Fractal Substrates Research Articles

Frequency-band programmable piezoelectric energy harvesters with variable substrate material, tip mass and fractal architectures: Experimental and numerical investigations

To automate the approach of assessing the health and efficacy of large structural systems globally through structural health monitoring systems, a vast network of sensors that must be mounted throughout the entire structure and connected to a continuous power supply is necessary. Clusters of wires need to be placed throughout the structures to support the network, or batteries must be changed frequently, adding to the network’s high maintenance expenses. The present study investigates the scope of powering such low-energy devices with a localized renewable energy source based on smart piezoelectric components such as PZT-patched energy harvesting systems. This paper analyses the performance of the PZT patch mounted on different structures that are predominantly activated in d 31 mode. A vibration testing rig is manufactured to perform experiments for investigating the effect of material properties, natural frequencies, vibrating structural mass, and their interaction with the output power of a PZT transducer. Optimal mass, material, and structural configurations are attempted to be identified experimentally. The hypothesis, predictions, and results are evaluated further based on a converged finite element model. Subsequently, we introduce a novel concept of chiral fractal substrates in piezoelectric energy harvesters, wherein a significant improvement is noticed in the energy output along with increased frequency-band programmability. The power output of such architected and optimized energy harvesters holds the potential to serve as a reliable and sustainable alternative to conventional batteries, effectively providing a renewable source of power to energize and sustain low-power micro-electro-mechanical systems (MEMS) and devices.

Deep learning assisted fractal slotted substrate MIMO antenna with characteristic mode analysis (CMA) for Sub-6 GHz n78 5 G NR applications: design, optimization and experimental validation

This article presents the design and optimization of a Deep Learning assisted MIMO antenna for 5 G New Radio (NR) applications in Sub-6 GHz band. The Prototype of the simulated geometry has been practically modelled and experimentally tested to validate the theoretical results. The optimized two-port MIMO antenna of 48 × 24 mm2 size is designed using fractal slotted substrate geometry. The concept of characteristic mode analysis (CMA) method is performed to characterize the performance of the proposed slotted substrate monopole MIMO Antenna. Usually, Optimization techniques based on traditional electromagnetic simulation tools (CST, HFSS, etc) are time-consuming for the design purpose of complex MIMO antenna geometries. The simulation studies using electromagnetic simulation tools are needed to be performed repeatedly to evaluate the optimum geometrical parameters for achieving better acceptable performance. In order to solve this issue, Deep Learning (DL) method-based design optimization approach is considered as an effective technique for determining the optimum physical parameters. In this article, Deep learning method based Dual-Channel type Deep Neural Network (DC-DNN) optimization technique is suggested to estimate the S-parameters. The generated data is fed to DC-DNN acting as a surrogate model to map the input features with the reflection and transmission coefficients, thereby enabling the search for the optimum design parameters to obtain the best performance. The diversity parameters are observed within acceptable limits and the characteristic parameters related to impedance and radiation performance are best suitable for lower sub-6 GHz n78 (3300–3800 MHz) 5 G NR network applications.

Designer quantum states on a fractal substrate: Compact localization, flat bands and the edge modes

Compact localized single particle eigenstates on a deterministic fractal substrate, modelled by a triangular Sierpinski gasket of arbitrarily large size, are unravelled and examined analytically. We prescribe an exact real space renormalization group (RSRG) decimation scheme within a tight binding formalism to discern these states, and argue that the number of such states can be infinite if the fractal substrate is enlarged to its thermodynamic limit. Interestingly, these localized states turn out to populate the non-dispersive, flat bands in a periodic array of Sierpinski gasket motifs, however large they may be. Our results match and corroborate the recently observed compact localized, flat band states engineered on two dimensional photonic waveguide networks with a fractal geometry, and provide a whole subset of them, which, in principle, should be observable in fractal photonic lattice experiments.

Controlled Architectures in Supported Photocatalysis: Exploring the Potential of Cold Plasma Discharge, Additive Manufacturing, and Fractal Geometry to Form Hierarchically Immobilized Ni-MOF/BiOI/AgVO3.

