Fractal Shape Research Articles

Quantitative evaluation of the characteristics of air voids and their relationship with the permeability and salt freeze–thaw resistance of hybrid steel-polypropylene fiber–reinforced concrete composites

Hybrid fiber affects the structure of air voids of hardened concrete and further affects the performance of concrete. A laboratory test quantitatively analyzes the characteristics of air voids and their relationship with the permeability and salt freeze-thaw (F-T) resistance of hybrid steel fiber (ST)–polypropylene fiber (PP) reinforced concrete. Quantitative parameters such as the fractal dimension, number, tortuosity, and shape factor of the air voids are used to characterize their structure. In addition, the relationship between the structural characteristics of air voids and the permeability and salt F-T resistance of concrete is analyzed using the rough set theory. The hybrid ST–PP fiber can reduce the total air-void content, spacing factor, average chord length, and total chord length of the air voids. However, the number and specific surface area of the air voids increased by 113.9–380.2% and 185.3–422.7%, respectively. In addition, the tortuosity of air voids with a diameter of 180–500 μm is more complex than that of other apertures. Moreover, hybrid ST–PP fibers can change the shape of air voids in concrete and make the shape of air voids in concrete simple and round. The compressive strength and splitting tensile strength of concrete after salt F-T cycles are enhanced by the hybrid ST–PP fiber. Nevertheless, this hybrid fiber has a negative effect on the permeability of the concrete. The total air–void content, number of air voids and tortuosity are the main factors affecting the permeability and F-T resistance of concrete.

Thermal efficiency and performance enhancement examination in a new PHE design

Due to its significant heat transfer area and its compactness, the plate heat exchangers PHEs are extensively used in several engineering applications compared to the tubular heat exchanger. For this reason, enhancing the PHE thermal efficiency seems a critical and essential purpose for many researchers and manufactures. This paper covers a numerical examination of a new proposed design of the PHE with a plate fitted with Y fractal shape obstacles with different steps. The intension of this work is to analyze and evaluate the impact of the Y fractal branches number, the distribution area and the Reynolds number Re. The standard k-ϵ turbulence model was chosen for this investigation. Aiming to ensure the numerical method accuracy and preciseness, an appropriate and suitable grid refinement study has been conducted. With the experimental method, the numerical results have been validated so that it is possible to confirm the method reliability. For a Reynolds number Re range 400–1400, significant parameters (the Nusselt number Nu, the friction factor Cf, the Thermo-hydraulic performance parameter THPP) are predicted and the temperature contours are presented using ANSYS19. Compared to the standard commercial chevron PHE, the new concept indicates an improvement and enhancement in the heat transfer.

Embroidered Βow-Tie Wearable Antenna for the 868 and 915 MHz ISM Bands

A textile, embroidered antenna, based on the fractal shape of the Sierpinski triangle, is designed in this paper for operation in the European free Industrial Scientific and Medical (ISM) 863–870 MHz band, as well as in the 902–928 MHz band designated for ISM applications in North and South America. Several prototypes have been fabricated by employing different stitch patterns and thread materials. The effect of the fabrication parameters on the performance of the proposed antenna is investigated through measurements and simulations, with the results being in good agreement. The antenna exhibits attractive characteristics such as wide bandwidth, relatively stable radiation patterns, as well as robustness in washing. Several tests reveal that convex and concave bent conditions do not affect the coverage of the aforementioned ISM bands, despite the shift of the resonant frequency in some cases. Moreover, the SAR values resulting from simulations are below the corresponding thresholds suggested by international guidelines.

Role of a fractal shape of the inclusions on acoustic attenuation in a nanocomposite

Phononic materials structured at the macro- or nano-scale are at the forefront of materials research for controlling transport of sound and heat, respectively. Besides the structure length scale, the exact geometry has been found to be of relevance as well. In this work, we provide an extensive finite element investigation of the effect of the shape of periodically dispersed inclusions in a 2D matrix on propagation and attenuation of an acoustic wave packet. We show that, by significantly complexifying the shape from circular to fractal-like (dendrite shape), phonon scattering at wavelengths comparable with the inner structure of the inclusion is enhanced, leading to a strong attenuation that can be fitted by a compressed exponential function, while in the circular case, the diffusive regime is observed.

