本文讨论了二维时间分数阶Caputo-Hadamard慢扩散方程的交替方向隐式(Alternating Direction Implicit,ADI)紧致差分格式。首先,在指数型网格上对Caputo-Hadamard型分数阶导数进行离散;其次,利用紧致ADI方法将高维问题转化为2个一维问题...本文讨论了二维时间分数阶Caputo-Hadamard慢扩散方程的交替方向隐式(Alternating Direction Implicit,ADI)紧致差分格式。首先,在指数型网格上对Caputo-Hadamard型分数阶导数进行离散;其次,利用紧致ADI方法将高维问题转化为2个一维问题;根据离散系数的性质,利用数学归纳法证明了差分格式的稳定性和收敛性;最后,对具体模型进行数值求解。算例验证了上述理论分析的有效性。展开更多
The microstructure of diamond films was studied by slow positron beam and Raman spectroscopy. For the Raman spectroscopy experiment on diamond films, a high fraction of the sp3 hybridized bond was detected in samples....The microstructure of diamond films was studied by slow positron beam and Raman spectroscopy. For the Raman spectroscopy experiment on diamond films, a high fraction of the sp3 hybridized bond was detected in samples. Positron annihilation spectra analysis further illuminated that the concentration and types of defects were different in each sample. S-E curves of all samples showed that diamond crystal structures had obvious variation in each sample. These results indicated that positron annihilation spectroscopy was an effective means to measure microstructure of diamond films.展开更多
文摘本文讨论了二维时间分数阶Caputo-Hadamard慢扩散方程的交替方向隐式(Alternating Direction Implicit,ADI)紧致差分格式。首先,在指数型网格上对Caputo-Hadamard型分数阶导数进行离散;其次,利用紧致ADI方法将高维问题转化为2个一维问题;根据离散系数的性质,利用数学归纳法证明了差分格式的稳定性和收敛性;最后,对具体模型进行数值求解。算例验证了上述理论分析的有效性。
基金V. ACKN0WLEDGMENT This work was supported by the National Natural Science Foundation of China （No.10425072） and the National High Technology Research and Development Program of China （2003AA84ts18）.
文摘The microstructure of diamond films was studied by slow positron beam and Raman spectroscopy. For the Raman spectroscopy experiment on diamond films, a high fraction of the sp3 hybridized bond was detected in samples. Positron annihilation spectra analysis further illuminated that the concentration and types of defects were different in each sample. S-E curves of all samples showed that diamond crystal structures had obvious variation in each sample. These results indicated that positron annihilation spectroscopy was an effective means to measure microstructure of diamond films.