Herein, we explore the potential of innovative manufacturing techniques based on green chemistry principles, for the fabrication of convenient, performant, and stable supported photocatalysts to be used for water depollution. After giving some insight into the use of fractal geometry for the fabrication of tunable polymer supports for photocatalysts, we investigated the use of liquid crystal display (LCD) 3D printing to generate the fractal resin substrates to be used for the immobilization of semiconductor photocatalysts. Notably, confocal laser imaging was used as a first attempt for assessing the surface area of the fractal substrate. Immobilization methods based on cold plasma discharge (CPD) were employed to modify the surface of the polymer substrates and permanently anchor three different phases, namely, nickel-based metal-organic framework (Ni-MOF), BiOI, and AgVO3, in a hierarchical configuration. Herein, for the first time, we developed a plasma-initiated condensed in situ complexation-assisted precipitation (c-ISCAP) method that allowed 2D Ni-MOF to be synthesized directly onto the surface of a polymer substrate, in a single step. Not only this MOF coating was found to be strongly bound to the surface of the polymer substrate but also very uniform and fully functional, even when other inorganic phases were immobilized on the top of this layer. This chemical approach opens the way for the fabrication of hybrid materials with complex polymer substrates and MOF coatings that could be used in a range of possible applications, for instance as chemical sensors, electrodes, adsorbents, optical devices, etc. Our hybrid photocatalysts were tested via photodegradation of Rhodamine B (RhB) dye upon visible light activation, with recycling runs to assess their durability. It was found that the hierarchical heterojunction Ni-MOF/BiOI/AgVO3 showed an outstanding ability for the removal of RhB dye, owing to the activity of the Ni-MOF layer in terms of charge transfer, and also partly because of its adsorbing potential. The three photoactive phases demonstrated a strong synergistic effect through coupling. However, more importantly, our findings show that their immobilization itself, regardless of the method used, significantly modified their optoelectronic properties, hence most likely changing the overall mechanism of charge transfer in the heterojunction. The Ni-MOF phase, notably, was found to display a reduced bandgap when obtained by c-ISCAP, which contributed to enhance its activation by visible light irradiation. Finally, it was established that the fractal geometry had a significant impact on the efficiency of the supported catalysts, probably thanks to an increased immobilization ratio of photocatalyst mostly, owing to the larger surface area available.

Biological Response Evaluation of Human Fetal Osteoblast Cells and Bacterial Cells on Fractal Silver Dendrites for Bone Tissue Engineering.

Prosthetic joint replacement is the most widely used surgical approach to repair large bone defects, although it is often associated with prosthetic joint infection (PJI), caused by biofilm formation. To solve the PJI problem, various approaches have been proposed, including the coating of implantable devices with nanomaterials that exhibit antibacterial activity. Among these, silver nanoparticles (AgNPs) are the most used for biomedical applications, even though their use has been limited by their cytotoxicity. Therefore, several studies have been performed to evaluate the most appropriate AgNPs concentration, size, and shape to avoid cytotoxic effects. Great attention has been focused on Ag nanodendrites, due to their interesting chemical, optical, and biological properties. In this study, we evaluated the biological response of human fetal osteoblastic cells (hFOB) and P. aeruginosa and S. aureus bacteria on fractal silver dendrite substrates produced by silicon-based technology (Si_Ag). In vitro results indicated that hFOB cells cultured for 72 h on the Si_Ag surface display a good cytocompatibility. Investigations using both Gram-positive (S. aureus) and Gram-negative (P. aeruginosa) bacterial strains incubated on Si_Ag for 24 h show a significant decrease in pathogen viability, more evident for P. aeruginosa than for S. aureus. These findings taken together suggest that fractal silver dendrite could represent an eligible nanomaterial for the coating of implantable medical devices.

Restricted curvature model on a tetrahedral fractal substrate

Restricted curvature model on a tetrahedral fractal substrate

Design and Analysis of a PDLC-Based Reconfigurable Hilbert Fractal Antenna for Large and Fine THz Frequency Tuning.

The proposed reconfigurable radiating antenna design is based on the integration of a reconfigurable fractal antenna and electro-optic substrate material. This antenna can be adjusted to achieve either re-configurability or tunability in the desired frequency range for wireless systems. The electromagnetic characteristics of the fractal antenna are manipulated at both the level of fractal geometry, electrical length and dielectric substrate. The designed antenna features multiband responses, in which the geometry and length change create a large frequency shift and the dielectric change using polymer dispersed liquid crystal (PDLC) creates fine and/or continuous tuning. The far field and scattering properties of the antenna are analyzed using the Computer Simulation Technology (CST) Microwave Studio Suite. The proposed approach has successfully demonstrated reconfigurable switching for up to four frequency bands between 0.2 and 0.6 THz. The dielectric constant change in the PDLC substrate shows fine and continuous frequency tuning with an 8% maximum frequency shift when operating around 0.54 THz and a high directivity of 7.35 dBi at 0.54 THz and 8.43 dBi at 0.504 THz. The antenna can also realize a peak gain of 4.29 dBi at 0.504 THz in the extraordinary polarization state of PDLC. The designed antenna can be readily integrated in the current communication devices, such as satellites, smart phones, laptops, and other portable electronic devices, due to its compact geometry and IC compatible design. In satellite applications, the proposed antenna can play a significant role in terms of security. The antenna could be extremely useful for satellites that want to keep their information secret; by constantly switching their operating frequency, spy satellites can evade detection and data collection from enemy ears.

