According to detonation theory and hydrodynamic principle, a physical model has been set up in this paper. Based on the model a methodology for calculating dynamic initial shock parameters such as shock pressure pm sh...According to detonation theory and hydrodynamic principle, a physical model has been set up in this paper. Based on the model a methodology for calculating dynamic initial shock parameters such as shock pressure pm shock wave velosity Dm etc. of coupling charge on borehole wall has ben developed. The shock parameters have been calculated when high explosives works on granite, limestone and marble respectively. The magnitude of every parameter on borehole wall has been obtained from ignited dot to the end of borehole along axial direction. Some important conclusions are also gained.展开更多
Because of the importance of gravity waves （GWs） in coupling different atmospheric regions, further studies are necessary to investigate the characteristics of GW propagation in a non-isothermal atmosphere. Using a ...Because of the importance of gravity waves （GWs） in coupling different atmospheric regions, further studies are necessary to investigate the characteristics of GW propagation in a non-isothermal atmosphere. Using a nonlinear numerical model, we simulate the propagation of small amplitude GWs with various wavelengths in different non-isothermal atmospheres. Our re- sults show that the GW vertical wavelength undergoes sharp changes above the stratopause and mesopause region. Specifically for a GW with an initial vertical wavelength of 5 km, the seasonal background temperature structure difference at 50° latitude can cause the vertical wavelength to vary by -2 krn in the mesosphere and by as large as -4.5 km in the lower thermosphere. In addition, the GW paths exhibit great divergence in the height range of -65-110 kin. Our results also show that the variations of GW path, vertical wavelength and horizontal phase velocity are not synchronized in a non-isothermal atmosphere as in an isothermal atmosphere. Despite the fact that all GWs change their characteristics as they propagate upward in a non-isothermal atmosphere, the variations relative to the initial parameters at a reference height are similar for different initial vertical wavelengths. Our results indicate that the changing characteristics of a gravity wave in a non-isothermal atmosphere need to be considered when investigating the relationship of GWs at two different heights.展开更多
The steady Eikonal equation is a prototypical first-order fully nonlinear equation. A numerical method based on elliptic solvers is presented here to solve two different kinds of steady Eikonal equations and compute s...The steady Eikonal equation is a prototypical first-order fully nonlinear equation. A numerical method based on elliptic solvers is presented here to solve two different kinds of steady Eikonal equations and compute solutions, which are maximal and minimal in the variational sense. The approach in this paper relies on a variational argument involving penalty, a biharmonic regularization, and an operator-splitting-based time-discretization scheme for the solution of an associated initial-value problem. This approach allows the decoupling of the nonlinearities and differential operators.Numerical experiments are performed to validate this approach and investigate its convergence properties from a numerical viewpoint.展开更多
The authors study the compressible limit of the nonlinear Schrdinger equation with different-degree small parameter nonlinearities in small time for initial data with Sobolev regularity before the formation of singula...The authors study the compressible limit of the nonlinear Schrdinger equation with different-degree small parameter nonlinearities in small time for initial data with Sobolev regularity before the formation of singularities in the limit system.On the one hand,the existence and uniqueness of the classical solution are proved for the dispersive perturbation of the quasi-linear symmetric system corresponding to the initial value problem of the above nonlinear Schrdinger equation.On the other hand,in the limit system,it is shown that the density converges to the solution of the compressible Euler equation and the validity of the WKB expansion is justified.展开更多
文摘According to detonation theory and hydrodynamic principle, a physical model has been set up in this paper. Based on the model a methodology for calculating dynamic initial shock parameters such as shock pressure pm shock wave velosity Dm etc. of coupling charge on borehole wall has ben developed. The shock parameters have been calculated when high explosives works on granite, limestone and marble respectively. The magnitude of every parameter on borehole wall has been obtained from ignited dot to the end of borehole along axial direction. Some important conclusions are also gained.
基金supported by the National Natural Science Foundation of China (Grant Nos. 40921063, 41004063, 41074109, 40890165, and 41174127)the National Important Basic Research Project (Grant No. 2011CB811405)+3 种基金the China Postdoctoral Science Foundation (Grant No. 20100470506)supported in part by the Specialized Research Fundthe Open Research Program of the State Key Laboratory of Space Weatherthe National Science Foundation of Unites States grant-ATM-0633418 to Miami University
文摘Because of the importance of gravity waves （GWs） in coupling different atmospheric regions, further studies are necessary to investigate the characteristics of GW propagation in a non-isothermal atmosphere. Using a nonlinear numerical model, we simulate the propagation of small amplitude GWs with various wavelengths in different non-isothermal atmospheres. Our re- sults show that the GW vertical wavelength undergoes sharp changes above the stratopause and mesopause region. Specifically for a GW with an initial vertical wavelength of 5 km, the seasonal background temperature structure difference at 50° latitude can cause the vertical wavelength to vary by -2 krn in the mesosphere and by as large as -4.5 km in the lower thermosphere. In addition, the GW paths exhibit great divergence in the height range of -65-110 kin. Our results also show that the variations of GW path, vertical wavelength and horizontal phase velocity are not synchronized in a non-isothermal atmosphere as in an isothermal atmosphere. Despite the fact that all GWs change their characteristics as they propagate upward in a non-isothermal atmosphere, the variations relative to the initial parameters at a reference height are similar for different initial vertical wavelengths. Our results indicate that the changing characteristics of a gravity wave in a non-isothermal atmosphere need to be considered when investigating the relationship of GWs at two different heights.
基金supported by the National Science Foundation(No.DMS-0913982)
文摘The steady Eikonal equation is a prototypical first-order fully nonlinear equation. A numerical method based on elliptic solvers is presented here to solve two different kinds of steady Eikonal equations and compute solutions, which are maximal and minimal in the variational sense. The approach in this paper relies on a variational argument involving penalty, a biharmonic regularization, and an operator-splitting-based time-discretization scheme for the solution of an associated initial-value problem. This approach allows the decoupling of the nonlinearities and differential operators.Numerical experiments are performed to validate this approach and investigate its convergence properties from a numerical viewpoint.
基金Project supported by the National Natural Science Foundation of China (Nos.10801102,10771151)the Sichuan Youth Sciences and Technology Foundation (No.07ZQ026-009)the China Postdoctoral Science Foundation
文摘The authors study the compressible limit of the nonlinear Schrdinger equation with different-degree small parameter nonlinearities in small time for initial data with Sobolev regularity before the formation of singularities in the limit system.On the one hand,the existence and uniqueness of the classical solution are proved for the dispersive perturbation of the quasi-linear symmetric system corresponding to the initial value problem of the above nonlinear Schrdinger equation.On the other hand,in the limit system,it is shown that the density converges to the solution of the compressible Euler equation and the validity of the WKB expansion is justified.
