Laboratoire de Physique de la Matière Condensée (UMR 7643), CNRS-Ecole Polytechnique, 91128 Palaiseau, France.
Interdisciplinary Scientific Center Poncelet (ISCP), (UMI 2615 CNRS/IUM/IITP RAS/Steklov MI RAS/Skoltech/HSE), Bolshoy Vlasyevskiy Pereulok 11, 119002 Moscow, Russia.
Phys Rev E. 2018 Jan;97(1-1):012148. doi: 10.1103/PhysRevE.97.012148.
We introduce a heterogeneous continuous-time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environments, weighted graphs or networks. We derive the exact form of the propagator and investigate the effects of spatiotemporal heterogeneities onto the diffusive dynamics via the spectral properties of the generalized transition matrix. In particular, we show how the distribution of first-passage times changes due to local and global heterogeneities of the medium. The HCTRW formalism offers a unified mathematical language to address various diffusion-reaction problems, with numerous applications in material sciences, physics, chemistry, biology, and social sciences.
我们引入了一种非均匀连续时间随机游走（HCTRW）模型，作为研究和模拟非均匀结构中扩散过程的通用分析形式，例如多孔或无序介质、多尺度或拥挤环境、加权图或网络。我们推导出了传播子的精确形式，并通过广义转移矩阵的谱性质研究了时空非均匀性对扩散动力学的影响。特别是，我们展示了由于介质的局部和全局非均匀性，首次通过时间的分布如何发生变化。HCTRW 形式提供了一种统一的数学语言来解决各种扩散-反应问题，在材料科学、物理、化学、生物和社会科学中有许多应用。
