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Title: A regularized continuum model for travelling waves and dispersive shocks of the granular chain
Abstract In this paper, we focus on a discrete physical model describing granular crystals, whose equations of motion can be described by a system of differential difference equations. After revisiting earlier continuum approximations, we propose a regularized continuum model variant to approximate the discrete granular crystal model through a suitable partial differential equation. We then compute, both analytically and numerically, its travelling wave and periodic travelling wave solutions, in addition to its conservation laws. Next, using the periodic solutions, we describe quantitatively various features of the dispersive shock wave (DSW) by applying Whitham modulation theory and the DSW fitting method. Finally, we perform several sets of systematic numerical simulations to compare the corresponding DSW results with the theoretical predictions and illustrate that the continuum model provides a good approximation of the underlying discrete one.  more » « less
Award ID(s):
2110030 2204702 2408988
PAR ID:
10634583
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Cambridge University Press
Date Published:
Journal Name:
Journal of Nonlinear Waves
Volume:
1
ISSN:
3033-4268
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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