Efficient Orbit Propagation of Orbital Elements Using Modified Chebyshev Picard Iteration Method

This paper focuses on propagating perturbed two-body motion using orbital elements combined with a novel integration technique.While previous studies show that Modified Chebyshev Picard Iteration(MCPI)is a powerful tool used to propagate position and velocity,the present results show that using orbital elements to propagate the state vector reduces the number of MCPI iterations and nodes required,which is especially useful for reducing the computation time when including computationally-intensive calculations such as Spherical Harmonic gravity,and it also converges for>5.5x as many revolutions using a single segment when compared with cartesian propagation.Results for the Classical Orbital Elements and the Modified Equinoctial Orbital Elements(the latter provides singularity-free solutions)show that state propagation using these variables is inherently well-suited to the propagation method chosen.Additional benefits are achieved using a segmentation scheme,while future expansion to the two-point boundary value problem is expected to increase the domain of convergence compared with the cartesian case.MCPI is an iterative numerical method used to solve linear and nonlinear,ordinary differential equations(ODEs).It is a fusion of orthogonal Chebyshev function approximation with Picard iteration that approximates a long-arc trajectory at every iteration.Previous studies have shown that it outperforms the state of the practice numerical integrators of ODEs in a serial computing environment;since MCPI is inherently massively parallelizable,this capability is expected to increase the computational efficiency of the method presented.

STUDY ON ENRICHMENT AND SEPARATION OF TRACE ELEMENTS WITH SILICA GELS MODIFIED BY HETEROCYCLIC AZO DYES

Two types of modified silica gels were prepared by adsorption method and bonding method respectively. Enrichment and separation of trace metal ions have been done by using the column packed with modified silica gels.

A modified discrete element model for sea ice dynamics

Considering the discontinuous characteristics of sea ice on various scales,a modified discrete element model（DEM） for sea ice dynamics is developed based on the granular material rheology.In this modified DEM,a soft sea ice particle element is introduced as a self-adjustive particle size function.Each ice particle can be treated as an assembly of ice floes,with its concentration and thickness changing to variable sizes under the conservation of mass.In this model,the contact forces among ice particles are calculated using a viscous-elastic-plastic model,while the maximum shear forces are described with the Mohr-Coulomb friction law.With this modified DEM,the ice flow dynamics is simulated under the drags of wind and current in a channel of various widths.The thicknesses,concentrations and velocities of ice particles are obtained,and then reasonable dynamic process is analyzed.The sea ice dynamic process is also simulated in a vortex wind field.Taking the influence of thermodynamics into account,this modified DEM will be improved in the future work.

Subduction-Modified Subcontinental Mantle in South China: Trace Element and Isotope Evidence in Basalts from Hainan Island

Cenozoc lavas from Hainan Island, bouth China, comprise quartz tholeiite. olivinethoeiite, alkali basalt, and basanite and form a continuous, thoeiite-dominated, comopitionalspectrum. Highly incompatible elements and their relationships with isotope in these lavas areshown to be useful in evaluating mantle-source composition, whereas modeling suggests that ra-tios of elements with bulk partition coefficients significantly larger than those of Nb and Ta maybe sensitive to patial melting. Th/Ta and La/Nb ratios of alkali basalts are lower than those ofthoeiites, and they are all fower than tbe of the primitive mantle. These ratios correlate posi-tively with 207Pb/204Pb and 87Sr/86Sr ratios. Such relatioships can be explained by mixing ofdepleted and enriched source componentS. A depleted component is indicated by alkali basaltcompositions and is similar to some depleted OIB (PREMA). The enriched component, similarto sediment compositios, is indicated by tholeiites with high LILE/HFSE, 207Pb/204Pb, and87/86Sr ratios.In general, basalts from Hainan and the South China Basin (SCB) share common geo-chemical charcters, e.g. high Rb/Sr, Th/Ta, 207Pb/206Pb, and low Ba/Th ratios. Such ageochemical trend is comparable to that of EMII-type OIB and best explained as the result ofsubduction. Occurrence of these charcteristics in both continennd Hainan basalts and SCBseamount basalts indicates the presence of a South China geochemical domain that exists in themantle region below the lithosphere.

