Fractal Design Research Articles

Effects of Fractal Electrode Geometry in Charge Injection Capacity of TiN Microelectrodes.

Microelectrodes are basic tools for investigating small-scale brain dynamics. Noble metals such as gold (Au), platinum (Pt), and iridium oxide (IrOx) have been used as an electrode material because of their biocompatibility and good charge transfer capability. Their main charge transfer mechanism is the Faradaic process with redox reactions. Unfortunately, the decrease in electrode size accelerates the irreversible electrochemical dissolution during electrical stimulation due to increased current density. The dissolution can be prevented by alternating the electrode material to capacitive charge injection materials such as titanium nitride (TiN). However, electrical conductivity of TiN is relatively lower than the noble metals, which results in a lower charge injection capability. Therefore, there is a need to increase the charge injection limit of TiN electrodes for a high-performing neurostimulation. Our previous work suggested that the Vicseck fractal design can increase the charge injection limit of the microelectrodes. In this work, the effects of the fractal design in capacitive charge injection material were experimentally investigated by using TiN microelectrodes with circular and fractal designs. We measured the cyclic voltammetry, electrochemical impedance spectroscopy, and voltage transients. In addition, the charge injection limits of theses microelectrodes were estimated to quantify the effects of planar geometry on TiN microelectrodes. Despite our previous results showing superior charge injection capability of fractal Pt microelectrodes, the TiN showed no significant improvements due to the fractal geometry. This may be because the increase in charge injection capability of fractal microelectrodes is due to increased Faradaic charge injection process, which is minimized for TiN materials. Thus, our data suggests that the material as well as the geometry of the microelectrodes play key roles in optimizing stimulation microelectrode performance.Clinical relevance-As with the Faradaic charge injection-dominant materials, the capacitive charge injection materials could also benefit from additional investigation to fully characterize effects of electrode geometry for improved neurostimulation performance.

Hydrogel-Fractal Piezoelectric Bilayer Transducer for Wireless Biochemical Sensing.

This paper reports on a novel transducer for wireless biochemical sensing. The bilayer transducer consists of a fractal piezoelectric membrane and pH-sensitive chemo-mechanical hydrogel, which overcomes many shortcomings in the chemical and biochemical sensing. The fractal design on the piezoelectric membrane enhances frequency response and linearity by employing periodically repeated pore architecture. As a basis of the pore, a Hilbert space-filling curve with modifications is used. On the surface of the fractal piezoelectric membrane, the hydrogel is laminated. When the bilayer transducer is introduced to a pH environment (e.g., pH = 4, 8, and 12), the hydrogel swells (or shrinks) and induces the curling of the bilayer transducer (10.47°/pH). The curvature then exhibits various ultrasound responses when the bilayer transducer was excited. The measured voltage outputs using an ultrasonic receiver were 0.393, 0.341, 0.250 mV/cm2 when curvature angles were 30°, 60°, and 120°, respectively. Overall pH sensitivity was 0.017 mV/cm2/pH. Ultimately, the biochemical sensing principle using a novel bilayer ultrasound transducer suggests a simple, low-cost, battery-less, and long-range wireless readout system as compared to traditional biochemical sensing.

A Preliminary Study of a Graphene Fractal Sierpinski Antenna

We provide a preliminary study of a Graphene fractal antenna operating at THz frequencies with the opportunity to modulate the emission. There are many advantages of the fractal design, namely multiband/wideband ability, and, a smaller, lighter and simpler configuration for higher gain, that can benefit from the coupling with Graphene, the thinnest and strongest of materials exhibiting very high electrical conductivity and tunability. This paper proposes a conceptual background for the study and presents some preliminary results on the electromagnetic emission simulations undertaken.

Switched-capacitor-convertors based on fractal design for output power management of triboelectric nanogenerator

Owing to the advantages of integration and being magnet-free and light-weight, the switched-capacitor-convertor plays an increasing role compared to traditional transformer in some specific power supply systems. However, the high output impedance and switching loss largely reduces its power efficiency, due to imperfect topology and transistors. Herein, we propose a fractal-design based switched-capacitor-convertors with characteristics including high conversion efficiency, minimum output impedance, and electrostatic voltage applicability. As a double-function output power management system for triboelectric nanogenerators, it delivers over 67 times charge boosting and 954 W m−2 power density in pulse mode, and achieves over 94% total energy transfer efficiency in constant mode. The establishment of the fractal-design switched-capacitor-convertors provides significant guidance for the development of power management toward multi-functional output for numerous applications. The successful demonstration in triboelectric nanogenerators also declares its great potential in electric vehicles, DC micro-grids etc.

