Fractal Shape Research Articles

Theoretical Study of fractal shape material of negative refractive index

Theoretical Study of fractal shape material of negative refractive index

A novel extended edge-based compact PIFA antenna for mobile devices

In this paper, an optimized ultra-compact planar inverted F antenna (PIFA) is proposed. Planar inverted F antenna (PIFA) is most commonly used antenna in modern day Mobile devices. While electronics industry is starving for compactness in their design, the concept used in the proposed design further reduces size of antenna. The overall dimensions of proposed antenna are 14.94×16mm for 3G/4G standards. In proposed design 21.61% size reduction is reported in comparison to conventional rectangular patch PIFA designs. The concept can be further utilized in designing antenna for different standards by optimizing size for specific frequency. A fractal shape Patch shorted at one end is used in the proposed design. The fractal patch is extended 6.59mm above the ground plane. The comparison is performed between measurement of fabricated and simulated S11 for proposed antenna. The novelty of design is inherited in extension of edges of patch towards ground which enable further reduction in size of antenna. Parametric optimization of antenna is performed for calculation of extended edge dimensions. Return loss for fabricated antenna is measured using vector network analyzer. The results of fabricated antenna show good agreement with simulated results and calculations.

Fractal Minkowski Antenna Loaded with Hilbert Curve as Complementary Split Ring Resonator

Fractal Minkowski patch antenna is proposed. Classical complementary split ring resonator (CSRR) is slotted on the patch. For comparison, fractal Hilbert shape split ring resonator also slotted on the patch. These slots make the patch behaves as a left-handed material in certain frequency band. Minkowski fractal antenna has three resonance frequencies. The complementary split ring resonator and Hilbert ring affects the upper two frequencies and make the antenna resonate at lower frequencies. Lowering the resonance frequencies cause a reduction in antenna size. More reduction of antenna size is obtained when fractal Hilbert is used as complementary split ring resonator. The simulated results have been done by using (HFSS) software, which is based on finite element modeling. The measurement of fabricated antenna shows good agreement with simulation results

Fractal Minkowski Antenna Loaded with Hilbert Curve as Complementary Split Ring Resonator

Fractal Minkowski patch antenna is proposed. Classical complementary split ring resonator (CSRR) is slotted on the patch. For comparison, fractal Hilbert shape split ring resonator also slotted on the patch. These slots make the patch behaves as a left-handed material in certain frequency band. Minkowski fractal antenna has three resonance frequencies. The complementary split ring resonator and Hilbert ring affects the upper two frequencies and make the antenna resonate at lower frequencies. Lowering the resonance frequencies cause a reduction in antenna size. More reduction of antenna size is obtained when fractal Hilbert is used as complementary split ring resonator. The simulated results have been done by using (HFSS) software, which is based on finite element modeling. The measurement of fabricated antenna shows good agreement with simulation results

Fractal Peano Antenna Covered by Two Layers of Modified Ring Resonator

Negative index of refraction has attracted a great attention in literatures. These materials are artificial structures named metamaterials has characteristics not found in nature. Microstrip antennas covered by metamaterial are very interesting areas of study. In this paper fractal Peano shape antenna is proposed and covered by two layers of modified ring resonator. The results show an enhancement in Reflection Coefficients, gain, and directivity.

Design of Rhombus Shaped Fractal Antenna for WLAN and X-Band Applications

Low profile features of microstrip antennas attract many researchers to investigate the performance of these antennas in various ways.Generation of multiband characteristic takes place when an antenna is introduced with some geometrical distortions i.e. fractal which is then used to increase data rates of communication system. Generally, an antenna tends to resonate at a single frequency but fractal antenna is a special type which has multiple resonances. Fabrication of miniaturized antennas have become possible due to fractal technology.This letter presents the design of Rhombus shaped fractal antenna using Sierpinski gasket structure.Two Sierpinski gasket structures has been combined, one in an inverted fashion which ultimately leads to a rhombus shape and the performance of second iteration antenna is studied.A 50ohms microstrip line is used to excite the patch.Analysis and Simulation of the proposed antenna has been done with the help of HFSS 13.0,an electromagnetic simulation software. The proposed antenna has been designed to resonate for LTE (long term evolution), WLAN and X-band Applications.

