Generation of a realistic 3D sand assembly using X‐ray micro‐computed tomography and spherical harmonic‐based principal component analysis

Three‐dimensional particle morphology is a significant problem in the discrete element modeling of granular sand. The major technical challenge is generating a realistic 3D sand assembly that is composed of a large number of random‐shaped particles containing essential morphological features of natural sands. Based on X‐ray micro‐computed tomography data collected from a series of image processing techniques, we used the spherical harmonics (SH) analysis to represent and reconstruct the multi‐scale features of real 3D particle morphologies. The SH analysis was extended to some highly complex particles with sharp corners and surface cavities. We then proposed a statistical approach for the generation of realistic particle assembly of a given type of sand based on the principle component analysis (PCA). The PCA aims to identify the major pattern of the coefficient matrix, which is made up of the SH coefficients of all the particles involved in the analysis. This approach takes into account the particle size effect on the variation of particle morphology, which is observed from the available results of micro‐computed tomography and QICPIC analyses of sand particle morphology. Using the aforementioned approach, two virtual sand samples were generated, whose statistics of morphological parameters were compared with those measured from real sand particles. The comparison shows that the proposed approach is capable of generating a realistic sand assembly that retains the major morphological features of the mother sand. Copyright © 2016 John Wiley & Sons, Ltd.     

Linear theory of rotating fluids using spherical harmonics part I: Steady flows

Abstract

It is shown that a systematic development of physical quantities using spherical harmonics provides analytical solutions to a whole class of linear problems of rotating fluids.

These solutions are regular throughout the whole domain of the fluid and are not much affected by the equatorial singularity of steady boundary layers in spherical geometries.

A comparison between this method and the one based on boundary layer theory is carried out in the case of the steady spin-up of a fluid inside a sphere.     

Transitions to chaotic thermal convection in a rapidly rotating spherical fluid shell

Abstract

Numerical simulations of thermal convection in a rapidly rotating spherical fluid shell heated from below and within have been carried out with a nonlinear, three-dimensional, time-dependent pseudospectral code. The investigated phenomena include the sequence of transitions to chaos and the differential mean zonal rotation. At the fixed Taylor number T _a =10⁶ and Prandtl number Pr=1 and with increasing Rayleigh number R, convection undergoes a series of bifurcations from onset of steadily propagating motions SP at R=R _c = 13050, to a periodic state P, and thence to a quasi-periodic state QP and a non-periodic or chaotic state NP. Examples of SP, P, QP, and NP solutions are obtained at R = 1.3R _c , R = 1.7 R _c , R = 2R _c , and R = 5 R _c , respectively. In the SP state, convection rolls propagate at a constant longitudinal phase velocity that is slower than that obtained from the linear calculation at the onset of instability. The P state, characterized by a single frequency and its harmonics, has a two-layer cellular structure in radius. Convection rolls near the upper and lower surfaces of the spherical shell both propagate in a prograde sense with respect to the rotation of the reference frame. The outer convection rolls propagate faster than those near the inner shell. The physical mechanism responsible for the time-periodic oscillations is the differential shear of the convection cells due to the mean zonal flow. Meridional transport of zonal momentum by the convection cells in turn supports the mean zonal differential rotation. In the QP state, the longitudinal wave number m of the convection pattern oscillates among m = 3,4,5, and 6; the convection pattern near the outer shell has larger m than that near the inner shell. Radial motions are very weak in the polar regions. The convection pattern also shifts in m for the NP state at R = 5R _c , whose power spectrum is characterized by broadened peaks and broadband background noise. The convection pattern near the outer shell propagates prograde, while the pattern near the inner shell propagates retrograde with respect to the basic rotation. Convection cells exist in polar regions. There is a large variation in the vigor of individual convection cells. An example of a more vigorously convecting chaotic state is obtained at R = 50R _c . At this Rayleigh number some of the convection rolls have axes perpendicular to the axis of the basic rotation, indicating a partial relaxation of the rotational constraint. There are strong convective motions in the polar regions. The longitudinally averaged mean zonal flow has an equatorial superrotation and a high latitude subrotation for all cases except R = 50R _c , at this highest Rayleigh number, the mean zonal flow pattern is completely reversed, opposite to the solar differential rotation pattern.     

Application of the exact constitutive relationship of modified Cam clay to the undrained expansion of a spherical cavity

The modified Cam clay (MCC) model is used to study the response of virgin‐compressed clay subjected to undrained triaxial compression. The MCC constitutive relationship is obtained in a closed form. Both elastic and plastic deviatoric strains are considered in the analysis. The solution allows to obtain total and effective stress paths followed by the clay in undrained spherical expansion. Pore water pressures are determined from the difference between total and effective mean stresses. For illustration purposes, the analysis is also applied to the well‐known reconstituted normally consolidated London clay and the results are compared with the recently published data obtained by a numerical approach. In addition, the Almansi large strains are used in the analysis, as these allow to obtain limit expansion and pore pressures, whereas both small‐strain and logarithmic‐strain approaches do not permit to determine them. Copyright © 2010 John Wiley & Sons, Ltd.     

