Numerical Solution of the Space Fractional Advection-Dispersion Equations and Applications

分数阶微分方程是指方程中含有非整数阶的导数，它非常有效地描述各种各样物质的记忆和遗传性质，在工程、物理、金融、水文等领域中发挥了越来越重要的作用。遗憾的是，大多数分数阶微分方程的解析解都含有复杂的级数或者特殊函数，不利于进行近似计算。于是对分数阶微分方程进行数值求解变得尤其重要。目前分数阶偏微分方程数值解的工作皆以抛物型方程为主要研究对象，数值方法多采用有限差分方法。本文也是采用差分法讨论抛物型方程，有所不同的是两类分数阶微分方程比较复杂。 本文所讨论的第一种抛物型方程是从随机游走和一种随机过程的稳定分布推导出的Lévy-Feller对流-扩散微分方程，方程中含有较复杂的分数阶导数—Ries...Fractional-order differential equation is obtained from the standard differential equation by replacing the integer-order derivative with fractional-order derivative. It describes more efficiently the property of memory and heredity of much material. It plays a more and more important role in various fields, especially in engineering, physics, finance and hydrology. Unfortuenately, most of the ana...学位：理学博士院系专业：数学科学学院信息与计算数学系_计算数学学号：B20042301

不同保水固沙措施对沙培番茄生长和基质环境的影响

针对我国荒漠化危害严重,不利于植物种植等系列问题,以番茄为试验材料,结合纸膜、保水剂、生物基固沙剂等不同保水固沙措施,分析各处理下基质的理化性质以及番茄的生物学性状,以探明各处理对沙地环境的改善效果及对番茄生长的影响,为沙漠的防治及沙产业的发展提供参考。结果表明:瓦楞纸处理显著提高了番茄果实的有机酸、可溶性糖含量,分别比CK高27. 78%、8. 87%,其pH值比CK高0. 89,速效氮含量是CK的40倍;牛皮纸处理20~40 cm含水量比CK高73. 40%;保水剂处理可明显促进根系的生长发育,其根长、根直径以及体积分别比CK高16. 25%、29. 17%、56. 58%,番茄可溶性固形物含量比CK高7. 17%,沙子的比重和总孔隙度分别比CK高12. 88%、38. 35%,但容重比CK低6. 88%;生物基B处理可明显提高果实内可溶性糖含量,比CK高15. 53%,可显著提高沙子中的速效钾含量,比CK高55. 99%,有机质含量比CK高10. 91%;生物基A处理对番茄的株高有明显的促进作用,比CK高19. 81%,叶绿素含量比CK高8. 24%,番茄根系的总长比CK高45. 95%,叶片净光合速率是CK的1. 66倍,蒸腾速率以及气孔导度都相对较高,果实内可溶性固形物以及可溶性糖的含量分别比CK高6. 33%、8. 87%,容重比CK高3. 33%,速效氮含量是CK的16倍。通过主成分分析,生物基A的综合得分最高。因此,生物基A处理对促进番茄生长发育以及改善沙地生态环境效果最显著。宁夏回族自治区“十三五”重大研发项目(2016BZ0902);;“十二五”国家科技支撑计划项目(2014BAD05B02);;吴忠国家园区专项(2016BN05);;宁夏回族自治区科技创新领军人才项目(KJT2017001

