A Study on the Assessment and Integration of Multi-Source Evapotranspiration Products over the Tibetan Plateau

Evapotranspiration(ET)is a crucial variable in the terrestrial water,carbon,and energy cycles.At present,a large number of multi source ET products exist.Due to sparse observations,however,great challenges exist in the evaluation and integration of ET products in remote and complex areas such as the Tibetan Plateau(TP).In this paper,the applicability of the multiple collocation(MC)method over the TP is evaluated for the first time,and the uncertainty of multisource ET products(based on reanalysis,remote sensing,and land surface models)is further analyzed,which provides a theoretical basis for ET data fusion.The results show that 1)ET uncertainties quantified via the MC method are lower in RS-based ET products(5.95 vs.7.06 mm month^(-1))than in LSM ET products(10.22 vs.17.97 mm month^(-1))and reanalysis ET estimates(7.27 vs.12.26 mm month-1).2)A multisource evapotranspiration(MET)dataset is generated at a monthly temporal scale with a spatial resolution of 0.25°across the TP during 2005-15.MET has better performance than any individual product.3)Based on the fusion product,the total ET amount over the TP and its patterns of spatiotemporal variability are clearly identified.The annual total ET over the entire TP is approximately 380.60 mm.Additionally,an increasing trend of 1.59±0.85 mm yr^(-1)over the TP is shown during 2005-15.This study provides a basis for future studies on water and energy cycles and water resource management over the TP and surrounding regions.

Review of Collocation Methods and Applications in Solving Science and Engineering Problems

The collocation method is a widely used numerical method for science and engineering problems governed by partial differential equations.This paper provides a comprehensive review of collocation methods and their applications,focused on elasticity,heat conduction,electromagnetic field analysis,and fluid dynamics.The merits of the collocation method can be attributed to the need for element mesh,simple implementation,high computational efficiency,and ease in handling irregular domain problems since the collocation method is a type of node-based numerical method.Beginning with the fundamental principles of the collocation method,the discretization process in the continuous domain is elucidated,and how the collocation method approximation solutions for solving differential equations are explained.Delving into the historical development of the collocation methods,their earliest applications and key milestones are traced,thereby demonstrating their evolution within the realm of numerical computation.The mathematical foundations of collocation methods,encompassing the selection of interpolation functions,definition of weighting functions,and derivation of integration rules,are examined in detail,emphasizing their significance in comprehending the method’s effectiveness and stability.At last,the practical application of the collocation methods in engineering contexts is emphasized,including heat conduction simulations,electromagnetic coupled field analysis,and fluid dynamics simulations.These specific case studies can underscore collocation method’s broad applicability and effectiveness in addressing complex engineering challenges.In conclusion,this paper puts forward the future development trend of the collocation method through rigorous analysis and discussion,thereby facilitating further advancements in research and practical applications within these fields.

A Novel Method for Linear Systems of Fractional Ordinary Differential Equations with Applications to Time-Fractional PDEs

This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.

A Collocation Technique via Pell-Lucas Polynomials to Solve Fractional Differential EquationModel for HIV/AIDS with Treatment Compartment

In this study,a numerical method based on the Pell-Lucas polynomials(PLPs)is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment.The HIV/AIDS mathematical model with a treatment compartment is divided into five classes,namely,susceptible patients(S),HIV-positive individuals(I),individuals with full-blown AIDS but not receiving ARV treatment(A),individuals being treated(T),and individuals who have changed their sexual habits sufficiently(R).According to the method,by utilizing the PLPs and the collocation points,we convert the fractional order HIV/AIDS epidemic model with a treatment compartment into a nonlinear system of the algebraic equations.Also,the error analysis is presented for the Pell-Lucas approximation method.The aim of this study is to observe the behavior of five populations after 200 days when drug treatment is applied to HIV-infectious and full-blown AIDS people.To demonstrate the usefulness of this method,the applications are made on the numerical example with the help of MATLAB.In addition,four cases of the fractional order derivative(p=1,p=0.95,p=0.9,p=0.85)are examined in the range[0,200].Owing to applications,we figured out that the outcomes have quite decent errors.Also,we understand that the errors decrease when the value of N increases.The figures in this study are created in MATLAB.The outcomes indicate that the presented method is reasonably sufficient and correct.

AHermitian C^(2) Differential Reproducing Kernel Interpolation Meshless Method for the 3D Microstructure-Dependent Static Flexural Analysis of Simply Supported and Functionally Graded Microplates

This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.

