,统计分析脊帆高度、龙骨宽度、龙骨深度、龙骨水平倾角等主要几何参数,并确定这些几何参数间的对应关系。将离散元模拟结果同冰脊现场观测资料对比分析以验证扩展多面体离散元方法模拟冰脊形成过程的可行性。在此基础上讨论冰厚、冰速、海冰强度等因素对冰脊形态的影响。本文采用离散元方法对冰脊形成过程及几何特性的数值分析可为深入开展冰脊的形成机理及其对船舶、海洋工程结构物的冰载荷分析提供参考依据。     

(Ca_(0.5),□_(0.5))BaCe_2(CO_3)_4F矿物晶体结构的测定

(Ca0.5□0.5)BaCe2(CO3)4F属于六方晶系,晶胞参数为:a=b=5.093(6),c=23.017(6),r=120°,Z=2。用强功率四圆单晶衍射仪在2=2—65°范围内共收集到821个原始衍射强度数据。晶体结构主要靠重原子法解出,采用空间群P62C,根据344个独立衍射点经多轮最小二乘修正后,获得其全部原子的三维坐标、占位度、各向同性及各向异性温度因子等参数,最终的偏离因子R=0.05。     

基于面片集合的三维地籍产权体的拓扑自动构建

在三维地籍应用需求下,分析当前三维表达和自动构造三维几何体的难点和不足;发展基于面片结构的三维拓扑数据模型,指出三维构体时对面片的基本空间约束;提出基于共享边的离散面片集合来自动构建最小三维封闭体及其拓扑关系的方法,并将该方法用于三维地籍的产权体构建和拓扑建立上,在群集产权体构建上体现较强适宜性,为实现三维产权体的管理提供技术方法。