Consider a network embedded in the 2D plane, where a particle diffuses along the edges of the network. It is clear that over short length scales a particle moves along a single edge and thus undergoes one-dimensional diffusion. However, on larger length scales it is no longer immediately clear how the transport will behave. One could intuit that as the network is embedded in two dimensions for "large enough" length scales the transport will also appear two-dimensional. Is this true for all networks? Can we quantify the length scales upon which this transition occurs? What is the transport behaviour on intermediate spatial scales? In this paper, we answer these question by presenting a numerical linear algebra approach that provides the exact moments of first passage times for a given network. Comparing these networked first-passage times to first-passage times for planar diffusion reveals several interesting properties of networked transport. In particular we can directly quantify the length scale upon which networked diffusion will appear planar if it does at all. Finally, we introduce an adaptation of the method of maximum entropy to use the moments of first-passage times to construct an analytical approximation to the first-passage times entire probability distribution.
Stochastic synthesis-degradation processes: first-passage properties and connections with resetting
Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普里茨克分子工程学院）；Instituto de Física, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理研究所）
Heterogeneous planar diffusion with axisymmetric power-law decaying diffusion coefficient under stochastic resetting
Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts（马其顿科学院与艺术院计算机科学与信息技术研究中心）；Institute of Physics, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University（圣西里尔和梅托迪乌斯大学自然科学与数学学院物理研究所）；Department of Physics, Korea University（高丽大学物理系）；Laboratoire de Physique et Chimie Théoriques (CNRS UMR 7019), Université de Lorraine Nancy（洛林大学南锡分校理论与物理化学实验室）；Centro de Física Teórica e Computacional, Universidade de Lisboa（里斯本大学理论与计算物理中心）；Departamento de Física, Universidade Estadual de Maringá（马里纳州立大学物理系）
First-Passage-Time Asymmetry for Biased Run-and-Tumble Processes
ICTP -- The Abdus Salam International Centre for Theoretical Physics（阿卜杜斯·萨拉姆国际理论物理中心）；International School for Advanced Studies (SISSA)（高级研究国际学院）；Imperial College London（伦敦帝国理工学院）；Ravenshaw University（拉文肖大学）；University College London（伦敦大学学院）
Dynamics of a flexible polymer in planar mixed flow
我们提出了精确的时空关联函数的劳斯聚合物链浸没在流体中的平面混合流，在稳态。使用这些修正器，确定与第一次通过翻滚事件相关的时间尺度分布函数通常是困难的;最近在Phys. Rev. Lett. 101，188301（2008），对于“简单剪切”流动的特殊情况。我们在这里表明，在后一份文件中使用的方法失败的一般混合流问题。在简单切变的情况下，我们也给出了与角翻滚时间分布的指数尾相关的指数$θ$的许多新的估计
Emergence of generic first-passage time distributions for large Markovian networks
University of Heidelberg（海德堡大学）；Institute for Theoretical Physics, University of Heidelberg（海德堡大学理论物理研究所）；BioQuant-Center for Quantitative Biology, University of Heidelberg（海德堡大学生物定量中心）