Development of Gas Sensor Based on Fractal Substrate Structures

Gas sensor plays a key role in many applications with sensitivity being a critical performance characteristic. Increasing the surface area of gas sensing material is one approach that can increase sensitivity. Fractal geometries, which have large specific surface area and special fractal dimension, have previously been successfully used in the design of macro and microstructures of gas sensors to improve their performance. In this paper, the influence of geometrical structure of the substrate on the gas sensor performance has been investigated. Two fractal structures (Koch snowflake and Menger sponge) and one traditional structure (Cylinder) were fabricated by 3D printing and coated in Ag:MWCNTs based sensing materials. The fabricated sensors were tested with nitrogen dioxide at different temperatures and humidity. Experimental results show that the sensitivity of gas sensors with fractal structures is increased more than twice that of those with traditional geometrical structures.

Nonlinear Friction Dynamics of Oil-in-Water and Water-in-Oil Emulsions on Hydrogel Surfaces.

In this study, the friction properties of emulsions in an oral environment were investigated to understand the food-texture recognition mechanisms occurring on biological surfaces. Numerous publications have suggested that the friction phenomena depend on friction conditions, such as the surface characteristics, as well as the shape and movement of contact probes. Traditional friction evaluation systems are unsuitable for mimicking the oral environment. Thus, in this study, the friction forces between two fractal agar gel substrates in an emulsion were examined using a sinusoidal motion friction evaluation system that effectively mimics the oral environment. The physical properties of the fractal agar gel, including the elasticity, hydrophilicity, and surface roughness, were analogous to those of the human tongue. Furthermore, the sinusoidal motion imitated the movements of living organisms. Depending on the samples, three friction profiles were observed. For water, the surfactant aqueous solution, and olive oil, the friction profiles of the outward and homeward processes were symmetric (stable pattern). Interestingly, for an oil-in-water (O/W) emulsion, friction behaviors with not only an asymmetric friction profile (unstable pattern I) but also a lubrication phenomenon, which temporarily decreased the friction force (unstable pattern II), were noted. The probability for the appearance of unstable patterns and adhesion force between the gel substrates increased with the oil content of the O/W emulsions. These characteristic friction phenomena were attributed to the strong adhesive force in the emulsion, which was sandwiched between the agar gel substrates. The findings obtained in this study would contribute significantly to understanding the food-texture recognition mechanisms and dynamic phenomena occurring on biological surfaces.

Persistence and coexistence of infinite attractors in a fractal Josephson junction resonator with unharmonic current phase relation considering feedback flux effect

Josephson junction resonators are the devices which exhibit complex behaviours as a consequence of their inductive properties. Even though the insulating medium between Josephson junctions (JJs) is normally considered homogeneous, the fact that lithography is used to form the layer, it has fractal substrates. Such JJs are identified as fractal Josephson junctions (FJJs). In this paper, a new chaotic oscillator based on memristor and FJJ has been investigated. Superconductor properties can dramatically change its operating points especially voltage and heat that are related to Josephson tunnelling. Some changes in the operating points can cause the Josephson tunnelling junctions to oscillate in different oscillation modes in very high frequencies. This can be achieved by considering the potential across the junction with its flux feedback. In order to model the magnetic flux effect, we use a memristor whose memductance function is considered as an exponential function. By varying the type of the bias current, we could observe the property of infinitely coexisting attractors in the memristor-fractal Josephson junction oscillator, which is considered as a rare phenomenon in physical circuits. The proposed Josephson-Memristor circuit model is developed, and its equilibrium points, bifurcation and Lyapunov exponents are computed. As an engineering application, modelling the trajectories of the moving object has been realized. First, the SURF algorithm, which is not affected by the scale and rotations of the object, is used in the images to identify an object that tracks the states of the proposed Josephson-Memristor circuit. In this way, the coordinates of the orbits on which the object moves were determined on the image. In order to reproduce the orbits of the specified object, the coordinate information of the object has been trained to the artificial neural network model and the orbits of the object have been reproduced.

