The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eige...The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.展开更多
Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their an...Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.展开更多
We derive a Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom. From the formulation and using the Hamiltonian perturbation theory, we obtain...We derive a Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom. From the formulation and using the Hamiltonian perturbation theory, we obtain effective Boussinesq equations that describe the motion of bidirectional long waves and unidirectional equations that are similar to the KdV equation for the case in which the bottom possesses short length scale. The computations for these results are performed in the framework of an asymptotic analysis of multiple scale operators.展开更多
We study the nonlinear propagation of dust-ion acoustic(DIA) shock waves in an un-magnetized dusty plasma which consists of electrons, both positive and negative ions and negatively charged immobile dust grains. Start...We study the nonlinear propagation of dust-ion acoustic(DIA) shock waves in an un-magnetized dusty plasma which consists of electrons, both positive and negative ions and negatively charged immobile dust grains. Starting from a set of hydrodynamic equations with the ion thermal pressures and ion kinematic viscosities included, and using a standard reductive perturbation method, the Kadomtsev–Petviashivili–Burgers(K-P-Burgers) equation is derived, which governs the evolution of DIA shocks. A stationary solution of the K-P-Burgers equation is obtained and its properties are analysed with different plasma number densities, ion temperatures and masses. It is shown that a transition from shocks with negative potential to positive one occurs depending on the negative ion concentration in the plasma and the obliqueness of propagation of DIA waves.展开更多
Perturbation method and Fourier-cosine-expansion method were used to solve a 3-D nonlinear super-cavitating flow in an inclined field under gravity effect at large Froude numbers. By expanding the velocity potential i...Perturbation method and Fourier-cosine-expansion method were used to solve a 3-D nonlinear super-cavitating flow in an inclined field under gravity effect at large Froude numbers. By expanding the velocity potential into a power series of a small parameter, the original 3-D nonlinear problem was reduced to a number of 2-D one. The solutions of the first three orders were derived and expressed in terms of the complete elliptic integrals of the first and second kinds. The boundary integral equations method was applied to getting the numerical solutions. Computational results were obtained for super-cavitating flow past cone under various flow conditions.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10875018 and 10773002)
文摘The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10875018 and 10773002)
文摘Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.
文摘We derive a Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom. From the formulation and using the Hamiltonian perturbation theory, we obtain effective Boussinesq equations that describe the motion of bidirectional long waves and unidirectional equations that are similar to the KdV equation for the case in which the bottom possesses short length scale. The computations for these results are performed in the framework of an asymptotic analysis of multiple scale operators.
文摘We study the nonlinear propagation of dust-ion acoustic(DIA) shock waves in an un-magnetized dusty plasma which consists of electrons, both positive and negative ions and negatively charged immobile dust grains. Starting from a set of hydrodynamic equations with the ion thermal pressures and ion kinematic viscosities included, and using a standard reductive perturbation method, the Kadomtsev–Petviashivili–Burgers(K-P-Burgers) equation is derived, which governs the evolution of DIA shocks. A stationary solution of the K-P-Burgers equation is obtained and its properties are analysed with different plasma number densities, ion temperatures and masses. It is shown that a transition from shocks with negative potential to positive one occurs depending on the negative ion concentration in the plasma and the obliqueness of propagation of DIA waves.
文摘Perturbation method and Fourier-cosine-expansion method were used to solve a 3-D nonlinear super-cavitating flow in an inclined field under gravity effect at large Froude numbers. By expanding the velocity potential into a power series of a small parameter, the original 3-D nonlinear problem was reduced to a number of 2-D one. The solutions of the first three orders were derived and expressed in terms of the complete elliptic integrals of the first and second kinds. The boundary integral equations method was applied to getting the numerical solutions. Computational results were obtained for super-cavitating flow past cone under various flow conditions.