Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurati...Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurations are considered, one in which a short-wave limit approximation is used, and another in which a long-wave limit approximation is used. In the short-wave limit, Wentzel-Kramers-Brillouin (WKB) methods are utilized to estimate the eigenvalues, and the eigenfunctions are approximated in terms of Green’s functions. The procedure consists of transforming the Orr-Sommerfeld equation into a system of two second order ordinary differential equations for which the eigenvalues and the eigenfunctions can be approximated. In the long-wave limit approximation, solutions are expressed in terms of generalized hypergeometric functions. Our procedure works regardless of the values of the Reynolds number.展开更多
Elastic scattering differential cross sections for a p- ~4He system are calculated within the framework of optical limit approximation of the Glauber multiple scattering model. Three different ranges for proton energy...Elastic scattering differential cross sections for a p- ~4He system are calculated within the framework of optical limit approximation of the Glauber multiple scattering model. Three different ranges for proton energy(E_(lab)), 19〈E_(lab)〈50 Me V, 100≤E_(lab)≤1730 Me V, and 45 ≤E_(lab)≤393 Ge V are considered. It is shown that the Pauli blocking fails to describe the data up to the proton energy, E_(lab)〈100 Me V. For higher proton energies, a qualitative agreement is obtained. The observed elastic scattering differential cross section is nicely reproduced in the whole range of scattering angles in the center of mass system up to Θ_(c.m.)〈200° for 19〈E_(lab) ≤100 Me V when the effect of both the nucleon–nucleon(NN) phase variation parameter γNN and higher-order momentum transfer components(λ_n; n = 1 and 2) of(NN) elastic scattering amplitude is included. In the range of 200 E_(lab) 1730 Me V, introducing λ_n plays a significant role in describing the data up to the momentum transfer, q^2≤1:2(Ge V/c)~2.Moreover, it is found that considering only the effect of phase variation parameter, cNN, improved the agreement in the region of minima for elastic scattering differential cross section for 45≤E_(lab)≤393 Ge V. The values of cNNand kn as a function of incident proton energies are presented.展开更多
文摘Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurations are considered, one in which a short-wave limit approximation is used, and another in which a long-wave limit approximation is used. In the short-wave limit, Wentzel-Kramers-Brillouin (WKB) methods are utilized to estimate the eigenvalues, and the eigenfunctions are approximated in terms of Green’s functions. The procedure consists of transforming the Orr-Sommerfeld equation into a system of two second order ordinary differential equations for which the eigenvalues and the eigenfunctions can be approximated. In the long-wave limit approximation, solutions are expressed in terms of generalized hypergeometric functions. Our procedure works regardless of the values of the Reynolds number.
文摘Elastic scattering differential cross sections for a p- ~4He system are calculated within the framework of optical limit approximation of the Glauber multiple scattering model. Three different ranges for proton energy(E_(lab)), 19〈E_(lab)〈50 Me V, 100≤E_(lab)≤1730 Me V, and 45 ≤E_(lab)≤393 Ge V are considered. It is shown that the Pauli blocking fails to describe the data up to the proton energy, E_(lab)〈100 Me V. For higher proton energies, a qualitative agreement is obtained. The observed elastic scattering differential cross section is nicely reproduced in the whole range of scattering angles in the center of mass system up to Θ_(c.m.)〈200° for 19〈E_(lab) ≤100 Me V when the effect of both the nucleon–nucleon(NN) phase variation parameter γNN and higher-order momentum transfer components(λ_n; n = 1 and 2) of(NN) elastic scattering amplitude is included. In the range of 200 E_(lab) 1730 Me V, introducing λ_n plays a significant role in describing the data up to the momentum transfer, q^2≤1:2(Ge V/c)~2.Moreover, it is found that considering only the effect of phase variation parameter, cNN, improved the agreement in the region of minima for elastic scattering differential cross section for 45≤E_(lab)≤393 Ge V. The values of cNNand kn as a function of incident proton energies are presented.