Design of a compact UWB MIMO‐diversity antenna incorporating fractal inspired isolation structure with band notch characteristics

AbstractIn this communication, a new compact ultra‐wideband (UWB) multiple‐input multiple‐output (MIMO) antenna with band notch characteristics is presented for wireless application. It comprises of two unique monopole antenna elements sharing a similar ground plane. To reduce the coupling between antenna elements, a modified T‐shaped stub equipped with Minkowski fractal shape elements are introduced on the ground plane which in turn establish a good isolation between radiating elements. A band notch is achieved at 5.45 GHz by adding two additional rectangular stubs at 45° where symmetric slots have been etched. The efficiency and gain of the antenna drops significantly at the centre of the notch band which indicates good interference suppression. Results show that the designed antenna delivers widest impedance bandwidth (−10 dB) throughout the operating band of 3.1–20 GHz (of 146% impedance bandwidth) which covers UWB as well as Ku‐band. The antenna also produces ‐18 dB isolation for most of the operating band and ‐16 dB up to 6 GHz. The optimized antenna is fabricated and tested showing |S11| characteristics below −10 dB from 3.1 to 20 GHz band. The dimension of the proposed antenna is 18 × 26 × 1.6 mm3. Results show that the simulated characteristics are in good agreement with the measured counterpart. The designed MIMO antenna is an appropriate candidate for UWB and other wireless applications.

Fractal Geometry as a Source of Innovative Formations in Interior Design

Fractal geometry is the best to describe natural shapes, as it can result to creating a complex shapes but with simple laws. After using technology, it became easy to understand and use fractal shapes in many aspects of our lives. Fractal science is a mathematical branch but this branch of science nowadays acts as an inspirational tool because of its aesthetic appeal and its ingenuity in describing natural objects. Ecosystems has an internal order that seems chaotic and fractal geometry offered new ways for understanding ecosystems. Across different historical design styles and different cultures, each one of them was aiming to reach the grace in each aspect of the design, ecosystems has always been the source of inspiration to reach what they were aiming for. Interior and furniture designer is the main responsible of enhancing the life of the space or furniture user, most of our local interior and furniture designers are not aware of the importance of fractal geometry in design, and how fractal geometry can give different taste to the designs. The research paper aims through the study of fractal geometry and its characteristics, the study of ecosystems as a source of inspiration and its characteristics aims to find the connection between them to help interior designers to create designs that copes with this modern era. Finding the connection was done by an analytical study to compare the characteristics of each of the fractal shapes, nature and how it can be found in interior, furniture and architectural design.

Design and experimental verification of fractal based MIMO antenna for lower sub 6-GHz 5G applications

This article presents fractal shape based MIMO antenna with microstrip feeding for sub 6-GHz applications. The proposed fractal based structure is a flower-shaped construct with added rectangular strips patch and circular, rectangular slots are introduced into the ground plane to reduce the isolation between the patches. The main purpose in designing 2 × 1 MIMO system antenna is to enhance the scattering signals and optimize the performance. The proposed structure uses FR-4 material with a dimension of 25 mm × 38 mm. The 2 × 1 MIMO structure resonate at 3.5 GHz for the sub 6 GHz 5 G communications with directional radiation pattern. The performance characteristics of the antenna such as surface current distributions, radiation patterns and S-parameters are investigated. In addition the performance of diversity system of MIMO structure including the total active reflection coefficient (TARC), multiplexing efficiency, envelope correlation coefficient (ECC) and diversity gain (DG) are studied. For this proposed MIMO structure all antenna parameters are found that within an acceptable range.

WITHDRAWN: Modelling and design of fractal antenna of multiband applications

Abstract This paper introduces the design as well as modelling of a multiband planar antenna based on fractal shapes. Sierpinski carpet as well as Minkowski fractal geometries are applied to a square shaped patch antenna. The result from this combination is multiband, small size, high gain as well as low return loss antenna. The proposed antenna cover multi-frequency bands such as, 3.4, 4.03, 5.8, 6.48, 6.78, 7.32, 8.26, 9.21, 10.09 GHz. Antenna parameters as well as performance have been calculated as well as tested by using FEKO software, where it is full wave electromagnetic software based on advanced numerical methods.

