Analytical tortuosity–porosity correlations for Sierpinski carpet fractal geometries

Khabbazi, Ali Ebrahimi; Hinebaugh, James; Bazylak, Aimy

doi:10.1016/j.chaos.2015.07.019

Cited by 29 publications

(3 citation statements)

References 28 publications

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“…The peculiar properties of standard Sierpi ński carpets and cubes and Menger sponges remain an active topic of research (see Refs. [151][152][153][154][155][156][157][158][159][160] and references therein).…”

Section: The Standard Sierpiński Carpetsmentioning

confidence: 99%

A Brief Survey of Paradigmatic Fractals from a Topological Perspective

Ortíz

Martínez-Cruz

et al. 2023

Fractal Fract

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The key issues in fractal geometry concern scale invariance (self-similarity or self-affinity) and the notion of a fractal dimension D which exceeds the topological dimension d. In this regard, we point out that the constitutive inequality D>d can have either a geometric or topological origin, or both. The main topological features of fractals are their connectedness, connectivity, ramification, and loopiness. We argue that these features can be specified by six basic dimension numbers which are generally independent from each other. However, for many kinds of fractals, the number of independent dimensions may be reduced due to the peculiarities of specific kinds of fractals. Accordingly, we survey the paradigmatic fractals from a topological perspective. Some challenging points are outlined.

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Section: The Standard Sierpiński Carpetsmentioning

confidence: 99%

A Brief Survey of Paradigmatic Fractals from a Topological Perspective

Ortíz

Martínez-Cruz

et al. 2023

Fractal Fract

View full text Add to dashboard Cite

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“…The Mandelbrot's method of describing fractals based on self-similarity, although relatively frequent in the literature (e.g. Oleschko, 2000, Khabbazi et al, 2015, is not a strict definition of fractals. One of the existing methods of defining fractals in the mathematical sense is the use of iterated function system (IFS) (Barnsley et al, 2005, Martyn, 2011.…”

Section: Introductionmentioning

confidence: 99%

Set of Suffosion Holes Occurring After a Water Supply Failure as a Structure with Fractal Features

Iwanek¹

2022

J. Ecol. Eng.

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As a result of a buried water pipe unsealing, water often flows from the pipe to the soil surface, washing out the solid particles of soil and creating the so-called suffosion holes. It is a dangerous phenomenon, especially in urbanized areas, where it poses a threat to human safety and the stability of infrastructure. Uncontrolled outflows of water from water pipes belong to the main causes of suffosion in cities, occur in all water networks around the world and are difficult to predict. Therefore, it seems to be important to determine the size of the so-called the protection zone, which is the area around the potential leak where, in the event of a water pipe failure, it would be possible for water to flow in the soil. The analysis of the suffosion holes distribution around the place of leakage may be helpful in determining the size of the protection zone. Previous studies have shown that this distribution is random. Thus, the structure consisting of suffusion holes creates a certain geometric shape, which is difficult to describe using the classical concepts of Euclidean geometry. The study showed that this structure meets the conditions for probabilistic fractals, which means that elements of fractal geometry can be used to determine the size of the protection zone.

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“…Khabbazi et al 12 analytically investigated a 2D fractal porous medium where they treated it as Sierpinski carpets. The goal of the study was to develop an improved model of tortuosity based on circular Sierpinski carpets.…”

Section: Introductionmentioning

confidence: 99%

Computational analysis of gas permeability of slip flow through microannulus replete by based‐circular Sierpinski porous medium

2021

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There are wide applications for flow in a microporous medium. In this study, a computational analysis of airflow through a porous microannulus constructed by circular‐based Sierpinski has been performed in a slip flow regime, where several parameters played an important role in the flow characteristics. These parameters are the Knudsen number, the average friction factor, radius ratio, and porosity. The impacts of these parameters on permeability and the gas flow characteristics are examined and analyzed thoroughly. The ranges of the investigated parameters are as follows (0.001 ≤ Kn ≤ 0.1 and the porosity range is 0.75 ≤ ε ≤ 0.95). The results showed that porosity has a significant impact on the velocity distribution and Darcy number. The Knudsen number has also a direct effect on the velocity distribution, while it has a positive logarithmic proportionality with a dimensionless permeability but the radius ratio does have a neglected effect on the Darcy number. Moreover, the effect of the average friction factor has an inverse proportional relationship to the Darcy number.

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Analytical tortuosity–porosity correlations for Sierpinski carpet fractal geometries

Cited by 29 publications

References 28 publications

A Brief Survey of Paradigmatic Fractals from a Topological Perspective

A Brief Survey of Paradigmatic Fractals from a Topological Perspective

Set of Suffosion Holes Occurring After a Water Supply Failure as a Structure with Fractal Features

Computational analysis of gas permeability of slip flow through microannulus replete by based‐circular Sierpinski porous medium

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