In this paper, we combine the perturbation method in supersymmetric quantum mechanics with the WKB method to restudy an angular equation coming from the wave equations for a Sehwarzschild black hole with a straight st...In this paper, we combine the perturbation method in supersymmetric quantum mechanics with the WKB method to restudy an angular equation coming from the wave equations for a Sehwarzschild black hole with a straight string passing through it. This angular equation serves as a naive model for our investigation of the combination of supersymmetric quantum mechanics and the WKB method, and will provide valuable insight for our further study of the WKB approximation in real problems, like the one in spheroidal equations, etc.展开更多
The mild-slope equation derived by Berkhoff (1972), has widely been used in the numerical calculation of refraction and diffraction of regular waves. However, it is well known that the random sea waves has a significa...The mild-slope equation derived by Berkhoff (1972), has widely been used in the numerical calculation of refraction and diffraction of regular waves. However, it is well known that the random sea waves has a significant effect in the refraction and diffraction problems. In this paper, a new form of time-dependent mild slope equation for irregular waves was derived with Fade approximation and Kubo's time series concept. The equation was simplified using WKB method, and simple and practical irregular mild slope equation was obtained. Results of numerical calculations are compared with those of laboratory experiments.展开更多
We investigate computationally the attenuation and reflection of Terahertz (THz) wave using targets coated with plasmas. The simulators are the Wentzel-Kramer-Brillouin (WKB) method and finite-difference timedoma...We investigate computationally the attenuation and reflection of Terahertz (THz) wave using targets coated with plasmas. The simulators are the Wentzel-Kramer-Brillouin (WKB) method and finite-difference timedomain (FDTD) method. The relation between the frequency of the incident electromagnetic (EM) wave and the attenuation caused by unmagnitized plasma is analyzed. The results demonstrate that the amount of absorbed power is a decreasing function of the EM wave frequency and the plasma collision frequency. For THz band incident wave, the attenuation that is caused by plasma is small when the plasma has common density and the collision frequency. This conclusion has fine applying foreground for plasma anti stealth.展开更多
Theoretical analysis and numerical calculations of Love wave propagation in layered graded composites with imperfectly bonded interface are described in this paper. On the basis of WKB method, the approximate analytic...Theoretical analysis and numerical calculations of Love wave propagation in layered graded composites with imperfectly bonded interface are described in this paper. On the basis of WKB method, the approximate analytic solutions for Love waves are obtained. By the interface shear spring model, the dispersion relations for Love waves in layered graded composite structures with rigid, slip, and imperfectly bonded interfaces are given, and the effects of the interface conditions on the phase velocities of Love waves in SiC/Al layered graded composites are discussed. Numerical analysis shows that the phase velocity decreases when the defined flexibility parameter is greater. For the general imperfectly bonded interface, the phase velocity changes in the range of the velocities for the rigid and slip interface conditions.展开更多
Because the nonlinearity of actual physical processes can be expressed more precisely by the introduction of a non- linear term, the weakly nonlinear Prandtl model is one of the most effective ways to describe the pur...Because the nonlinearity of actual physical processes can be expressed more precisely by the introduction of a non- linear term, the weakly nonlinear Prandtl model is one of the most effective ways to describe the pure katabatic flow (no backgrotmd flow). Features of the weak nonlinearity are reflected by two factors: the small parameter c and the gradually varying eddy thermal conductivity. This paper first shows how to apply the Wentzel-Kramers-Brillouin (WKB) method for the approximate solution of the weakly nonlinear Prandtl model, and then describes the retrieval of gradually varying eddy thermal conductivity from observed wind speed and perturbed potential temperature. Gradually varying eddy thermal conductivity is generally derived from an empirical parameterization scheme. We utilize wind speed and potential temperature measurements, along with the variational assimilation technique, to de- rive this parameter. The objective function is constructed by the square of the differences between the observation and model value. The new method is validated by numerical experiments with simulated measurements, revealing that the order of the root mean squre error is 10-2 and thus confirming the method's robustness. In addition, this me- thod is caoable of anti-interference, as it effectivelv reduces the influence of observation error.展开更多
In this paper,by the WKB method the relation between the energy increase of internal inertial gravity waves and heterogeneous atmospheric stratification is derived,and a new generalized wave action is defined and its ...In this paper,by the WKB method the relation between the energy increase of internal inertial gravity waves and heterogeneous atmospheric stratification is derived,and a new generalized wave action is defined and its conservation is proved.展开更多
In this paper the influences of nonuniform stratification on the propagating paths of internal inertial-gravity and pure gravity wave energy are discussed by using the WKB approximation method.The conditions for conse...In this paper the influences of nonuniform stratification on the propagating paths of internal inertial-gravity and pure gravity wave energy are discussed by using the WKB approximation method.The conditions for conservation of wave energy,generalized wave action and wave enstrophy are obtained.The necessary condition of instability for inter- nal gravity waves and the equation governing the refraction of wave rays are derived.Two types of critical levels are giv- en.Finally,the wave rays for different distributions of stratification are calculated by using the fourth-order Runge-Kutta method.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10875018)
文摘In this paper, we combine the perturbation method in supersymmetric quantum mechanics with the WKB method to restudy an angular equation coming from the wave equations for a Sehwarzschild black hole with a straight string passing through it. This angular equation serves as a naive model for our investigation of the combination of supersymmetric quantum mechanics and the WKB method, and will provide valuable insight for our further study of the WKB approximation in real problems, like the one in spheroidal equations, etc.