Edge-Coupled Parasitic Split Ring Resonator based Metamaterial Inspired Low-Cost Diamond Shaped Fractal Antenna for Multiband Wireless Applications

ABSTRACT The metamaterial inspired low-cost diamond-shaped fractal antenna (DSFA) based on edge-coupled (EC) parasitic split ring resonator (SRR) for multiband wireless application is presented and investigated in this manuscript. Initially, three iterations of DSFA are designed and found that second iteration reveals the more number of frequency bands as compared to the other iterations. For proper impedance matching characteristics, partial ground plane has been introduced in the designing of antenna and low-cost FR4 glass epoxy substrate with thickness of 1.6 mm is used with an overall size of 32 × 36 mm2. Further, the EC parasitic SRR is loaded in the geometry of the proposed antenna and compared with the unloaded antenna and noted that the loaded antenna reports the better results in terms of bandwidth and reflection coefficient. The loaded antenna exhibits the maximum bandwidth of 5.68 GHz (1.67–7.34 GHz) and a maximum gain of 8.63 dB at 2.3 GHz and 9.90 dB at 19.9 GHz. The prototype of the proposed DSFA has been fabricated and tested for the authentication of measured results with the simulated results and found both are in agreement with each other. Proposed DSFA with EC parasitic SRR is best suitable for different wireless applications because of its multiband behaviour.

Absorption enhanced thin‐film solar cells using fractal nano‐structures

In this article, a new structure for development of thin film solar cells is proposed in which elements with fractal shapes are integrated inside the cell to enhance its performance in a wide range of wavelengths. Two different structures are studied. In the first structure, a metallic fractal nano-carpet is integrated inside the silicon layer in order to trap and absorb sunlight by exciting surface plasmon polaritons and local surface plasmons at different wavelengths. Numerical analysis shows that this technique increases the short circuit current provided by the cell by a factor of 2.40 for both TM and TE polarisations of the incident light. The second structure has an active layer shaped as a fractal structure, and absorbs sunlight through Mie and Fabry-Perot resonances occurring at different wavelengths. The short circuit current enhancement for this structure is 2.97 for both TM and TE polarisations of the incident light, representing a significant improvement when compared with the previous works.

Spatial structure and aggregation of carbon allotrope nanofillers in isotactic polypropylene composites studied by small-angle neutron scattering

We study the aggregation of carbon allotrope nanofillers in the matrix of isotactic polypropylene with direct small-angle neutron scattering measurements. With the ATSAS software, we analyzed the data and determined the fractal shape, dimension, and sizes of nanofiller aggregation in the bulk of isotactic polypropylene over the range of the scattering angles. We estimated the volume distributions and aggregation of different types of carbon nanofillers at different concentrations: nanographite, graphene nanoplatelets (GNP), fullerenes, single-walled carbon nanotubes (SWCNT), multi-walled carbon nanotubes (MWCNT) and binary fillers MWCNT/GNP. We reconstructed the shape of nanoscale particles and aggregates of a few nanofillers SWCNT, MWCNT and MWCNT/GNP and found that the systems are polydisperse; nanofillers associate in the volume of isotactic polypropylene as fractal dense aggregates with rugged surface, their sizes exceeding original dimensions of nanofillers several times.

In Situ Assembly of Gold Nanoparticles in the Presence of Poly-DADMAC Resulting in Hierarchical and Highly Fractal Nanostructures

The presence of the polycationic macromolecule poly(diallyldimethylammonium chloride) (poly-DADMAC) has a strong effect on the shape and size of colloidal gold nanoparticles formed by the reduction of tetrachloroauric acid with ascorbic acid in aqueous solution. It slows down nanoparticle growth and supports the formation of nonspherical, partially highly fractal and hierarchical nanoparticle shapes. Four structural levels have been recognized from the near-spherical gold nanoparticles in the lower nanometer range over compact aggregates in the midnanometer range and flower and star-like particles in the submicron range up to larger filamentous aggregates. High-contrast scanning electron microscope (SEM) images show that single gold nanoparticles and clusters of them are connected by bundles of macromolecules in large aggregates. The investigation showed that a large spectrum of different nanoparticle shapes and sizes can be accessed by tuning the poly-DADMAC concentrations and their ratio to other reactants. The nanoassemblies with a very high specific surface area might be of interest for SERS and heterogeneous catalysis.

