This chapter introduces a family of fractional-order oscillators based on a single operational amplifier (Op-Amp) with two fractional-order capacitors. Twelve different fractional-order oscillator circuits are investigated where the state matrix, oscillation frequency, and oscillation condition for each circuit are presented. The phase difference between the two oscillatory outputs is deduced in terms of the fractional-order parameters. The fractional-order parameter enhances the oscillator performance by providing an extra degree-of-freedom. Also, the resulting circuits provide independent controllability for the phase difference and the oscillation frequency. Numerical simulations using MATLAB® are performed to study the effect of the fractional-order parameters on the circuit response. Moreover, PSpice simulations are performed on different cases using two different fractional-order capacitors. Selected cases are verified experimentally to confirm the theoretical findings. © 2022 Elsevier Inc. All rights reserved.
On the Approximation of Fractional-Order Circuit Design
Despite the complex nature of fractional calculus, it is still fairly possible to reduce this complexity by using integer-order approximation. Each integer-order approximation has its own trade-offs from the complexity, sensitivity, and accuracy points of view. In this chapter, two different fractional-order electronic circuits are studied: the Wien oscillator and the CCII-based KHN filter with two different fractional elements of orders ? and ?. The investigation is concerned with changes in the response of these two circuits under two approximations: Oustaloup and Matsuda. A detailed review of each approximation technique is provided as well as its design procedure. Oscillator and filter responses are simulated using MATLAB. Foster-I realization is used to implement the approximated Wien oscillator and filter transfer functions as circuits in order to simulate them in PSpice. The responses are compared to the exact solution to investigate which achieves the lowest error. For oscillators, the comparison is based on oscillation condition and oscillation frequency while for filters, the focus is on filter fundamental frequencies. This is a big issue in filter design: maximum or minimum frequency, right phase frequency, and half-power frequency. © 2018 Elsevier Inc. All rights reserved.
Survey on Two-Port Network-Based Fractional-Order Oscillators
This chapter merges the fractional calculus and two-port networks in oscillator design. The fractional-order elements ? and ? add extra degrees of freedom that increase the design flexibility and frequency band while providing control over the phase difference. A prototype of the fractional-order two-port network oscillators is introduced. It consists of a general two-port network and three impedances distributed as input, output, and a feedback impedance. Three different two-port network classifications are obtained according to the ground location. This chapter focuses on one of these classifications from which two derived prototypes can be extracted. The general analytical formulas of the oscillation frequency and condition as well as the phase difference are derived in terms of the transmission matrix parameter of a general two-port network. Different active building blocks are used to serve as a two-port network. Numerical, Spice simulations, and experimental results are given to validate the presented analysis. © 2018 Elsevier Inc. All rights reserved.
FPGA Implementation of Fractional-Order Chaotic Systems
This chapter introduces two FPGA implementations of the fractional-order operators: the Caputo and the Grünwald-Letnikov (GL) derivatives. First, the Caputo derivative is realized using nonuniform segmentation to reduce the size of the Look-Up Table. The Caputo implementation introduced can generate derivatives of previously defined functions only. Generic and complete hardware architecture of the GL operator is realized with different memory window sizes. The generic architecture is used as a block to implement several fractional-order chaotic systems. The investigated systems include Borah, Chen, Liu, Li, and Arneodo fractional-order chaotic systems. Different interesting attractors are realized under various parametric changes with distinct step sizes for different fractional orders. To verify the chaotic behavior of the generated attractors, the Maximum Lyapunov Exponent is calculated for each system at different parameter values. © 2018 Elsevier Inc. All rights reserved.
FPGA implementation of integer/fractional chaotic systems
Chaotic systems have remarkable importance in capturing some complex features of the physical process. Recently, fractional calculus becomes a vigorous tool in characterizing the dynamics of complex systems. The fractional-order chaotic systems increase the chaotic behavior in new dimensions and add extra degrees of freedom, which increase system controllability. In this chapter, FPGA implementation of different integer and fractional-order chaotic systems is presented. The investigated integer-order systems include Chua double scroll chaotic system and the modified Chua N-scroll chaotic system. The investigated fractional-order systems include Chua, Yalcin et al., Ozuogos et al., and Tang et al., chaotic systems. These systems are implemented and simulated based on the Grunwald–Letnikov (GL) definition with different window sizes. The parameters effect, along with different GL window sizes is investigated where some interesting chaotic behaviors are obtained. The proposed FPGA implementation utilizes fewer resources and has high throughput. Experimental results are provided on a digital oscilloscope. © Springer Nature Switzerland AG 2020.