LFSR-Fractal ANN Model applied in R-IEDs for Smart Energy

In this research, a novel VHDL model was developed for implementation of self-similar circuits, in reconfigurable hardware. A Reed Solomon coding system (255,k) was selected as a case study. Fractal design techniques and concurrent modeling were applied. A theoretical contribution was achieved, with the logic model of a Fractal ANN. Likewise; practical advances are obtained with the optimization in terms of hardware resources and energy efficiency. The correspondence of these circuits has been interpreted through LFSR schemes, which constitutes a significant contribution for Reconfigurable IEDs applications in Reconfigurable Systems of Renewable Energy, under criteria of hardware re-usability.

Fractal solar panels: Optimizing aesthetic and electrical performances.

Solar energy technologies have been plagued by their limited visual appeal. Because the electrical power generated by solar panels increases with their surface area and therefore their occupancy of the observer’s visual field, aesthetics will play an increasingly critical role in their future success in urban environments. Inspired by previous psychology research highlighting the aesthetic qualities of fractal patterns, we investigated panel designs featuring fractal electrodes. We conducted behavioral studies which compared observers’ preferences for fractal and conventional bus-bar electrode patterns, along with computer simulations which compared their electrical performances. This led us to develop a hybrid electrode pattern which best combines the fractal and bus-bar designs. Here we show that the new hybrid electrode matches the electrical performance of bus-bars in terms of light transmission and minimizing electrical power losses, while benefiting from the superior aesthetics of fractal patterns. This innovative integration of psychology and engineering studies provides a framework for developing novel electrode patterns with increased implementation and acceptance.

Epidermal electronics for respiration monitoring via thermo-sensitive measuring

The depth and rate of human respiration reveal important and diverse sets of physiological information for evaluating human health. Here, we introduce an ultrathin, skin-integrated respiration sensor based on the thermal convection effect. The device features a filamentary fractal design of the gold heating electrode, a mini sensor (0.6 mm × 0.3 mm × 0.23 mm) with high thermal sensitivity and an ultrasoft encapsulation package to enhance the overall flexibility and biaxial stretchability of the system. Adjusting the input power of the heating electrode, i.e., increasing the temperature difference between the thermal sensor and environment, can further improve the sensitivity of the respiration sensor. The real-time monitoring respiration sensor can competently distinguish various breathing patterns (sitting, frightening, sleeping, meditating, and gasping) through breath rate/depth of detection subjects. In addition, the respiration sensor can effectively capture, in real time, the respiration of a volunteer while exercising, resting, or sleeping for prolonged periods of time. The combination of advanced mechanics, high sensitivity, and good stability make this respiration sensor a great candidate for potential use in real-time monitoring of human health.

Statistical evaluation of growth parameters in biofuel waste as a culture medium for improved production of single cell protein and amino acids by Yarrowia lipolytica

Yarrowia lipolytica is an oleaginous yeast species with the ability to grow on a number of substrates types, especially industrial wastes. This paper concerns the statistical optimization of fermentation parameters and media to ensure consistent and improved Y. lipolytica protein production. A strain of Y. lipolytica A-101 was observed to be proficient in producing single cell protein, amino acids, and vitamin B12 while utilizing biofuel waste instead of a complete YPD medium for yeast growth. A fractional fractal design experiment was then applied, and the two fermentation parameters of temperature and pH were recognized to have a significant effect on the protein and amino acid production. Subsequently, the response surface methodology with a three-level complete factorial design was employed to optimize these influential parameters. Therefore, five different measuring systems were utilized to construct a quadratic model and a second-order polynomial equation. Optimal levels of parameters were then obtained by analysis of the model and the numerical optimization method. When the Y. lipolytica A-101 was cultivated at optimized pH (5.0) using biofuel waste as a medium, the protein concentration was increased to 8.28—a 44% enhancement as compared to the original (3.65). This study has thus demonstrated a beneficial way to cultivate Y. lipolytica A-101 on biofuel waste for enhanced production of single cell protein and amino acids for use in human diet and in animal feed.

