颅骨点云曲面重建的Euler’s Elastica模型

为从具有复杂拓扑关系的颅骨点云数据中重建精确、光滑的隐式曲面,提出了基于Euler’s Elastica的变分水平集方法.首先,将Euler’s Elastica作为正则化约束引入变分能量泛函,采用增广拉格朗日方法将变分能量泛函最小化问题转化为一系列子问题;其次,分别采用广义软阈值公式、解析公式和快速傅里叶变换求解;最后,在计算过程中采用投影算法,有效地避免了水平集函数的重新初始化过程.实验结果表明,相较于现有方法,所提基于Euler’s Elastica的变分水平集方法具有更好的收敛性和有效性,能够提高重建的精确性,避免曲面边缘的缺失.

基于Gauss滤波和Euler修复模型的SAR图像去噪

针对二阶偏微分模型(Total variation,TV)在合成孔径雷达(Synthetic aperture radar,SAR)图像去噪时会产生阶梯效应的问题,结合Euler修复正则项的优点,提出一种基于Euler修复正则项的高阶变分模型应用到图像去噪。为有效求解模型,采用加性算子分裂(Additive operating splitting,AOS)方法进行数值离散。迭代方式为半隐式,克服了显示格式对步长的限制。试验结果表明,仿真实验取得了很好的效果,而对真实的SAR图像,去噪图像会有明显的孤立大颗粒噪声存在,使视觉效果不好。针对此问题,本文又提出一种将Gauss滤波和Euler修复模型相结合的复合模型,数值实验表明,该方法有效地消除了大颗粒噪声,阶梯效应也被有效抑制。

Analysis of mathematical model for micromechanical vibratory wheel gyroscope

By the sketch of structure of MVWG,the working laws of this kind of gyroscope we re explained.To the aid of Euler′s Dynamics Equation,a mathematical model of the gyroscope was constructed,and then by the basic working laws of MVWG the model was simplified.Under the conditions of the three axial direction rotations and general rotation,the mathematical model was resolved.And finally by the solutions, the working laws of the gyroscope, the working disparity among all sorts of gyrations and the influences from the gyrations in the axial directions were analysed.

Stability analysis of helical rod based on exact Cosserat model

Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff＇s kinetic analogy is an effective approach to the stability analysis of equilibrium of a thin elastic rod. The main hypotheses of Kirchhoff＇s theory without the extension of the centerline and the shear deformation of the cross section are not adoptable to real soft materials of biological fibers. In this paper, the dynamic equations of a rod with a circular cross section are established on the basis of the exact Cosserat model by considering the tension and the shear deformations. Euler＇s angles are applied as the attitude representation of the cross section. The deviation of the normal axis of the cross section from the tangent of the centerline is considered as the result of the shear deformation. Lyapunov＇s stability of the helical equilibrium is discussed in static category. Euler＇s critical values of axial force and torque are obtained. Lyapunov＇s and Euler＇s stability conditions in the space domain are the necessary conditions of Lyapunov＇s stability of the helical rod in the time domain.

Consistency and Validity of the Mathematical Models and the Solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and Non-Homogeneous Non-Isotropic Solid Continua

Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (I) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (δI) set to zero is a necessary condition for an extremum of I. In this approach one could use δI = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from δI = 0, which is also satisfied by a solution obtained from δI = 0. The Euler’s equations obtained from δI = 0 indeed are the mathematical model associated with the energy functional I. In case of BVPs we follow the same approach except in this case, the energy functional I consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles i.e. conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.

Modeling of Plane Arrays Using a Variational Approach

The variational statement of synthesis problem is generalized in order to account the additional requirements to the synthesized radiation pattern (RP) and field distribution in the specified points of near zone. For this aim, the minimizing functional is supplemented by term providing the possibility to minimize the values of field in these points;creating the deep zeros in the RP for the certain angular coordinates is realized too. The approach foresees reduction of an explicit formula for field values in a near zone. The results of computational modeling testify the possibility to create zeros in the given RP and to minimize the values of field in a near zone of plane arrays in a great extent.

