The unsteady oscillatory flow of an incompressible second grade fluid in a cylindrical tube with large wall suction is studied analytically. Flow in the tube is due to uniform suction at the permeable walls, and the o...The unsteady oscillatory flow of an incompressible second grade fluid in a cylindrical tube with large wall suction is studied analytically. Flow in the tube is due to uniform suction at the permeable walls, and the oscillations in the velocity field are due to small amplitude time harmonic pressure waves. The physical quantities of interest are the velocity field, the amplitude of oscillation, and the penetration depth of the oscillatory wave. The analytical solution of the governing boundary value problem is obtained, and the effects of second grade fluid parameters are analyzed and discussed.展开更多
The frequency of the Love-type surface waves in a bedded structure con- sisting of a porous piezoelectric (PP) medium and a functionally graded material (FGM) substrate is approximated. The FGM layer is assumed to hav...The frequency of the Love-type surface waves in a bedded structure con- sisting of a porous piezoelectric (PP) medium and a functionally graded material (FGM) substrate is approximated. The FGM layer is assumed to have a constant initial stress. The Wentzel-Kramers-Brillouin (WKB) approximation technique is used for the wave solution in the FGM layer, and the method of separation of variables is applied for the solution in the porous piezoelectric medium. The dependence of the wave frequency on the wave number is obtained for both electrically open and short cases. The effects of the gradient coefficient of the FGM layer, the initial stresses (tensile stress and compressive stress), and the width of the FGM layer are marked distinctly and shown graphically. The findings may contribute towards the design and optimization of acoustic wave devices.展开更多
A new analytical model was developed to predict the gravity wave drag （GWD） induced by an isolated 3-dimensional mountain, over which a stratified, nonrotating non-Boussinesq sheared flow is impinged. The model is c...A new analytical model was developed to predict the gravity wave drag （GWD） induced by an isolated 3-dimensional mountain, over which a stratified, nonrotating non-Boussinesq sheared flow is impinged. The model is confined to small amplitude motion and assumes the ambient velocity varying slowly with height. The modified Taylor-Goldstein equation with variable coefficients is solved with a Wentzel-Kramers-Brillouin （WKB） approximation, formally valid at high Richardson numbers. With this WKB solution, generic formulae of second order accuracy, for the GWD and surface pressure perturbation （both for hydrostatic and non-hydrostatic flow） are presented, enabling a rigorous treatment on the effects by vertical variations in wind profiles. In an ideal test to the circular bell-shaped mountain, itwas found that when the wind is linearly sheared, that the GWD decreases as the Richardson number decreases. However, the GWD for a forward sheared wind （wind increases with height） decreases always faster than that for the backward sheared wind （wind deceases with height）. This difference is evident whenever the model is hydrostatic or not.展开更多
We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with Poisson jumps and small multiplicative noises by using weak convergence method.
Spontaneous fission(SF) with a new formula based on a liquid drop model is proposed and used in the calculation of the SF half-lives of heavy and superheavy nuclei(Z = 90–120). The predicted half-lives are in agreeme...Spontaneous fission(SF) with a new formula based on a liquid drop model is proposed and used in the calculation of the SF half-lives of heavy and superheavy nuclei(Z = 90–120). The predicted half-lives are in agreement with the experimental SF half-lives. The half-lives of decay(AD) for the same nuclei are obtained by using the Wentzel-Kramers-Brillouin(WKB) method together with Bohr-Sommerfeld(BS) quantization condition considering the isospin-dependent effects for the cosh potential. The decay modes and branching ratios of superheavy nuclei(Z =104-118) with experimental decay modes are obtained, and the modes are compared with the experimental ones and with the predictions found in the literature. Although some nuclei have predicted decay modes that are different from their experimental decay modes, decay modes same as the experimental ones are predicted for many nuclei. The SF and AD half-lives, branching ratios, and decay modes are obtained for superheavy nuclei(Z = 119–120) with unknown decay modes and compared with the predictions obtained in a previous study. The present results provide useful information for future experimental studies performed on both the AD and SF of superheavy nuclei.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
We study the properties of proton rich nuclei reported as proton emitters in the region from I to Bi with Z =53 to 83 and N = 56 to 102 as a crucial application to the existence of exotic nuclei. The effective relativ...We study the properties of proton rich nuclei reported as proton emitters in the region from I to Bi with Z =53 to 83 and N = 56 to 102 as a crucial application to the existence of exotic nuclei. The effective relativistic meanfield formalism(E-RMF), with NL3, FSUGarnet, G3 and IOPB-I interactions, is adopted for analysis of the ground state properties of proton emitters. Furthermore, in the E-RMF background, the Wentzel-Karmers-Brillouin(WKB)barrier penetration method is used for the calculation of proton emission half-lives. It is found that the calculated halflives are in good agreement with the experimental results for all emitters considered in this study.展开更多
文摘The unsteady oscillatory flow of an incompressible second grade fluid in a cylindrical tube with large wall suction is studied analytically. Flow in the tube is due to uniform suction at the permeable walls, and the oscillations in the velocity field are due to small amplitude time harmonic pressure waves. The physical quantities of interest are the velocity field, the amplitude of oscillation, and the penetration depth of the oscillatory wave. The analytical solution of the governing boundary value problem is obtained, and the effects of second grade fluid parameters are analyzed and discussed.