Fractal-Like Flow-Fields with Minimum Entropy Production for Polymer Electrolyte Membrane Fuel Cells

The fractal-type flow-fields for fuel cell (FC) applications are promising, due to their ability to deliver uniformly, with a Peclet number Pe~1, the reactant gases to the catalytic layer. We review fractal designs that have been developed and studied in experimental prototypes and with CFD computations on 1D and 3D flow models for planar, circular, cylindrical and conical FCs. It is shown, that the FC efficiency could be increased by design optimization of the fractal system. The total entropy production (TEP) due to viscous flow was the objective function, and a constant total volume (TV) of the channels was used as constraint in the design optimization. Analytical solutions were used for the TEP, for rectangular channels and a simplified 1D circular tube. Case studies were done varying the equivalent hydraulic diameter (Dh), cross-sectional area (DΣ) and hydraulic resistance (DZ). The analytical expressions allowed us to obtain exact solutions to the optimization problem (TEP→min, TV=const). It was shown that the optimal design corresponds to a non-uniform width and length scaling of consecutive channels that classifies the flow field as a quasi-fractal. The depths of the channels were set equal for manufacturing reasons. Recursive formulae for optimal non-uniform width scaling were obtained for 1D circular Dh -, DΣ -, and DZ -based tubes (Cases 1-3). Appropriate scaling of the fractal system providing uniform entropy production along all the channels have also been computed for Dh -, DΣ -, and DZ -based 1D models (Cases 4-6). As a reference case, Murray’s law was used for circular (Case 7) and rectangular (Case 8) channels. It was shown, that Dh-based models always resulted in smaller cross-sectional areas and, thus, overestimated the hydraulic resistance and TEP. The DΣ -based models gave smaller resistances compared to the original rectangular channels and, therefore, underestimated the TEP. The DZ -based models fitted best to the 3D CFD data. All optimal geometries exhibited larger TEP, but smaller TV than those from Murray’s scaling (reference Cases 7,8). Higher TV with Murray’s scaling leads to lower contact area between the flow-field plate with other FC layers and, therefore, to larger electric resistivity or ohmic losses. We conclude that the most appropriate design can be found from multi-criteria optimization, resulting in a Pareto-frontier on the dependencies of TEP vs TV computed for all studied geometries. The proposed approach helps us to determine a restricted number of geometries for more detailed 3D computations and further experimental validations on prototypes.

The Fractal Artistic Design Based on Interactive Genetic Algorithm

The Fractal Artistic Design Based on Interactive Genetic Algorithm

Computational Batik Motif Generation: Innovation of Traditional Heritage by Fractal Computation

Human-computer interaction has been the cause of the emerging innovations in many fields, including in design and art, architectural, technological artifacts, and even traditional heritage. In the case of Indonesian traditional heritages, the computation of fractal designs has been introduced to develop batik design – the genuine textile art and skill that becomes a symbol of Indonesian culture. The uniqueness of Batik, which depicted in the richness of its motifs, is regarded as one of interesting aspect to be researched and innovated using computational techniques. Recent studies of batik motifs have discovered conjecture to the existence of fractal geometry in batik designs. This finding has given some inspiration of implementing certain fractal concepts, such escape-time fractal (complex plane) and iterated function system to generate batik motifs. We develop motif generator based upon the Collage Theorem by using Java TM platform. This software is equipped by interface that can be used by user to generate basic patterns, which could be interpreted and painted as batik motif. Experimentally, we found that computationally generated fractal motifs are appropriated to be implemented as batik motif. However, human made batik motifs are less detail and some of them differ significantly with the computationally generated ones for tools used to draw batik and human aesthetic constraints.

Design and Evaluation of General Purpose, Barrier, and Multichannel Plasticating Extrusion Screws