Combined Electromagnetic and Drift Diffusion Models for Microwave Semiconductor Device

In this work, we present a numerical model to solve the drift diffusion equations coupled with electromagnetic model, where all simulations codes are implemented using MATLAB code software. As first, we present a one-dimensional (1-D) PIN diode structure simulation achieved by solving the drift diffusion model (DDM). Backward Euler algorithm is used for the discretization of the proposed model. The aim is to accomplish time-domain integration. Also, finite different method (FDM) is considered to achieve space-Domain mesh. We introduced an iterative scheme to solve the obtained matrix systems, which combines the Gummel’s iteration with an efficient direct numerical UMFPACK method. The obtained solutions of the proposed algorithm provide the time and space distribution of the unknown functions like electrostatic potential and carrier’s concentration for the PIN diode. As second case, the finite-difference time-domain (FDTD) technique is adopted to analyze the entire 3-D structure of the stripline circuit including the lumped element PIN diode. The microwave circuit is located in an unbounded medium, requiring absorbing boundaries to avoid nonphysical reflections. Active device results were presented and show a good agreement with other reference. Electromagnetic results are qualitatively in agreement with other results obtained using SILVACO-TCAD.

Modeling of Orientation-Dependent Photoelastic Constants in Cubic Crystal System

Euler’s rotation theorem and tensor rotation technique are applied to develop a generalized mathematical model for determining photoelastic constants in arbitrary orientation of cubic crystal system. Two times rotations are utilized in the model relating to crystallographic coordinates with Cartesian coordinates. The symmetry of photoelastic constants is found to have strong dependence with rotation angle. Using the model, one can determine photoelastic constants in any orientation by selecting appropriate rotation angle. The outcome of this study helps to characterize spatial variation of residual strain in crystalline as well as polycrystalline materials having cubic structure using the experimental technique known as scanning infrared polariscope.

EULER弹性模型在图像修复中的应用

由于全变分模型修复的图像只能沿直线修复,不能满足人的视觉连接性效果,本文将Euler弹性曲线能量引入到全变分模型中,采用改进的EULER弹性模型对图像进行修复,实验结果表明:欧拉弹性修复模型能有效、稳定地沿曲线修复破损区域的图像信息,由于引入了曲线能量使得修复后的图像满足人的视觉连接性效果。

A Fast Augmented Lagrangian Method for Euler’s Elastica Models

In this paper,a fast algorithm for Euler’s elastica functional is proposed,in which the Euler’s elastica functional is reformulated as a constrained minimization problem.Combining the augmented Lagrangian method and operator splitting techniques,the resulting saddle-point problem is solved by a serial of subproblems.To tackle the nonlinear constraints arising in the model,a novel fixed-point-based approach is proposed so that all the subproblems either is a linear problem or has a closed-form solution.We show the good performance of our approach in terms of speed and reliability using numerous numerical examples on synthetic,real-world and medical images for image denoising,image inpainting and image zooming problems.

Fast Linearized Augmented Lagrangian Method for Euler’s Elastica Model

Recently,many variational models involving high order derivatives have been widely used in image processing,because they can reduce staircase effects during noise elimination.However,it is very challenging to construct efficient algo-rithms to obtain the minimizers of original high order functionals.In this paper,we propose a new linearized augmented Lagrangian method for Euler’s elastica image denoising model.We detail the procedures of finding the saddle-points of the aug-mented Lagrangian functional.Instead of solving associated linear systems by FFTor linear iterative methods(e.g.,the Gauss-Seidel method),we adopt a linearized strat-egy to get an iteration sequence so as to reduce computational cost.In addition,we give some simple complexity analysis for the proposed method.Experimental results with comparison to the previous method are supplied to demonstrate the efficiency of the proposed method,and indicate that such a linearized augmented Lagrangian method is more suitable to deal with large-sized images.

Domain Decomposition of an Optimal Control Problem for Semi-Linear Elliptic Equations on Metric Graphs with Application to Gas Networks

We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a semi-linear model derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a given network and introduce a time discretization thereof. We then study the well-posedness of the corresponding time-discrete optimal control problem. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a non-overlapping domain decomposition of the semi-linear elliptic optimal control problem on the graph into local problems on a small part of the network, ultimately on a single edge.

基于变分法的超声图像斑点噪声自适应滤波算法

各向异性扩散模型在去除超声图像斑点噪声时不能有效保护图像细节,针对上述问题本文提出基于变分法的自适应最小能量去噪模型。首先直接将由微分方程表示的各向异性扩散模型转化为最小能量变分模型;然后引入欧拉弹性能量模型,在去除噪声的同时有效地保护和增强图像细节。同时为了解决数值求解过程中出现的迭代次数与迭代步长的矛盾,本文还提出迭代停止准则和自适应变步长去噪算法。仿真和真实超声图像的实验结果表明基于变分法的超声图像斑点噪声自适应滤波算法在去噪的同时能够很好地保护细节信息,而且能有效地减少迭代次数。

