Porter Mason A, Daraio Chiara, Herbold Eric B, Szelengowicz Ivan, Kevrekidis P G
Oxford Centre for Industrial and Applied Mathematics, University of Oxford, Oxford OX1 3LB, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jan;77(1 Pt 2):015601. doi: 10.1103/PhysRevE.77.015601. Epub 2008 Jan 28.
We investigate the propagation of highly nonlinear solitary waves in heterogeneous, periodic granular media using experiments, numerical simulations, and theoretical analysis. We examine periodic arrangements of particles in experiments in which stiffer and heavier beads (stainless steel) are alternated with softer and lighter ones (polytetrafluoroethylene beads). We find good agreement between experiments and numerics in a model with Hertzian interactions between adjacent beads, which in turn agrees very well with a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments and general bead interactions. Our analysis encompasses previously studied examples as special cases and also provides key insights into the influence of the dimer lattice on the properties (width and propagation speed) of the highly nonlinear wave solutions.
我们通过实验、数值模拟和理论分析，研究了高度非线性孤立波在非均匀周期性颗粒介质中的传播。我们在实验中研究了颗粒的周期性排列，其中较硬较重的珠子（不锈钢）与较软较轻的珠子（聚四氟乙烯珠子）交替排列。我们发现，在一个相邻珠子间存在赫兹相互作用的模型中，实验结果与数值模拟结果吻合良好，而该模型又与我们针对非均匀环境和一般珠子相互作用推导的长波长区域模型的理论分析非常吻合。我们的分析将先前研究的例子作为特殊情况包含在内，还为二聚体晶格对高度非线性波解的性质（宽度和传播速度）的影响提供了关键见解。
