We study numerically propagation of energy in a one dimensional Ding-Ding lattice, composed of linear oscillators with ellastic collisions. Wave propagation is suppressed by breaking translational symmetry, we consider three way to do this: a position disorder, a mass disorder, and a dimer lattice with alternating distances between the units. In all cases the spreading of an initially localized wavepacket is irregular, due to appearance of chaos, and subdiffusive. Guided by a nonlinear diffusion equation, we establish that the mean waiting times of spreading obey a scaling law in dependence on energy. Moreover, we show that the spreading exponents very weakly depend on the level of disorder.

中文翻译：

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无序叮咚晶格中能量扩散的标度

我们研究了一维丁丁晶格中能量的数值传播，该晶格由具有弹性碰撞的线性振荡器组成。通过打破平移对称性来抑制波传播，我们考虑三种方法来做到这一点：位置无序、质量无序和单元之间具有交替距离的二聚体晶格。在所有情况下，初始局部波包的传播都是不规则的，因为出现了混沌和次扩散。在非线性扩散方程的指导下，我们确定扩散的平均等待时间服从依赖于能量的标度定律。此外，我们表明传播指数非常微弱地依赖于无序程度。