论文标题
带有小内部谐振器的质量质量晶格
Mass-in-Mass Lattices with Small Internal Resonators
论文作者
论文摘要
当内部谐振器很小时，我们考虑质量质量（MIM）晶格。当没有内部谐振器时，晶格将减少到标准的费米 - 帕斯塔 - 乌拉姆 - tsingou（fput）系统。我们表明，使用合适的初始数据，MIM系统的解决方案会长时间阴影。使用一些经典的振荡积分估计值，我们可以得出结论，近似值（在某些设置中）的误差比人们预期的要高。
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.
