Sussman Daniel M, Goodrich Carl P, Liu Andrea J, Nagel Sidney R
Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104, USA.
Soft Matter. 2015 Apr 14;11(14):2745-51. doi: 10.1039/c4sm02905d.
We study the vibrational properties near a free surface of disordered spring networks derived from jammed sphere packings. In bulk systems, without surfaces, it is well understood that such systems have a plateau in the density of vibrational modes extending down to a frequency scale ω*. This frequency is controlled by ΔZ = 〈Z〉 - 2d, the difference between the average coordination of the spheres and twice the spatial dimension, d, of the system, which vanishes at the jamming transition. In the presence of a free surface we find that there is a density of disordered vibrational modes associated with the surface that extends far below ω*. The total number of these low-frequency surface modes is controlled by ΔZ, and the profile of their decay into the bulk has two characteristic length scales, which diverge as ΔZ(-1/2) and ΔZ(-1) as the jamming transition is approached.
我们研究了由紧密堆积的球体衍生出的无序弹簧网络自由表面附近的振动特性。在没有表面的体系统中，人们很清楚这样的系统在振动模式密度上有一个平台，一直延伸到频率尺度ω*。这个频率由ΔZ =〈Z〉 - 2d控制，即球体的平均配位数与系统空间维度d的两倍之间的差值，它在堵塞转变时消失。在存在自由表面的情况下，我们发现存在与表面相关的无序振动模式密度，其延伸到远低于ω*的频率范围。这些低频表面模式的总数由ΔZ控制，并且它们向体内衰减的轮廓有两个特征长度尺度，当接近堵塞转变时，它们分别按ΔZ(-1/2)和ΔZ(-1)发散。