Effects of Collocational Congruency,Frequency and L2 Proficiency on the Processing of English Adjective-Noun Collocations

The present study investigates the effects of congruency and frequency on adjective-noun collocational processing for Chinese learners of English at two proficiency levels based on the data obtained in an online acceptability judgment task.The subject pool of this research included 60 English majors studying at a university in China;30 were selected as a higher-proficiency group and 30 as a lower-proficiency group according to their Vocabulary Levels Test(Schmitt et al.,2001)scores and their self-reported proficiency in English.The experimental materials were programmed to E-prime 2.0 and included six types of collocations:(1)15 high-frequency congruent collocations,(2)15 low-frequency congruent collocations,(3)15 high-frequency incongruent collocations,(4)15 low-frequency incongruent collocations,(5)15 Chinese-only items,and(6)75 unrelated items for baseline data.The collected response times(RTs)and accuracy rates data were statistically analyzed by the use of an ANOVA test and pairwise comparisons through SPSS 16.0 software.The results revealed that:(1)the adjective-noun collocational processing of Chinese English learners is influenced by collocational frequency,congruency and L2 proficiency;(2)the processing time is affected by the interaction of congruency and frequency;and(3)the interactive effect of L2 proficiency in conjunction with congruency and frequency also influences the processing quality.

耦合拉格朗日-欧拉方法及其在海洋工程中的应用

Combining the strengths of Lagrangian and Eulerian descriptions,the coupled Lagrangian–Eulerian methods play an increasingly important role in various subjects.This work reviews their development and application in ocean engineering.Initially,we briefly outline the advantages and disadvantages of the Lagrangian and Eulerian descriptions and the main characteristics of the coupled Lagrangian–Eulerian approach.Then,following the developmental trajectory of these methods,the fundamental formulations and the frameworks of various approaches,including the arbitrary Lagrangian–Eulerian finite element method,the particle-in-cell method,the material point method,and the recently developed Lagrangian–Eulerian stabilized collocation method,are detailedly reviewed.In addition,the article reviews the research progress of these methods with applications in ocean hydrodynamics,focusing on free surface flows,numerical wave generation,wave overturning and breaking,interactions between waves and coastal structures,fluid–rigid body interactions,fluid–elastic body interactions,multiphase flow problems and visualization of ocean flows,etc.Furthermore,the latest research advancements in the numerical stability,accuracy,efficiency,and consistency of the coupled Lagrangian–Eulerian particle methods are reviewed;these advancements enable efficient and highly accurate simulation of complicated multiphysics problems in ocean and coastal engineering.By building on these works,the current challenges and future directions of the hybrid Lagrangian–Eulerian particle methods are summarized.

An Extended Numerical Method by Stancu Polynomials for Solution of Integro-Differential Equations Arising in Oscillating Magnetic Fields

In this study, the Bernstein collocation method has been expanded to Stancu collocation method for numerical solution of the charged particle motion for certain configurations of oscillating magnetic fields modelled by a class of linear integro-differential equations. As the method has been improved, the Stancu polynomials that are generalization of the Bernstein polynomials have been used. The method has been tested on a physical problem how the method can be applied. Moreover, numerical results of the method have been compared with the numerical results of the other methods to indicate the efficiency of the method.

LEO卫星轨道预报精度分析

利用动力学拟合法,以HY-2A卫星为例分析不同拟合区间对预报不同弧长的轨道精度的影响。基于CNES提供的事后精密星历和采用非差简化动力学方法获得的厘米级快速轨道两种产品,进行卫星轨道预报。结果表明:采用24 h和12 h拟合区间分别预报12 h轨道时,其3DRMS优于6 dm;当预报24 h轨道时,3DRMS优于1 m。

基于Triple Collocation方法的土壤湿度误差分析

土壤湿度作为水循环中重要的驱动参数之一,对天气变化有着显著影响。遥感技术的发展促使土壤湿度的大范围动态性观测变为可能,但对其误差的准确估计仍需进一步的研究。利用ASCAT散射计、AMSR-E辐射计反演得到的2种卫星遥感土壤湿度数据以及ERA-Interim土壤湿度再分析资料,通过三重组合(Triple Collocation,TC)方法得到了研究区域(15°N^55°N,73°E^135°E) 3种土壤湿度数据的误差方差和信噪比估计,并结合MODIS土地覆盖类型数据分析了3种土壤湿度数据的误差特征。结果表明:植被覆盖会影响遥感土壤湿度的TC误差方差估计;从TC误差方差估计值来看,ERA土壤湿度精度最高,AMSR-E精度次之,ASCAT精度最低;从信噪比来看,ASCAT土壤湿度信噪比最高,ERA的信噪比低于ASCAT高于AMSR-E,AMSR-E信噪比最低;通过研究区MODIS土地覆盖类型数据与TC结果的分析可知TC结果多分布在草原、农田和裸地,TC结果比较符合客观实际情况。

Thermal-hydro-mechanical coupling stress intensity factor of brittle rock

A new calculation formula of THM coupling stress intensity factor was derived by the boundary collocation method, in which an additional constant stress function was successfully introduced for the cracked specimen with hydraulic pressure applied on its crack surface. Based on the newly derived formula, THM coupling fracture modes （including tensile, shear and mixed fracture mode） can be predicted by a new fracture criterion of stress intensity factor ratio, where the maximum axial load was measured by self-designed THM coupling fracture test. SEM analyses of THM coupling fractured surface indicate that the higher the temperature and hydraulic pressure are and the lower the confining pressure is, the more easily the intergranular （tension） fracture occurs. The transgranular （shear） fracture occurs in the opposite case while the mixed-mode fracture occurs in the middle case. The tested THM coupling fracture mechanisms are in good agreement with the predicted THM coupling fracture modes, which can verify correction of the newly-derived THM coupling stress intensity factor formula.