A Study of Palm Oil-Methanol Mixing in a Stirred Tank Equipped with a Fractal Baffles

Palm oil and methanol do not form a single phase mixture in transesterification process in stirred tank due to a poor surface contact between them; hence give a relatively slow mixing process of the mixing. Introduction of new baffles in the stirred tank with a fractal pattern due to the fractal shape can give a high turbulent level when a fluid flow through the fractal pattern is the new idea in optimizing the using of the fractal pattern in engineering especially in mixing industries. Hence, in the present study, a new concept of baffles with a fractal design was proposed to enhance a palm oil-methanol mixing in stirred tank. In order to achieve the objective, the simulation of palm oil-methanol mixing was carried out by using ANSYS Fluent software. The simulation was carrying out primarily in the stirred tank equipped with the fractal baffles and the levels of mixing were observed at 60, 120, 180 and 240 seconds after the beginning of introduction of methanol in the stirred tank. An effectiveness of the fractal baffles will be evaluated by determining the Coefficient of Variation (COV). The simulation results also were compared in term of homogeneity level of palm oil-methanol mixing to the normal baffles in order to determine the significant effect of the fractal baffles. Based on the simulation results, the value of COV for the mixing process in the stirred tank equipped with fractal baffles at the selected time interval are 0.066, 0.0436, 0.0326 and 0.0226 respectively. Since the values of COV between 0.01 and 0.05 are a reasonable target for many industry applications, the results for new approach of stirred tank with fractal baffles represent completely homogeneous mixing for the palm oil-methanol simulated in this study. Definitely this new approach of fractal baffles gave better results because of lower number of COV compared to the stirred tank with normal baffles.

Facile synthesis of hematite nanoplates and their self-assembly generated by domain growth of NaCl

Hematite nanoplates with exposed (001) facets were fabricated through a solvothermal process using FeCl3 and CH3COONa in an ethanol solution because of CH3COO− groups ascribed on the (001) facets of Fe2O3. Hexagonal-like nanoplates, octahedron, and nanoplates were created through adjusting the amount of CH3COONa. Solvents were crucial for the preparation of the nanoplates because irregular Fe2O3 particles rather than nanoplates were created once isopropanol or the mixture of water and ethanol instead of ethanol. The growth process of Fe2O3 with various morphologies was discussed. Additionally, we observed the self-assembly of the nanoplates into one- or three-dimensional dendritic morphology through a droplet dewetting technique by using NaCl molecules as scaffolds. This phenomenon is ascribed to the domain growth of NaCl to form fractal shapes and a hydrodynamic mechanism through outward capillary flow. The morphologies of the assemblies are related to the evaporation speed of solvent during droplet dewetting.

Analysis of tristable energy harvesting system having fractional order viscoelastic material.

A particular attention is devoted to analyze the dynamics of a strongly nonlinear energy harvester having fractional order viscoelastic flexible material. The strong nonlinearity is obtained from the magnetic interaction between the end free of the flexible material and three equally spaced magnets. Periodic responses are computed using the KrylovBogoliubov averaging method, and the effects of fractional order damping on the output electric energy are analyzed. It is obtained that the harvested energy is enhanced for small order of the fractional derivative. Considering the order and strength of the fractional viscoelastic property as control parameter, the complexity of the system response is investigated through the Melnikov criteria for horseshoes chaos, which allows us to derive the mathematical expression of the boundary between intra-well motion and bifurcations appearance domain. We observe that the order and strength of the fractional viscoelastic property can be effectively used to control chaos in the system. The results are confirmed by the smooth and fractal shape of the basin of attraction as the order of derivative decreases. The bifurcation diagrams and the corresponding Lyapunov exponents are plotted to get insight into the nonlinear response of the system.

