Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric d...Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the ＂k/2π scale＂ and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.展开更多
In this paper, exact solutions of scattering states of the Klein-Gordon equation with Coulomb potential plus a new ring-shaped potential are studied under the condition that the scalar potential is equal to the vector...In this paper, exact solutions of scattering states of the Klein-Gordon equation with Coulomb potential plus a new ring-shaped potential are studied under the condition that the scalar potential is equal to the vector potential. The normalized wave functions of scattering states on the “k/27π scale” and the calculation formula of phase shifts are presented. Analytical properties of the scattering amplitude are discussed.展开更多
The knowledge of the equation of state(EOS)and the compressibility of a solid are of central importance for the understanding of the behavior and the application of a condensed matter.The compression behavior of Zr41T...The knowledge of the equation of state(EOS)and the compressibility of a solid are of central importance for the understanding of the behavior and the application of a condensed matter.The compression behavior of Zr41Ti14Cu12.5Ni10Be22.5 bulk metallic glass(BMG)is investigated at room temperature up to 24 GPa using in-situ high pressure energy dispersive X-ray diffraction with synchrotron radiation.A model of basic cell volume has been established and the equation of state of BMG is determined by the calculation of radial distribution function.The experimental results indicate that the BMG contains a large amount of vacancy-like free volume.Low pressure(below 7 GPa)induces the collapse of the free volume to some extent and structure relaxation in the BMG.展开更多
A two-body equation of the kaon-proton system with the lowest order relativistic corrections is derived and solved. The scattering lengths and the energy of an unstable bound state are calculated.
Within a Pekeris-type approximation to the centrifugal term, we examine the approximately analytical scattering state solutions of the l-wave Schrdinger equation with the modified Rosen–Morse potential. The calculati...Within a Pekeris-type approximation to the centrifugal term, we examine the approximately analytical scattering state solutions of the l-wave Schrdinger equation with the modified Rosen–Morse potential. The calculation formula of phase shifts is derived, and the corresponding bound state energy levels are also obtained from the poles of the scattering amplitude.展开更多
Black lenses with L(n,1) horizon topology in five dimensions have many unusual properties shared by neither Myers-Perry black holes with event-horizon topology S 3,nor 5-dimensional black rings with event-horizon topo...Black lenses with L(n,1) horizon topology in five dimensions have many unusual properties shared by neither Myers-Perry black holes with event-horizon topology S 3,nor 5-dimensional black rings with event-horizon topology S 2 × S 1.In this work,by constructing appropriate matrices γμ for the general covariant Dirac equation,we further extend the fermion tunnelling method to 5-dimensional static and rotating black lenses.As a result,it is interesting to find as in black hole cases,fermions tunnelling can also result in correct Hawking temperatures for the static and rotating black lenses.展开更多
We have quantitatively investigated the radiation belt's dynamic variations of 1.5-6.0 MeV electrons during 54 CME (coronal mass ejection)-driven storms from 1993 to 2003 and 26 CIR (corotating interaction region)...We have quantitatively investigated the radiation belt's dynamic variations of 1.5-6.0 MeV electrons during 54 CME (coronal mass ejection)-driven storms from 1993 to 2003 and 26 CIR (corotating interaction region)-driven recurrent storms in 1995 by utilizing case and statistical studies based on the data from the SAMPEX satellite. It is found that the boundaries determined by fitting an exponential to the flux as a function of L shell obtained in this study agree with the observed outer and inner boundaries of the outer radiation belt. Furthermore, we have constructed the Radiation Belt Content (RBC) index by integrating the number density of electrons between those inner and outer boundaries. According to the ratio of the maximum RBC index during the recovery phase to the pre-storm average RBC index, we conclude that CME-driven storms produce more relativistic electrons than CIR-driven storms in the entire outer radiation belt, although the relativistic electron fluxes during CIR-related storms are much higher than those during CME-related storms at geosynchronous orbit. The physical radiation belt model STEERB is based on the three-dimensional Fokker-Planck equation and includes the physical processes of local wave-particle interactions, radial diffusion, and adiabatic transport. Due to the limitation of numerical schemes, formal radiation belt models do not include the cross diffusion term of local wave-particle interactions. The numerical experiments of STEERB have shown that the energetic electron fluxes can be overestimated by a factor of 5 or even several orders (depending on the pitch angle) if the cross diffusion term is ignored. This implies that the cross