Extrusion screw designs and validation are presented for three multiple channel, fractal screws for comparison with common general purpose, and barrier screws using an instrumented single screw extruder with high impact polystyrene (HIPS) and low density polyethylene (LDPE) at varying screw speeds. The fractal screws are designed with multiple channels and pressure–volume–temperature relations to control shear heating with cooling by adiabatic decompression. The general‐purpose design had the highest throughput but did not provide sufficient mixing and so resulted in excessive variation in the melt temperature and pressure at screw speeds above 40 RPM. The barrier screw was a capable design with good performance for LDPE and HIPS with screw speeds from 20 to 60 RPM. However, it tended to provide excessive shear heating at higher screw speeds due to the large surface area of the barrier and mixing sections. The first fractal screw design was a multichannel variant of the general‐purpose design and exhibited good consistency but excessive heating due to the large bearing area between the flights and barrel. The second fractal screw design provided decompression in the feed zone and metering zone to improve throughput but was limited by a poor transition section design. The third fractal screw design remedied these deficiencies with an improved transition section and intermittent clearances for dispersive mixing. Its performance rivaled that of the barrier screw with respect to volumetric output and energy efficiency but provided better melt pressure consistency. Cold screw freezing experiments were performed for all five screws with 5% black, blue, and violet colorants serially added to neat HIPS. The cold screw pulls showed that the general purpose and barrier screws exhibited significant racing of the materials within their screw channels and, thus, broad residence time distributions. Examination of the material cross sections indicated persistent coiled sheet morphologies, which were best dispersed with the third fractal screw. POLYM. ENG. SCI., 60:752–764, 2020. © 2020 The Authors. Polymer Engineering & Science published by Wiley Periodicals, Inc. on behalf of Society of Plastics Engineers.

Sparse Array Design via Fractal Geometries

Sparse sensor arrays have attracted considerable attention in various fields such as radar, array processing, ultrasound imaging and communications. In the context of correlation-based processing, such arrays enable to resolve more uncorrelated sources than physical sensors. This property of sparse arrays stems from the size of their difference coarrays, defined as the differences of element locations. Thus, the design of sparse arrays with large difference coarrays is of great interest. In addition, other array properties such as symmetry, robustness and array economy are important in different applications. Numerous studies have proposed diverse sparse geometries, focusing on certain properties while lacking others. Incorporating multiple properties into the design task leads to combinatorial problems which are generally NP-hard. For small arrays these optimization problems can be solved by brute force, however, in large scale they become intractable. In this paper, we propose a scalable systematic way to design large sparse arrays considering multiple properties. To that end, we introduce a fractal array design in which a generator array is recursively expanded according to its difference coarray. Our main result states that for an appropriate choice of the generator such fractal arrays exhibit large difference coarrays. Furthermore, we show that the fractal arrays inherit their properties from their generators. Thus, a small generator can be optimized according to desired requirements and then expanded to create a fractal array which meets the same criteria. This approach paves the way to efficient design of large arrays of hundreds or thousands of elements with specific properties.

A Sustainable Biomimetic Fractal Design Method to Illuminate the Interior Environment of a Single-Floor Building

A Sustainable Biomimetic Fractal Design Method to Illuminate the Interior Environment of a Single-Floor Building

A NEW FRACTAL DESIGN OF POROUS AlN/BN/SiOC COMPOSITES WITH LOW-k AND HIGH THERMAL CONDUCTIVITY

In this work, we propose a new model for the dielectric constant and thermal conductivity, and apply it to the design of composites with low dielectric constant and high thermal conductivity based on fractal theory and effective medium theory. In particular, we use this model to prepare porous AlN/BN/SiOC composites with low dielectric constant and high thermal conductivity in different component fractions. We successfully synthesize ceramic samples with low dielectric constants [Formula: see text] and high thermal conductivity ([Formula: see text]). These results indicate that the proposed fractal design is valid.

Fractal design in streetscape: Rethinking the visual aesthetics of building elevation composition

Each stylistic movement in building design and within its context throughout history is meant to possess a distinct visual character that is measurable in some way. From another perspective, building aesthetic measures in architecture have regularity included both experience and theories. Current styles of architecture are full of irregularity using a series of geometric construction which parametrically repeat themselves to produce complex images that could be defined as fractal. Recently, studying contemporary fractal dimensions in architecture has become significant as has been the metallic ratios in the past. In this study, fractal analysis is used to interpret current building elevation composition in a mathematical quantifiable way (boxcounting method). These measures are then verified by comparing results of questionnaires focused on habitats' perception of visual aesthetics of building elevation composition. This paper attempts to try to understand how fractal geometry contributes to the perception of buildings in their context and its participation in aesthetics measures. Findings confirm that highly dense fractals are not necessarily visually unpleasant, and that visual aesthetics are not correlated to fractal dimensions. This is due to the too many variables and conditions that are involved.