价层电子对互斥理论的一种简洁推导

价层电子对互斥理论在推测分子构型方面有着广泛的应用,是现代分子结构理论的一个重要知识点,通过简洁的数学推导证明了分子构型与价层电子对之间的对应关系,并根据解析几何学分析多面体各顶点与其中心的距离,借以判断多原子分子中中心原子的孤对电子应处的位置,其结论完全符合价层电子对互斥理论的预测。

基于模板的图像修复算法优先权的改进

研究了基于块填充的图像修复算法,修复图像的质量容易受到待修复区域边界像素修复顺序的影响,通过分析待修复区域像素点所在模块的图像特征,改进了填充算法的优先权,分别是基于P-Laplace算子和Euler’s elastica模型的优先权计算方法的改进。实验结果证实了文中所介绍算法能有效提高重建图像的感知质量。

水轮机蜗壳和固定导叶内部流动的数值模拟研究

为探求蜗壳内部的流动规律,优化蜗壳设计,对三峡混流式水轮机组模型蜗壳和固定导叶内部的流动进行了紊流解和欧拉解的全三维数值模拟。文中基于Navier—Stokes方程的标准K—ε紊流模型、欧拉方程模型,采用贴体座标和交错网格系统,用SIMPLEC算法.对蜗壳和固定导叶内部流动的联合计算结果进行对比分析.并与实验值进行了比较。最后对流动的不均匀性进行了分析.首次提出了改进和优化蜗壳及固定导叶设计的较为可信的解决方案。

Segmentation by Elastica Energy with L^(1) and L^(2) Curvatures: a Performance Comparison

In this paper,we propose an algorithm based on augmented Lagrangian method and give a performance comparison for two segmentation models that use the L^(1)-and L^(2)-Euler’s elastica energy respectively as the regularization for image seg-mentation.To capture contour curvature more reliably,we develop novel augmented Lagrangian functionals that ensure the segmentation level set function to be signed dis-tance functions,which avoids the reinitialization of segmentation function during the iterative process.With the proposed algorithm and with the same initial contours,we compare the performance of these two high-order segmentation models and numerically verify the different properties of the two models.

运输类飞机高升力构型数值模拟研究

高升力装置对大多数运输机的大小、吨位、经济性及安全性都有重要的影响。由于复杂的流动机理、几何外形、支撑机构及驱动系统之间的矛盾关系,导致高升力系统的设计周期很长并且很大程度上依赖于试验[1]。然而,随着计算机软件和硬件的迅速发展,近几年的工程设计中N-S方程应用日趋广泛。在空气动力学设计领域,计算机辅助设计手段已经逐步替代了过去的经验设计手段,并且国内飞机设计单位的科研人员也开始花费越来越多的时间应用流体仿真软件来达到设计目标,而不是像过去那样完全依赖试验结果去设计和分析飞机气动力特性,高升力装置设计也是如此。本文着重对著名的MSES软件和CFX软件在高升力装置模拟中的工程应用进行探索,并和风洞试验结果进行比较,初步研究了高升力装置数值模拟在飞机设计工程应用中存在的一些问题。

S形通道中金属熔体与固体颗粒流动混合的数值模拟研究

金属基复合材料的性能、应用、成本等在很大程度上取决于材料的制造技术,因此研究和发展有效的制造技术一直是金属基复合材料研究中的最重要的问题之一。本文提出了一种基于S形流道的固体颗粒-金属流体混合方法,并采用欧拉-离散相模型分析计算了该流道内的颗粒-流体混合过程。研究结果表明,S形流道内流体具有周期性变化的流动方向及流速,同时在横截面内存在旋转方向周期性改变的涡流,能够强化颗粒在金属流体中的分散过程。分析了颗粒在S形通道内的均匀度,在第三级出口处的颗粒均匀度达到0.915,表明该方法能够较好的实现固体颗粒在金属液内的均匀分散,进而实现颗粒增强金属基复合材料的制备。

企业资本性支出实证模型选择及检验

检验企业资本性支出的实证模型的优化选择,无疑会为实证研究企业投资奠定良好基础。本文首先对国外以往文献中常用的投资模型进行了分析评价,根据我国资本市场的独有特点,选择出理论上更适用于我国上市公司的投资模型。其次,本文采用我国上市公司1999—2005年的数据资料。进一步实证检验了所选模型对中国资本市场的适用性。结果表明,我国上市公司企业内部现金流与其资本性支出之间存在着显著的正相关关系,即企业资本性支出对内部现金流具有显著的敏感性,并且在非国有控制的上市公司中敏感性更强;所选模型在解释我国资本市场中企业的资本性支出时具有较强的稳健性。