Diffusion dynamics in branched spherical structure

doi:10.1088/1674-1056/ac7a16

中国物理B ›› 2022, Vol. 31 ›› Issue (11): 110202-110202.doi: 10.1088/1674-1056/ac7a16

Diffusion dynamics in branched spherical structure

Kheder Suleiman^1,2, 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

收稿日期:2022-04-21 修回日期:2022-06-07 接受日期:2022-06-18 出版日期:2022-10-17 发布日期:2022-10-25
通讯作者: Lian-Cun Zheng E-mail:liancunzheng@ustb.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11772046 and 81870345).

Diffusion dynamics in branched spherical structure

Kheder Suleiman^1,2, 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

Received:2022-04-21 Revised:2022-06-07 Accepted:2022-06-18 Online:2022-10-17 Published:2022-10-25
Contact: Lian-Cun Zheng E-mail:liancunzheng@ustb.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11772046 and 81870345).

摘要/Abstract

摘要： 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.

关键词: anomalous diffusion, Fokker-Planck equation, branched spherical structure

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.

Key words: anomalous diffusion, Fokker-Planck equation, branched spherical structure

中图分类号: (Stochastic analysis)

02.50.Fz

02.50.Ey (Stochastic processes) 05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion) 05.60.-k (Transport processes)

Kheder Suleiman, Xue-Lan Zhang(张雪岚), Sheng-Na Liu(刘圣娜), and Lian-Cun Zheng(郑连存). Diffusion dynamics in branched spherical structure[J]. 中国物理B, 2022, 31(11): 110202-110202.

Kheder Suleiman, Xue-Lan Zhang(张雪岚), Sheng-Na Liu(刘圣娜), and Lian-Cun Zheng(郑连存). Diffusion dynamics in branched spherical structure[J]. Chin. Phys. B, 2022, 31(11): 110202-110202.

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Diffusion dynamics in branched spherical structure

Diffusion dynamics in branched spherical structure

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