Novel Minimum Passive Element Realization of All-Pass Network Using A Modified Current Conveyor

1. IntroductionA large number of networks for realizing first and second order transfer functions using a currentconveyor have been reported in the literature. Especially, the networks that can offer highinput impedance attract attention, for high input impedance has the advantage that the networksmay be used in cascade without requiring impedance matching device. In the Higashimura and

A modified Johnson–Cook model for 7N01 aluminum alloy under dynamic condition

Tensile tests at different strain rates(0.0002, 0.002, 0.02, 1000 and 3000 s^(-1)) were carried out for 7N01 aluminum alloy. Low strain rate experiments(0.0002, 0.002 and 0.02 s^(-1)) were conducted using an electronic mechanical universal testing machine, while high strain rate experiments(1000, 3000 s^(-1)) were carried out through a split Hopkinson tensile bar. The experimental results showed that 7N01 aluminum alloy is strain rate sensitive. By introducing a correction scheme of the strain rate hardening coefficient, a modified Johnson–Cook model was proposed to describe the flow behaviors of 7N01 aluminum alloy. The proposed model fitted the experimental data better than the original Johnson–Cook model in plastic flow under dynamic condition. Numerical simulations of the dynamic tensile tests were performed using ABAQUS with the modified Johnson–Cook model. Digital image correlation was used together with high-speed photography to study the mechanical characters of specimen at high strain rate. Good correlations between the experiments results, numerical predictions and DIC results are achieved. High accuracy of the modified Johnson-Cook model was validated.

NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS

Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an ellip- tic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two con- centrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.

Systematic Synthesis on Pathological Models of CCCII and Modified CCCII

According to the equivalent view for the terminal current-voltage constraint relationship between pathological elements and the various second-generation current-controlled convegors （CCCIIs）, four patholo- gical models for the CCCII are first derived by means of the nodal admittance matrix expansion in this paper. Moreover, 48 new pathological models for the modified CCCII are also synthesized. The derived pathological models for the various CCCIIs are expected to be useful in circuit analysis and synthesis.

Determination of processing power and optimum billet radius of modified backward extrusion by upper bound approach

A recently developed backward extrusion method entitled “modified backward extrusion” was presented using an upper bound analysis. For this purpose deformation area was divided into four distinct zones and a kinematically admissible velocity field for each of them was suggested. Total dissipated power was calculated for the deformation zones and the extrusion power wascomputed. The correlations of important geometrical parameters with extrusion force and dissipated powers were shown. Finding the initial billet size, a challenging area in the modified backward extrusion method, was discussed and the optimum billet radius was obtained, considering the minimum relative extrusion pressure. Finite element analyses were conducted and the results werecompared with the upper bound analysis. Finally, experiments were executed on commercially pure aluminium and a good agreement between upper bound and finite element analyses with experimental values was observed.

Buckling Analysis of Tapered Continuous Columns by Using Modified Buckling Mode Shapes

Elastic critical buckling load of a column depends on various parameters,such as boundary conditions,material,and crosssection geometry.The main purpose of this work is to present a new method for investigating the buckling load of tapered columns subjected to axial force.The proposed method is based on modified buckling mode shape of tapered structure and perturbation theory.The mode shape of the damaged structure can be expressed as a linear combination of mode shapes of the intact structure.Variations in length in piecewise form can be positive or negative.The method can be used for single-span and continuous columns.Comparison of results with those of finite element and Timoshenko methods shows the high accuracy and efficiency of the proposed method for detecting buckling load.

Mechanism of the Pyroelectric Response under Direct-Current Bias in La-Modified Lead Zirconate Titanate Stannate Ceramics

Dielectric and pyroelectric properties of Pb_(0.97)La_(0.02)(Zr_(0.42)Sn_(0.40)Ti_(0.18))O_(3) ceramics are investigated as functions of temperature and dc bias field.Induced and intrinsic pyroelectric coefficients pind and p0 are calculated and analyzed.It is found that the sign,value and variation of the net pyroelectric coefficient p with increasing dc bias all are dominated by p0 under applied biases.Polarization and depolarization processes under dc biases are analyzed.Besides the contribution of pind,the diffuse and decreased pyroelectric response under dc bias compared with that of an identical field poled sample without dc bias is mainly attributed to the depolarization process under dc bias.

