| 引用本文格式: Lu Ming-Liang,Zhang Zhen-Jun,Yuan Xiao-Li. Energy equipartition Properties of Fermi-Pasta-Ulam-Tsingou system for small number of particles with fixed boundary conditions [J]. J. At. Mol. Phys., 2023, 40(3): 036003 (in Chinese) 鲁明亮,张振俊,苑晓丽. 固定边界条件下Fermi-Pasta-Ulam-Tsingou短链能量均分性质研究 [J]. 原子与分子物理学报, 2023, 40(3): 036003] |
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| 固定边界条件下Fermi-Pasta-Ulam-Tsingou短链能量均分性质研究 |
| Energy equipartition Properties of Fermi-Pasta-Ulam-Tsingou system for small number of particles with fixed boundary conditions |
| 摘要点击 482 全文点击 181 投稿时间：2021-12-31 修订日期：2022-02-21 |
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| DOI编号
10.19855/j.1000-0364.2023.036003 |
| 中文关键词
FPUT短链 固定边界条件 能量均分 共振 |
| 英文关键词
FPUT system with small number of particles fixed boundary conditions energy equipartition resonance |
| 基金项目
中央高校基本科研业务经费专项基金（批准号：B210202148）;省级农业科技创新与推广专项（NJ2021-21） |
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| 中文摘要
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| 采用固定边界条件，数值研究了Fermi-Pasta-Ulam-Tsingou (FPUT) 短链的能量均分性质. 研究发现，在较强的非线性强度区间内，能量均分时间teq与能量密度ε 满足teq～ε-4.0的标度关系. 在该非线性强度区间内，能量通过相邻本征模之间的共振不停的传输，并最终达到能量均分状态. 这说明，即使不存在非平庸的六波共振，只要相邻本征模间的共振可以发生，teq～ε-4.0的标度关系就能出现. 随着非线性强度的减小，该标度关系不再成立. 此时，能量是通过高频本征模的共振逐渐向低频本征模传输的。 |
| 英文摘要
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| The properties of energy equipartition in Fermi-Pasta-Ulam-Tsingou (FPUT) system using fixed boundary conditions for small number of particles are studied. Energy equipartition time teq depending on system’s energy density ε shows a power law scaling teq～ε-4.0 within a certain range of nonlinearity. In this range of nonlinearity, energies can interchange between the adjacent eigenmodes continuously with time through the mechanism of overlap of frequencies until reaching the energy equipartition state. It suggests that even if there are no nontrivial six-wave resonances, as long as the resonances between adjacent eigenmodes occur, the power law teq～ε-4.0 will appear. With a further decreasing nonlinearity, there will be a steeper growth than teq～ε-4.0. In this range of nonlinearity, energy transport process is found to be related with the resonances of high frequency modes. |