二流—四流球谐函数谱展开累加辐射传输方案在全球气候模式中的应用

本文首先构建了二流—四流球谐函数谱展开累加辐射传输的新方案,然后将其应用于国家气候中心第二代大气环流模式BCC_AGCM2.0.1的新版本中,并与模式中原有的Eddington累加方案进行了比较。由于新方案本质上是单层Eddington近似方案在四流上的推广。因此新方案在计算精度上要优于原方案。通过在全球气候模式中的应用与比较,本文发现新方案对气候模拟会产生比较大的影响。在晴空条件下,新方案计算的在南纬30°到60°区间、北大西洋东北部以及非洲北部的撒哈拉沙漠区域的地表向下年平均短波辐射通量要小于原方案结果,最大差别可以达到3.5 W/m2;同时,新方案计算的在南纬30°到60°区间和北大西洋东北部的大气顶向上年平均短波辐射通量要大于原方案结果,最大差别达到3 W/m2。在有云大气情况下,新方案计算的地表向下年平均短波辐射通量要小于原方案结果,并随着纬度的增加,新旧两种方案的差别逐渐变大,在南北极时达到最大5.5 W/m2;同时,新方案计算的在赤道区域的大气顶的年平均短波向上辐射通量要小于原方案结果,最大差别为2.5 W/m2,而在南北纬30°到60°区间,新方案计算的在大气顶的年平均短波向上辐射通量则要大于原方案结果,最大差别为1.5 W/m2。新方案计算的年平均短波加热率普遍高于原方案结果,特别是在800 hPa到地表之间的低层大气以及50 hPa到100 hPa的高层大气,最大差别可达0.03 K/d。因此,新方案有助于改善全球气候模式中普遍存在的赤道平流层中下层的温度冷偏差现象。     

Earth2014: 1 arc-min shape,topography, bedrock and ice-sheet models – Available as gridded data and degree-10,800 spherical harmonics

Since the release of the ETOPO1 global Earth topography model through the US NOAA in 2009, new or significantly improved topographic data sets have become available over Antarctica, Greenland and parts of the oceans. Here, we present a suite of new 1′ (arc-min) models of Earth’s topography, bedrock and ice-sheets constructed as a composite from up-to-date topography models: Earth2014. Our model suite relies on SRTM30_PLUS v9 bathymetry for the base layer, merged with SRTM v4.1 topography over the continents, Bedmap2 over Antarctica and the new Greenland bedrock topography (GBT v3). As such, Earth2014 provides substantially improved information of bedrock and topography over Earth’s major ice sheets, and more recent bathymetric depth data over the oceans, all merged into readily usable global grids. To satisfy multiple applications of global elevation data, Earth2014 provides different representations of Earth’s relief. These are grids of (1) the physical surface, (2) bedrock (Earth’s relief without water and ice masses), (3) bedrock and ice (Earth without water masses), (4) ice sheet thicknesses, (5) rock-equivalent topography (ice and water masses condensed to layers of rock) as mass representation. These models have been transformed into ultra-high degree spherical harmonics, yielding degree 10,800 series expansions of the Earth2014 grids as input for spectral modelling techniques. As further variants, planetary shape models were constructed, providing distances between relief points and the geocenter. The paper describes the input data sets, the development procedures applied, the resulting gridded and spectral representations of Earth2014, external validation results and possible applications. The Earth2014 model suite is freely available via http://ddfe.curtin.edu.au/models/Earth2014/.     

球形标靶的固定式扫描大点云自动定向方法

根据目前地面激光扫描数据获取速度快、数据量大、测量距离远、专用特殊材料制作的标靶识别距离近、点云定向数据处理相对滞后、自动化程度低、不能适应远距离地形测量的现状,提出了从大点云中(每站1亿点以上)自动探测远距离标靶的点云定向方法。该方法首先根据标靶控制点的工程测量坐标信息,搜索到标靶所在点云环,然后对各点云环进行扇形分区,快速探测标靶,获取标靶中心扫描坐标,最后平差计算扫描仪位置参数和姿态参数,实现点云坐标到工程测量坐标的转换。该方法在普通配置的计算机上得到实现,并成功用于远距离山区地形测量,其中定向标靶半径0.162m,标靶到扫描站距离在180~700m之间。     

航空重力梯度数据的模拟研究

针对提高模拟航空重力梯度的精度研究不足的现状,文章运用地球重力场模型构建了计算单点的扰动重力梯度分量的数学模型,推导了Legendre函数及其导数的无奇异性递推计算公式,克服了计算高阶次Legendre函数Pnm(cosθ)的下溢问题,随之对数学模型进行优化;最后利用EGM2008地球位模型模拟生成4km飞行高度处的扰动重力梯度张量作为航空重力梯度观测值。模拟试算表明,该模型能够满足当前航空重力梯度测量的精度要求。     

利用体应变观测资料检测地球自由振荡

选用通河地震台体应变观测数据,采用功率谱密度估计方法,获得2015年5月30日日本小笠原群岛地区8.0级大地震和2017年9月8日墨西哥沿岸近海8.2级大地震激发的_0S_4—_0S_(35)基频球型自由振荡频率,并与地球初步参考模型(PREM)的理论自由振荡频率进行对比,结果发现:前者共被检测到11个基频信号,有7个信号与理论值存在偏差,1个存在频谱分裂现象;后者共被检测到17个基频信号,有9个信号与理论值存在偏差,1个存在频谱分裂现象。     

三维隔震单层球面网壳结构频率相关变阻尼半主动控制

在不同频率特征的地震动作用下,三维隔震单层球面网壳结构隔震层最优阻尼设计不同.文中基于单自由度体系加速度传递率函数,提出一种地震动主频相关的加速度阈值变阻尼半主动控制方法以及地震动主频分区识别方法.基于ABAQUS软件的DLOAD子程序,开展了三维隔震单层球面网壳被动控制与半主动控制有限元计算,对节点加速度、杆件轴力进...