A Pythagorean tree fractal shape stub-loaded resonator as a UWB bandpass filter with wide stopband

AbstractA compact ultrawideband (UWB) bandpass filter (BPF) is designed by harnessing the efficacy of a Pythagorean tree fractal shape stub-loaded resonator. The design inherently provides the passband transmission poles, which make it convenient to be used in wide passband filtering circuits. The number and the position of the resonating modes can be controlled by increasing the iterations of the Pythagorean tree, as analyzed using odd- and even-mode analysis. Design steps of the BPF are detailed. The designed UWB BPF takes up a small circuit area of (12.13 × 9.59) mm2. The proposed design is fabricated and measured to verify the simulated results. The stopband is extended up to 17.5 GHz with a maximum attenuation of 15 dB.

Ultra-wideband fractal antenna using rhombus shaped patch with stub loaded defected ground plane: Design and measurement

The Rhombus Shaped Fractal Antenna with stub loaded defected ground plane is presented for UWB wireless applications. Proposed antenna bears the overall compact size of 30 × 24 × 1.6 mm3. The proposed geometry of antenna generates the higher impedance bandwidth in comparison to the other structures such as antenna with partial ground plane and ground plane with defects. The modification in the ground plane has been investigated and analyzed to obtain the optimized results of the designed antenna. Finally, the stub is employed in the geometry of antenna with defected ground plane and the bandwidth of antenna has been enhanced as 17.53 GHz (167.19%) in the 1.72 to 19.25 GHz frequency range. The peak realized gain of antenna is calculated and found as 6.48 dB (maximum gain) at 2.4 GHz frequency band. Far – field radiation patterns of proposed antenna are measured and presented at points 2.4, 7.8, 13.4 and 18.5 GHz. The performance of designed antenna has been analyzed by using HFSS V13 simulator based on finite element method (FEM) and then the optimized final structure is fabricated for the experimental results. The wider bandwidth of proposed antenna made it a suitable candidate for different wireless standards in the desired frequency range.

Assessing the regional policies of Italian regions in managing the Cesarean delivery phenomenon: a fractal analysis.

Objectives.Assessing the 2017 administrative data on Cesareans delivery in Italy by using fractal statistic.Methods.2017 administrative data on Italian Cesarean deliveries are freely available as crude numbers and rates according to each Italian region, according to Italian health institute type and according to first or repeated Cesarean. As already reported, the Italian Cesarean delivery phenomenon is in relationship with hospital, regional, cultural perspectives in caring pregnancy and delivery. Fractal statistics can best assess the biocomplexity underlying the Italian Cesarean section phenomenon. Fractal shapes and self-organized criticality of the Cesarean section phenomenon for each Italian region were done. Fractal shapes were compared to find similarities by using global test of coincidence among regression lines.Results.In the regions where the health care institutes are more than a type, there are evanescent similar fractal shapes. Self-organized criticality assessment demonstrates that chaos is largely involved in Cesarean delivery phenomenon in all Italian regions and in Italy. The fractal images for each region are able to highlight the item causing the deviation from fractal shapes in each region.Conclusion.Fractal statistics could be used to compare regional or hospital policies in performing Cesareans, starting from Cesareans rates extracted from administrative data. (www.actabiomedica.it)

Assessing the ratio between new Covid-19 cases and new tests for Sars-Cov-2 in Italy by fractal investigation.

Aim:processing the heterogeneous data on the Italian Covid-19 epidemic by fractal investigation on the trend curve of the ratio between new Covid19 cases/new Sars-Cov-2 tests.Methods:New cases of Covid-19 disease and new tests were calculated from raw data freely available on the Italian governing website. The effectiveness of Italian government Decrees aiming to obtain lock-down was assessed by fractal investigation. Self-similarity parameters of presumed fractal shapes obtained 6 days after each Decree were estimated, when possible. Self-organized criticality was also assessed to check for chaos involvement in disturbing the fractal shapes. Shapes were then compared and were used to estimate the number of new tests for Sars-Cov-2 that Italy would be able to perform.Results:The full lock-down changed the biocomplexity of the Covid-19 epidemic in Italy. If the biocomplexity of Covid-19 did not change after the lock-down, Italy should have been able to perform at least 25490 tests daily (±8940) on average, while real data show that a larger number of tests were done (p<0.001) (thereby obtaining the lowering of contagions). If the same biocomplexity was observed before full lock down, Italy would be able to perform 7088 tests daily (±5163) on average, while real data show that a lower number of tests were done (p=0.029) (thereby observing the worsening of contagions).Conclusion:in case of heterogeneous data, fractal investigation would be prove useful for assessing and estimating trends. (www.actabiomedica.it)