On the fractional order generalized discrete maps
Chaos theory describes the dynamical systems which exhibit unpredictable, yet deterministic, behavior. Chaotic systems have a remarkable importance in both modeling and information processing in many fields. Fractional calculus has also become a powerful tool in describing the dynamics of complex systems such as fractional order (FO) chaotic systems. The FO parameter adds extra degrees of freedom which increases the design flexibility and adds more control on the design. The extra parameters increase the chaotic range. This chapter provides a review of several generalized discrete time one-dimensional maps. The generalizations include a signed control parameter, scaling parameters, and shaping parameters. The properties of the generalized fractional logistic map are presented. The generalized fractional tent map is presented and its properties are studied and validated using numerical simulations. Various simulations are conducted including time series, bifurcation diagrams, and various chaotic properties against the system parameters and FO parameter. © 2018 Elsevier Inc. All rights reserved.
Carbon Nanomaterials and Their Composites as Adsorbents
Carbon nanomaterials with various nanostructures (carbon nanotubes, graphene, graphene oxide, fullerene, nano diamonds, carbon quantum dots, carbon nanofibers, graphitic carbon nitrides, and nano porous carbons) are the decade’s most distinguishing and popular materials. They have distinctive physicochemical qualities such as chemical stability, mechanical strength, hardness, thermal and electrical conductivities, and so on. Furthermore, they are easily surface functionalized and tweaked, modifying them for high-end specific applications. Carbon nanostructures’ properties and surface characteristics are determined by the synthesis method used to create them. Nanoscience and nanotechnology have the potential to create materials with unexpected functions and qualities, which are transforming all industries. Carbon nanoparticles such as fullerene, carbon nanotubes, and graphene stand out among the various kinds of nanomaterials. These nanoparticles offer a wide range of practical applications, particularly in adsorption processes. Carbon nanoparticles exhibit unique structures that could be used in the construction of extremely sensitive, selective, and effective adsorbent devices for the removal of inorganic, organic, and biological pollutants from water solutions, as well as nano sensors and drug delivery systems. In this chapter, we demonstrated the number of studies published in recent years that used carbon nanomaterials as adsorbents. Furthermore, this chapter discusses essential features of adsorption and different nanocarbon carbon composite material, such as the contrast between physical and chemical absorption. Furthermore, diverse carbon nanomaterial synthesis such as AC–FeO ?Cu and Bimetallic FeO ?Cu/algae activated carbon composites AC–Fe0 ?Cu methodologies, functionalization, and characteristics are provided and logically addressed. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
A review of coagulation explaining its definition, mechanism, coagulant types, and optimization models; RSM, and ANN
The textile business is one of the most hazardous industries since it produces several chemicals, such as dyes, which are released into water streams with ef-fluents. For the survival of the planet’s life and the advancement of humanity, water is a crucial resource. One of the anthropogenic activities that pollute and consume water is the textile industry. Thus, the purpose of the current effort is to Apply coagulation as a Physico-chemical and biological treatment strat-egy with different techniques and mechanisms to treat the effluent streams of textile industries. The discharge of these effluents has a negative impact on the environment, marine life, and human health. Therefore, the treatment of these effluents before discharging is an important matter to reduce their adverse ef-fect. Many physico-chemical and biological treatment strategies for contaminants removal from polluted wastewater have been proposed. Coagulation is thought to be one of the most promising physico-chemical strategies for removing con-taminants and colouring pollutants from contaminated water. Coagulation is accompanied by a floculation process