耗散流体中的慢程和长程动力学非均匀性
Slow and Long-ranged Dynamical Heterogeneities in Dissipative Fluids
摘要：
一个二维的双分散颗粒流体表现出显着的长程动力学不均匀性的动态逮捕接近。在这里，我们专注于最直接的方法来研究这些异质性：我们确定集群的慢粒子，并确定其大小，$N_c$，和他们的回转半径，$R_G$。我们表明，$N_c\propto R_G^{d_f}$，提供直接的证据表明，最不动的颗粒排列在分形对象的分形维数，$d_f$，这是观察到的填充分数$ϕ$增加。簇大小分布服从缩放，接近结构停滞极限的代数衰减，即，$ϕ\toϕ_c$。另外，通过四点结构因子$S_4(q,t)$和动力学磁化率$χ_4(t)$分析动力学不均匀性。$S_4(q,t)$服从缩放在整个范围内的包装分数，$0.6\leqϕ\leq 0.805$，并成为越来越长的范围为$ϕ\toϕ_c$。$χ_4(t)$的有限尺寸缩放为先前分析的$χ_4(t)\propto (ϕ-ϕ_c)^{-γ_χ}$和相关长度$ξ\propto (ϕ-ϕ_c)^{-γ_ξ}$的发散提供了一致性检查。我们检查我们的结果的鲁棒性方面，我们的定义的流动性。的分歧和缩放$ϕ\toϕ_c$建议的非平衡玻璃化转变，似乎定性的恢复系数无关。
英文摘要：
A two-dimensional bidisperse granular fluid is shown to exhibit pronounced long-ranged dynamical heterogeneities as dynamical arrest is approached. Here we focus on the most direct approach to study these heterogeneities: we identify clusters of slow particles and determine their size, $N_c$, and their radius of gyration, $R_G$. We show that $N_c\propto R_G^{d_f}$, providing direct evidence that the most immobile particles arrange in fractal objects with a fractal dimension, $d_f$, that is observed to increase with packing fraction $ϕ$. The cluster size distribution obeys scaling, approaching an algebraic decay in the limit of structural arrest, i.e., $ϕ\toϕ_c$. Alternatively, dynamical heterogeneities are analyzed via the four-point structure factor $S_4(q,t)$ and the dynamical susceptibility $χ_4(t)$. $S_4(q,t)$ is shown to obey scaling in the full range of packing fractions, $0.6\leqϕ\leq 0.805$, and to become increasingly long-ranged as $ϕ\toϕ_c$. Finite size scaling of $χ_4(t)$ provides a consistency check for the previously analyzed divergences of $χ_4(t)\propto (ϕ-ϕ_c)^{-γ_χ}$ and the correlation length $ξ\propto (ϕ-ϕ_c)^{-γ_ξ}$. We check the robustness of our results with respect to our definition of mobility. The divergences and the scaling for $ϕ\toϕ_c$ suggest a non-equilibrium glass transition which seems qualitatively independent of the coefficient of restitution.
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