DUAL-BAND SUBSTRATE INTEGRATED WAVEGUIDE RESONATOR BASED ON SIERPINSKI CARPET

In this paper, a dual-band Substrate Integrated Waveguide (SIW) resonator with Sierpinski fractal geometry is proposed. The space-filling property of the employed fractal shape allows to reduce the resonator size. The bandwidth, the minimum insertion loss, the maximum return loss and the stop band rejection are considered for evaluating the effect of the fractal geometry on the resonator characteristics. An accurate electromagnetic investigation is made using a full wave finite element method solver (Ansoft HFSS). Simulated and measured results are in good agreement. The second iteration fractal resonator exhibits two simulated bands centered at the frequencies f1 =1 1.57 GHz and f2 =2 5.7 GHz, while the measured frequencies are f1 =1 1.33 GHz, f2 =2 3.67 GHz. The measured bandwidths are BW = 1.15 GHz and BW = 2 GHz and the minimum insertion losses are close to −1.36 dB and −1.97 dB, respectively. The prototypes of the square resonator without, with first and with second iteration fractal geometry are fabricated via standard printed circuit board process (PCB). A Rogers Duroid 5880 substrate with thickness t =0 .381 mm is employed.

English

The main concept of Cross Field Antenna is getting phase shift between electric fields of the two cylinders of the antenna equals to 90 degrees. This is done by connecting a coil to the antenna circuit. The objective of doing this is to get rid of near field region and make far field region starting from antenna surface. Fractal shape antennas have many characteristics that not find in classical antennas. Among them is, multiband and wide band behaviour, antenna size is not depend on the operating frequency and easy matching of the antenna circuit. Here, combination of cross field antenna and fractal antenna is done; to get fractal shape cross field antenna. The proposed fractal shape is Sierpinski Carpet. Fractal shape cross field antenna has attracted wide band behaviour and self-tuning.

Design of planar inverted‐F antenna over uniplanar EBG structure for laptop mimo applications

ABSTRACTThree uniplanar shapes of electromagnetic band gap (EBG) structure as T‐shape, fractal shape, and interdigital capacitors are investigated for antenna applications. The proposed EBG shapes are etched on the ground plane of the planar inverted‐F antenna (PIFA) to improve the impedance bandwidth, reduce the antenna size, increase the gain, and improve radiation pattern. Next, two trapezoidal shaped slots are etched on the radiating plate of PIFA antenna to excite two resonant frequencies. The proposed antenna is designed to cover two narrow bands at GSM 1.8 GHz, upper WLAN 5.2 GHz and a wideband from 2.4 to 4 GHz. Effect of the laptop is investigated on the performance of the proposed antenna. Finally, the effect of these new EBG shapes on mutual coupling reduction between two pair of antennas is studied for multiple input multiple output application in laptop device. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:277–285, 2015

3D Printing of Fractal Deterministic Shapes into Polymer Matrix with Respect to Final Composite Mechanical Properties

This paper deals with mechanical properties research of innovative polymer multiphase composite materials consisting of matrix and isotropic or anisotropic oriented deterministic fractal shapes made by 3D printing. Standard polymer composite materials consisting for example of polypropylene matrix and glass fibres have mechanical properties which depend mainly on matrix-fibre interface strength, fibre length, fibre strength and fibres orientation. [1] In case of under critical fibre length is fibres orientation stochastic in for example injection moulded composites. So is possible to say that mechanical properties of these (standard) composites with short fibres are isotropic and thus all direction limited. However by creating of reinforcing internal structure consisting of deterministic fractal connected shapes is possible to gain unlimited mechanical properties directing. These fractal shapes – placed in multiphase system matrix – are significantly influencing whole material system mechanical properties mainly in case of stress on the limit of strength, proportional elongation on the limit of strength or tensile/ flexural modulus. Fractal shapes are also possible to properly locate, orient or shape modify according to potential material using with goal to gain maximal efficiency of fractal shapes occurrence. Producing of this multiphase system is realized by the help of two component 3D printing technology. So is possible to create any fractal shapes placed in polymer matrix which are by another technology unmanufacturable. Mechanical properties analyse is performed with respect to fractal shape type, fractal dimension, fractal shape orientation and shear and tensile strength of matrix.

