A theoretical study of the multigrid three-dimensional variational data assimilation scheme using a simple bilinear interpolation algorithm

In order to solve the so-called ＂bull-eye＂ problem caused by using a simple bilinear interpolation as an observational mapping operator in the cost function in the multigrid three-dimensional variational （3DVAR） data assimilation scheme, a smoothing term, equivalent to a penalty term, is introduced into the cost function to serve as a means of troubleshooting. A theoretical analysis is first performed to figure out what on earth results in the issue of ＂bull-eye＂, and then the meaning of such smoothing term is elucidated and the uniqueness of solution of the multigrid 3DVAR with the smoothing term added is discussed through the theoretical deduction for one-dimensional （1D） case, and two idealized data assimilation experiments （one- and two-dimensional （2D） cases）. By exploring the relationship between the smoothing term and the recursive filter theoretically and practically, it is revealed why satisfied analysis results can be achieved by using such proposed solution for the issue of the multigrid 3DVAR.

Three-Dimensional Space Interpolation of Grey / Depth Image Sequence-A New Technique of Computer Graphics Synthesis

This paper advances a three-dimensional space interpolation method of grey / depth image sequence, which breaks free from the limit of original practical photographing route. Pictures can cruise at will in space. By using space sparse sampling, great memorial capacity can be saved and reproduced scenes can be controlled. To solve time consuming and complex computations in three-dimensional interpolation algorithm, we have studied a fast and practical algorithm of scattered space lattice and that of 'Warp' algorithm with proper depth. By several simple aspects of three dimensional space interpolation, we succeed in developing some simple and practical algorithms. Some results of simulated experiments with computers have shown that the new method is absolutely feasible.

Analysis of Multi-Scale Fractal Dimension for Image Interpolation

This article presents a novel image interpolation based on rational fractal fimction. The rational function has a simple and explicit expression. At the same time, the fi＇actal interpolation surface can be defined by proper parameters. In this paper, we used the method of ＇covering blanket＇ combined with multi-scale analysis; the threshold is selected based on the multi-scale analysis. Selecting different parameters in the rational function model, the texture regions and smooth regions are interpolated by rational fractal interpolation and rational interpolation respectively. Experimental results on benchmark test images demonstrate that the proposed method achieves very competitive performance compared with the state-of-the-art interpolation algorithms, especially in image details and texture features.

A Novel Multi-Stage Interpolation Filter Design Technique for High-Resolution Σ-Δ DAC

This paper presents an efficient way to implement an interpolation filter in a 20bit ∑-△ DAC with an oversampling ratio of 128. A multistage structure is used to reduce the complexity of filter coefficients and the fi- nite word length effect. A novel method based on mixed-radix number representation is proposed to realize a poly- phase multiplier-free half-band subfilter with a high resolution. This approach reduces the complexity of the con- trol system and saves chip area dramatically. The IC is realized in a standard 0.13μm CMOS process and the inter- polation filter occupies less than 0.63mm^2 . This realization has desirable properties of regularity with simple hard- ware devices which are suitable for VLSI and can be applied to many other high resolution data converters.

THE SMOOTHNESS AND DIMENSION OF FRACTAL INTERPOLATION FUNCTIONS

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DIMENSION AND DIFFERENTIABILIIY OF A CLASS OF FRACTAL INTERPOLATION FUNCTIONS

In this paper, a new iterated function system consisting of non-linear affinemaps is constructed. We investigate the fractal interpolation functions generated bysuch a system and get its differentiability, its box dimension, its packing dimension,and a lower bound of its Hansdorff dimension.

Sub-pixel high precision dimensional measurement method for aero-engine hollow turbine blade based on industrial computed tomography image

Aero-engine hollow turbine blades are work under prolonged high temperature,requiring high dimensional accuracy.Blade profile and wall thickness are important parameters to ensure the comprehensive performance of blades,which need to be measured accurately during manufacturing process.In this study,a high accuracy industrial computed tomography(ICT)measuring method was developed based on standard cylindrical pin and ring workpieces of different sizes.Combining ICT with cubic spline interpolation,a sub-pixel accuracy was achieved in measuring the dimension of component.Compared with the traditional and whole-pixel level image measurement method,the cubic spline interpolation algorithm has the advantages of high accuracy in image edge detection and thus high accuracy of dimensional measurement.Further,the technique was employed to measure the profile and wall thickness of a typical aerospace engine turbine blade,and an accuracy higher than 0.015 mm was obtained.

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.

