Fractal dimensions in fluid dynamics and their effects on the Rayleigh problem, the Burger's Vortex and the Kelvin–Helmholtz instability

El-Nabulsi, Rami Ahmad; Anukool, Waranont

doi:10.1007/s00707-021-03128-9

Cited by 29 publications

(6 citation statements)

References 162 publications

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“…Theoretical applications of fractal analysis that have been of interest to various studies include the physical phenomena of hierarchical structure, thermal conductivity in micro-channels, diffusion, dynamics of the atmosphere and ocean, petroleum and nuclear engineering, meteorology, material design, and thermo-elasticity [25][26][27][28][29][30][31][32][33] . Through a porous structure, Sheng et al 34 investigated a fractal model, and Miao et al 35 looked into another fractal model of shale.…”

Section: Introductionmentioning

confidence: 99%

An instrumental insight for a periodic solution of a fractal Mathieu–Duffing equation

El‐Dib

Elgazery

Alyousef

2023

Journal of Low Frequency Noise, Vibration and Active Control

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The primary goal of the present study is to investigate how to obtain a periodic solution for a fractal Mathieu–Duffing oscillator. To achieve this, the fractal oscillator in the fractal space has been transformed into a damping Mathieu–Duffing equation in the continuous space by employing a new modification of He’s definition of the fractal derivative. The required analytical periodic solution has been based on the rank upgrade technique (RUT) presented. The RUT successfully generates a periodic solution without sacrificing the damping coefficient by creating an alternate equation, aside from any challenges in managing the impact of the linear damping component. The homotopy perturbation method (HPM) has been used to find the required periodic solution for the alternate equation. A comparison of the numerical solutions of the original equation and the alternative equation showed good agreement. The stability behavior in the non-resonance case as well as in the sub-harmonic resonance case has also been discussed. Further, another method, “the non-perturbative approach”, that deals with the obtained equation has been introduced.

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Section: Introductionmentioning

confidence: 99%

An instrumental insight for a periodic solution of a fractal Mathieu–Duffing equation

El‐Dib

Elgazery

Alyousef

2023

Journal of Low Frequency Noise, Vibration and Active Control

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“…The fractal studying is an interesting idea that has distinctive applications in assorted areas, for instance, the physical phenomena of the hierarchical structure, diffusion, thermal conductivity within branched networks, meteorology, fluids flow resistance in micro-channels, ocean and atmosphere dynamics, nuclear and petroleum engineering, thermo elasticity, and materials design [30][31][32][33][34][35][36][37][38]. As a result of these important applications, the study of fractals was a fertile field for many scientists.…”

Section: Introductionmentioning

confidence: 99%

An innovative technique to solve a fractal damping Duffing-jerk oscillator

El‐Dib

Elgazery

Khattab

et al. 2023

Commun. Theor. Phys.

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The idea of the present article is to look into the nonlinear dynamics and vibration of a damping Duffing-jerk oscillator in fractal space exhibiting the non-perturbative approach. Using a new analytical technique, namely, the modification of He's a fractal derivative that converts the fractal derivative to the traditional derivative in continuous space, this study provides an effective and easy-to-apply procedure that is dependent on He's fractal derivative approach. The analytic approximate solution has significant match with the results of the numerical simulation as the fractal parameter is very closer to unity, which proves the reliability of the method. Stability behavior is discussed and illustrated graphically. These new powerful analytical tools are developed in an attempt to obtain effective analytical tools, valid for any fractal nonlinear problems.

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“…Mandelbrot was the first to suggest that fractals could be an ideal tool in applied mathematics to model diverse phenomena-from physical objects to stock market behavior. Since its inception, the fractal concept has spawned a new system of geometry that has had significant implications for fields as diverse as physical chemistry, physiology, and fluid mechanics [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

Placental Growth and Development Analyzed through 2D and 3D Fractals

Shah¹,

Salafia²,

Girardi³

et al. 2023

Fractal Analysis - Applications and Updates

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Fractal geometry has many applications in physiology and anatomy, providing novel insights into the structure and function of biological systems and organs, including the placenta. The placenta is a vital fetal organ that is the means by which essential nutrients and oxygen are extracted from maternal blood and transferred to the developing fetus. Anatomically, the placenta is a highly intricate structure exhibiting self-similarity at different scales. The complex relationship between placental function in nutrient transfer and fetal growth follows the allometric metabolic scaling law. Variability of shape of the placental chorionic plate, a 2D plane which contains the major chorionic arteries and veins, has been linked to measures of child health and neurodevelopmental outcomes. The microscopic arrangement of chorionic villi have also been demonstrated to have fractal properties that vary by gestational age and in different pathological conditions. Geographical Information Systems theory could be used to analyze the placental topography in the context of its surface vasculature and measures of spatial autocorrelation can model placental growth and development over gestation. An ideal model would mark timing, nature, and severity of gestational pathology modifying placental growth and, by extension, fetal development that leads to poor pregnancy outcomes.

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Fractal dimensions in fluid dynamics and their effects on the Rayleigh problem, the Burger's Vortex and the Kelvin–Helmholtz instability

Cited by 29 publications

References 162 publications

An instrumental insight for a periodic solution of a fractal Mathieu–Duffing equation

An instrumental insight for a periodic solution of a fractal Mathieu–Duffing equation

An innovative technique to solve a fractal damping Duffing-jerk oscillator

Placental Growth and Development Analyzed through 2D and 3D Fractals

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