diffusion term is indispensable for the evaluation of radiation belt electron fluxes. Formal radiation belt models often adopt dipole magnetic field; the time varying Hilmer-Voigt geomagnetic field was adopted by the STEERB model, which self-consistently included the adiabatic transport process. The test simulations clearly indicate that the adiabatic process can significantly affect the evolution of radiation belt electrons. The interactions between interplanetary shocks and magnetosphere can excite ULF waves in the inner magnetosphere; the excited polodial mode ULF wave can cause the fast acceleration of "killer electrons". The acceleration mechanism of energetic electrons by poloidal and toroidal mode ULF wave is different at different L shells. The acceleration of energetic electrons by the toroidal mode ULF waves becomes important in the region with a larger L shell (the outer magnetosphere); in smaller L shell regions (the inner magnetosphere), the poloidal mode ULF becomes responsible for the acceleration of energetic electrons.展开更多
A numerical investigation has been performed on supersonic mixing of hydrogen with air in a Scramjet (Supersonic Combustion Ramjet) combustor and its flame holding capability by solving Two-Dimensional full Navier-Sto...A numerical investigation has been performed on supersonic mixing of hydrogen with air in a Scramjet (Supersonic Combustion Ramjet) combustor and its flame holding capability by solving Two-Dimensional full Navier-Stokes equations. The main flow is air entering through a finite width of inlet and gaseous hydrogen is injected perpendicularly from the side wall. An explicit Harten-Yee Non-MUSCL Modified-flux-type TVD scheme has been used to solve the system of equations, and a zero-equation algebraic turbulence model to calculate the eddy viscosity coefficient. In this study the enhancement of mixing and good flame holding capability of a supersonic combustor have been investigated by varying the distance of injector position from left boundary keeping constant the backward-facing step height and other calculation parameters. The results show that the configuration for small distance of injector position has high mixing efficiency but the upstream recirculation can not evolved properly which is an important factor for flame holding capability. On the other hand, the configuration for very long distance has lower mixing efficiency due to lower gradient of hydrogen mass concentration on the top of injector caused by the expansion of side jet in both upstream and downstream of injector. For moderate distance of injector position, large and elongated upstream recirculation can evolve which might be activated as a good flame holder.展开更多
基金＊Supported by the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2010291, the Professor and Doctor Foundation of Yancheng Teachers University under Grant No. 07YSYJB0203
文摘Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the ＂k/2π scale＂ and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.
基金The project supported by the Protessor and Doctor Foundation of Yancheng Teachers College
文摘In this paper, exact solutions of scattering states of the Klein-Gordon equation with Coulomb potential plus a new ring-shaped potential are studied under the condition that the scalar potential is equal to the vector potential. The normalized wave functions of scattering states on the “k/27π scale” and the calculation formula of phase shifts are presented. Analytical properties of the scattering amplitude are discussed.
基金Sponsored by the National Natural Science Foundation of China(Grant No.10004014).
文摘The knowledge of the equation of state(EOS)and the compressibility of a solid are of central importance for the understanding of the behavior and the application of a condensed matter.The compression behavior of Zr41Ti14Cu12.5Ni10Be22.5 bulk metallic glass(BMG)is investigated at room temperature up to 24 GPa using in-situ high pressure energy dispersive X-ray diffraction with synchrotron radiation.A model of basic cell volume has been established and the equation of state of BMG is determined by the calculation of radial distribution function.The experimental results indicate that the BMG contains a large amount of vacancy-like free volume.Low pressure(below 7 GPa)induces the collapse of the free volume to some extent and structure relaxation in the BMG.
基金the National Natural Science Foundation of China under，the High Performance Computing Center of China (Beijing) and partly undertaken on IBM RS/6000 SP at CCSE of Peking University，北京大学校科研和校改项目
文摘A two-body equation of the kaon-proton system with the lowest order relativistic corrections is derived and solved. The scattering lengths and the energy of an unstable bound state are calculated.
基金Supported by the National Natural Science Foundation of China under Grant No.11405128Natural Science Basic Research Plan in Shaanxi Province of China under Grant No.15JK2093
文摘Within a Pekeris-type approximation to the centrifugal term, we examine the approximately analytical scattering state solutions of the l-wave Schrdinger equation with the modified Rosen–Morse potential. The calculation formula of phase shifts is derived, and the corresponding bound state energy levels are also obtained from the poles of the scattering amplitude.
