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
运用边界积分方法(boundary integral method,简称BIM)求解Sinai台球低能区的能谱及其相应的本征态波函数.将Sinai台球和1/4 Sinai台球对应能量的本征态波函数进行对照,由于两者对称性的显著差异,故其部分能级的本征态波函数表现出明显...运用边界积分方法(boundary integral method,简称BIM)求解Sinai台球低能区的能谱及其相应的本征态波函数.将Sinai台球和1/4 Sinai台球对应能量的本征态波函数进行对照,由于两者对称性的显著差异,故其部分能级的本征态波函数表现出明显的不同.展开更多
In order to consider the viscous effect,the introduction of a parametric dissipation and new results are realized by applying the new formulation combining and dynamic conditions over the free-surface with viscous ter...In order to consider the viscous effect,the introduction of a parametric dissipation and new results are realized by applying the new formulation combining and dynamic conditions over the free-surface with viscous terms. The dispersion equation is then modified by assuming an additional term in the boundary condition at the free-surface and wave-number becomes complex number with a small imaginary part which ensures the decay of wave amplitudes. The comparisons of numerical results and model test measurement on wave elevation at the moon-pool center is obtained both for the peak period and for the amplitude at resonance by choosing an appropriated dissipation coefficient. The results show that the introduce dissipation is not only effective but also reliable to provide realistic predictions.展开更多
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Sponsored by the National Natural Science Foundation of China(Grant No.51079032)
文摘In order to consider the viscous effect,the introduction of a parametric dissipation and new results are realized by applying the new formulation combining and dynamic conditions over the free-surface with viscous terms. The dispersion equation is then modified by assuming an additional term in the boundary condition at the free-surface and wave-number becomes complex number with a small imaginary part which ensures the decay of wave amplitudes. The comparisons of numerical results and model test measurement on wave elevation at the moon-pool center is obtained both for the peak period and for the amplitude at resonance by choosing an appropriated dissipation coefficient. The results show that the introduce dissipation is not only effective but also reliable to provide realistic predictions.
