A Review of Fractals Properties: Mathematical Approach

Nurujjaman, Md.; Hossain, Ahammad; Ahmed, Payer

doi:10.11648/j.sjams.20170503.11

Cited by 11 publications

(10 citation statements)

References 6 publications

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“…The Sierpinski carpet fractals and box fractals are examples of the successive removal method of making fractals. [29] Fractal-like hierarchical honeycombs [30] gave insights into how incorporating hierarchy in the material structure can create low-density structural material with desired properties. Fractals also exist in 3D space like Menger sponge, which has an infinite surface but contains zero volume.…”

Section: Introductionmentioning

confidence: 99%

Mechanical and Acoustic Behavior of 3D‐Printed Hierarchical Mathematical Fractal Menger Sponge

et al. 2021

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Structural materials that feature hierarchical architectures (e.g., fractals) display remarkable mechanical properties. Menger sponge is one of the fractal geometries defined in Mathematics and made up of a unit cube with three orthogonal cavities. The precise fractal dimensions are fabricated using 3D printing. Experiments and simulations are conducted on the structure under uniaxial compression. The effect of increasing the levels of orthogonal cavities of the Menger sponge structure as well as the changing shape of the cavity are studied. The results show an interesting correlation between mechanical properties and the effective density of the structure. Multiple levels of hierarchy are analyzed in terms of different cavity shapes. These comparisons suggest that hierarchical structures are used to obtain better performance with a lower effective density of the resulting structures. Damage initiation for the different cavity shapes shows how each of the cavity shapes behaves under compressive loading. Herein, it is discerned how hierarchical architecture is used to access the unique properties of structures, providing insight into the role of design in regulating the mechanical properties of such mechanical structures. The result of acoustic investigation shows that it is a better absorber as compared with commercial sponge in the low‐frequency regime.

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Section: Introductionmentioning

confidence: 99%

Mechanical and Acoustic Behavior of 3D‐Printed Hierarchical Mathematical Fractal Menger Sponge

et al. 2021

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“…The fractal concept gained life through the necessity of understanding complex natural architectures like the tree's crowns, inflorescences, snowflakes, waves, seashores, etc. [21,25,28]. Moreover, the fractal interpretation can be transposed further from natural elements to components of the human body: the brain and the neural network, the circulatory system, DNA structure, etc.…”

Section: Introductionmentioning

confidence: 99%

“…a point-D = 0, a line-D = 1, a plane-D = 2, a cube-D = 3, etc.). In other words, the fractal dimension is a complexity indicator of an object's auto-similarity [23,25]. Fractal interpretations gained popularity in the cartographic field, offering the possibility to approximate dimensions, depending on the zoom level and determination scale [19,22].…”

Section: Introductionmentioning

confidence: 99%

Perspectives to Describe Surface Properties of Raw Pharmaceutical Materials. A Fractal Approach on the Wetting of Powders

Prisada¹

2020

FARMACIA

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Surface science is a currently expanding field which attracts attention through numerous possible correlations between different superficial phenomena. Modern approaches regarding superficial properties include extreme wetting interpretations through adapted regimes. Moreover, innovative applications arise from special surface properties like superhydrophilicity/ superhydrophobicity, through biomimicry, improving classic materials or generating new better artificial ones, of important interest in many domains. Liquid marbles, known as superhydrophobic-like structures also gained researcher's attention due to their special superficial properties. Experimental data in this direction are scarce, especially regarding active ingredients in the pharmaceutical domain and taking into account different morphologies and formulation versatility of liquid marbles. This paper focuses on anti-inflammatory powders and their superficial properties as raw pharmaceutical materials, but also as liquid marbles' components (external phases). Interpretations concern powders wettability degree expressed through contact angles and apparent contact angles of corresponding liquid marbles. These wetting parameters are correlated through a mathematical model, which also allows evaluation of fractal quantitative indexes: rugosity and fractal dimension. Applying a fractal wetting model to anti-inflammatory powders represents a step forward towards proposing contact angles and other wetting parameters as key indicators in pre-formulation processes. Dissolution and absorption of active ingredients are only two examples of processes in which a drug's pharmacokinetic profile is directly correlated to wetting parameters of its components. The importance of predicting a pharmaceutical products' behaviour is crucial in designing new products, making superficial properties investigations mandatory steps of the process. Rezumat Domeniul "Ştiința suprafețelor" este unul aflat în curs de expansiune şi atrage atenția prin numeroase posibile corelații înt re fenomenele superficiale. Abordări moderne ale proprietăților superficiale includ interpretări ale fenomenelor extreme de umectare, realizate prin intermediul regimurilor de udare adaptate. Mai mult, aplicații inovative derivă din proprietăți superficiale speciale precum superhidrofobia/superhidrofilia. Prin intermediul biomimetismului, materiale clasice sunt îmbunătățite. Totodată, sunt fabricate materiale noi cu caracteristici superioare, de interes în numeroase domenii. "Liquid marbles", exponenți ai comportamentului de tip superhidrofob, au atras atenția cercetătorilor prin proprietățile superficiale deosebite. Având în vedere versatilitatea formulării şi morfologiei "liquid marbles", datele experimentale în direcția caracterizării lor sunt insuficiente. Aceasta se aplică mai ales în legătură cu domeniul farmaceutic, referitor la substanţele active. Prezenta lucrare se concentrează asupra pulberilor antiinflamatorii și proprietăților superficiale, atât ca materii prime farmaceutice, cât și ca faze ...

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“…They are said to be statistically self-similar natural fractals. The complex geometry of these objects made them highly complex and rich in geometric properties [2,3,6]. Irrespective of the complexity fractals posses self-similarity [6,7].…”

Section: Introductionmentioning

confidence: 99%

“…The complex geometry of these objects made them highly complex and rich in geometric properties [2,3,6]. Irrespective of the complexity fractals posses self-similarity [6,7]. This nature of fractals is greatly exploited in the nano to the macro world [8,9].…”

Section: Introductionmentioning

confidence: 99%

Untitled

2019

OABB

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We live in a world of high complexity in all means. The present article is an attempt to elucidate the potential of fractal analysis in understanding and quantifying the complexity. Of several methods of fractal analysis, we have used only the box counting and power spectral methods for explaining the potential of the technique. The application of fractal analysis in bio-nanosystems, thin films, are forensic science are exemplified though our own work.

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A Review of Fractals Properties: Mathematical Approach

Cited by 11 publications

References 6 publications

Mechanical and Acoustic Behavior of 3D‐Printed Hierarchical Mathematical Fractal Menger Sponge

Mechanical and Acoustic Behavior of 3D‐Printed Hierarchical Mathematical Fractal Menger Sponge

Perspectives to Describe Surface Properties of Raw Pharmaceutical Materials. A Fractal Approach on the Wetting of Powders

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