Flow pattern analysis of linear gradient flow distribution

This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An Lx-function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement.

A Node-Based Smoothed Finite Element Method with Linear Gradient Fields for Elastic Obstacle Scattering Problems

In this paper,a node-based smoothed finite element method(NS-FEM)with linear gradient fields(NS-FEM-L)is presented to solve elastic wave scattering by a rigid obstacle.By using Helmholtz decomposition,the problem is transformed into a boundary value problem with coupled boundary conditions.In numerical analysis,the perfectly matched layer(PML)and transparent boundary condition(TBC)are introduced to truncate the unbounded domain.Then,a linear gradient is constructed in a node-based smoothing domain(N-SD)by using a complete order of polynomial.The unknown coefficients of the smoothed linear gradient function can be solved by three linearly independent weight functions.Further,based on the weakened weak formulation,a system of linear equation with the smoothed gradient is established for NS-FEM-L with PML or TBC.Some numerical examples also demonstrate that the presented method possesses more stability and high accuracy.It turns out that the modified gradient makes the NS-FEM-L-PML and NS-FEM-L-TBC possess an ideal stiffness matrix,which effectively overcomes the instability of original NS-FEM.Moreover,the convergence rates of L 2 and H1 semi-norm errors for the two NS-FEM-L models are also higher.

Accurate assessment of antibiotic susceptibility and screening resistant strains of a bacterial population by linear gradient plate

The dynamics of a bacterial population exposed to theminimum inhibitory concentration (MIC) of an antibiotic is an important issue in pharmacological research.Therefore,a novel antibiotic susceptibility test is urgently needed that can both precisely determine the MIC and accurately select antibiotic-resistant strains from clinical bacterial populations.For this purpose,we developed a method based on Fick's laws of diffusion using agar plates containing a linear gradient of antibiotic.The gradient plate contained two layers.The bottom layer consisted of 15 mL agar containing the appropriate concentration of enrofloxacin and allowed to harden in the form of a wedge with the plate slanted such that the entire bottom was just covered.The upper layer consisted of 15 mL plain nutrient agar added with the plate held in the horizontal position.After allowing vertical diffusion of the drug from the bottom agar layer for 12 h,the enrofloxacin concentration was diluted in proportion to the ratio of the agar layer thicknesses.The uniform linear concentration gradient was verified by measuring the enrofloxacin concentration on the agar surface.When heavy bacterial suspensions were spread on the agar surface and incubated for more than 12 h,only resistant cells were able to form colonies beyond the boundary of confluent growth of susceptible cells.In this way,the true MIC of enrofloxacin was determined.The MICs obtained using this linear gradient plate were consistent with those obtained using conventional antibiotic susceptibility tests.Discrete colonies were then spread onto a gradient plate with higher antibiotic concentrations;the boundary line increased significantly,and gene mutations conferring resistance were identified.This new method enables the rapid identification of resistant strains in the bacterial population.Use of the linear gradient plate can easily identify the precise MIC and reveal the dynamic differentiation of bacteria near the MIC.This method allows the study of genetic and physiological characteristics of individual strains,and may be useful for early warning of antibiotic resistance that may occur after use of certain antimicrobial agents,and guide clinical treatment.

The principle of optimization of binary mobile phase composition of multi-step linear gradient elution

The basic principle of optimal method called “moving overlapping resolution mapping Method” to select the optimal binary mobile phase composition of multi-step linear gradient liquid chromatography is discussed with simultaneously considering effects of position of solute inside the column and mobile phase composition on peak resolution and retention value, then a BASIC program based on this principle is developed in IBM-PC computer. The validities of both principle of optimization and BASIC program are confirmed by separation of samples Containing bile acids and PAHs in RP-HPLC.

C^1 natural element method for strain gradient linear elasticity and its application to microstructures

C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation （NNI）, with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions （EBCs） can be imposed directly in a Galerkin scheme for partial differential equations （PDEs）. In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor （SCF） are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.

GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR LINEAR AND NONLINEAR PARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS

In this article, we will derive local elliptic type gradient estimates for positive solutions of linear parabolic equations （△-e/et）u（x,t）＋q（x,t）u^p（x,t）=0 and nonlinear parabolic equations （△-e/et）u（x,t）＋h（x,t）u^p（x,t）=0（p 〉 1） on Riemannian manifolds.As applications, we obtain some theorems of Liouville type for positive ancient solutions of such equations. Our results generalize that of Souplet-Zhang （[1], Bull. London Math. Soc. 38（2006）, 1045-1053） and the author （[2], Nonlinear Anal. 74 （2011）, 5141-5146）.

Multi-segment linear gradient optimization strategy based on resolution map in HPLC

Based on the mechanism of chromatographic retention (the relationship between the retention of solute and the mobile phase conditions) and method of resolution map, several methods of optimizing multi-segment linear gradient elution conditions were proposed according to the different separation requirements of various samples. These methods were verified using literature data. Moreover, the advantages and disadvantages of these methods were compared. It was proved that the third method is a fast optimization method which is capable of separating all the components with relatively high resolution.

Linear Regression and Gradient Descent Method for Electricity Output Power Prediction

Regulating the power output for a power plant as demand for electricity fluctuates throughout the day is important for both economic purpose and the safety of the generator. In this work, gradient descent method together with regularization is investigated to study the electricity output related to vacuum level and temperature in the turbine. Ninety percent of the data was used to train the regression parameters while the remaining ten percent was used for validation. Final results showed that 99% accuracy could be obtained with this method. This opens a new window for electricity output prediction for power plants.

High-efciency improved symmetric successive over-relaxation preconditioned conjugate gradient method for solving large-scale finite element linear equations

Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.

A New Conjugate Gradient Projection Method for Solving Stochastic Generalized Linear Complementarity Problems

In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.

一种基于线性零磁场的动脉血管扫描成像方法仿真

基于磁电耦合效应的血流检测及血管成像是实现心血管疾病早期诊疗的有效方法之一。该文基于磁场与血流耦合电效应,设计一种用于动脉血管扫描成像的组合线圈结构,产生带有零磁场线(FFL)区域的线性梯度磁场;在此结构的基础上,通过控制激励电流驱动FFL实现成像区域双向扫描;结合卷积神经网络(CNN)实现磁电耦合信号与血管信息的非线性映射,进而提出一种基于线性零磁场的动脉血管扫描成像新方法。采用多物理场仿真软件COMSOL对基于线性零磁场的血管扫描成像方法进行建模,求解磁电耦合信号,验证了所提出方法的合理性和有效性。结果表明,线性梯度磁场模式下的磁电耦合信号含有血管位置、半径等信息;CNN重建血管位置误差平均值为1.5694 mm,重建血管半径的方均误差(MSE)和相关系数(CC)平均值分别为0.0548和0.9870。研究结果可用于血管成像装置设计及后续相关临床应用提供研究支撑。

考虑用户负荷率因素的电力市场偏差电量定价方法

针对偏差电量定价中尚未考虑用户的负荷率变化,导致电力交易各方的经济利益不均衡问题,提出考虑用户负荷率因素的电力市场偏差电量定价方法。以售电量时间序列为基准,完成基于多元线性回归的电力市场售电量预测。在此基础上,建立基于月用电量偏差率的惩罚机制,考虑负荷率和偏差率的变化确定对应偏差电量的电价。通过某区域电力市场交易数据试验,负荷率的波动直接影响购电公司收益,提出的偏差电量定价方法能够降低偏差考核电费对整体收益的影响,规范电量市场交易行为,在一定程度上均衡用户和售电企业各方的利益。

