二维线性化Navier-Stokes-Poisson方程解的逐点估计

本文研究了二维空间线性化的等熵可压缩Navier-Stokes-Poisson方程柯西问题.通过把方程组转变成关于单个函数的方程,求解出各个函数,得到方程组的格林函数.利用对格林函数的详细分析,获得了方程组解的逐点估计.结果显示方程组中电流密度以热核的速度衰减,动量密度衰减慢得多,且其L2范数不衰减.

My Jump 2应用程序测量大学生下肢垂直刚度的信度和效度

背景:证实My Jump 2应用程序测量下肢垂直刚度的信效度水平,可为其作为Kistler三维测力台测量下肢垂直刚度的替代方法提供可能性。目的:验证My Jump 2应用程序测量大学生下肢垂直刚度的信效度。方法:通过Kistler三维测力台和My Jump 2应用程序采集受试者的跳深数据并计算受试者的下肢垂直刚度。采用组内相关系数分析My Jump 2应用程序与Kistler三维测力台测得的数据,以验证My Jump 2应用程序的信度。将2个设备之间的偏倚值和平均值绘制成Bland-Altman图,验证2种测试方法之间的一致性。最后,使用克朗巴哈系数(α)和变异系数分析My Jump 2应用程序在30,40 cm高度的重测信度,使用皮尔逊积矩相关系数分析My Jump 2应用程序的相关性。结果与结论:①My Jump 2应用程序在测量下肢垂直刚度时具有较高的信效度;②同时由于其具有低成本、携带便捷和可用于大样本的场地测试的优势,可作为测力台的替代工具在大学生以及类似人群中对下肢垂直刚度进行测试。

通过嵌合管来增强负Poisson比结构的耐撞性能

为了提高结构耐撞性,从而实现车辆轻量化,提出了一种嵌合管(由薄壁方形管嵌入双箭头格子而组成的)具有负Poisson比的增强型结构。通过负Poisson比的收缩效应,来增强负Poisson比结构和嵌合管的耦合作用。建立了增强型结构的有限元模型,并通过压缩试验,来验证其准确性;通过数值方法,在轴向载荷下,比较双箭头点阵结构、结构填充管和嵌合管负Poisson比增强型结构的耐撞性能,并进行了参数分析。结果表明:与双箭头点阵结构和填充管结构相比,增强型结构的总吸收能量为1.12 MJ,提升了约40%;比吸能13.2 kJ/kg,提升了约30%;短梁的夹角70°、长梁的夹角40°、长梁厚度1.4~1.6 mm、短梁厚度1.2 mm的结构填充管结构,具有较大的比吸能和较小的碰撞峰值力;增加嵌管厚度显著提升耐撞性能,但结构质量急剧增加,嵌管厚度达到1.2 mm左右时,兼顾耐撞性和轻量化的需求。

基于DP算法的Poisson回归模型的变量选择

利用已有的DP算法,对Poisson回归模型的似然函数进行优化估计出模型的参数,分别写出Lasso、Adaptive Lasso、SCAD、MCP 4种惩罚似然函数,用DP算法进行求解,实现变量选择.为了实现算法的自动变量选择,在对惩罚参数的选择上,使用了AIC、BIC信息准则.为了验证DP算法的可行性,通过随机模拟的方式生成数据进行求解.在各项指标下,将DP算法与已有的相关算法进行对比.

广义结构Poisson括号与Casimir函数

证明了广义结构Poisson括号恒等于零的相关结果并得到验证,改进了广义Poisson括号的Casimir函数的结果,并得到了一个推论。

任意特征域上sl(2)的Poisson结构

利用李代数上Poisson代数的定义与双线性决定了任意特征域上李代数sl(2)的所有Poisson结构,得到结论:特征不为2的域上,sl(2)的Poisson结构由一个参数完全决定,都是非交换且非结合的;特征为2的域上,sl(2)的Poisson结构由8个参数完全决定,而且既有结合的Poisson结构、交换的Poisson结构,也有非交换且非结合的Poisson结构.

