Anomalous diffusion in inclined comb-branch structure

Zhaoyang Wang and Liancun Zheng

Physica A: Statistical Mechanics and its Applications, 2020, vol. 549, issue C

Abstract: This paper presents a research for anomalous diffusion in inclined comb branch structure which has the potential in modeling many problems in medical science and nature. Mathematical model are formulated for two types of branch diffusion, i.e., bilateral branch and unilateral branch. Exact solutions are obtained by Laplace transform and separate variable techniques. The particle distribution on the backbone is represented by the Fox H-function. Results show that both types of diffusion are anomalous sub-diffusion and the inclination angle of branches has remarkable effect on particles transport behavior. For bilateral branch, the total number of particles on x axis is 〈P〉=sinθ∕[2(πt)1∕2], the mean square displacement (MSD) is 〈ξ2(t)〉=(πt)1∕2∕sinθ with invariant 〈ξ2P〉=1∕2, and with a symmetric particle distribution. For unilateral branch, the total number of particles on ξ axis is twice to that of bilateral branch diffusion. Moreover, some other characteristics of solutions are also graphically analyzed in detail.

Keywords: Anomalous diffusion; Inclined comb branch; Particles transport; MSD (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:549:y:2020:i:c:s0378437119321594

DOI: 10.1016/j.physa.2019.123889

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