As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the researc...As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.展开更多
The Robin problem for the Helmholtz equation in normal-polar shells is addressed by using a suitable spherical harmonic expansion technique. Attention is in particular focused on the wide class of domains whose bounda...The Robin problem for the Helmholtz equation in normal-polar shells is addressed by using a suitable spherical harmonic expansion technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by a generalized version of the so-called “superformula” introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica? is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained.展开更多
Mie theory is a rigorous solution to scattering problems in spherical coordinate system. The first step in applying Mie theory is expansion of some arbitrary incident field in terms of spherical harmonics fields in te...Mie theory is a rigorous solution to scattering problems in spherical coordinate system. The first step in applying Mie theory is expansion of some arbitrary incident field in terms of spherical harmonics fields in terms of spherical which in turn requires evaluation of certain definite integrals whose integrands are products of Bessel functions, associated Legendre functions and periodic functions. Here we present analytical results for two specific integrals that are encountered in expansion of arbitrary fields in terms of summation of spherical waves. The analytical results are in terms of finite summations which include Lommel functions. A concise analytical expression is also derived for the special case of Lommel functions that arise, rendering expensive numerical integration or other iterative techniques unnecessary.展开更多
The expansion coefficient C-\L\(D) Of Coulomb potential 1/r(12) of atomic system in hyper-spherical harmonics is derived and the explicit expression is given.
本文首先构建了二流—四流球谐函数谱展开累加辐射传输的新方案,然后将其应用于国家气候中心第二代大气环流模式BCC_AGCM2.0.1的新版本中,并与模式中原有的Eddington累加方案进行了比较。由于新方案本质上是单层Eddington近似方案在四...本文首先构建了二流—四流球谐函数谱展开累加辐射传输的新方案,然后将其应用于国家气候中心第二代大气环流模式BCC_AGCM2.0.1的新版本中,并与模式中原有的Eddington累加方案进行了比较。由于新方案本质上是单层Eddington近似方案在四流上的推广。因此新方案在计算精度上要优于原方案。通过在全球气候模式中的应用与比较,本文发现新方案对气候模拟会产生比较大的影响。在晴空条件下,新方案计算的在南纬30°到60°区间、北大西洋东北部以及非洲北部的撒哈拉沙漠区域的地表向下年平均短波辐射通量要小于原方案结果,最大差别可以达到3.5 W/m2;同时,新方案计算的在南纬30°到60°区间和北大西洋东北部的大气顶向上年平均短波辐射通量要大于原方案结果,最大差别达到3 W/m2。在有云大气情况下,新方案计算的地表向下年平均短波辐射通量要小于原方案结果,并随着纬度的增加,新旧两种方案的差别逐渐变大,在南北极时达到最大5.5 W/m2;同时,新方案计算的在赤道区域的大气顶的年平均短波向上辐射通量要小于原方案结果,最大差别为2.5 W/m2,而在南北纬30°到60°区间,新方案计算的在大气顶的年平均短波向上辐射通量则要大于原方案结果,最大差别为1.5 W/m2。新方案计算的年平均短波加热率普遍高于原方案结果,特别是在800 h Pa到地表之间的低层大气以及50 h Pa到100 h Pa的高层大气,最大差别可达0.03 K/d。因此,新方案有助于改善全球气候模式中普遍存在的赤道平流层中下层的温度冷偏差现象。展开更多
基金Supported by the NSF of China under the Grant 10471010partially by the NSERC Canada under Grant G121211001
文摘As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.
文摘The Robin problem for the Helmholtz equation in normal-polar shells is addressed by using a suitable spherical harmonic expansion technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by a generalized version of the so-called “superformula” introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica? is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained.
文摘Mie theory is a rigorous solution to scattering problems in spherical coordinate system. The first step in applying Mie theory is expansion of some arbitrary incident field in terms of spherical harmonics fields in terms of spherical which in turn requires evaluation of certain definite integrals whose integrands are products of Bessel functions, associated Legendre functions and periodic functions. Here we present analytical results for two specific integrals that are encountered in expansion of arbitrary fields in terms of summation of spherical waves. The analytical results are in terms of finite summations which include Lommel functions. A concise analytical expression is also derived for the special case of Lommel functions that arise, rendering expensive numerical integration or other iterative techniques unnecessary.
基金Project supported by the National Natural Science Foundation of China (NO. 29503019) and partially by the U. S. National Science Foundation Grant of PHY-9540854.
文摘The expansion coefficient C-\L\(D) Of Coulomb potential 1/r(12) of atomic system in hyper-spherical harmonics is derived and the explicit expression is given.
文摘本文首先构建了二流—四流球谐函数谱展开累加辐射传输的新方案,然后将其应用于国家气候中心第二代大气环流模式BCC_AGCM2.0.1的新版本中,并与模式中原有的Eddington累加方案进行了比较。由于新方案本质上是单层Eddington近似方案在四流上的推广。因此新方案在计算精度上要优于原方案。通过在全球气候模式中的应用与比较,本文发现新方案对气候模拟会产生比较大的影响。在晴空条件下,新方案计算的在南纬30°到60°区间、北大西洋东北部以及非洲北部的撒哈拉沙漠区域的地表向下年平均短波辐射通量要小于原方案结果,最大差别可以达到3.5 W/m2;同时,新方案计算的在南纬30°到60°区间和北大西洋东北部的大气顶向上年平均短波辐射通量要大于原方案结果,最大差别达到3 W/m2。在有云大气情况下,新方案计算的地表向下年平均短波辐射通量要小于原方案结果,并随着纬度的增加,新旧两种方案的差别逐渐变大,在南北极时达到最大5.5 W/m2;同时,新方案计算的在赤道区域的大气顶的年平均短波向上辐射通量要小于原方案结果,最大差别为2.5 W/m2,而在南北纬30°到60°区间,新方案计算的在大气顶的年平均短波向上辐射通量则要大于原方案结果,最大差别为1.5 W/m2。新方案计算的年平均短波加热率普遍高于原方案结果,特别是在800 h Pa到地表之间的低层大气以及50 h Pa到100 h Pa的高层大气,最大差别可达0.03 K/d。因此,新方案有助于改善全球气候模式中普遍存在的赤道平流层中下层的温度冷偏差现象。
