A corrected explicit method of double time steps(CEMDTS) was introduced to accurately simulate nonlinear vibration problems in engineering. The CEMDTS, the leapfrog central difference method, the Newmark method, the g...A corrected explicit method of double time steps(CEMDTS) was introduced to accurately simulate nonlinear vibration problems in engineering. The CEMDTS, the leapfrog central difference method, the Newmark method, the generalized-a method and the precise integration method were implemented in typical nonlinear examples for the purpose of comparison. Both conservative and non-conservative systems were examined. The results show that it isn't unconditionally stable for the precise integration method, the Newmark method and the generalized-a method in nonlinear systems. The stable interval of the three methods is less than that of the CEMDTS. When a small time step(?t≤T_(min)/20) is employed, the precise integration method is endowed with the highest accuracy while the CEMDTS possesses the smallest computation effort. However, the CEMDTS becomes the most accurate one when the time step is large(?t≥0.3T_(min)) or the system is strongly nonlinear. Therefore, the CEMDTS is more applicable to the nonlinear vibration systems.展开更多
We restrict purely kinetic k-essence.Assuming that the equation of state is a power law of the kinetic energy,i.e.w=w0Xα,we find thatαmust be positive to obtain accelerated phases,constrained from the conditions for...We restrict purely kinetic k-essence.Assuming that the equation of state is a power law of the kinetic energy,i.e.w=w0Xα,we find thatαmust be positive to obtain accelerated phases,constrained from the conditions for stability and causality.In this case the k-essence behaves like a phantom.We also study the evolutions of the equation of state and the speed of sound with numerical simulations.展开更多
基金Projects(51405402,51505390)supported by the National Natural Science Foundation of ChinaProjects(2016YFB1200404,2016YFB1200505)supported by the National Key Research and Development Program of China
文摘A corrected explicit method of double time steps(CEMDTS) was introduced to accurately simulate nonlinear vibration problems in engineering. The CEMDTS, the leapfrog central difference method, the Newmark method, the generalized-a method and the precise integration method were implemented in typical nonlinear examples for the purpose of comparison. Both conservative and non-conservative systems were examined. The results show that it isn't unconditionally stable for the precise integration method, the Newmark method and the generalized-a method in nonlinear systems. The stable interval of the three methods is less than that of the CEMDTS. When a small time step(?t≤T_(min)/20) is employed, the precise integration method is endowed with the highest accuracy while the CEMDTS possesses the smallest computation effort. However, the CEMDTS becomes the most accurate one when the time step is large(?t≥0.3T_(min)) or the system is strongly nonlinear. Therefore, the CEMDTS is more applicable to the nonlinear vibration systems.
基金Supported in part by the Natural Science Foundation of Hebei Province under Grant No.A2011201147the Research Fund for Doctoral Programs of Hebei University under Grant No.2009-155the Open Research Topics Fund of Key Laboratory of Particle Astrophysics,Institute of High Energy Physics,Chinese Academy of Sciences,under Grant No.0529410T41-200901.
文摘We restrict purely kinetic k-essence.Assuming that the equation of state is a power law of the kinetic energy,i.e.w=w0Xα,we find thatαmust be positive to obtain accelerated phases,constrained from the conditions for stability and causality.In this case the k-essence behaves like a phantom.We also study the evolutions of the equation of state and the speed of sound with numerical simulations.
