一个简洁的最小二乘法拟合程序

一个简洁的最小二乘法拟合程序陈乃强（河北师范学院物理系石家庄０５００９１）用最小二乘法对含有随机误差的离散数据进行曲线拟合，能将变量ｘ与ｙ间变化关系的ｍ对测量值，总结成ｘ、ｙ间最可几的函数表达式ｙ＝ｆ（ｘ）．但由于此方法所需计算量甚大，故只有在微机已...     

核磁共振弛豫时间测量数据处理方法的讨论

分析和讨论了在超小型核磁共振成像仪测量弛豫时间T1的数据处理方法中存在的问题,并提出了测量方法和数据拟合的改进方案.     

基于改进非线性拟合的核磁共振T2谱多指数反演

核磁共振T₂谱多指数反演算法是开展复杂体系样品核磁共振(NMR)弛豫研究最重要的数学工具. 常用的T₂谱多指数反演算法一般都是事先给出弛豫时间T₂分布的布点, 然后转化为线性拟合问题进行求解. 在求解的T₂谱较为分散的时候, 反演得到的T₂谱精确度不高, 分辨率较低. 非线性拟合是解决这个问题的有效办法. 本文针对分散T₂谱反演利用非线性拟合时遇到的初值依赖及运算复杂问题, 利用线性回归最小二乘方法, 改进了其中的带非负约束非线性优化模型, 将搜索的反演参数从T₂, f 减少为T₂, 加快了收敛速度, 减少了对初值的依赖, 提高了反演精度, 使算法更加稳健. 通过用改进的Levenberg-Marquardt算法和差分进化算法进行计算机模拟反演及实验数据反演, 验证了改进方法在核磁共振T₂ 谱反演中的有效性.     

最小二乘法直线拟合基本假定的几点讨论

本文讨论物理实验中因不满足基本假定不宜用最小二乘法进行直线拟合的几种情况。     

基于二维核磁共振弛豫谱的雷四段孔隙度计算方法

基于常规测井资料的体积模型和一维核磁共振（NMR）测井资料的固定截止值法,可以计算地层孔隙度,但是扩径段孔隙度计算结果偏大.本文通过川西海相雷四段岩心样品NMR实验和实测二维NMR测井资料,开展扩径段的T₂、T₁孔隙度计算方法研究.首先总结不同孔径流体在T₂谱和T₁谱上的响应特征,分析钻井液流体峰截止值的分布范围和影响因素,建立钻井液流体弛豫时间截止值的计算模型;然后根据未扩径段和扩径段的粘土束缚水弛豫时间截止值确定原则,确立变粘土束缚水弛豫时间截止值的有效孔隙度计算方法.多口井的应用效果表明,基于T₁谱的孔隙度计算结果精度更高、定量分析误差小,能有效解决扩径段孔隙度计算结果偏大的问题,满足储层评价的要求.     

基于Matllab的约束最小二乘法拟合磁滞回线

由实验测得的磁滞回线数据的是一系列离散、带噪声的值。通过约束最小二乘方法对曲线进行分段拟合,使曲线的畸变程度得到了改善,准确地表达磁滞回线的特性,为磁材料的定量分析述提供了基础。     

用最小二乘法进行直线拟合的讨论

文章讨论了实验数据一元线性回归中应该注意的两个问题：自变量选择和线性关系检验，并扼要介绍了回归分析中常用的Ｆ检验方法，     

最小二乘法线性拟合的一个问题

指出在一些物理实验教材中，讲述最小二乘法线性拟合时的一个问题，以期引起注意。     

数据区对最小二乘法拟合函数系数偏差的影响

一、问题提出在许多问题的研究中需要对实验结果作出理论解释。提出理论模型,用最小二乘法进行测量数据拟合,以此来验证理论模型的正确性。在组合测量的数据处理过程中,同时给出各拟合参量(系数)的估计偏差。拟合结果有时是曲线与实验点符合很好,而有些参量的估计偏差却很大,怎样解释这些大偏差呢?     

核磁共振实验教学内容的重组与优化

探索研究了一种将连续核磁共振和脉冲核磁共振有机融合的实验教学方法.在实验中,利用多媒体课件展示核磁共振的物理原理,学生分别采用连续和脉冲核磁共振方法测量同样浓度的CuSiO4水溶液的表观弛豫时间和横向弛豫时间,了解样品浓度、磁场非均匀度等因素对横向弛豫时间测量的影响.     

Solution dynamics of the natural bioactive molecule capsaicin: a relaxation study

Nuclear magnetic resonance spectroscopy is a straightforward technique for studying molecular dynamics that range in timescale from picosecond (motions faster than molecular reorientation) to those that occur in real-time. This approach is important to highlight the behavior of bioactive molecules in solution, and to acquire information about action mechanisms and potential pharmacological effects. Proton and carbon-13 spin–lattice relaxation experiments were performed to calculate the reorientational correlation time for protonated carbons. Capsaicin showed complex dynamical properties and the results revealed two regions with different dynamical properties: the aliphatic region with fast reorientation motions and the aromatic region with slow motions.     

