Research Alliance Center for Mathematical Sciences, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan.
WPI-Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan.
Phys Rev E. 2019 Jan;99(1-1):012906. doi: 10.1103/PhysRevE.99.012906.
We numerically study the evolution of elastic standing waves in disordered disk systems with a focus on the dispersion relations of rotational sound. As on a lattice, the rotational mode exhibits an optical-like dispersion relation in the high frequency regime, representing a shoulder in the vibrational density of states and fast oscillations of the autocorrelations of rotational velocities. If tangential stiffness between the disks is large enough, a lattice-based model perfectly describes the dispersion relation of the rotational mode. If it is comparable to or smaller than the normal stiffness, the model fails for short wavelengths. However, the dispersion relation then follows the model prediction for the transverse mode, implying that the fast oscillations of disks' rotations switch to acousticlike behavior. We evidence such a transition from rotational to transverse modes by analyzing their respective participation of different degrees of freedom to the eigenvectors.
我们通过数值研究了无序盘系统中弹性驻波的演化，重点关注旋转声的频散关系。与晶格类似，旋转模式在高频区表现出类光色散关系，在振动态密度中表现为一个肩峰，并表现出旋转速度自相关的快速振荡。如果盘之间的切向刚度足够大，则基于晶格的模型可以完美描述旋转模式的频散关系。如果它与正常刚度相当或更小，则对于短波长，模型将失败。但是，频散关系随后遵循横向模式的模型预测，这意味着圆盘旋转的快速振荡转变为类声波行为。通过分析它们各自的本征向量对不同自由度的参与程度，我们证明了这种从旋转模式到横向模式的转变。