Fractal-Based Generative Design of Structural Trusses Using Iterated Function System

The purpose of this study is to apply the notion of fractal geometry in designing structural roof trusses. Fractal geometry, commonly characterized by the features of recursive self-similarity, is considered as a rule-based geometric system that can be generated by using the process of the Iterated Function System (IFS). Lattice configurations of conventional trusses generally show some extend of ‘self-similarity’ features that loosely and sometimes closely resemble with the properties of fractal shapes. The typical configurations of these regular trusses are strategically designed to provide adequate strength and stability to the structures for carrying enough vertical and wind loads. This paper, using the Iterated Function System based on Barnsely's contraction mapping as a generative design method, proposes a new family of truss designs that follow the concept of fractal geometry. The Hausdorff dimensions and the Box Counting dimensions are evaluated to measure the fractality and detailness of the lattices of proposed fractal-based trusses. It also briefly investigates their mechanical properties for analyzing their practical feasibility in construction.

Review article: methods of fractal geometry used in the study of complex geomorphic networks

Fractal geometry methods allow one to quantitatively describe self-similar or self-affined landscape shapes and facilitate the complex/holistic study of natural objects in various scales. They also allow one to compare the values of analyses from different scales (Mandelbrot 1967; Burrough 1981). With respect to the hierarchical scale (Bendix 1994) and fractal self-similarity (Mandelbrot 1982; Stuwe 2007) of the fractal landscape shapes, suitable morphometric characteristics have to be used, and a suitable scale has to be selected, in order to evaluate them in a representative and objective manner. This review article defines and compares: 1) the basic terms in fractal geometry, i.e. fractal dimension, self-similar, self-affined and random fractals, hierarchical scale, fractal self-similarity and the physical limits of a system; 2) selected methods of determining the fractal dimension of complex geomorphic networks. From the fractal landscape shapes forming complex networks, emphasis is placed on drainage patterns and valley networks.

Slot Cut Ultra Wide Band Antennas

The ultra wide band antennas are required in applications where larger bandwidth for the transmitting signal is needed. They cover wide bandwidth in the range from 500 MHz to the frequencies above 8000 MHz. In this paper, a review of various techniques to realize ultra wide band microstrip antennas (MSA) is presented. They are realized by using different techniques like basic planar monopole antenna and the variations of the same by using different shapes of radiating monopole antenna, like, bi-conical, Bowtie, etc. They are also realized by using modifying the feeding strip shape or by cutting the slot inside the patch. The ultra wide band (UWB) response has also been realized by using fractal shapes in the radiating monopole antenna. Towards the end of paper, the scope of future work is proposed, wherein the exact formulation of resonant length is needed for planar monopole antenna at its fundamental and higher order modes as well as the explanation for the ultra wide band response in terms of operating modes in slot cut and fractal geometries.

The traffic linked urban ambient air superfine and ultrafine PM1 mass concentration, contents of pro–oxidant chemicals, and their seasonal drifts in Lucknow, India

