变时间分数阶反应扩散方程的数值分析

考虑时变分数阶反应扩散方程的数值逼近问题。采用分段线性插值法结合对一阶时间导数的一个二阶近似离散Coimbra时变分数阶导数,用中心差分离散二阶空间分数阶导数通过数值例子验证了提出的数值方法,说明了数值方法的有效性。     

从孔子学院看中国文化的传播与传承现状及反思

在全球汉语热潮的推动下,随着孔子学院走向世界,中国文化在更加广阔的辖域中得到传播和发扬。孔子学院以阶梯式的文化传播模式完成光大与创新汉民族文化的传承,同时,也给国内的文化传播与传承现状带来新的思考,文化传承一定践行认知体系的开放、知识体系的构建、行为体系的创新和价值体系的与时俱进,实现文化的软实力强国目标。     

具有零磁扩散的3维广义磁流体方程的一个爆破准则

This paper proves a new regularity criterion ω： = rotu∈L1（0,T;B·0∞,∞） for the 3D generalized MHD system with fractional diffusion terms（-Δ）αu with α 〉9/8 and zero magnetic diffusivity. Here u is the fluid velocity,ω is the vorticity and B·0∞,∞is the homogeneous Besov space.     

考虑再生粗骨料随机分布的混凝土氯离子扩散细观数值模拟

考虑粗骨料分布的随机性及氯离子结合的非线性对氯离子扩散性的影响,对再生混凝土中氯离子扩散进行数值建模与细观仿真分析,并将数值模拟结果与已有试验数据进行对比;通过改变老硬化砂浆扩散系数、新硬化砂浆扩散系数、老界面过渡区扩散系数及浸泡时间,对比研究了不同情况下再生混凝土中氯离子的扩散特性.结果表明:数值模拟结果与试验结果接近;再生混凝土中氯离子沿扩散深度方向呈波浪式下降;随着扩散系数的增大及浸泡时间的增长,氯离子扩散速度加快;随着再生粗骨料取代率的增加,氯离子扩散速度也增加;相同扩散深度处,不同随机骨料模型中氯离子含量最大值接近,说明所采用的随机骨料模型模拟结果具有较好的稳定性.     

扩散模型复合分位回归估计的渐近正态性

主要研究扩散模型中漂移函数的复合分位回归估计的渐近正态性.基于离散观测样本,利用复合分位回归的方法得到了漂移参数函数的局部估计量,并证明了估计量的渐近正态性.     

一类反应扩散系统的振幅方程及其斑图稳定性分析

分析了Brusselator模型产生斑图的必要条件,求得系统在图灵分岔处的振幅方程,进一步讨论了对应斑图的稳定性.在此基础上,通过数值模拟,验证了理论分析的正确性.     

Spatiotemporal characteristics of freezing and thawing of the active layer in the source areas of the Yellow River （SAYR）

Based on the analysis of data on temperatures and moisture of soils in the active layer at four different permafrost sites in the source areas of the Yellow River(SAYR)in 2010–2012,the freeze–thaw processes of soils in the active layer were compared and contrasted for understanding the spatiotemporal variations.At the four studied sites,the thickness and mean annual temperature of permafrost are different.The temperatures at the top of permafrost(TTOP),i.e.,the maximum depth(s)of seasonal frost and/or thaw penetration,are-1.9°C at the Chalaping site(CLP),-0.9°C at the site on the southern bank of the Zhaling Lake(ZLH),-0.4°C at the Maduo Town site(MDX),and 1.1°C at the site on the northern bank of the Eling Lake(ELH).Differences in the mean annual ground temperature of permafrost and TTOPs may be responsible for the differentiations in the freeze–thaw processes of soils in the active layer.With rising TTOPs,the ground thawing started earlier:CLP in early June,ZLH in late May,MDX in early May,and ELH in mid-April,while the freezing began later:CLP in early October,ZLH in early to midOctober,MDX in mid-October,and ELH in the mid-to late October.With increasing TTOPs,the freeze-up periods for permafrost sites were shortened:202 days at CLP,130 days at ZLH,100 days at MDX,and the period of complete thaw was 89 days at ELH.At the CLP and ZLH sites,the two-directional ground freezing(downwards from ground surfaces and upwards from the permafrost table)and thawing finished in the same year,but the ground freezing at the MDX continued to the end of the nextJanuary,with very slow freezing rates in the end.At the ELH site,ground freezing kept on until early May when thawing began on the surface,and upward and downward thawing became increasingly stable in late June to early July.At each site,with rising TTOPs,the downward freezing accelerated in comparison with the upward freezing,and with an increasing proportion of downward frozen depth,and with the larger ratios of freezing to thawing duration.In summary,the patterns of thawing and freezing processes in the active layer in the SAYR differ from those in other parts of the Qinghai–Tibet Plateau to a noticeable extent.     

Computational diffusion kinetics and its applications in study and design of rare metallic materials

Computational diffusion kinetics(CDK),with a spirit of and being coupled with the computational thermodynamics(CT,or called as the CALPHAD technique),plays increasingly important role in the alloy design/optimization and microstructure control during the processing of advanced metallic materials.This paper is to highlight recent progress of CDK in research with great focus on novel Ti and Zr alloys,which was largely performed in the authors’group.It ends with one representative example of the applications of CDK,coupled with CT,quantitative phase field,and three-dimensional(3D)statistical calculation,in designing the heattreatment schedule for the dual phase(αβ)Ti–6Al–4V alloys.     

时域光学拓扑成像方法的模拟和实验研究

针对现有的以修正的朗伯-比尔定律(modified Lambert-Beer law,MLBL)为理论模型的光学拓扑方法存在量化度不准确的问题,提出了一种基于最小二乘拟合算法的时域光学拓扑成像方法.该方法利用时域扩散方程在半无限空间条件下的解析解和测量曲线实现最佳匹配以计算相邻的源点与探测点之间的待测组织吸收系数变化值.对该时域光学拓扑成像方法进行了一系列的模拟验证,并以基于时间相关单光子计数(time-correlated single photon counting,TCSPC)技术的多通道时间分辨测量系统为平台进行了实验验证.结果表明:所提出的最小二乘拟合算法总体上优于传统的基于经验值光程的MLBL方法.     

破产准则下修正Heston波动的最优再保-投资决策

为了研究修正Heston随机波动率下保险公司最优再保-投资策略问题,在盈余水平服从扩散过程的假设下,运用随机动态规划原理,建立最小化破产概率准则的HJB方程,通过求解方程得到最优再保-投资策略和最小化破产概率的显式解,并分析了随机波动率对最优投资决策,最优比例再保险策略和最小破产概率的影响。