Numerical study on three-dimensional flow field of continuously rotating detonation in a toroidal chamber

Gaseous detonation propagating in a toroidal chamber was numerically studied for hydrogen/oxygen/nitrogen mixtures. The numerical method used is based on the three-dimensional Euler equations with detailed finiterate chemistry. The results show that the calculated streak picture is in qualitative agreement with the picture recorded by a high speed streak camera from published literature. The three-dimensional flow field induced by a continuously rotating detonation was visualized and distinctive features of the rotating detonations were clearly depicted. Owing to the unconfined character of detonation wavelet, a deficit of detonation parameters was observed. Due to the effects of wall geometries, the strength of the outside detonation front is stronger than that of the inside portion. The detonation thus propagates with a constant circular velocity. Numerical simulation also shows three-dimensional rotating detonation structures, which display specific feature of the detonation- shock combined wave. Discrete burning gas pockets are formed due to instability of the discontinuity. It is believed that the present study could give an insight into the interest- ing properties of the continuously rotating detonation, and is thus beneficial to the design of continuous detonation propulsion systems.

Numerical Filling Simulation of Injection Molding Using Three-Dimensional Model

Most injection molded parts are three-dimensional, with complex geometrical configurations and thick/thin wall sections. A 3D simulation model will predict more accurately the filling process than a 2.5D model. This paper gives a mathematical model and numeric method based on 3D model, in which an equal-order velocity-pressure interpolation method is employed successfully. The relation between velocity and pressure is obtained from the discretized momentum equations in order to derive the pressure equation. A 3D control volume scheme is employed to track the flow front. Th e validity of the model has been tested through the analysis of the flow in cavity.

Infinite Three-Dimensional Coordination Polymers: Synthesis and Structures of [Cd (4,4'-bpy)_2 (H_2O)_2]_n (pic)_(2n),[Zn (4,4'-bpy)_2 (H_2O)_2]_n(pic)_(2n) (H_2O)_(2n), and [Zn (4,4'-bpy)_2 (H_2O)_2]_n (4,4'-bpy)_n(H_2O)_n (pic)_(2n)

Three Complexes of the formula [Cd (4,4'-bpy)_2 (H_2O)_2]_n. (pic)_(2n) (1) [Zn (4,4'-bpy)_2 (H_2O)]_n (4,4'-bpy)_n(H_2O)_n (pic)-(2n) (2) and [Zn (4,4'-bpy)_2 (H_2O)]_n (4,4'-bpy)_n (pic)-(2n)(H_2O)_n (3) (4.4'-bpy = 4.4'-bipyridine. pic = picric anion ) have been synthesized and characterized by elemental analysis and single-crystal x-ray diffraction. They all have infinite three-dimensional network structure. crystallizing in the monoclinic space group C2/c (1) and Cc (2.3).

3-Dimensional Body Measurement Technology

3 - dimensional body measurement technology, the basis of developing high technology in industry, accelerates digital development of aplparel industry. This paper briefly introduces the history of 3 - dimensional body measurement technology, and recounts the principle and primary structure of some types of 3 - dimensional automatic body measurement system. With this understanding, it discusses prospect of 3- dimensional CAD and virtual technology used in apparel industry.

Parametric study on single shot peening by dimensional analysis method incorporated with finite element method

Shot peening is a widely used surface treatment method by generating compressive residual stress near the surface of metallic materials to increase fatigue life and re- sistance to corrosion fatigue, cracking, etc. Compressive re- sidual stress and dent profile are important factors to eval- uate the effectiveness of shot peening process. In this pa- per, the influence of dimensionless parameters on maximum compressive residual stress and maximum depth of the dent were investigated. Firstly, dimensionless relations of pro- cessing parameters that affect the maximum compressive residual stress and the maximum depth of the dent were de- duced by dimensional analysis method. Secondly, the in- fluence of each dimensionless parameter on dimensionless variables was investigated by the finite element method. Fur- thermore, related empirical formulas were given for each di- mensionless parameter based on the simulation results. Fi- nally, comparison was made and good agreement was found between the simulation results and the empirical formula, which shows that a useful approach is provided in this pa- per for analyzing the influence of each individual parameter.

Numerical Solution of Two Dimensional Fredholm Integral Equations of the Second Kind by the Barycentric Lagrange Function

This paper solves the two dimensional linear Fredholm integral equations of the second kind by combining the meshless barycentric Lagrange interpolation functions and the Gauss-Legendre quadrature formula. Inspired by this thought, we convert the equations into the associated algebraic equations. The results of the numerical examples are given to illustrate that the approximated method is feasible and efficient.