基于监督下降法的大地电磁二维反演及应用研究

传统的大地电磁二维反演方法较为成熟,但仍存在反演结果依赖初始模型和正则化参数选取、容易陷入局部极小值等问题。监督下降法是一种学习平均下降方向来预测数据残差的机器学习算法。本文尝试采用监督下降法解决传统的大地电磁二维反演存在的问题,基于监督下降法理论开发了大地电磁二维反演算法,设计理论模型合成算例验证了算法的正确性,并对西藏高原实测数据进行反演,检验了监督下降法的实用性。理论模型合成数据和实测数据反演结果表明,相较于传统的非线性共轭梯度反演,基于监督下降法的反演具有收敛速度快、反演效果好、抗噪能力强等特点。

结合机器学习的SA湍流模型闭合系数修正

将修正Morris分类筛选法与极端梯度提升(extreme gradient boosting,XGBoost)相结合,在计算流体动力学(computational fluid dynamics,CFD)数据驱动下,用于SA(Spalart-Allmaras)湍流模型闭合系数的修正.利用分类筛选法有效缩小闭合系数研究范围,同时依据XGBoost方法在小规模数据集下取得精度较高的拟合模型,有效提升系数修正效率.在三维DLR-F6-WB构型下进行了数值实验,实验结果显示利用本方法能够在三维复杂模型上基于小样本数据进行系数修正,修正后的升阻力系数计算精度得到了显著提升.

InGaN基蓝光激光器p型覆盖层和波导层优化

[目的]为了进一步提升蓝光激光器的性能,基于实验样品结构,研究了p型覆盖层和波导层对InGaN基边发射蓝光激光器性能的综合影响.[方法]将p型覆盖层优化为多层Al组分渐变的结构,以降低p型覆盖层与电子阻挡层的Al组分差值;优化波导层的In组分浓度,以提高波导层的光限制能力.利用PICS3D软件模拟计算其光输出功率、能带结构、光场分布、载流子电流密度分布等特性.[结果]随着p型覆盖层层数的增加,以及p型覆盖层与电子阻挡层之间Al组分差值的减小,光输出功率和斜率效率不断提高;随着上波导层In组分的增加,光输出功率提升明显.同时优化两者得到的最终优化结构,光输出功率可达到0.421 W,相较标准结构提升了65.75%.[结论]降低p型覆盖层与电子阻挡层之间的Al组分差值,可以有效降低两者之间的晶格失配和势垒差,进而提高有源区的空穴注入;增加p型覆盖层的层数可降低晶格失配,进而降低载流子的传输损耗.增加波导层的In组分浓度可以提高有效提高光限制因子,尤其是上波导的In组分增加对提高光限制因子非常明显.

液相色谱中线性溶剂强度模型的快速建立

目的通过一组单线性梯度洗脱实验获取线性溶剂强度模型的参数值,为色谱图的预测提供所必须的参数值。方法首先,在实验中固定流动相组成的起始和结束值,通过改变梯度洗脱的时间,从而改变梯度的斜率(B)。测定溶质在这些梯度条件下的保留时间,计算其流出色谱柱时所对应的流动相组成(φR)。然后,将描述φR与B之间关系的数学公式对实验数据进行非线性拟合,从而获取线性溶剂强度模型的参数值。拟合基于Levenberg-Marquardt算法,通过Excel中的Visual Basic for Applications(VBA)语言编程实现。结果计算机程序的可靠性通过实验进行验证。以12种芳环化合物为分离的对象,以C18柱为固定相,含1%乙酸的甲醇-水溶液为流动相,应用所编写的程序对单线性梯度洗脱实验数据进行处理,获取溶剂强度模型的参数值。然后,根据所得到的参数值预测多线性梯度洗脱条件下的色谱图,得到的理论色谱图与实验色谱图吻合。结论所建立的方法可快速准确地获取线性溶剂强度模型的参数值,具有良好的实用价值。