The anthropogenic PM2.5 in ambient air is implicated in the increased health risks and morbidities of urban subjects. However in the literature, there is a limited information on mass concentrations and size segregated chemical profile of ultrafine and superfine PM1 fractions of traffic linked urban ambient air. The size, and the adsorbed chemicals, and response to seasonal change in this submicron range of particles have seldom been studied so far. We have looked into these aspects in urban ambient air of Lucknow Uttar Pradesh India. A 10–stage MOUDI cascade impactor sampled the superfine (PM0.56, PM0.32, PM0.18) and ultrafine particles (PM0.1, PM0.056) distributed in traffic linked ambient air. We studied their morphology, mass concentrations, the adsorbed metal contents and organic chemical moieties using TEM, gravimetric analyses, AAS, and FTIR spectroscopy. A change in their contents and profile with season was also examined. Results revealed spherical and fractal shapes of PM0.1, 50nm–2μm size range of PM0.56 fractions, and 10–100nm size range of constituent spherules. Gravimetric analyses disclosed mass concentrations and multifold increases in their levels in winter. Cr, Cd, Ni, Pb and transition element Cu, Fe were found to be present in the studied particles. The presence of aliphatic and aromatic hydrocarbons with hydroxyl, carbonyl, and ketone groups were also found and displayed changes in their levels with season. Presence of organonitrate compounds indicated the role of submicron and nanosize particulates in secondary aerosol formation also. Results are important for epidemiological studies and public policy on superfine and ultrafine particulate matter in urban ambient air for identification of toxicity risk or health hazard, air quality monitoring and regulation.

Pull-out capacity of tree root inspired anchors in shallow granular soils

The pull-out capacity of anchors inspired by tree roots was evaluated using model tests to investigate the effect of anchor geometry on pull-out capacity. Experimental pull-out tests were performed on anchors with fractal geometries buried at shallow depths in a model granular medium. The results show that an existing pull-out model for plain shape anchors can be extended to fractal shape anchors by introducing an additional shape factor. The values of this shape factor reveal that fractal anchors can achieve the same pull-out capacity as plain shape anchors but the amount of material needed for their construction is much less. As a consequence, the use of fractal shape anchors may be a cost-effective solution in a number of geotechnical applications.

Dendritic, transferable, strictly monolayer MoS2 flakes synthesized on SrTiO3 single crystals for efficient electrocatalytic applications.

Controllable synthesis of macroscopically uniform, high-quality monolayer MoS2 is crucial for harnessing its great potential in optoelectronics, electrocatalysis, and energy storage. To date, triangular MoS2 single crystals or their polycrystalline aggregates have been synthesized on insulating substrates of SiO2/Si, mica, sapphire, etc., via portable chemical vapor deposition methods. Herein, we report a controllable synthesis of dendritic, strictly monolayer MoS2 flakes possessing tunable degrees of fractal shape on a specific insulator, SrTiO3. Interestingly, the dendritic monolayer MoS2, characterized by abundant edges, can be transferred intact onto Au foil electrodes and serve as ideal electrocatalysts for hydrogen evolution reaction, reflected by a rather low Tafel slope of ∼73 mV/decade among CVD-grown two-dimensional MoS2 flakes. In addition, we reveal that centimeter-scale uniform, strictly monolayer MoS2 films consisting of relatively compact domains can also be obtained, offering insights into promising applications such as flexible energy conversion/harvesting and optoelectronics.

Multifractal breakage patterns of thick maltodextrin agglomerates

Breakage of food materials affects operations in industry such as storage, transport and quality control, and has an influence on sensorial attributes. However, the geometry of the breakage pattern is a complex and rarely studied subject. Maltodextrin has been used as an ingredient in food related systems. The aim of this work is to characterise the geometry of the breakage patterns in thick maltodextrin agglomerates (MDAs), by digital image analysis (DIA) and multifractal spectra. Results showed that morphology of the breakage pattern was independent of the powder particle size, agglomerate thickness and compaction force. On the other hand, significant differences in pattern's lacunarity were found between the different loads applied whereas different distributions of the irregularity of the breaking pattern measured from the centre to the border of the MDA were obtained. Multifractal spectra reported different generalised fractal dimensions and shapes. Therefore, the breakage profile has a heterogeneous shape with microstructural differences along the breakage line. To the best of our knowledge, this is the first time that multifractal analysis has been used to characterise the breakage pattern geometry in thick MDAs. Size distributions of residual particles (RP) generated during the fracturing process were correlated with the breakage pattern of the material. This study contributes to the quantitative analysis and understanding of the complex structure of the breakage pattern and provides valuable information for further research on brittle food products.