Silbert Leonardo E, Liu Andrea J, Nagel Sidney R
James Franck Institute, University of Chicago, Chicago, IL 60637, USA.
Phys Rev Lett. 2005 Aug 26;95(9):098301. doi: 10.1103/PhysRevLett.95.098301. Epub 2005 Aug 24.
We numerically study the vibrations of jammed packings of particles interacting with finite-range, repulsive potentials at zero temperature. As the packing fraction phi is lowered towards the onset of unjamming at phi(c), the density of vibrational states approaches a nonzero value in the limit of zero frequency. For phi >phi(c), there is a crossover frequency, omega* below which the density of states drops towards zero. This crossover frequency obeys power-law scaling with phi-phi(c). Characteristic length scales, determined from the dominant wave vector contributing to the eigenmode at omega*, diverge as power laws at the unjamming transition.
我们对零温度下与有限范围排斥势相互作用的颗粒堵塞堆积的振动进行了数值研究。当堆积分数φ朝着φ(c)处的解堵塞起始点降低时，在零频率极限下，振动态密度趋近于一个非零值。对于φ>φ(c)，存在一个交叉频率ω*，在其以下态密度降至零。这个交叉频率遵循与φ - φ(c)的幂律标度关系。由对ω*处本征模贡献的主导波矢确定的特征长度尺度，在解堵塞转变处按幂律发散。
