arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1401.0960cond-mat.soft
收藏

玻璃态动力学的准一维模型

Quasi-One Dimensional Models for Glassy Dynamics

Prasanta Pal, Jerzy Blawzdziewicz, Corey S. O'Hern

摘要:

我们描述了一个准一维(Q1D)模型的玻璃态动力学的数值模拟和分析。在该模型中,硬棒通过一系列由$J$交叉点连接的狭窄通道进行布朗动力学。我们不允许杆在交叉点处转弯,因此系统中只有一条连续的路线。这个Q1D模型显示了笼化行为,集体粒子重排,以及结构弛豫时间的快速增长,这些也在过冷液体和玻璃中发现。该Q1D模型的均方位移$Σ(t)$显示了几种动力学状态:1)短时扩散$Σ(t) \sim t$,2)由锁定行为引起的均方位移的平台,3)以中间时间的异常缩放$Σ(t) \sim t^{0.5}$为特征的单行扩散,以及4)随着电路复杂性的增加,时间$t$交叉到长时扩散$Σ(t) \sim t$。我们开发了一个通用的程序,用于确定的结构弛豫时间$t_D$,超过该系统进行长时间的扩散,作为包装分数$ϕ$和系统拓扑结构的函数。此程序包括几个步骤:1)在系统的配置空间中定义一组不同的微观状态,2)构建微观状态和它们之间的转换的有向网络,3)识别网络中引起结构松弛的最小闭环,4)确定控制缓慢动态的“瓶颈”微观状态的频率和从它们转换出来所需的时间,以及5)使用微态频率和寿命来推导$t_D(ϕ)$。我们发现,$t_D$服从幂律标度,$t_D\sim (ϕ^* - ϕ)^{-α}$,其中$ϕ^*$(信号完全动力学逮捕)和$α>0$依赖于系统的拓扑结构。

英文摘要:

We describe numerical simulations and analyses of a quasi-one-dimensional (Q1D) model of glassy dynamics. In this model, hard rods undergo Brownian dynamics through a series of narrow channels connected by $J$ intersections. We do not allow the rods to turn at the intersections, and thus there is a single, continuous route through the system. This Q1D model displays caging behavior, collective particle rearrangements, and rapid growth of the structural relaxation time, which are also found in supercooled liquids and glasses. The mean-square displacement $Σ(t)$ for this Q1D model displays several dynamical regimes: 1) short-time diffusion $Σ(t) \sim t$, 2) a plateau in the mean-square displacement caused by caging behavior, 3) single-file diffusion characterized by anomalous scaling $Σ(t) \sim t^{0.5}$ at intermediate times, and 4) a crossover to long-time diffusion $Σ(t) \sim t$ for times $t$ that grow with the complexity of the circuit. We develop a general procedure for determining the structural relaxation time $t_D$, beyond which the system undergoes long-time diffusion, as a function of the packing fraction $ϕ$ and system topology. This procedure involves several steps: 1) define a set of distinct microstates in configuration space of the system, 2) construct a directed network of microstates and transitions between them, 3) identify minimal, closed loops in the network that give rise to structural relaxation, 4) determine the frequencies of `bottleneck' microstates that control the slow dynamics and time required to transition out of them, and 5) use the microstate frequencies and lifetimes to deduce $t_D(ϕ)$. We find that $t_D$ obeys power-law scaling, $t_D\sim (ϕ^* - ϕ)^{-α}$, where both $ϕ^*$ (signaling complete kinetic arrest) and $α>0$ depend on the system topology.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