文摘The frequency of the Love-type surface waves in a bedded structure con- sisting of a porous piezoelectric (PP) medium and a functionally graded material (FGM) substrate is approximated. The FGM layer is assumed to have a constant initial stress. The Wentzel-Kramers-Brillouin (WKB) approximation technique is used for the wave solution in the FGM layer, and the method of separation of variables is applied for the solution in the porous piezoelectric medium. The dependence of the wave frequency on the wave number is obtained for both electrically open and short cases. The effects of the gradient coefficient of the FGM layer, the initial stresses (tensile stress and compressive stress), and the width of the FGM layer are marked distinctly and shown graphically. The findings may contribute towards the design and optimization of acoustic wave devices.
基金Project supported by the National Basic Research Program of China (973 Program) (No.2004CB418301)the National Natural Science Foundation of China(Nos.40575017 and 40333031)
文摘A new analytical model was developed to predict the gravity wave drag （GWD） induced by an isolated 3-dimensional mountain, over which a stratified, nonrotating non-Boussinesq sheared flow is impinged. The model is confined to small amplitude motion and assumes the ambient velocity varying slowly with height. The modified Taylor-Goldstein equation with variable coefficients is solved with a Wentzel-Kramers-Brillouin （WKB） approximation, formally valid at high Richardson numbers. With this WKB solution, generic formulae of second order accuracy, for the GWD and surface pressure perturbation （both for hydrostatic and non-hydrostatic flow） are presented, enabling a rigorous treatment on the effects by vertical variations in wind profiles. In an ideal test to the circular bell-shaped mountain, itwas found that when the wind is linearly sheared, that the GWD decreases as the Richardson number decreases. However, the GWD for a forward sheared wind （wind increases with height） decreases always faster than that for the backward sheared wind （wind deceases with height）. This difference is evident whenever the model is hydrostatic or not.
文摘We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with Poisson jumps and small multiplicative noises by using weak convergence method.
基金Supported by the Turkish Science and Research Council(TüB?TAK)with Grant Number 118R028
文摘Spontaneous fission(SF) with a new formula based on a liquid drop model is proposed and used in the calculation of the SF half-lives of heavy and superheavy nuclei(Z = 90–120). The predicted half-lives are in agreement with the experimental SF half-lives. The half-lives of decay(AD) for the same nuclei are obtained by using the Wentzel-Kramers-Brillouin(WKB) method together with Bohr-Sommerfeld(BS) quantization condition considering the isospin-dependent effects for the cosh potential. The decay modes and branching ratios of superheavy nuclei(Z =104-118) with experimental decay modes are obtained, and the modes are compared with the experimental ones and with the predictions found in the literature. Although some nuclei have predicted decay modes that are different from their experimental decay modes, decay modes same as the experimental ones are predicted for many nuclei. The SF and AD half-lives, branching ratios, and decay modes are obtained for superheavy nuclei(Z = 119–120) with unknown decay modes and compared with the predictions obtained in a previous study. The present results provide useful information for future experimental studies performed on both the AD and SF of superheavy nuclei.
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.
基金Supported by the Department of Science and Technology,Govt.of India(EMR/2015/002517)
文摘We study the properties of proton rich nuclei reported as proton emitters in the region from I to Bi with Z =53 to 83 and N = 56 to 102 as a crucial application to the existence of exotic nuclei. The effective relativistic meanfield formalism(E-RMF), with NL3, FSUGarnet, G3 and IOPB-I interactions, is adopted for analysis of the ground state properties of proton emitters. Furthermore, in the E-RMF background, the Wentzel-Karmers-Brillouin(WKB)barrier penetration method is used for the calculation of proton emission half-lives. It is found that the calculated halflives are in good agreement with the experimental results for all emitters considered in this study.
