基于MATLAB图像处理技术计算微纳米级磨损量

利用Hysitron纳米压痕仪对聚碳酸酯/二氧化硅(PC/SiO2)纳米复合材料进行微/纳米级(10-6～10-9m)磨损实验.本文首先指出了常用微纳米级磨损量计算方法的不足之处,并结合MATLAB数字图像处理技术的优点分析了MATLAB用来改进磨损量计算方法的可行性.然后,利用MATLAB编程结合Photoshop处理提取了完整连续的磨损区边缘,并用模板法实现了对磨损前后图片的配准.最后,使用改进的方法计算了不同载荷条件下材料的磨损体积,并将结果与常用微纳米级磨损量计算方法所得结果进行比较,结果表明改进后的方法过程更加合理,所得结果更加精确.     

A GUI tool for beta function measurement using MATLAB

The beta function measurement is used to detect the shift in the betatron tune as the strength of an individual quadrupole magnet is varied. A GUI (graphic user interface) tool for the beta function measurement is developed using the MATLAB program language in the Linux environment, which facilitates the commissioning of the Shanghai Synchrotron Radiation Facility (SSRF) storage ring. In this paper, we describe the design of the application and give some measuring results and discussions about the definition of the measurement. The program has been optimized to solve some restrictions of the AT tracking code. After the correction with LOCO (linear optics from closed orbits), the horizontal and the vertical root mean square values (rms values) can be reduced to 0.12 and 0.10.     

方形自聚焦透镜折射率分析

利用MATLAB 偏微分方程工具箱(PDE)实现方形玻璃纤维边界条件下离子扩散的有限元解法,给出一般步骤,对离子交换制备方形自聚焦透镜过程进行计算机模拟.运用分离变量法求解方形玻璃纤维中Tl+离子浓度定解方程,由离子浓度与折射率的线性关系,得到了方形自聚焦透镜折射率分布的数学表达式,计算出折射率分布图以及理论值.与实验值校验表明,相对误差小于0.33%.     

利用莫尔条纹测量物体三维形貌新方法研究

提出了以计算机控制光栅产生莫尔条纹来测量物体三维形貌的新方法.利用计算机控制空间光调制器（Space Light Modulator,SLM）产生可控制幅度及位相的理想光栅,将平行光波投影到待测物体上,其反射光通过参考光栅形成莫尔条纹,利用CCD接收并进行数字图像处理,恢复出待测物体的三维形貌.对此方法进行了理论分析,推导了变形莫尔条纹与待测物形貌变化的关系式.利用MATLAB对此关系式进行仿真计算,其准确度可达0.011 μm.     

用MATLAB简化溶液氢离子浓度计算的教学内容

溶液氢离子浓度计算涉及大量公式及繁杂的使用条件,是公认的教学重点和学习难点。将分布分数代入质子条件式即得关于氢离子浓度的一元高次方程,可用MATLAB方便地求解。因此,只要会写质子条件式就能迅速得到氢离子浓度,从而摆脱大量公式的烦扰,便于学生将精力更有效地集中于分析化学主体知识的学习。     

MATLAB在有限元教学中的应用与实践

 利用MATLAB在有限元教学中进行公式推导和程序编写, 可极大地降低学生掌握有 限元理论和进行程序设计的难度, 从而提高学习兴趣和效率. 另外, 利用MATLAB强大的图形 处理功能, 也可方便地进行有限元分析的后处理, 增加学生对计算结果的感性认识, 提 高教学效果. 经过几年的教学实践, 发现学生经过本课程后, 均具有独立使用MATLAB进行有 限元程序设计的能力.     

Minimum principle sufficiency

We characterize the property of obtaining a solution to a convex program by minimizing over the feasible region a linearization of the objective function at any of its solution points (Minimum Principle Sufficiency). For the case of a monotone linear complementarity problem this MPS property is completely equivalent to the existence of a nondegenerate solution to the problem. For the case of a convex quadratic program, the MPS property is equivalent to the span of the Hessian of the objective function being contained in the normal cone to the feasible region at any solution point, plus the cone generated by the gradient of the objective function at any solution point. This in turn is equivalent to the quadratic program having a weak sharp minimum. An important application of the MPS property is that minimizing on the feasible region a linearization of the objective function at a point in a neighborhood of a solution point gives an exact solution of the convex program. This leads to finite termination of convergent algorithms that periodically minimize such a linearization.This material is based on research supported by National Science Foundation Grants DCR-8521228 and CCR-8723091, and Air Force Office of Scientific Research Grants AFOSR 86-0172 and AFOSR and AFOSR 89-0410.     

Computing the Matrix Cosine

An algorithm is developed for computing the matrix cosine, building on a proposal of Serbin and Blalock. The algorithm scales the matrix by a power of 2 to make the -norm less than or equal to 1, evaluates a Padé approximant, and then uses the double angle formula cos(2A)=2cos(A)²–I to recover the cosine of the original matrix. In addition, argument reduction and balancing is used initially to decrease the norm. We give truncation and rounding error analyses to show that an [8,8] Padé approximant produces the cosine of the scaled matrix correct to machine accuracy in IEEE double precision arithmetic, and we show that this Padé approximant can be more efficiently evaluated than a corresponding Taylor series approximation. We also provide error analysis to bound the propagation of errors in the double angle recurrence. Numerical experiments show that our algorithm is competitive in accuracy with the Schur–Parlett method of Davies and Higham, which is designed for general matrix functions, and it is substantially less expensive than that method for matrices of -norm of order 1. The dominant computational kernels in the algorithm are matrix multiplication and solution of a linear system with multiple right-hand sides, so the algorithm is well suited to modern computer architectures.     

用MATLAB解决高等数学中的图形问题

本文通过实例将 MATLAB与 Mathematica的图形功能做了比较 ,指出了 MATLAB在解决高等数学图形问题时的优势 .     

Global Optimization of Nonconvex Polynomial Programming Problems Having Rational Exponents

This paper considers the solution of nonconvex polynomial programming problems that arise in various engineering design, network distribution, and location-allocation contexts. These problems generally have nonconvex polynomial objective functions and constraints, involving terms of mixed-sign coefficients (as in signomial geometric programs) that have rational exponents on variables. For such problems, we develop an extension of the Reformulation-Linearization Technique (RLT) to generate linear programming relaxations that are embedded within a branch-and-bound algorithm. Suitable branching or partitioning strategies are designed for which convergence to a global optimal solution is established. The procedure is illustrated using a numerical example, and several possible extensions and algorithmic enhancements are discussed.