Anomalous diffusion in inclined comb-branch structure

Wang, Zhaoyang; Zheng, Liancun

doi:10.1016/j.physa.2019.123889

Cited by 2 publications

(2 citation statements)

References 16 publications

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“…[43] Moreover, several complex extensions of comb-like structure, through introducing a modification on the geometry of the backbone or finger shape of the structure, is introduced to describe geometrically induced complex diffusion in nature, for example, comb with a finite finger length, [40,44,45] cylindrical comb, [46,47] random comb models, [48,49] comb with ramified teeth, [40,41] fractal mesh and grid structures, [50][51][52] and more complex structure. [53][54][55][56][57] Diffusion along the backbone in both two and three-dimensional comb-like structures with a finite finger is a transient sub-diffusion followed by normal diffusion at long times, and the same result is obtained in using a trap model of energetic nature. [58] Whereas, diffusion along the backbone in a three-dimensional comb-like structure with an infinite two-dimensional branch is ultra-slow diffusion/enhanced sub-diffusion if normal/sub-diffusion occurs inside branches.…”

Section: Introductionmentioning

confidence: 56%

Anomalous diffusion in branched elliptical structure

et al. 2023

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Diffusion in narrow curved channels with dead-ends as in extracellular space in the biological tissues, e.g. brain, tumors, muscles, etc. is a geometrically induced complex diffusion and is relevant to different kinds of biological, physical, and chemical systems. In this paper, we study the effects of geometry and confinement on the diffusion process in an elliptical comb-like structure and analyze its statistical properties. The ellipse domain whose boundary has the polar equation: ρ(θ)=$\frac{b}{{\sqrt {1 - {e^2}{{\cos }^2}\theta } }}$ with 0<e<1, θ∈[0,2π], and b is constant, can be obtained through stretched radius r such that Υ=r ρ(θ) with r∈[0,1]. We suppose that, for fixed radius r=R, an elliptical motion takes place and interspersed with a radial motion inward and outward of the ellipse. The probability distribution function (PDF) in the structure and the marginal PDF and mean square displacement (MSD) along the backbone are obtained numerically. Results show a transient sub-diffusion behavior dominates the process for a time followed by a saturating state. The sub-diffusion regime and saturation threshold are affected by the length of the elliptical channel lateral branch and its curvature.

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Section: Introductionmentioning

confidence: 56%

Anomalous diffusion in branched elliptical structure

et al. 2023

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“…Which mean, D x → D x (t) and D y → D y (t). This assumption is motivated by experimental and simulation results, which shows that anomalous diffusion is due to the structure of the comb rather than the nature of the diffusing particles [19,37]. The time dependent diffusivity in comb-models leads us to cumbersome analytical calculations.…”

Section: Introductionmentioning

confidence: 99%

Tempered fractional diffusion in comb-like structures with numerical investigation

Mokhtar Hefny,

Tawfik

2023

Phys. Scr.

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This paper presents two models for describing anomalous transport in comb-like structures. First, we analytically solve the tempered fractional diffusion model using the Laplace-Fourier technique. The probability distributions along the backbone (x-axis) and branches (y-axis) are represented by the M-Wright and Fox’s H functions. The probability distributions are illustrated according to the time-fractional order α and the tempered parameter λ. Additionally, we determine the mean square displacement to classify the degree of diffusivity in the comb structure based on the values of the time-fractional and tempered orders. Second, we introduce a power-law time-dependent diffusion coefficient as an extension of the comb-like models. In this section, we investigate the solution of the proposed comb-like via numerical simulation and explore the connection between the presence of a time-dependent diffusion coefficient and anomalous transport based on the particle density and mean square displacements.

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Anomalous diffusion in inclined comb-branch structure

Cited by 2 publications

References 16 publications

Anomalous diffusion in branched elliptical structure

Anomalous diffusion in branched elliptical structure

Tempered fractional diffusion in comb-like structures with numerical investigation

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