Cubic Spline Interpolation on a Class of Triangulations

In this paper, we consider spaces of cubic C^1-spline on a class of triangulations. By using the inductive algorithm, the posed Lagrange interpolation sets are constructed for cubic spline space. It is shown that the class of triangulations considered in this paper are nonsingular for S1/3 spaces. Moreover, the dimensions of those spaces exactly equal to L. L. Schuraaker＇s low bounds of the dimensions. At the end of this paper, we present an approach to construct triangulations from any scattered planar points, which ensures that the obtained triangulations for S1/3 space are nonsingular.

基于反距离加权法的磁记忆信号插值及力-磁效应研究

铁磁性材料是石化工业中重要受力部件的组成材料,石化管道逐渐日益高压输送的趋势对其安全性检测提出了更高的要求。金属磁记忆检测方法(MMM)是一种灵敏便捷的无损检测技术,为使磁记忆检测技术在管件早期缺陷快速检测中广泛应用,需对石化管件材料的磁记忆信号特征进行进一步的研究。通过反距离加权法对四条平行路径上采集的磁记忆信号进行空间插值,将一维磁记忆信号拓展到三维空间,从而以曲面的偏导及全导的形式将传统的磁记忆信号的特征参量演化为空间域的磁记忆信号特征值。为石化管道早期缺陷的快速识别做出了铺垫性研究,对磁记忆检测技术在管道内检测领域的应用具有参考性价值。

INFINITE DIMENSIONAL KOLMOGOROV WIDTH AND OPTIMAL INTERPOLATION ON SOBOLEV-WIENER SPACE

In this paper, we introduce a kind of Sobolev-Wiener spaces defined on the whole realaxis and discuss their infinite dimensional width and optimal interpolation problems. Wegive the exact values (of strong asymptotics) of the infinite dimensional Kolmogorov widthand linear width of W_(∞,p)~r(R) in the metric L_p(R). Meanwhile, we also solve its optimalinterpolation problem.

Elevation data compression using IFS-based three-dimensional fractal interpolation

This paper presents the application of iterated function system (IFS) based three-dimensional (3D) fractal interpolation to elevation data compression. The parameters of contractive transformations are simplified by a concise fractal iteration form with geometric meaning. A local iteration algorithm is proposed, which can solve the non-separation problem when Collage theorem is applied to find the appropriate fractal parameters. The elevation data compression is proved experimentally to be effective in. reconstruction quality and time-saving.

基于特征分解的2-D多边形渐变

二维多边形渐变在二维角色动画、模式匹配、几何造型等领域有着重要的应用.已有的方法大多根据多边形的边长、角度、面积、骨架等几何属性来完成多边形之间的最佳对应和渐变,而忽略了多边形的内在视觉特征.提出了一种基于视觉特征对应的 2-D 多边形渐变方法,该方法把源多边形和目标多边形按照视觉特征进行同构特征分解,得到若干对对应的特征子多边形.在渐变过程中,每个源特征子多边形光滑地过渡到目标特征子多边形.通过引入特征分解点,用户可以灵活和直观地改变特征子多边形,按照预想的效果控制多边形的渐变.实验效果表明,基于特征分解的顶点对应和插值算法不仅可以得到光滑的多边形渐变序列,而且可以实现多特征保留.

MR 3D-VIBE序列多期动态增强扫描在原发性肝细胞癌中的应用

【目的】通过对原发性肝细胞癌(HCC)的MR三维容积插入屏气检查(3D-VIBE)多期动态增强扫描与多层螺旋CT(MSCT)增强扫描的对照研究,探讨MR 3D-VIBE序列动态增强扫描在显示HCC的动态强化特点中的价值。【方法】收集23例在我院行上腹部3.0T MR 3D-VIBE多期动态增强扫描及MSCT双期增强扫描的HCC的患者的临床及影像学资料,对比3D-VIBE序列动态增强扫描及MSCT增强扫描显示肿瘤的强化特点。【结果】23例经手术证实共发现23个HCC,MRI 3DVIBE序列检出全部23个病灶,CT检出21个病灶。MRI 3D-VIBE序列多期动态增强扫描中病灶显示为"快进快退"征象者占78.3%(18/23),MSCT增强扫描具有此征象者占54.5%。直径≤3 cm的肿瘤更易在3D-VIBE序列多期动态增强扫描中观察到明显强化征象(P=0.037)。【结论】MR 3D-VIBE序列肝脏进行多期动态增强扫描,提高了HCC尤其是小HCC诊断的敏感性与准确性。