强非线性格的首阶拟连续逼近的证明
Justification of Leading Order Quasicontinuum Approximations of Strongly Nonlinear Lattices
摘要：
本文研究了受Hertz接触定律支配的一维颗粒介质在预压下的首阶准连续极限。在此极限下导出的近似模型是合理的，通过建立渐近界的帮助下的能量估计的错误。连续介质模型预测的冲击波的发展，这也是在整个系统中的数值模拟的帮助下进行研究。我们还表明，现有的非线性薛定谔（NLS）和Korteweg de-Vries（KdV）近似FPU模型的结果直接适用于一个预压缩的颗粒介质中的弱非线性制度。
英文摘要：
We consider the leading order quasicontinuum limits of a one-dimensional granular medium governed by the Hertz contact law under precompression. The approximate model which is derived in this limit is justified by establishing asymptotic bounds for the error with the help of energy estimates. The continuum model predicts the development of shock waves, which are also studied in the full system with the aid of numerical simulations. We also show that existing results concerning the Nonlinear Schrodinger (NLS) and Korteweg de-Vries (KdV) approximation of FPU models apply directly to a precompressed granular medium in the weakly nonlinear regime.
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