to aid precipitation, as well as the collection of the created sludge following the treatment phase. Different commercial, and natural coagulants have been applied as a coagulants in the process of coagulation. Additionally, many factors such as; pH, coagulant dose, pollu-tants concentration are optimized to obtain high coagulants removal capacity. This review will discuss the coagulation process, coagulant types and aids in addition to the factors affecting the coagulation process. Additionally, a brief comparison between the coagulation process, and the other processes; princi-ple, advantages, disadvantages, and their efficiency were discussed throgh the review. Furthermore, it discusses the models and optimization techniques used for the coagulation process including response surface methodology (RSM), ar-tificial neural network (ANN), and several metaheuristic algorithms combined with ANN and RSM for optimization in previous work. The ANN model has more accurate results than RSM. The ANN combined with genetic algorithm gives an accurate predicted optimum solution. © 2023 The Authors
Crystal violet removal using bimetallic Fe0–Cu and its composites with fava bean activated carbon
Nano zero-valent iron (nZVI), bimetallic nano zero-valent iron-copper (Fe0– Cu), and fava bean activated carbon-supported bimetallic nano zero-valent iron-copper (AC-Fe0-Cu) are synthesized and characterized using DLS, zeta potential, FT-IR, XRD, and SEM. The maximum removal capacity is demonstrated by bimetallic Fe0–Cu, which is estimated at 413.98 mg/g capacity at pH 7, 180 min of contact duration, 120 rpm shaking speed, ambient temperature, 100 ppm of C.V. dye solution, and 1 g/l dosage. The elimination capability of the H2SO4 chemical AC-Fe0-Cu adsorbent is 415.32 mg/g under the same conditions but with a 150 ppm C.V. dye solution. The H3PO4 chemical AC-Fe0-Cu adsorbent achieves a removal capacity of 413.98 mg/g under the same conditions with a 350 ppm C.V. dye solution and a 1.5 g/l dosage. Optimal conditions for maximum removal efficiency are determined by varying pH (3–9), time intervals (15–180 min), and initial dye concentrations (25–1000 ppm). Kinetic and isothermal models are used to fit the results of time and concentration experiments. The intra-particle model yields the best fit for bimetallic Fe0–Cu, H2SO4 chemical AC- Fe0–Cu, and H3PO4 chemical AC-Fe0-Cu, with corrected R-Squared values of 0.9656, 0.9926, and 0.964, respectively. The isothermal results emphasize the significance of physisorption and chemisorption in concentration outcomes. Response surface methodology (RSM) and artificial neural networks (ANN) are employed to optimize the removal efficiency. RSM models the efficiency and facilitates numerical optimization, while the ANN model is optimized using the moth search algorithm (MSA) for optimal results. © 2023
Preparation and Characterization of nZVI, Bimetallic Fe 0-Cu, and Fava Bean Activated Carbon-Supported Bimetallic AC-F e 0-Cu for Anionic Methyl Orange Dye Removal
Nano zero-valent iron (nZVI), bimetallic Nano zero-valent iron-copper (Fe 0- Cu), and fava bean activated carbon-supported with bimetallic Nano zero-valent iron-copper (AC-F e 0-Cu) were prepared and characterized by DLS, FT-IR, XRD, and SEM. The influence of the synthesized adsorbents on the adsorption and removal of soluble anionic methyl orange (M.O) dye was investigated using UV-V spectroscopy. The influence of numerous operational parameters was studied at varied pH (3–9), time intervals (15–180 min), and dye concentrations (25–1000 ppm) to establish the best removal conditions. The maximum removal efficiency of M.O. using the prepared adsorbent materials reached about 99%. The removal efficiency is modeled using response surface methodology (RSM). The Bimetallic Fe -Cu, the best experimental and predicted removal efficiency is 96.8% RE. For the H2SO4 chemical AC- Fe -Cu, the best experimental and removal efficiency is 96.25% RE. The commercial AC-Fe0–Cu, the best experimental and predicted removal efficiency is 94.93%RE. This study aims to produce low-cost adsorbents such as Bimetallic Fe0-Cu, and Fava Bean Activated Carbon-Supported Bimetallic AC-Fe0-Cu to treat the industrial wastewater from the anionic methyl orange (M.O) dye and illustrate its ability to compete H2SO4 chemical AC-Fe0-Cu, and commercial AC-Fe0-Cu. © 2023, The Author(s).