基金supported by the Scientific Research Foundation of the Education Department of Liaoning Province,China (Grant No.L2011195)
文摘Black lenses with L(n,1) horizon topology in five dimensions have many unusual properties shared by neither Myers-Perry black holes with event-horizon topology S 3,nor 5-dimensional black rings with event-horizon topology S 2 × S 1.In this work,by constructing appropriate matrices γμ for the general covariant Dirac equation,we further extend the fermion tunnelling method to 5-dimensional static and rotating black lenses.As a result,it is interesting to find as in black hole cases,fermions tunnelling can also result in correct Hawking temperatures for the static and rotating black lenses.
基金supported by the National Basic Research Program of China (Grant No. 2012CB825603)the Specialized Research Fund for State Key Laboratories
文摘We have quantitatively investigated the radiation belt's dynamic variations of 1.5-6.0 MeV electrons during 54 CME (coronal mass ejection)-driven storms from 1993 to 2003 and 26 CIR (corotating interaction region)-driven recurrent storms in 1995 by utilizing case and statistical studies based on the data from the SAMPEX satellite. It is found that the boundaries determined by fitting an exponential to the flux as a function of L shell obtained in this study agree with the observed outer and inner boundaries of the outer radiation belt. Furthermore, we have constructed the Radiation Belt Content (RBC) index by integrating the number density of electrons between those inner and outer boundaries. According to the ratio of the maximum RBC index during the recovery phase to the pre-storm average RBC index, we conclude that CME-driven storms produce more relativistic electrons than CIR-driven storms in the entire outer radiation belt, although the relativistic electron fluxes during CIR-related storms are much higher than those during CME-related storms at geosynchronous orbit. The physical radiation belt model STEERB is based on the three-dimensional Fokker-Planck equation and includes the physical processes of local wave-particle interactions, radial diffusion, and adiabatic transport. Due to the limitation of numerical schemes, formal radiation belt models do not include the cross diffusion term of local wave-particle interactions. The numerical experiments of STEERB have shown that the energetic electron fluxes can be overestimated by a factor of 5 or even several orders (depending on the pitch angle) if the cross diffusion term is ignored. This implies that the cross diffusion term is indispensable for the evaluation of radiation belt electron fluxes. Formal radiation belt models often adopt dipole magnetic field; the time varying Hilmer-Voigt geomagnetic field was adopted by the STEERB model, which self-consistently included the adiabatic transport process. The test simulations clearly indicate that the adiabatic process can significantly affect the evolution of radiation belt electrons. The interactions between interplanetary shocks and magnetosphere can excite ULF waves in the inner magnetosphere; the excited polodial mode ULF wave can cause the fast acceleration of "killer electrons". The acceleration mechanism of energetic electrons by poloidal and toroidal mode ULF wave is different at different L shells. The acceleration of energetic electrons by the toroidal mode ULF waves becomes important in the region with a larger L shell (the outer magnetosphere); in smaller L shell regions (the inner magnetosphere), the poloidal mode ULF becomes responsible for the acceleration of energetic electrons.
文摘A numerical investigation has been performed on supersonic mixing of hydrogen with air in a Scramjet (Supersonic Combustion Ramjet) combustor and its flame holding capability by solving Two-Dimensional full Navier-Stokes equations. The main flow is air entering through a finite width of inlet and gaseous hydrogen is injected perpendicularly from the side wall. An explicit Harten-Yee Non-MUSCL Modified-flux-type TVD scheme has been used to solve the system of equations, and a zero-equation algebraic turbulence model to calculate the eddy viscosity coefficient. In this study the enhancement of mixing and good flame holding capability of a supersonic combustor have been investigated by varying the distance of injector position from left boundary keeping constant the backward-facing step height and other calculation parameters. The results show that the configuration for small distance of injector position has high mixing efficiency but the upstream recirculation can not evolved properly which is an important factor for flame holding capability. On the other hand, the configuration for very long distance has lower mixing efficiency due to lower gradient of hydrogen mass concentration on the top of injector caused by the expansion of side jet in both upstream and downstream of injector. For moderate distance of injector position, large and elongated upstream recirculation can evolve which might be activated as a good flame holder.