Modified OFS-RDS bat algorithm for IFS encoding of bitmap fractal binary images

This work is an extension of a previous paper (presented at the Cyberworlds 2019 conference) introducing a new method for fractal compression of bitmap binary images. That work is now extended and enhanced through three new valuable features: (1) the bat algorithm is replaced by an improved version based on optimal forage strategy (OFS) and random disturbance strategy (RDS); (2) the inclusion of new similarity metrics; and (3) the consideration of a variable number of contractive maps, whose value can change dynamically over the population and over the iterations. The first feature improves the search capability of the method, the second one improves the reconstruction accuracy, and the third one computes the optimal number of contractive maps automatically. This new scheme is applied to a benchmark of two binary fractal images exhibiting a complex and irregular fractal shape. The graphical and numerical results show that the method performs very well, being able to reconstruct the input images with high accuracy. It also computes the optimal number of contractive maps in a fully automatic way. A comparative work with other alternative methods described in the literature is also carried out. It shows that the presented method outperforms the previous approaches significantly.

Fractal Dynamics in the RR Interval of Craniopharyngioma and Adrenal Tumor in Adolescence.

Heart rate variability (HRV) is the physiological phenomenon of variation in the time interval between heartbeats. It is measured by the variation in the beat-to-beat interval and/or RR variability (where R is a point corresponding to the peak of the QRS complex of the ECG wave and RR is the interval between successive Rs) and other components extracted from these. HRV is a field of research interest in pathophysiology (in general) and cancer prognosis (more specifically). Adolescents with adrenal tumor or craniopharyngioma were investigated, herein. Αutonomic nervous system recordings were performed with Task Force® Monitor (gold standard of the Task Force of the European Society of Cardiology and the North American Society of Electrophysiology). The RR interval (RRI) time series calculations were performed with the MatLab® computational environment and included the estimation of fractal dimension and Lyapunov exponent. Fractal dimensions were calculated by estimating N and R, where N represents the number of "squares" needed for a fractal shape to be completed and their respective "square size" R. By definition, if the first derivative of d ln N/d ln R remains constant for a space of R, this is the fractal dimension of the shape, in the present case of the time series trajectory. We found that RRI manifested different fractal dynamics, thus, a complex pattern of progression in these two morbid entities, suggesting the need for further investigation in ANS contribution to tumor pathophysiology.

Modified Koch curve broadband fractal antenna for spectrum sensing in cognitive radio

AbstractThis paper presents the design and development of broadband modified Koch curve microstrip patch antenna with multiband characteristics for spectrum sensing in cognitive radio applications. The proposed spectrum sensing antenna is designed specifically for its efficient operation in the spectrum (1.683–3.05, 4.246–9.714, and 11.25–18 GHz) specified for L, S, C, X, Ku with broadband characteristics and omnidirectional radiation pattern. The validity of the proposed shape is proved by having a comparison with other fractal shapes available in the literature.

Investigation of wakes generated by fractal plates in the compressible flow regime using large-eddy simulations

We investigate flows interacting with square and fractal shape multi-scale structures in the compressible regime for Mach numbers under subsonic and supersonic upstream conditions using large-eddy simulations. We also aim at identifying similarities and differences that these interactions have with the corresponding interactions in the canonical incompressible flow problem. To account for the geometrical complexity associated with the fractal structures, we apply an immersed boundary method to model the no-slip boundary condition at the solid surfaces, with adequate mesh resolution in the vicinity of the small fractal features. We validate the numerical results through extensive comparisons with experimental wind tunnel measurements at a low Mach number. Similar to the incompressible flow case results, we find a breakup of the flow structures by the fractal plate and an increase in turbulent mixing in the downstream direction. As the Mach number increases, we observe noticeable wake meandering and higher spread rate of the wake in the lateral direction perpendicular to the streamwise–spanwise plane. Although not significant, we quantify the difference between the square and the fractal plates using two-point velocity correlations across the Mach number range. The wakes generated by the fractal plate in the compressible regime showed lower turbulent kinetic energy and energy spectra levels compared to those of the square case. Moreover, results in terms of the near-field pressure spectra seem to indicate that the fractal plate has the potential to reduce the aerodynamic noise.