基金The research was financially supported by the Doctor degree Program Foundation of State Education Commission of China
文摘The mild-slope equation derived by Berkhoff (1972), has widely been used in the numerical calculation of refraction and diffraction of regular waves. However, it is well known that the random sea waves has a significant effect in the refraction and diffraction problems. In this paper, a new form of time-dependent mild slope equation for irregular waves was derived with Fade approximation and Kubo's time series concept. The equation was simplified using WKB method, and simple and practical irregular mild slope equation was obtained. Results of numerical calculations are compared with those of laboratory experiments.
基金the National Natural Science Foundation of China (60771017)the China Postdoctoral ScienceFoundation (20060390272)
文摘We investigate computationally the attenuation and reflection of Terahertz (THz) wave using targets coated with plasmas. The simulators are the Wentzel-Kramer-Brillouin (WKB) method and finite-difference timedomain (FDTD) method. The relation between the frequency of the incident electromagnetic (EM) wave and the attenuation caused by unmagnitized plasma is analyzed. The results demonstrate that the amount of absorbed power is a decreasing function of the EM wave frequency and the plasma collision frequency. For THz band incident wave, the attenuation that is caused by plasma is small when the plasma has common density and the collision frequency. This conclusion has fine applying foreground for plasma anti stealth.
基金Engineering Research Institute of Peking University (ERIPKU) Joint Building Project of Beijing Education Committee
文摘Theoretical analysis and numerical calculations of Love wave propagation in layered graded composites with imperfectly bonded interface are described in this paper. On the basis of WKB method, the approximate analytic solutions for Love waves are obtained. By the interface shear spring model, the dispersion relations for Love waves in layered graded composite structures with rigid, slip, and imperfectly bonded interfaces are given, and the effects of the interface conditions on the phase velocities of Love waves in SiC/Al layered graded composites are discussed. Numerical analysis shows that the phase velocity decreases when the defined flexibility parameter is greater. For the general imperfectly bonded interface, the phase velocity changes in the range of the velocities for the rigid and slip interface conditions.
基金Supported by the National Natural Science Foundation of China(41575026)
文摘Because the nonlinearity of actual physical processes can be expressed more precisely by the introduction of a non- linear term, the weakly nonlinear Prandtl model is one of the most effective ways to describe the pure katabatic flow (no backgrotmd flow). Features of the weak nonlinearity are reflected by two factors: the small parameter c and the gradually varying eddy thermal conductivity. This paper first shows how to apply the Wentzel-Kramers-Brillouin (WKB) method for the approximate solution of the weakly nonlinear Prandtl model, and then describes the retrieval of gradually varying eddy thermal conductivity from observed wind speed and perturbed potential temperature. Gradually varying eddy thermal conductivity is generally derived from an empirical parameterization scheme. We utilize wind speed and potential temperature measurements, along with the variational assimilation technique, to de- rive this parameter. The objective function is constructed by the square of the differences between the observation and model value. The new method is validated by numerical experiments with simulated measurements, revealing that the order of the root mean squre error is 10-2 and thus confirming the method's robustness. In addition, this me- thod is caoable of anti-interference, as it effectivelv reduces the influence of observation error.
文摘In this paper,by the WKB method the relation between the energy increase of internal inertial gravity waves and heterogeneous atmospheric stratification is derived,and a new generalized wave action is defined and its conservation is proved.
基金This research is supported by the National Natural Science Foundation of China.
文摘In this paper the influences of nonuniform stratification on the propagating paths of internal inertial-gravity and pure gravity wave energy are discussed by using the WKB approximation method.The conditions for conservation of wave energy,generalized wave action and wave enstrophy are obtained.The necessary condition of instability for inter- nal gravity waves and the equation governing the refraction of wave rays are derived.Two types of critical levels are giv- en.Finally,the wave rays for different distributions of stratification are calculated by using the fourth-order Runge-Kutta method.