Investigation on novel wideband fractal antenna design based on cylindrical shape dielectric resonator

This article explains a novel approach for achieving wideband characteristics in case of dielectric resonator antenna (DRA). Wideband characteristic has been realized by uniting the concept of vastu purusha mandala (VPM)-based fractal geometry with dielectric resonator antenna. VPM is Hindu religion-based fractal geometry, which provides the advantage of decrease in volume to surface area of the radiator. This concept is useful to enhance impedance bandwidth of proposed antenna. For the purpose of validation, prototype of proposed antenna design has been fabricated as well as tested. After experimental testing, it is confirmed that the proposed radiator functions over the frequency range 2.6-4.34 GHz with a percentage bandwidth of 46.52%. The proposed radiating arrangement provides peak gain of 6.3 dBi and stable far-field characteristics. All these features make it applicable for WiMAX application (3.3 GHz).

Design of Wavy Ag Microwire Array for Mechanically Stable, Multimodal Vibrational Haptic Interface

AbstractA vibrotactile interface is an actuator device to convey haptic information intuitively from electronics to users. For the next‐generation of user‐friendly interface applications, the vibrotactile actuator is required to be vibration intensity/frequency controllable, mechanically stable, transparent, and have large scalability. Previously, although these requirements are satisfied via several approaches using a random network film of Ag wires or a mixture with conductive polymers, the random‐network‐based materials only have limited control on material density and uniformity, which in turn hinders precise control over vibration intensity and device transparency. Here, a new approach to assemble large‐scale Ag microwire arrays is demonstrated by involving an evaporative assembly method and is presented to overcome the current limitations. In particular, the 1D wavy structure derived from fractal designs promotes vibration intensity and cycling due to greater areal coverage and improved mechanical stability. Furthermore, by taking advantage of the precisely aligned microwires array, tunable multimode vibration frequencies are obtained by generating two different voltage frequencies. The large‐scale wavy Ag microwire array with precise spatial controllability will be directly adaptable as a user‐friendly interface in electronic applications like wearable devices, computer interfaces, and flexible mobile phones.

Photoactive Hybrid Materials with Fractal Designs Produced via 3D Printing and Plasma Grafting Technologies.

The present paper partly aims at exploring the potential of fractal geometry for concrete applications in the field of materials science. It is more specifically a study about the conception of hybrid polymer-based materials with photocatalytic activity. The concept behind this work is to investigate the use of polymer fractal structures manufactured by 3D-printing technology, as a highly ordered substrate with an important surface area to immobilize catalyst nanoparticles, by means of plasma grafting technology. Two types of fractal units, fractal pyramids (fracmids) and fractal cones (fracones), have been described and the former has been extensively characterized on a geometrical aspect. Various complex superstructures have also been described using fractal units as building blocks. 3D structures based on the aforementioned theoretical models have been designed using computer-aided design (CAD). On the basis of CAD models, several structures have been 3D-printed with PLA using fused deposition modeling. PLA substrates have been successfully coated with nanoparticles of ZnO using a combination of core-shell synthesis and plasma grafting. Finally, the photocatalytic activity of a hybrid material has been assessed with a positive outcome, showing the relevance of the concept developed in this study.

Graphene prevents neurostimulation-induced platinum dissolution in fractal microelectrodes

Platinum (Pt) is one of the most commonly used materials for neural interface owing to its excellent biocompatibility and good charge transfer characteristics. Although Pt is generally regarded to be a safe and inert material, it is known to undergo irreversible electrochemical dissolution during neurostimulation. The byproducts of these irreversible electrochemical reactions are known to be cytotoxic that can damage the surrounding neural substrate. With decreasing size of microelectrodes for more advanced high-density neural interfaces, there is a need for a more reliable, safe, and high-performance neurostimulating electrodes. In this work, we demonstrate that a monolayer of graphene can significantly suppress Pt dissolution while maintaining excellent electrochemical functionality. We microfabricated bare and graphene-coated Pt microelectrodes with circular and fractal designs and measured their Pt dissolution rate using inductively coupled plasma mass spectrometry. In addition, we measured changes in electrochemical characteristics of these microelectrodes before and after a prolonged stimulation period to quantify the effects of Pt dissolution and graphene protective layer. We confirm that fractal microelectrodes do have a better charge transfer performance than conventional circular designs but bare Pt fractal microelectrodes had significantly faster dissolution rate than the circular ones. When coated with monolayer of graphene, however, Pt dissolution was reduced >97% for fractal microelectrodes while they retained the superior charge transfer characteristics. The results of our work suggest that graphene can serve as an excellent diffusion barrier that can ameliorate the concerns for Pt dissolution in chronically implanted neurostimulation microelectrodes.