一种三维Poisson-Nernst-Planck方程的虚单元计算

利用虚单元方法在多面体网格上求解一种三维稳态Poisson-Nernst-Planck(PNP)方程,并给出PNP方程的虚单元离散形式,推导电势方程及离子浓度方程的刚度矩阵与荷载向量的矩阵表达式.数值实验结果表明,在3种不同的多面体网格下实现了PNP方程的虚单元计算,数值解在L^(2)和H^(1)范数下均达到最优阶.

A fringe jump counting method for the phase measurement in the HCN laser interferometer on EAST and its FPGA-based implementation

Electron density in fusion plasma is usually diagnosed using laser-aided interferometers. The phase difference signal obtained after phase demodulation is wrapped, which is also called a fringe jump. A method has been developed to unwrap the phase difference signal in real time using FPGA, specifically designed to handle fringe jumps in the hydrogen cyanide(HCN) laser interferometer on the EAST superconducting tokamak. This method is designed for a phase demodulator using the fast Fourier transform(FFT) method at the front end. The method is better adapted for hardware implementation compared to complex mathematical analysis algorithms, such as field programmable gate array(FPGA). It has been applied to process the phase measurement results of the HCN laser interferometer on EAST in real time. Electron density results show good confidence in the fringe jump unwrapping method. Further possible application in other laser interferometers, such as the POlarimeter-INTerferometer(POINT)system on EAST tokamak is also discussed.

Fault Estimation for a Class of Markov Jump Piecewise-Affine Systems: Current Feedback Based Iterative Learning Approach

In this paper, the issues of stochastic stability analysis and fault estimation are investigated for a class of continuoustime Markov jump piecewise-affine(PWA) systems against actuator and sensor faults. Firstly, a novel mode-dependent PWA iterative learning observer with current feedback is designed to estimate the system states and faults, simultaneously, which contains both the previous iteration information and the current feedback mechanism. The auxiliary feedback channel optimizes the response speed of the observer, therefore the estimation error would converge to zero rapidly. Then, sufficient conditions for stochastic stability with guaranteed performance are demonstrated for the estimation error system, and the equivalence relations between the system information and the estimated information can be established via iterative accumulating representation.Finally, two illustrative examples containing a class of tunnel diode circuit systems are presented to fully demonstrate the effectiveness and superiority of the proposed iterative learning observer with current feedback.

Study of a Hydraulic Jump in an Asymmetric Trapezoidal Channel with Different Sluice Gates

In this study,the main properties of the hydraulic jump in an asymmetric trapezoidal flume are analyzed experimentally,including the so-called sequent depths,characteristic lengths,and efficiency.In particular,an asymmetric trapezoidal flume with a length of 7 m and a width of 0.304 m is considered,with the bottom of the flume transversely inclined at an angle of m=0.296 and vertical lateral sides.The corresponding inflow Froude number is allowed to range in the interval(1.40<F1<6.11).The properties of this jump are compared to those of hydraulic jumps in channels with other types of cross-sections.A relationship for calculating hydraulic jump efficiency is proposed for the considered flume.For F1>5,the hydraulic jump is found to be more effective than that occurring in triangular and symmetric trapezoidal channels.Also,when■mes>8 and■>5,the hydraulic jump in the asymmetrical trapezoidal channel downstream of a parallelogram sluice gate is completely formed as opposed to the situation where a triangular sluice is considered.

Asynchronous Learning-Based Output Feedback Sliding Mode Control for Semi-Markov Jump Systems: A Descriptor Approach

This paper presents an asynchronous output-feed-back control strategy of semi-Markovian systems via sliding mode-based learning technique.Compared with most literature results that require exact prior knowledge of system state and mode information,an asynchronous output-feedback sliding sur-face is adopted in the case of incompletely available state and non-synchronization phenomenon.The holonomic dynamics of the sliding mode are characterized by a descriptor system in which the switching surface is regarded as the fast subsystem and the system dynamics are viewed as the slow subsystem.Based upon the co-occurrence of two subsystems,the sufficient stochastic admissibility criterion of the holonomic dynamics is derived by utilizing the characteristics of cumulative distribution functions.Furthermore,a recursive learning controller is formulated to guarantee the reachability of the sliding manifold and realize the chattering reduction of the asynchronous switching and sliding motion.Finally,the proposed theoretical method is substantia-ted through two numerical simulations with the practical contin-uous stirred tank reactor and F-404 aircraft engine model,respectively.