A Modified Polynomial Preserving Recovery and Its Applications to A Posteriori Error Estimates

A modified polynomial preserving gradient recovery technique is proposed. Unlike the polynomial preserving gradient recovery technique,the gradient recovered with the modified polynomial preserving recovery(MPPR) is constructed element-wise, and it is discontinuous across the interior edges.One advantage of the MPPR technique is that the implementation is easier when adaptive meshes are involved.Superconvergence results of the gradient recovered with MPPR are proved for finite element methods for elliptic boundary problems and eigenvalue problems under adaptive meshes. The MPPR is applied to adaptive finite element methods to construct asymptotic exact a posteriori error estimates.Numerical tests are provided to examine the theoretical results and the effectiveness of the adaptive finite element algorithms.

A Table That Produces Elements

How do elements originate, how atoms are formed, and what are the laws? According to the unified logic of “Tong Yi Lun Thought”, combined with the elements’ attributes and the atomic composition that have been discovered now, after determining that the mechanism of increasing yang in the atomic system is the increase of proton number, the Bian Zheng relationship among proton, neutron and electron determines that there are only 128 kinds of elements in the atomic system. At the same time, element atoms have corresponding logical relations when they are generated.

Modified Layer-Removal Method for Measurement of Residual Stress in Pre-stretched Aluminium Alloy Plate

Residual stress is one of the factors affecting the machining deformation of monolithic structure parts in the aviation industry. Thus, the studies on machining deformation rules induced by residual stresses largely depend on correctly and efficiently measuring the residual stresses of workpieccs. A modified layer-removal method is proposed to measure residual stress by analysing the characteristics of a traditional, layer-removal method. The coefficients of strain release are then deduced according to the simulation results using the finite element method （FEM）. Moreover, the residual stress in a 7075T651 aluminium alloy plate is measured using the proposed method, and the results are then analyzed and compared with the data obtained by the traditional methods. The analysis indicates that the modified layer-removal method is effective and practical for measuring the residual stress distribution in pre-stretched aluminium alloy plates.

Derivative of a Determinant with Respect to an Eigenvalue in the Modified Cholesky Decomposition of a Symmetric Matrix, with Applications to Nonlinear Analysis

In this paper, we obtain a formula for the derivative of a determinant with respect to an eigenvalue in the modified Cholesky decomposition of a symmetric matrix, a characteristic example of a direct solution method in computational linear algebra. We apply our proposed formula to a technique used in nonlinear finite-element methods and discuss methods for determining singular points, such as bifurcation points and limit points. In our proposed method, the increment in arc length (or other relevant quantities) may be determined automatically, allowing a reduction in the number of basic parameters. The method is particularly effective for banded matrices, which allow a significant reduction in memory requirements as compared to dense matrices. We discuss the theoretical foundations of our proposed method, present algorithms and programs that implement it, and conduct numerical experiments to investigate its effectiveness.

A Modified Paving Approach and Automatic Mesh Grading Method to Quadrilateral Mesh Generation

A modified paving technique for automatic generation of all-quadrilateral mesh fromarbitrary 2-D geometry is presented. The generated mesh elementS are nearly square andperpendicular to boundaries. Aner the nodes and elementS formation is completed. a fully automaticgrading method is applied to increase the accuracy and reliability of engineering analysis. In thispaper, we mainly describe the theory of mathematical algorithm and present some examples ofautomatically generated mesh.

