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arXiv 0707.4178cond-mat.soft
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干扰附近的拓扑持续性和动力学不均匀性

Topological persistence and dynamical heterogeneities near jamming

A. R. Abate, D. J. Durian

摘要:

我们引入拓扑方法量化空间异质动力学,并使用这些工具来分析颗粒跟踪数据的准二维颗粒系统的空气流化珠的方法堵塞。特别是,我们定义了两个重叠的序参量,它量化了粒子配置之间的相关性,在不同的时间,基于Voronoi建设和持久性在所产生的细胞和最近的邻居。持久区和键序参量衰减的时间波动定义了两个可供选择的动态四点极化率,XA(t)和XB(t),非常适合于表征空间非均匀动态。这些类似于标准的四点动态磁化率X4(l,t),但是其中空间依赖性通过拓扑而不是通过任意选择截止函数唯一地固定。虽然这三个quantibilities产生的特征时间尺度是有些不同的,他们给域大小的动态的不均匀性,是在良好的协议和分歧的方法干扰。

英文摘要:

We introduce topological methods for quantifying spatially heterogeneous dynamics, and use these tools to analyze particle-tracking data for a quasi-two-dimensional granular system of air-fluidized beads on approach to jamming. In particular we define two overlap order parameters, which quantify the correlation between particle configurations at different times, based on a Voronoi construction and the persistence in the resulting cells and nearest neighbors. Temporal fluctuations in the decay of the persistent area and bond order parameters define two alternative dynamic four-point susceptibilities, XA(t) and XB(t), well-suited for characterizing spatially-heterogeneous dynamics. These are analogous to the standard four-point dynamic susceptibility X4(l,t), but where the space-dependence is fixed uniquely by topology rather than by discretionary choice of cutoff function. While these three susceptibilities yield characteristic time scales that are somewhat different, they give domain sizes for the dynamical heterogeneities that are in good agreement and that diverge on approach to jamming.

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