基于重心插值配点法求解变系数广义Poisson方程

提出了一种求解二维变系数广义Poisson方程的重心插值配点法,重心插值配点法是一种真正的无网格配点方法,其在计算域内不用划分网格,得出的数值解在一定误差范围内可以无限接近精确解,同时具有很好的数值稳定性.本文中的数值算例均采用重心有理插值配点法和重心Lagrange插值配点法来计算,然后通过与解析解的比较,可以得出该方法具有快速、准确和易于数值计算的优点,是一种较好的数值计算方法.

线性Poisson-Boltzmann方程的虚单元L^(2)误差估计

针对一类线性Poisson-Boltzmann方程的虚单元L^(2)误差估计进行分析.首先引入正则化的线性Poisson-Boltzmann方程,将原问题转化为非奇性Poisson-Boltzmann方程.然后给出L^(2)范数的误差估计.最后在四边形和五边形混合多边形网格上进行数值实验,数值结果验证了理论分析的正确性.

Modified filter for mean elements estimation with state jumping

To investigate the real-time mean orbital elements(MOEs)estimation problem under the influence of state jumping caused by non-fatal spacecraft collision or protective orbit trans-fer,a modified augmented square-root unscented Kalman filter(MASUKF)is proposed.The MASUKF is composed of sigma points calculation,time update,modified state jumping detec-tion,and measurement update.Compared with the filters used in the existing literature on MOEs estimation,it has three main characteristics.Firstly,the state vector is augmented from six to nine by the added thrust acceleration terms,which makes the fil-ter additionally give the state-jumping-thrust-acceleration esti-mation.Secondly,the normalized innovation is used for state jumping detection to set detection threshold concisely and make the filter detect various state jumping with low latency.Thirdly,when sate jumping is detected,the covariance matrix inflation will be done,and then an extra time update process will be con-ducted at this time instance before measurement update.In this way,the relatively large estimation error at the detection moment can significantly decrease.Finally,typical simulations are per-formed to illustrated the effectiveness of the method.

Topology Optimization of Metamaterial Microstructures for Negative Poisson’s Ratio under Large Deformation Using a Gradient-Free Method

Negative Poisson’s ratio(NPR)metamaterials are attractive for their unique mechanical behaviors and potential applications in deformation control and energy absorption.However,when subjected to significant stretching,NPR metamaterials designed under small strain assumption may experience a rapid degradation in NPR performance.To address this issue,this study aims to design metamaterials maintaining a targeted NPR under large deformation by taking advantage of the geometry nonlinearity mechanism.A representative periodic unit cell is modeled considering geometry nonlinearity,and its topology is designed using a gradient-free method.The unit cell microstructural topologies are described with the material-field series-expansion(MFSE)method.The MFSE method assumes spatial correlation of the material distribution,which greatly reduces the number of required design variables.To conveniently design metamaterials with desired NPR under large deformation,we propose a two-stage gradient-free metamaterial topology optimization method,which fully takes advantage of the dimension reduction benefits of the MFSE method and the Kriging surrogate model technique.Initially,we use homogenization to find a preliminary NPR design under a small deformation assumption.In the second stage,we begin with this preliminary design and minimize deviations in NPR from a targeted value under large deformation.Using this strategy and solution technique,we successfully obtain a group of NPR metamaterials that can sustain different desired NPRs in the range of[−0.8,−0.1]under uniaxial stretching up to 20% strain.Furthermore,typical microstructure designs are fabricated and tested through experiments.The experimental results show good consistency with our numerical results,demonstrating the effectiveness of the present gradientfree NPR metamaterial design strategy.

