Christopher Chong , Ari Geisler , Panayotis G. Kevrekidis , Gino Biondini
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引用次数: 0
摘要
在本研究中,我们重新探讨了预压缩颗粒链中的冲击波动力学。通过用 α-Fermi-Pasta-Ulam-Tsingou 链近似模型,我们利用后者在应变变量公式中与两个独立可积分模型的联系,一个是连续模型,即 KdV 方程,另一个是离散模型,即 Toda 晶格。我们利用惠瑟姆调制理论对这种可积分系统进行分析,并对它们的色散冲击波进行分析近似,以便通过与粒状晶体的还原联系提供粒状问题的冲击波近似。对原始粒状链及其基于可积分系统的近似色散冲击波的详细数值比较证明,在广泛的参数范围内都非常有利。随着求解振幅参数的增加,(近似)理论与数值计算之间的渐进偏差得到了量化和讨论。
Integrable approximations of dispersive shock waves of the granular chain
In the present work we revisit the shock wave dynamics in a granular chain with precompression. By approximating the model by an -Fermi–Pasta–Ulam–Tsingou chain, we leverage the connection of the latter in the strain variable formulation to two separate integrable models, one continuum, namely the KdV equation, and one discrete, namely the Toda lattice. We bring to bear the Whitham modulation theory analysis of such integrable systems and the analytical approximation of their dispersive shock waves in order to provide, through the lens of the reductive connection to the granular crystal, an approximation to the shock wave of the granular problem. A detailed numerical comparison of the original granular chain and its approximate integrable-system-based dispersive shocks proves very favorable in a wide parametric range. The gradual deviations between (approximate) theory and numerical computation, as amplitude parameters of the solution increase are quantified and discussed.
期刊介绍:
Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics.
The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.