Hu Yanqing, Johnson David L, Valenza John J, Santibanez Francisco, Makse Hernán A
Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA.
Schlumberger-Doll Research, One Hampshire, Cambridge, Massachusetts 02139, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):062202. doi: 10.1103/PhysRevE.89.062202. Epub 2014 Jun 9.
A zero-temperature critical point has been invoked to control the anomalous behavior of granular matter as it approaches jamming or mechanical arrest. Criticality manifests itself in an anomalous spectrum of low-frequency normal modes and scaling behavior near the jamming transition. The critical point may explain the peculiar mechanical properties of dissimilar systems such as glasses and granular materials. Here we study the critical scenario via an experimental measurement of the normal modes frequencies of granular matter under stress from a pole decomposition analysis of the effective mass. We extract a complex-valued characteristic frequency which displays scaling |ω (σ)| ∼ σΩ' with vanishing stress σ for a variety of granular systems. The critical exponent is smaller than that predicted by mean-field theory opening new challenges to explain the exponent for frictional and dissipative granular matter. Our results shed light on the anomalous behavior of stress-dependent acoustics and attenuation in granular materials near the jamming transition.
零温度临界点已被用来控制颗粒物质在接近堵塞或机械停滞时的异常行为。临界性表现为低频正常模式的异常频谱以及堵塞转变附近的标度行为。该临界点可能解释诸如玻璃和颗粒材料等不同系统的特殊力学性质。在此，我们通过对颗粒物质在应力作用下正常模式频率的实验测量，从有效质量的极点分解分析来研究临界情形。对于各种颗粒系统，我们提取了一个复数值特征频率，其在应力σ趋于零时呈现出|ω (σ)| ∼ σΩ' 的标度关系。临界指数小于平均场理论预测的值，这为解释摩擦耗散颗粒物质的指数带来了新的挑战。我们的结果揭示了颗粒材料在堵塞转变附近与应力相关的声学和衰减的异常行为。
