2015/05/19 by Tadeusz Kosztołowicz, Kosztołowicz, Tadeusz
Chemistry · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Electrostatics and Colloid Interactions #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.1505.05199
openalex publication_date 2015/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study subdiffusion in a system with a thin membrane. At the\nbeginning, the random walk of a particle is considered in a system with a\ndiscrete time and space variable and then the probability describing the\nevolution of the particle's position (Green's function) is transformed into a\ncontinuous system. Two models are considered differing here from each other\nregarding the assumptions about how the particle is stopped or reflected by the\nmembrane when the particle attempts to pass through the membrane fails. We show\nthat for a system in which a membrane is partially permeable with respect to\nboth its sides the Green's functions obtained for both models within the it\ncontinuous time random walk formalism are equivalent to each other and\nexpressed by the functions presented in the paper: T. Koszto lowicz, Phys.\nRev. E \91, 022102 (2015), except the values defined at the membrane's\nsurfaces. We also show that for a system with a one--sidedly fully permeable\nmembrane, the Green's functions obtained within both models are not equivalent\nto each other.\n We also present the generalized method of images which provides the Green's\nfunctions for the membrane system, obtained in this paper. This method, which\nhas a simple physical interpretation, is of a general nature and, in our\nopinion, can be used to find the Green's functions for a system with a thin\nmembrane in which various models of subdiffusion can be applied. As an example,\nwe find the Green's functions for the particular case of a `slow--subdiffusion'\nprocess in a system with a thin membrane.\n