论文标题
通过周期性负载，能量供应到半无限的$β$β$ -FERMI-PASTA-ULAM-TSINGOU链
Energy supply into a semi-infinite $β$-Fermi-Pasta-Ulam-Tsingou chain by periodic force loading
论文作者
论文摘要
我们处理〜$β$ -FERMI-PASTA-PASTA-TSINGOU链的动力学，并具有一个自由端，受到正弦周期性的作用。我们检查了大量提供的总能量的演变。在谐波情况〜（$β= 0 $）中，能量在非零组速度上线性增长，对应于激发频率，并以〜$ \ sqrt {t} $在零组速度下生长。通过分析获得粒子速度场的近似闭合形式表达，提出了能量时间的行为的解释。 在弱的非谐疾病中，通过使用重新归一化的分散关系获得了总能量的大渐近近似。运行近似值，我们在驾驶频率下分析能量转移，均位于传递频带和谐波链的停止频段中。讨论了与数值模拟结果的渐近评估的一致性。
We deal with dynamics of the~$β$-Fermi-Pasta-Ulam-Tsingou chain with one free end, subjected to the sinusoidal periodic force. We examine evolution of the total energy, supplied at large times. In the harmonic case~($β=0$), the energy grows in time linearly at non-zero group velocities, corresponding to the excitation frequency and grows in time as~$\sqrt{t}$ at zero group velocity. Explanation of behavior in time of the energy is proposed by analysis of obtained approximate closed-form expression for the field of particle velocities. In the weak anharmonic case, large-time asymptotic approximation for the total energy is obtained by using the renormalized dispersion relation. Operating of the approximation, we analyze energy transfer at the driving frequencies, lying both in the pass-band and in the stop-band of the harmonic chain. Consistency of the asymptotic assesses with the results of numerical simulations is discussed.
