具有小谐振腔的质量中质量晶格
Mass-in-Mass Lattices with Small Internal Resonators
摘要：
我们考虑的质量中的质量（MiM）晶格时，内部谐振器是非常小的。当没有内部谐振器时，晶格简化为标准的Fermi-Pasta-Ulam-Tsingou（FPUT）系统。我们表明，解决方案的MiM系统，具有合适的初始数据，阴影的FPUT系统很长一段时间。使用一些经典的振荡积分估计，我们可以得出结论，近似的误差（在某些设置）高于人们可能期望的。
英文摘要：
We consider the mass-in-mass (MiM) lattice when the internal resonators are very small. When there are no internal resonators the lattice reduces to a standard Fermi-Pasta-Ulam-Tsingou (FPUT) system. We show that the solution of the MiM system, with suitable initial data, shadows the FPUT system for long periods of time. Using some classical oscillatory integral estimates we can conclude that the error of the approximation is (in some settings) higher than one may expect.
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