Functional Supported ZnO/Bi2MoO6 Heterojunction Photocatalysts with 3D-Printed Fractal Polymer Substrates and Produced by Innovative Plasma-Based Immobilization Methods.

Inorganic photocatalysts became an essential and powerful tool for the remediation of polluted water. However, important limitations of photocatalysts in their colloidal form, especially nanosized, remain. For instance, their separation from water after use and recovery, which can be particularly demanding, time- and energy-wise. Considering such aspects, supported catalysts bear significant advantages. However, efforts still have to be made to develop processes that allow the permanent and efficient immobilization of inorganic photocatalysts in sustainable conditions, in order to maintain the advantages of supported catalysts over colloidal ones. Herein, we report the use of an aqueous-phase plasma-aided grafting (APPAG) process to produce functional and efficient hybrid photocatalysts. More specifically, based on cold plasma discharge (CPD), ZnO/Bi2MoO6 heterojunctions were permanently immobilized on polymer supports generated by 3D-printing, with fractal-inspired designs. Three different approaches of the APPAG process have been successfully used for the immobilization of the inorganic phase, that is core-shell-assisted direct grafting, indirect grafting and in situ complexation-assisted precipitation (ISCAP). Noticeably, the latter technique has never been reported before to our knowledge. These three immobilization routes rely on different strategies and yield to distinct morphological specificities, but all allow using mild synthesis conditions and producing stable, active, permanently immobilized coatings of photocatalysts. Regarding the preparation of the organic supports, two sorts of additive manufacturing (AM) technologies were employed, namely fused-deposition modeling (FDM) and liquid crystal diode (LCD)-based SLA (stereolithography). The use of fractal geometries combined with AM permits the production of supports with relatively high surface areas, in a single processing step. Overall, the three plasma-based immobilization methods revealed to be efficient and the performance of the different hybrid photocatalysts have later been assessed through the photodegradation of Rhodamine B dye under simulated sunlight irradiation and visible light only, with promising results.

Synthesis and Mechanical Reconfiguration of Ground Plane Tilted Microstrip Antennas Based on Tetra-Circle Fractals

Abstract A synthesis procedure of a mechanically reconfigurable antenna based on tetra-circle fractal patch elements is presented, enabling to change both resonant frequencies and radiation pattern performance. The antenna geometry reconfiguration is implemented by tilting the ground plane of the microstrip antenna with respect to the fractal patch and substrate layer. The tilt angle is defined as the angle between the back of the dielectric substrate and the tilted ground plane and is electromechanically varied using a thin rod of dielectric material sliding up and down, in a simple geometry. Simulation results for the proposed antenna parameters are obtained using Ansoft HFSS software. In addition to promoting frequency and pattern reconfiguration, the tilting of the ground plane has proven to be an alternative to increase the antenna gain and enable single-band or dual-band operation. Prototypes were fabricated and measured for comparison purpose showing a good agreement between simulation and measurement results.

The Influence of Electric Fields on Self-Organization Processes in an Ultradispersed Solution of Multi-Walled Carbon Nanotubes

The influence of the electric field on the ordering processes in sediments of an ultradispersed solution of functionalized carbon nanotubes is investigated. The features and regularities of self-assembling and/or self-organization, leading to the formation of linear, fractal, and cluster substrates are examined via confocal (with video recording) and atomic force microscopy, scanning electron microscopy and transmission electron microscopy, as well as via IR Fourier spectroscopy, Raman spectroscopy and X-ray diffraction. It is established that dimensions of fractal structures decrease inversely to the electric field strength and their growth rate is a quadratic function of strength. Single-walled carbon nanotubes with metallic and semiconducting conductivities are detected and characterized with respect to chirality inside linear and cluster structures.