Effect of flow on the apparent transverse relaxation time in a microfluidic nuclear magnetic resonance chip

The detection of samples in a microfluidic nuclear magnetic resonance chip is generally performed under flow condition. To study the effect of sample flow on the apparent transverse relaxation time in a microfluidic nuclear magnetic resonance chip, theoretical calculations were performed on three microfluidic samples (including deionized water, absolute ethanol, and copper sulfate pentahydrate) for flow velocities in the range 1.7–25?mm/s. A microfluidic nuclear magnetic resonance device with a low cost microfluidic solenoid coil was fabricated to verify the theoretical calculations by experiments. The results show that the apparent transverse relaxation time of the sample is a monoexponential decay with respect to flow velocity. In addition, it was found that the experimental values and the theoretical values of the apparent transverse relaxation time are identical when the samples are prepolarized completely; but for the samples that are not prepolarized completely, all the experimental values are smaller than the theoretical values and their difference increases with the flow velocity of the sample. After further study, it was discovered that the relative error between the experimental values and the theoretical values is a monoexponential decay to the level of the sample to be prepolarized. This discovery is very useful, because it can be used to modify the theoretical calculation model of the apparent transverse relaxation time for the samples that are prepolarized incompletely, as well as improve the application of microfluidics on nuclear magnetic resonance.     

利用核磁共振测量乙醇汽油溶液浓度

利用核磁共振成像分析仪测量了不同汽油体积含量的乙醇汽油溶液的核磁共振信号,分析了横向弛豫时间、信号强度与汽油浓度的关系.结果表明乙醇汽油溶液中汽油的体积含量与信号强度呈线性关系,因此利用低磁场核磁共振可以测量乙醇汽油浓度.     

A new method for multi-exponential inversion of NMR relaxation measurements

The NMR technique has been widely applied to petroleum well logging and rock core analysis since the 1990s when NUMAR introduced a reliable NMR logging tool to the oil industry. It has been playing an important role for prospecting and exploiting resource of oil and gas for the last ten years. In an oil well, NMR can provide parameters of reservoir and fluid properties, such as porosity, pore size distribution, bound water volume, bulk volume of free water, permeability, in-situ fluid dif…     

低场核磁共振扩散-横向弛豫二维反演算法

针对低场核磁共振一维反演中无法分辨一维谱中重叠组分和目前报道的扩散-横向弛豫二维反演算法计算量大、计算耗时长的问题,提出了一种计算量小、计算效率高、耗时短的扩散-横向弛豫二维反演算法. 首先对扩散系数D-和横向弛豫时间T₂进行布点;其次根据信号采集条件计算出两个核心矩阵,并分别进行奇异值分解;然后,由所采集信号计算出两个核心矩阵的奇异值截断值,分别对两个核心矩阵的奇异值矩阵进行截断并求其逆矩阵;最后计算出初始反演结果,并添加非负约束经过多次迭代得到最终反演结果. 实验结果证明,提出的扩散-横向弛豫二维反演算法在不影响反演结果准确性的基础上,能极大提高计算效率.     

Probing the analogy of the proton relaxation in biological tissues and porous media

Summary Experimental data are reported that show the analogy of longitudinal and transverse proton relaxation in heterogeneous systems as different as biological tissues and water-saturated rocks. Published data on the τ-dependence of the transverse-relaxation rate for biological tissues with magnetite grains, used as a contrast agent in MRI, are discussed in the light of our recent results on water-saturated porous media, and give for the liver another case of a behaviour parallel to that in rocks. There are enough similarities between NMR relaxation in tissues and in other porous media that, for work in either area, attention to the other is likely to be fruitful. Work supported by Italian CNR and MURST grants     

自旋回波的简易观测方法及共振弛豫分析

在脉冲核磁共振实验中,通常采用自旋回波法测量共振弛豫时间,但模拟示波器观测难以获得准确的实验数据.通过对计算机标准配置资源声卡的性能检测及标定,使其达到物理实验测量数据定量分析的教学要求,同时利用免费的简易程序实现多通道数字信号采集功能并用于观测记录脉冲核磁共振信号.配合实验操作技术改进,既准确地测量了横向弛豫时间,又展现了符合物理实验教学的计算机应用方法.     

Four complementary theoretical approaches for the analysis of NMR paramagnetic relaxation

Four theoretical and computational approaches used at the University of Michigan to analyze NMR paramagnetic relaxation enhancement (NMR-PRE) are described. The primary objective of the theory is to describe the relationship of the NMR-PRE phenomenon to the electron spin hamiltonian and the spin energy level structure when zero field splitting interactions are significant. Four formulations of theory are discussed: (1) spin dynamics simulation; (2) the laboratory frame "constant H(S)" formulation; (3) the Molecular Frame "constant H(S)" formulation; and (4) the zfs-limit "constant H(S)" formulation. No single theoretical approach describes all important aspects of the relaxation mechanism in a fully satisfactory way. We use the four formulations in a complementary manner to provide as complete a picture of the relaxation mechanism as possible. We also discuss the integration of NMR-PRE theory and recently developed theory of electron spin relaxation which accounts for effects of the permanent zfs hamiltonian.