Study on the prothymosin α as vaccine adjuvant of P.yoelii

目的:研究胸腺素α原(PrOTHyMOSInα,PrOTα)作为约氏疟原虫疫苗免疫佐剂的作用。方法:提取P.yOElII-17Xnl全蛋白作为抗原,用胸腺素α原作为免疫佐剂,免疫小鼠。具体方案为:昆明小鼠分为4组,每组6只,A组免疫P.yOElII-17Xnl全蛋白+PrOTα;b组免疫P.yOElII-17Xnl全蛋白;C组只注射PrOTα;d组为空白对照,以相同体积的生理盐水代替。免疫结束后感染致死的P.yOElII-17Xl,1x107个虫/只小鼠。结果:感染后的前10天A组小鼠疟原虫血症平均值要低于其他三组,且最终有3只小鼠存活下来,存活率50%,C组有一只小鼠存活,b、d组小鼠全部死亡。结论:用P.yOElII-17Xnl全蛋白做抗原,用PrOTα作为佐剂,比单独用P.yOElII-17Xnl全蛋白对小鼠有更好的免疫保护作用,提示了PrOTα可以成为一种有潜力的蛋白疫苗。Objective:To investigate the function of prothymosin α(ProTα) as vaccine adjuvant of P.yoelii.Methods:The mice were immunized with the total protein extracted from P.yoelii-17XNL as antigen,together with prothymosin α as adjuvant.Programs:Kunming mice were divided into A,B,C and D group.A group was immunized with P.yoelii-17XNL total protein and ProTα;B group was immunized with P.yoelii-17XNL;C group was only injected with ProTα;D group was the control,only injected with physiological saline.And then,the mice of each group was infected with P.yoelii-17XL,the dosage was 1×107/mice.Results:The parasitemia of A group-mice was lower than the other three groups in the first 10 days after infection,and eventually there were three mice survived in A group,the survival rate was 50%,one mouse survived in C group,all of mice in B group and D group died.Conclusion:Mice immunized with P.yoelii-17XNL total protein as antigen together with ProTα as adjuvants,had better immune protection than those immunized with P.yoelii-17XNL protein only.The present results suggest that the ProTα can act as a potential adjuvant in protein vaccine.厦门市科技项目(3502Z20083004);国家“973”项目(2007CB513103)资

CCCCC pentadentate chelates with planar Möbius aromaticity and unique properties

本课题充分发挥了厦门大学多学科协同研究优势，通讯作者为夏海平教授（合成、表征）、刘刚教授（生物医学应用）和吕鑫教授（理论计算）。合成实验和结构表征由朱从青（第一作者，目前在麻省理工学院、2005年诺贝尔化学奖得主Richard Schrock教授课题组从事博士后研究）完成；生物医学应用由杨彩霞（共同第一作者）、林凎、杨宇惠、王晓勇合作完成；理论计算由朱军、王永恒、朱从青完成。美国NIH的陈小元教授参与了生物医学应用的讨论。该研究工作得到国家自然科学基金委、科技部项目的支持。The coordinating atoms in polydentate chelates are primarily heteroatoms. We present the first examples of pentadentate chelates with all binding atoms of the chelating agent being carbon atoms, denoted as CCCCC chelates. Having up to five metal-carbon bonds in the equatorial plane has not been previously observed in transition metal chemistry. Density functional theory calculations showed that the planar metallacycle has extended Craig-Möbius aromaticity arising from 12-center–12-electron dπ-pπ π-conjugation. These planar chelates have broad absorption in the ultraviolet-visible–near-infrared region and, thus, notable photothermal performance upon irradiation by an 808-nm laser, indicating that these chelates have potential applications in photothermal therapy. The combination of facile synthesis, high stability, and broad absorption of these complexes could make the polydentate carbon chain a novel building block in coordination chemistry.the National Basic Research Program of China (nos. 2012CB821600 and 2014CB744503) , the National Science Foundation of China (nos. 21332002, 81422023, 51273165, 21490573, and 21573179)

NUMERICAL SOLUTION of THE TWO-DIMENSIONAL FRACTIONAL ORDER ADVECTION-DISPERSION EQUATION WITH VARIABLE COEFFICIENTS

1引言在古典的微分方程中,利用阶数为实数的分数阶导数代替整数阶导数,能更好地模拟许多物理现象.特别是具有复杂结构的多孔介质中的反常扩散问题.近年来分数阶微分方程在很多科学工程领域得到了广泛的应用[4,6,7,9].作为分数阶微分方程的一种,分数阶对流-扩散方程在物理学和地下水文学研究中已被用来模拟多孔介质中流体的流动情In this paper,we consider a two-dimensional fractional advection-dispersion equation(2D-FADE) with variable coefficients on a finite domain.We adopt the Gr(u|¨)nwald-Letnikov definition of fractional derivative,and propose a fractional Peaceman-Rachford scheme based on the alternating direction method for 2D-FADE.The stability and convergence of the fractional Peaceman-Rachford scheme are proved.A method is combined with spatial extrapolation to obtain temporally and spatially second order accurate numerical method.Some numerical examples are presented to support our theoretical analysis.福建省自然科学基金(2010J01011;2010J05009);国家自然科学基金(11026094);澳大利亚国家研究基金(DP0559807)资

MODIFIED ALTERNATING DIRECTION METHODS FOR SOLVING A TWO-DIMENSIONAL NON-CONTINUOUS SEEPAGE FLOW WITH FRACTIONAL DERIVATIVES