稀疏过程在常利率环境下的广义Poisson风险模型中的应用

风险理论是连接数学与金融问题的一座桥梁,它是保险精算学(即实际寿险精算)的重要组成部分,是保险精算人员对保险业务进行风险管理的重要理论工具,同时也是保险公司发展业务进行有效营运的理论保证。破产概率是风险理论研究的核心问题,而利息是影响破产概率的重要因素。本文讨论了常利率环境下离散时间风险模型的破产概率,给出了模型的破产概率的上界。首先构造了风险模型,通过鞅方法得到模型的破产概率满足的Lundberg不等式和相关公式;然后给出了离散时间情形下的双险种风险模型,得到了与破产相关的一些变量的表达式和性质。

A gated recurrent unit model to predict Poisson’s ratio using deep learning

Static Poisson’s ratio(vs)is crucial for determining geomechanical properties in petroleum applications,namely sand production.Some models have been used to predict vs;however,the published models were limited to specific data ranges with an average absolute percentage relative error(AAPRE)of more than 10%.The published gated recurrent unit(GRU)models do not consider trend analysis to show physical behaviors.In this study,we aim to develop a GRU model using trend analysis and three inputs for predicting n s based on a broad range of data,n s(value of 0.1627-0.4492),bulk formation density(RHOB)(0.315-2.994 g/mL),compressional time(DTc)(44.43-186.9 μs/ft),and shear time(DTs)(72.9-341.2μ s/ft).The GRU model was evaluated using different approaches,including statistical error an-alyses.The GRU model showed the proper trends,and the model data ranges were wider than previous ones.The GRU model has the largest correlation coefficient(R)of 0.967 and the lowest AAPRE,average percent relative error(APRE),root mean square error(RMSE),and standard deviation(SD)of 3.228%,1.054%,4.389,and 0.013,respectively,compared to other models.The GRU model has a high accuracy for the different datasets:training,validation,testing,and the whole datasets with R and AAPRE values were 0.981 and 2.601%,0.966 and 3.274%,0.967 and 3.228%,and 0.977 and 2.861%,respectively.The group error analyses of all inputs show that the GRU model has less than 5% AAPRE for all input ranges,which is superior to other models that have different AAPRE values of more than 10% at various ranges of inputs.

Inverse Spectral Problem for Sturm-Liouville Operator with Boundary and Jump Conditions Dependent on the Spectral Parameter

In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem and the eigenvalue properties are given, then the asymptotic formulas of eigenvalues and eigenfunctions are presented. Finally, the uniqueness theorems of the corresponding inverse problems are given by Weyl function theory and inverse spectral data approach.

基于Jump-SBERT的二进制代码相似性检测技术研究

二进制代码相似性检测技术在不同的安全领域中有着重要的作用。针对现有的二进制代码相似性检测方法面临计算开销大且精度低、二进制函数语义信息识别不全面和评估数据集单一等问题,提出了一种基于Jump-SBERT的二进制代码相似性检测技术。Jump-SBERT有两个主要创新点,一是利用孪生网络构建SBERT网络结构,该网络结构能够在降低模型的计算开销的同时保持计算精度不变;二是引入了跳转识别机制,使Jump-SBERT可以学习到二进制函数的图结构信息,从而更加全面地捕获二进制函数的语义信息。实验结果表明,Jump-SBERT在小函数池(32个函数)中的识别准确率可达96.3%,在大函数池(10000个函数)中的识别准确率可达85.1%,比最先进(State-of-the-Art,SOTA)的方法高出36.13%,且Jump-SBERT在大规模二进制代码相似性检测中的表现更加稳定。消融实验表明,两个主要创新点对Jump-SBERT均有积极作用,其中,跳转识别机制的贡献最高可达9.11%。

基于混合Gamma-Poisson分布模型的参数估计与异质性研究

针对连续离散型混合分布的参数估计方法较少,且大多存在高维矩阵求逆或估计效率较低等问题,本文考虑将最小最大化(MM)算法以及组装分解技术应用在Gamma-Poisson混合分布的参数估计中,目的是将高维目标函数分离组装成一系列的低维函数的线性组合,有效地避开高维矩阵求逆的困难。模拟研究表明:MM算法及其组装分解在Gamma-Poisson混合分布模型参数估计中具有较强的准确性和稳定性。将Gamma-Poisson混合分布模型应用到比利时离婚期限数据中,发现Gamma-Poisson混合分布模型对这一组异质性的连续离散型数据具有较好的拟合效果。