Quasi scale-free geographically embedded networks over DLA-generated aggregates

This paper proposes a novel model to construct quasi scale-free geographically-embedded networks, in which the network’s nodes have been generated by means of a Diffusion Limited Aggregation (DLA) process, and the links connecting a new node i to others are generated using a link radiusRli based on the Euclidean distance. The network is constructed by means of an evolutionary-based algorithm, aiming at minimizing the error between the actual degree distribution of the network under construction and that of the scale free networks, k−γ. Several algorithms for generating scale-free geographically-embedded networks over regular Euclidean lattices can be found in the literature but, to the best of our knowledge, the general case over complex or fractal substrates had not been tackled up until now. Although well-known in very large complex networks (with a huge number of nodes and links), the scale-free property has received much less attention for small geographically-embedded networks, in which the study of networks’ properties is much more difficult. The idea of this work is to evolve the link radii for all the nodes in the network, aiming at finally fulfilling the scale-free property, if possible. Our experimental work shows that the proposed model is actually able to generate quasi scale-free geographically embedded networks in an efficient way. Discussions on the algorithm’s performance to generate scale-free networks, a special encoding to improve the search, and the algorithm’s computational evolution are given in the paper. Alternative possibilities of distribution objective (such as Poissonian, which leads to random geographically-embedded networks) are also tested and discussed in this work.

Friction Dynamics on Rough Agar Gel Surfaces

Gels exhibit complex friction behavior. This study aims to evaluate the friction forces between two fractal agar gel substrates under sinusoidal motion to show the effect of rough surfaces on friction dynamics. In a previous study, we observed an asymmetric friction profile during reciprocating motion and an ultra-low friction state on flat agar gel surfaces. On the other hand, these distinct friction profiles were not observed on rough agar gel surfaces. We determined that this distinction was caused by the contact state between fractal agar gel surfaces; no thick water film was formed on the fractal surfaces because the rough structure provided channels to drain water from the interface. These physical insights are useful not only for developing biofunctional materials but also for understanding surface phenomena on biosurfaces including tongues and small intestinal walls.

On the dilemma of fractal or fractional kinetics in drug release studies: A comparison between Weibull and Mittag-Leffler functions

We compare two of the most successful models for the description and analysis of drug release data. The fractal kinetics approach leading to release profiles described by a Weibull function and the fractional kinetics approach leading to release profiles described by a Mittag-Leffler function. We used Monte Carlo simulations to generate artificial release data from euclidean and fractal substrates. We have also used real release data from the literature and found that both models are capable in describing release data up to roughly 85% of the release. For larger times both models systematically overestimate the number of particles remaining in the release device.

A Conserved Current Solid-on-Solid Model on a Sierpinski Tetrahedron Substrate

A conserved current solid-on-solid model with conservative noise on a 3D Sierpinski tetrahedron substrate is studied. The interface width W grows as t β , with β = 0.0396 ± 0.0009, and becomes saturated as Lα, with α = 0.195±0.005, where L is the system size. The dynamic exponent z ≈ 4.92 is estimated from the relation z = α/β. These values satisfy a scaling relation α+z = 2z rw , where z rw is the random walk exponent of the fractal substrate. Our results are consistent with the values estimated from a fractional Langevin equation with a conservative noise.

Random walk diffusion model with restricted solid on solid condition on fractal substrates

A random walk diffusion model with a restricted solid-on-solid (RSOS) condition is studied on both Sierpinski gasket and checkerboard fractal substrates. A deposited particle is allowed to hop randomly until finding a site satisfying the RSOS condition. The interface width W of the model grows as at the beginning and becomes saturated at for , where L is the system size. We obtain , , and the dynamic exponent for a Sierpinski gasket substrate. A scaling relation is well satisfied, where zrw is the random walk exponent of the fractal substrate. Also, they are in good agreement with the predicted values of a suggested Langevin equation.

Influences of Fractal Substrate Structures on Dynamic Scaling Behaviors of Etching Model**Supported by the Fundamental Research Funds for the Central Universities under Grant No. 2015XKMS074-CUMT

The Etching model on various fractal substrates embedded in two dimensions was investigated by means of kinetic Mento Carlo method in order to determine the relationship between dynamic scaling exponents and fractal parameters. The fractal dimensions are from 1.465 to 1.893, and the random walk exponents are from 2.101 to 2.578. It is found that the dynamic behaviors on fractal lattices are more complex than those on integer dimensions. The roughness exponent increases with the increasing of the random walk exponent on the fractal substrates but shows a non-monotonic relation with respect to the fractal dimension. No monotonic change is observed in the growth exponent.

Evaluation of the Frictional Properties of Oil-in-water Emulsions on Fractal Agar Gel Surface

We evaluated the frictional properties of emulsions on fractal agar gel substrates. The friction force and its temporal profile depend on the ternary mixed state. An unstable emulsion containing a large amount of oil shows a significant lubricating effect.