Fractional-time random walk subdiffusion and anomalous transport with finite mean residence times: faster, not slower.
Fractional-time random walk subdiffusion and anomalous transport with finite mean residence times: faster, not slower.
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DOI：
10.1103/physreve.86.021113
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发表时间：
2012-06
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影响因子：
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通讯作者：
I. Goychuk
中科院分区：
文献类型：
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作者：
I. Goychuk
传统上，连续时间随机漫步（CTRW）子扩散及其相关的分数阶Fokker-Planck方程（FFPE）是以平均周期发散的随机时钟为前提的。这项工作考虑了另一种CTRW和FFPE描述，其特征是在任何有限大小的空间域中具有有限的平均停留时间（MRTs）。瞬态亚扩散输运可以发生在非常大的时间尺度τ(c)上，它可以大大超过任何阱的平均停留时间τ(c) >>(τ)，甚至与之无关。渐近地，在宏观尺度上，t >> τ(c)为正常输运。然而，介观输运是反常的。与粘弹性亚扩散不同，不需要位置增量之间的远程反相关关系。此外，我们的研究表明，瞬态亚扩散和输运在宏观尺度上比从它们的正常渐近极限所期望的要快。这一观察结果对生物细胞中异常介观运输过程具有深远的意义，因为细胞质的宏观粘度是有限的。
Continuous time random walk (CTRW) subdiffusion along with the associated fractional Fokker-Planck equation (FFPE) is traditionally based on the premise of random clock with divergent mean period. This work considers an alternative CTRW and FFPE description which is featured by finite mean residence times (MRTs) in any spatial domain of finite size. Transient subdiffusive transport can occur on a very large time scale τ(c) which can greatly exceed mean residence time in any trap, τ(c) >>(τ), and even not being related to it. Asymptotically, on a macroscale transport becomes normal for t >> τ(c). However, mesoscopic transport is anomalous. Differently from viscoelastic subdiffusion no long-range anticorrelations among position increments are required. Moreover, our study makes it obvious that the transient subdiffusion and transport are faster than one expects from their normal asymptotic limit on a macroscale. This observation has profound implications for anomalous mesoscopic transport processes in biological cells because the macroscopic viscosity of cytoplasm is finite.