By using the super-symmetric quantum mechanics （SUSYQM） method, this paper obtains the analytical solutions for the spin-weighted spheroidal wave equation in the case of s = 2. Based on the derived W0 to W4 the gene...By using the super-symmetric quantum mechanics （SUSYQM） method, this paper obtains the analytical solutions for the spin-weighted spheroidal wave equation in the case of s = 2. Based on the derived W0 to W4 the general form for the n-th-order super-potential is summarized and is proved correct by mathematical induction. Hence the ground eigenvalue problem is completely solved. Particularly, the novel solutions of the excited state are investigated according to the shape-invariance property.展开更多
For steady-state heat conduction,a new variational functional for a unit cell of composites with periodic microstructures is constructed by considering the quasi-periodicity of the temperature field and in the periodi...For steady-state heat conduction,a new variational functional for a unit cell of composites with periodic microstructures is constructed by considering the quasi-periodicity of the temperature field and in the periodicity of the heat flux fields. Then by combining with the eigenfunction expansion of complex potential which satisfies the fiber-matrix interface conditions, an eigenfunction expansion-variational method （EEVM）based on a unit cell is developed. The effective transverse thermal conductivities of doubly-periodic fiber reinforced composites are calculated, and the first-order approximation formula for the square and hexagonal arrays is presented, which is convenient for engineering application. The numerical results show a good convergency of the presented method,even though the fiber volume fraction is relatively high. Comparisons with the existing analytical and experimental results are made to demonstrate the accuracy and validity of the first-order approximation formula for the hexagonal array.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 10875018 and 10773002)
文摘By using the super-symmetric quantum mechanics （SUSYQM） method, this paper obtains the analytical solutions for the spin-weighted spheroidal wave equation in the case of s = 2. Based on the derived W0 to W4 the general form for the n-th-order super-potential is summarized and is proved correct by mathematical induction. Hence the ground eigenvalue problem is completely solved. Particularly, the novel solutions of the excited state are investigated according to the shape-invariance property.
基金National Natural Science Foundation of China(90716002)The Open Fund of LNM
文摘For steady-state heat conduction,a new variational functional for a unit cell of composites with periodic microstructures is constructed by considering the quasi-periodicity of the temperature field and in the periodicity of the heat flux fields. Then by combining with the eigenfunction expansion of complex potential which satisfies the fiber-matrix interface conditions, an eigenfunction expansion-variational method （EEVM）based on a unit cell is developed. The effective transverse thermal conductivities of doubly-periodic fiber reinforced composites are calculated, and the first-order approximation formula for the square and hexagonal arrays is presented, which is convenient for engineering application. The numerical results show a good convergency of the presented method,even though the fiber volume fraction is relatively high. Comparisons with the existing analytical and experimental results are made to demonstrate the accuracy and validity of the first-order approximation formula for the hexagonal array.