本文考虑在二维均匀介质中带有分数阶导数的非连续渗流问题,此模型修正了众所周知的dArCy原理.利用rIEMAnn-lIOuVIllE和grünWAld-lETnIkOV分数阶导数之间的关系,提出了求解在二维均匀介质中带有分数阶导数的非连续渗流问题的两种修正的交替方向法:修正的交替方向隐式EulEr方法和修正的PEACEMAn-rACHfOrd方法.我们讨论了这两种方法的稳定性,相容性和收敛性.最后给出数值例子.In this paper,a two-dimensional non-continuous seepage flow with fractional derivatives (2D-NCSF-FD) in uniform media is considered,which has modified the well-known Darcy law.Using the relationship between Riemann-Liouville and Grünwald-Letnikov fractional derivatives,two modified alternating direction methods:a modified alternating direction implicit Euler method and a modified Peaceman-Rachford method,are proposed for solving the 2D-NCSF-FD in uniform media.The stability and consistency,thus convergence of the two methods in a bounded domain are discussed.Finally,numerical results are given.国家自然科学基金(10271098)资助项目

Lévy-Feller Advection-dispersion Equation

考虑Lévy-Feller对流-扩散过程,应用Laplace和Fourier变换及其逆变换导出了用格林函数表示的Lévy-Feller对流-扩散方程的解析解,结果中去掉对流项的特殊情况与Mainardi等的研究结果是一致的.利用Riesz-Feller,Riemann-Li-ouville和Grünwald-Letnikov分数阶导数之间的关系,按照Grünwald-Letnikov定义对Riesz-Feller分数阶导数进行离散,得到了近似Lévy-Feller对流-扩散方程的一种两层的有限差分格式.最后,对上述的两层有限差分格式在一定条件下进行了离散随机游走的解释.In this paper,a Lévy-Feller advection-dispersion process was considered.Using Laplace and Fourier transform,the analytic solution of the Lévy-Feller advection-dispersion equation was derived by the corresponding Green's function.The result without the advection term was found to be in good agreement with previous research by Mainardi et al.Using the relationship between Riesz-Feller,Riemann-Liouville and Grünwald-Letnikov fractional-order derivatives,and discretizing Riesz-Feller fractional-order derivative by the definition of Grünwald-Letnikov,a two-level finite difference scheme was proposed for approximating the Lévy-Feller advection-dispersion equation.Finally,the finite difference scheme was interpreted by a discrete random walk model under a certain condition.国家自然科学基金(10271098)资

Finite Element Approximation for the Anomalous Sub-diffusion Process

讨论一类反常次扩散问题,进行了有限元数值模拟,分别给出了其时间半离散、时间空间全离散形式,并且讨论了两种形式的稳定性、收敛性.最后给出数值例子显示所提出的数值方法的有效性.Recently fractional diffusion equations are widely used to describe anomalous diffusion processes,then the research for diffusion processes plays an important role in many fields such as engineering,physics,etc.In this paper,we consider a sub-diffusion equation by finite element method.The semi-discrete approximation and full discrete approximation are proposed.And the stability and convergence are discussed.Finally some numerical examples are presented to demonstrate the effectiveness of theoretical analysis.国家自然科学基金(11101344;11301194); 福建省自然科学基金(2013J01021

An Effective Numerical Method of the Rayleigh-Stokes Problem for a Heated Generalized Second Grade Fluid With Fractional Derivative

考虑加热下分数阶广义二阶流体的rAylEIgH-STOkES问题(rSP-HgSgf),提出了一种逼近有界区域内rSP-HgSgf的有效数值方法.并且讨论了所提出方法的稳定性和收敛性.最后,利用数值例子体现数值方法的有效性.The Rayleigh-Stokes problem for a heated generalized second grade fluid(RSP-HGSGF) with fractional derivative was considered.An effective numerical method for approximating RSP-HGSGF in a bounded domain was presented.And the stability and convergence of the numerical method were analyzed.Finally,some numerical examples were presented to show the application of the present technique

active measurement model for software process control and improvement

提出了一种支持软件过程控制与改进的主动度量模型 AMM(active measurement model)和度量方法.模型形式化描述了软件过程的目标、特征和度量指标等关键元素以及相互间的关系,给出了确定软件过程度量的原则、方法和步骤.基于该度量模型,软件组织一方面可以依据确定的过程目标,主动导出合适的度量过程;另一方面还可以依据度量的结果,识别过程改进的机会,并主动导出过程改进的方向.为正确的决策和成功的结果提供有效的支持