We study the behaviors of thermalization in Fermi–Pasta–Ulam–Tsingou(FPUT) system with small number of particles using periodic boundary conditions. The total energy has initially equidistributed among some of the ...We study the behaviors of thermalization in Fermi–Pasta–Ulam–Tsingou(FPUT) system with small number of particles using periodic boundary conditions. The total energy has initially equidistributed among some of the lowest frequency modes. The thermalization time t_(eq) depending on system's energy density ε scales as t_(eq) ∝ε^(-4) only within a certain range of nonlinearity. In this range of nonlinearity, energies can interchange between the initial excited modes and other modes continuously with time until reaching the thermalized state. With a further decreasing nonlinearity, a steeper growth than ε^(-4) will appear. In the very weakly nonlinear regime, energies on low frequency modes are found to be frozen on large time scales. Redistribution of mode energies happens through the resonances of high frequency modes.展开更多
In this paper,the process of many particles hitting the same point of the substrate has been studied and an approximated formula to estimate maximum number of impact on the same point has been obtained through analyti...In this paper,the process of many particles hitting the same point of the substrate has been studied and an approximated formula to estimate maximum number of impact on the same point has been obtained through analytical analysis.Particles number of impacting on the same point of substrate;ust be small than this critical number to prevent substrate failure.The calculation results shows that for 45 steel,it is 21 when initial velocity is 40m/s,15 when initial velocity is 60 m/s,12 when initial velocity is 80 m/s and 4 when initial velocity is 240 m/s.With the increase of the particles initial velocity,the maximum number of speculation by the analytical model becomes linear.Accordingly we can deduce that this treatment does not cause the damage of substrate material.展开更多
基金supported by the Fundamental Research Funds for the Central Universities,China (Grant Nos. 2017B17114 and B210202152)。
文摘We study the behaviors of thermalization in Fermi–Pasta–Ulam–Tsingou(FPUT) system with small number of particles using periodic boundary conditions. The total energy has initially equidistributed among some of the lowest frequency modes. The thermalization time t_(eq) depending on system's energy density ε scales as t_(eq) ∝ε^(-4) only within a certain range of nonlinearity. In this range of nonlinearity, energies can interchange between the initial excited modes and other modes continuously with time until reaching the thermalized state. With a further decreasing nonlinearity, a steeper growth than ε^(-4) will appear. In the very weakly nonlinear regime, energies on low frequency modes are found to be frozen on large time scales. Redistribution of mode energies happens through the resonances of high frequency modes.
基金Item Sponsored by National Natural Science Foundation of China[No.50874027,51074044]National High Technology Research and Development Program[2010AA03A405]the Fundamental Research Funds for the Central Universities[N100402013]
文摘In this paper,the process of many particles hitting the same point of the substrate has been studied and an approximated formula to estimate maximum number of impact on the same point has been obtained through analytical analysis.Particles number of impacting on the same point of substrate;ust be small than this critical number to prevent substrate failure.The calculation results shows that for 45 steel,it is 21 when initial velocity is 40m/s,15 when initial velocity is 60 m/s,12 when initial velocity is 80 m/s and 4 when initial velocity is 240 m/s.With the increase of the particles initial velocity,the maximum number of speculation by the analytical model becomes linear.Accordingly we can deduce that this treatment does not cause the damage of substrate material.