基于多尺度梯度域引导滤波的煤矿井下图像增强方法

煤矿井下图像存在较严重的光照不均匀和噪声干扰,现有基于Retinex的方法直接应用于煤矿井下图像增强易出现光晕伪影、边缘模糊、过增强和噪声放大等问题。针对上述问题,提出了一种基于多尺度梯度域引导滤波的煤矿井下图像增强方法。首先,将多尺度思想引入梯度域引导滤波中,实现对非均匀光照的准确估计,有效解决了增强图像时光晕伪影及边缘模糊的问题。然后,利用Retinex模型分离出光照分量和反射分量:对于光照分量,通过自适应伽马校正函数逐像素地修正光照信息,实现对图像暗区域增强的同时,抑制亮区域过增强,并使用限制对比度自适应直方图均衡化方法调整图像对比度;对于反射分量,将梯度域引导滤波与多尺度细节提升相结合,在准确去除噪声后提升纹理细节,避免了增强图像时噪声放大的问题。最后,将处理后的光照分量及反射分量融合,计算图像增益系数,并使用线性色彩恢复方法实现对原始RGB图像的逐像素增强,提升方法处理效率。实验结果表明,从主客观角度与现有方法相比,经所提方法处理后的图像在色彩保持、对比度、噪声抑制、细节保留等方面均取得了较好的增强效果,同时处理效率较高。

基于L0梯度平滑与图像分块聚类的海天线检测

海天线检测在海洋工程安防活动中具有重要的意义,真实海洋环境中的海天线检测易受云朵、海浪、光照变化、目标遮挡物、边界模糊等外界干扰。为了实现对真实海洋环境中海天线的检测,本研究提出一种基于L0梯度平滑和图像分块聚类的海天线检测算法。首先,对图像进行L0梯度平滑滤波,以增强海天线边缘,弱化非海天线因素干扰;接着,将图像沿着竖直方向分割成若干等宽图像块,以降低整体环境干扰,加强局部海天线检测效果;然后,通过Canny算子和霍夫变换提取每个分割图像块中的直线段;最后,采取K-means聚类算法提取每个图像块中的海天线段,拟合生成完整海天线。实验结果表明,在真实的海天线数据集中,本研究方法获取的矩形框重叠率平均精度为93.22%,角度差平均精度为7.66%,均高于文中选取的近年典型对比算法。满足实际海天线检测抗干扰强、准确率高、适应性广等要求。

Mathstudio在大学物理实验数据处理中应用

将数学软件Mathstudio应用到大学物理实验数据处理中,进行描述性统计、推断统计、求不确定度、线性回归等运算。Mathstudio具备数值运算和符号运算功能,使用数组和切片(Slice)操作,内置大量数学函数,微积分、统计等功能很强大,作图和动画也方便。Mathstudio不用安装、编译,浏览器打开网址即可运行,可逐行调试,命令格式简单。示例结合线性代数理论,使用了雅可比矩阵、海森矩阵、范数、线性回归、作图等命令,实现Mathstudio编程计算空心圆柱体体积的不确定度、铜-康铜热电偶温差电势的线性回归模型,程序简短精练,结构清晰,提高了数据处理效率。Mathstudio编程效率高,难度较低,适合小规模数据快速分析,也能进一步开发更专业的数据处理功能。

考虑相含量的TC17钛合金线性摩擦焊中的残余应力

为了获得准确的TC17钛合金线性摩擦焊中的残余应力,建立TC17钛合金弹性常数与相分数之间的数值关系。结合焊接区域的相分数,获得呈梯度分布的弹性常数,并将其引入轮廓法进行计算。结果表明,TC17钛合金的弹性常数与α相分数呈正相关,在宽度约4 mm的焊接区域呈现明显的梯度分布特征;若忽略相分数的梯度分布,计算残余应力时相对误差可达36.06%;修正后的残余应力呈双峰分布,在热影响区边缘处达到峰值,约为442 MPa。这说明考虑相分数的梯度分布是必要的。