Chin. Phys. B, 2022, Vol. 31(11): 110202    DOI: 10.1088/1674-1056/ac7a16
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# Diffusion dynamics in branched spherical structure

Kheder Suleiman1,2, Xue-Lan Zhang(张雪岚)2, Sheng-Na Liu(刘圣娜)1, and Lian-Cun Zheng(郑连存)2,†
1 School of Energy and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China;
2 School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
Abstract  Diffusion on a spherical surface with trapping is a common phenomenon in cell biology and porous systems. In this paper, we study the diffusion dynamics in a branched spherical structure and explore the influence of the geometry of the structure on the diffusion process. The process is a spherical movement that occurs only for a fixed radius and is interspersed with a radial motion inward and outward the sphere. Two scenarios govern the transport process in the spherical cavity: free diffusion and diffusion under external velocity. The diffusion dynamics is described by using the concepts of probability density function (PDF) and mean square displacement (MSD) by Fokker-Planck equation in a spherical coordinate system. The effects of dead ends, sphere curvature, and velocity on PDF and MSD are analyzed numerically in detail. We find a transient non-Gaussian distribution and sub-diffusion regime governing the angular dynamics. The results show that the diffusion dynamics strengthens as the curvature of the spherical surface increases and an external force is exerted in the same direction of the motion.
Keywords:  anomalous diffusion      Fokker-Planck equation      branched spherical structure
Received:  21 April 2022      Revised:  07 June 2022      Accepted manuscript online:  18 June 2022
 PACS: 02.50.Fz (Stochastic analysis) 02.50.Ey (Stochastic processes) 05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion) 05.60.-k (Transport processes)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11772046 and 81870345).
Corresponding Authors:  Lian-Cun Zheng     E-mail:  liancunzheng@ustb.edu.cn