小步长低阶Collocation方法轨道积分性能研究

介绍了Collocation方法的原理及误差构成,以Collocation方法在逐历元滤波轨道解算中的应用为切入点对小步长低阶Collocation方法轨道积分的性能进行了研究。分别就二体问题及真实GPS星座卫星轨道为对象进行了一系列验算,得到了一些有益结论:就积分方法本身性能而言,Collocation积分方法较传统数值积分法精度要高且稳定性要好;在一定长度的积分步长范围内,将小步长低阶Collocation方法用于滤波轨道解算是可行且有效的。但在积分步长很小的情形下,从计算效率方面考虑,不推荐使用Collocation方法;利用小步长低阶Collocation方法取代大步长高阶方法能提高效率且可抑制蚀现象引起的积分结果发散。经试验表明:选用积分步长为900s的4阶方法是合适的。

Collocation-PECE算法在低轨卫星精密定轨中的应用

在精密轨道确定中,PECE算法已成为目前最通用的轨道积分算法。利用Collocation方法的外推公式和内插公式可构造一种新的PECE算法,新算法以两种方式进行二阶微分方程的求解:将二阶微分方程降为一阶微分方程然后积分以及直接积分二阶微分方程。分别采用这两种类型的算法求解二体问题和低轨卫星的受摄轨道,并将计算结果与Adams-PECE算法及一般的PECE算法的积分结果进行了比较分析。结果表明,这两种类型的Collo-cation-PECE算法在实际轨道积分中较其它几种算法更有效。

Nonlinear Auto-Companding Method for Behavioral Modeling of Switched-Current Circuits

A wavelet collocation method with nonlinear auto companding is proposed for behavioral modeling of switched current circuits.The companding function is automatically constructed according to the initial error distribution obtained through approximating the input output function of the SI circuit by conventional wavelet collocation method.In practical applications,the proposed method is a general purpose approach,by which both the small signal effect and the large signal effect are modeled in a unified formulation to ease the process of modeling and simulation.Compared with the published modeling approaches,the proposed nonlinear auto companding method works more efficiently not only in controlling the error distribution but also in reducing the modeling errors.To demonstrate the promising features of the proposed method,several SI circuits are employed as examples to be modeled and simulated.

Idioms,Collocations,Formulaic Phrases and Second Language Acquisition

Idioms,collocations,and formulaic phrases are three factors playing the important role in the second language acquisition(SLA).This essay firstly deals with the definitions of these concepts,then it illustrates the importance of them to SLA on two perspectives—idioms,collocations,and formulaic phrases respectively and they regarded as a whole.Therefore,in this way,the essay may lead to the answer the question“How are idioms,collocations,and formulaic phrases important to SLA?”

THE ACCURACY COMPARISON BETWEEN CHEBYSHEV-τ METHOD AND CHEBYSHEV COLLOCATION METHOD

This paper is devoted to investigate the accuracy of the Pseudo spectral scheme with the Chebyshev tau method and Chebyshev collocation method. The computational results of the nonlinear disturbance development in plane Poiseuille flow for both methods are presented and compared in detail. It is acknowledged that the Chebyshev collocation method has higher precision than the other one, especially for near netural situation.

英语词汇记忆方法:语篇语境记忆法

在记忆单词的过程中,很多同学都遇到过这样的情况,即一个自己曾经学过或者背过的单词,放在阅读的文章中却仍然很陌生,即使套用自己背过的词义似乎也解释不通。例如下面的三个例子,没有一个复杂的单词,可是它们的意思你都能看得懂吗?

一种改进的collocation方法及其在动态定价问题中的应用

涉及多个状态变量的动态定价问题往往难以求解。基于此,引入多维插值与张量积,提出一种改进的collocation方法用于求解多状态变量的动态优化问题,并从理论上分析了改进后的collocation方法的收敛性。首先,将改进的collocation方法应用于求解多个状态变量的动态经济问题;给出了改进后的collocation方法的实际运用,应用于解决有限记忆的动态定价问题;利用状态变量的切比雪夫格点与其估计值构造出时序的状态转移,并依据状态转移模拟最优价格路径。通过数值分析表明,改进后的collocation方法比线性二次逼近法更快的收敛于稳态。

Study on the Collocation between Small Garden Ornaments and Other Elements

Starting with the basic elements of small garden ornaments, this research discusses its collocation art with other landscape elements such as plants, water, stones and environment, in order to offer useful references for the garden planning in a city.

An Explorative Research into the Factors Affecting Chinese Students＇ Retention and Application of English New Words

Vocabulary has a direct impact on people＇s communication competence. A good mastery of an English word covers its pronunciation, spelling, part of speech, meaning and application. This article will focus only on factors affecting the retention and application of a word from the perspective of semantic disparities, different defining angles in English and Chinese, emotional coloring and styles, morphological changes, and collocation. The author hopes that this article will be able to provide some insights into vocabulary teaching.