软黏土地区深大基坑工程桩-连续墙体系空间变形效应

土体开挖过程中深大基坑存在明显的空间变形效应,对其主体结构力学行为产生影响。以新建苏州南站枢纽深大基坑为工程背景,考虑地连墙厚度及工程桩的影响,基于ABAQUS建立三维空间有限元模型,采用修正剑桥模型考虑软黏土的应变硬化特征,从地连墙侧向位移、墙后地表沉降、工程桩和坑底土体隆起3个方面,研究软黏土地区深大基坑工程桩-连续墙体系的变形特征及空间效应。研究结果表明:深大基坑地连墙的侧向位移和地表沉降均呈现明显的角部效应,基坑A区(地连墙厚度1 m、桩径1 m)地连墙侧向位移角部效应的影响范围为1.05~1.71倍开挖深度,基坑B区(地连墙厚度0.8 m、桩径1.5 m)地连墙侧向位移角部效应的影响范围为0.91~1.48倍开挖深度;基坑A区、B区地表沉降角部效应的影响范围分别为1.24~2.10和1.77~2.47倍开挖深度;深大基坑空间变形角部效应与工程桩桩径及地连墙厚度有关,并且对基坑长边的影响效果大于短边。工程桩可有效增大基坑开挖面以下土体的刚度,减小地连墙的侧向位移;增大地连墙厚度可有效降低基坑的整体变形。基坑工程桩与坑底土体隆起总体呈现中间大、周边小的特征,工程桩周边土体受其约束,隆起较小;在一定范围内,工程桩对土体隆起抑制作用与其桩径呈正相关,与其桩间距呈负相关。软黏土地区深大基坑设计计算中需关注工程桩-连续墙结构体系的空间变形效应。

基于属性的概念化:制度本体研究的必要性与路径

制度本体的研究现状与制度之于人类生活的重要性并不相称,制度研究有必要返回本体,明确存在。解读制度理论的制度理解并指出它所引发的本体认知困惑,确立了制度本体研究的必要性。本体在于内涵,内涵首要是本质,有抱负的研究者都试图给出事物的本质性定义,但此定义往往可欲难求。一个可行的操作化步骤是,确定本体的属性。制度学界普遍接受的“制度即结构”可以明确为“制度即要素结构”,并可解构为要素之制、载体之制与结构之制。确定本体属性、要素化属性并将其概念化,应是可行的本体研究策略或路径。由此获得的概念语言暨制度本体词汇有助于校准本体描述,同时可作为中介术语沟通制度研究,推动制度知识的共享与交流。

局部环向变厚度方钢管混凝土柱偏压力学性能研究

针对海洋环境中飞溅区造成的钢管混凝土柱局部环向腐蚀现象,采用机械削减方式模拟钢管壁厚局部环向腐蚀,进行了7个方钢管混凝土柱偏压试验,揭示了削弱率和偏心率对其偏压承载力的影响,并通过数值模拟对削弱率进行拓展分析.提出了基于削弱率的偏压承载力降低系数,代入中、美规范进行偏压承载力计算.结果表明:钢管的局部环向变厚度严重削弱了方钢管混凝土柱的偏压承载力和侧向挠曲能力;较大的加载偏心率也降低了其偏压承载力,但增大了其侧向挠曲能力.引入偏压承载力降低系数后,根据中、美规范计算得到的偏压承载力与试验值均吻合较好;相比于我国规范,美国规范在计算偏压承载力时相对更加保守.

考虑化学反应的高聚物压密劈裂注浆仿真研究

考虑浆液化学反应原理,综合运用扩展有限元理论、修正剑桥模型和高聚物浆液膨胀力计算模型,建立了模拟高聚物在土体中压密劈裂注浆动态过程的二维仿真分析方法。通过模型试验验证了所提出方法的适用性,进而分析了浆液膨胀力、浆脉形态、土体孔隙比随时间变化规律及注浆孔埋深、土体断裂韧度对浆脉扩展过程的影响。结果表明:受高聚物化学反应进程驱动,在浆液与土体耦合作用下,浆液膨胀力初期随时间近似呈线性增长,达到峰值后快速下降并趋于稳定;浆脉长度和宽度发展速度不同步,裂缝启裂至二次扩展阶段,浆脉长度基本保持不变,宽度线性增大,裂缝二次扩展后,浆脉长度近似线性增大,而宽度增长速率趋缓;受浆液挤密作用影响,裂缝两侧一定范围内土体孔隙比显著降低,沿垂直于裂缝面方向,距注浆孔中心越近,孔隙比越小;孔隙比随时间整体呈下降趋势,随着裂缝的扩展和后期膨胀压力的下降,紧邻裂缝面两侧土体孔隙比有一定恢复,随后趋于稳定;随着注浆孔埋深和土体断裂韧度的增加,浆脉长度逐渐减小,宽度不断增大,两者变化速率基本保持不变;浆脉扩展稳定时间随埋深的增大而提前,随断裂韧度的增大而延后。