Application of fractional order concepts in the study of electrical potential

The Maxwell equations, expressing the fundamental laws of electricity and magnetism, only involve the integer-order calculus. However, several effects present in electromagnetism, motivated recently an analysis under the fractional calculus (FC) perspective. In fact, this mathematical concept allows a deeper insight into many phenomena that classical models overlook. On the other hand, genetic algorithms (GA) are an important tool to solve optimization problems that occur in engineering. In this work we use FC and GA to implement the electrical potential of fractional order. The performance of the GA scheme and the convergence of the resulting approximations are analyzed.

Application of genetic algorithms in the design of an electrical potential of fractional order

Fractional calculus (FC) is currently being applied in many areas of science and technology. In fact, this mathematical concept helps the researches to have a deeper insight about several phenomena that integer order models overlook. Genetic algorithms (GA) are an important tool to solve optimization problems that occur in engineering. This methodology applies the concepts that describe biological evolution to obtain optimal solution in many different applications. In this line of thought, in this work we use the FC and the GA concepts to implement the electrical fractional order potential. The performance of the GA scheme, and the convergence of the resulting approximation, are analyzed. The results are analyzed for different number of charges and several fractional orders.

Crossing genetic and swarm intelligence algorithms to generate logic circuits

Genetic Algorithms (GAs) are adaptive heuristic search algorithm based on the evolutionary ideas of natural selection and genetic. The basic concept of GAs is designed to simulate processes in natural system necessary for evolution, specifically those that follow the principles first laid down by Charles Darwin of survival of the fittest. On the other hand, Particle swarm optimization (PSO) is a population based stochastic optimization technique inspired by social behavior of bird flocking or fish schooling. PSO shares many similarities with evolutionary computation techniques such as GAs. The system is initialized with a population of random solutions and searches for optima by updating generations. However, unlike GA, PSO has no evolution operators such as crossover and mutation. In PSO, the potential solutions, called particles, fly through the problem space by following the current optimum particles. PSO is attractive because there are few parameters to adjust. This paper presents hybridization between a GA algorithm and a PSO algorithm (crossing the two algorithms). The resulting algorithm is applied to the synthesis of combinational logic circuits. With this combination is possible to take advantage of the best features of each particular algorithm.

Calculation of fractional derivatives of noisy data with genetic algorithms

This paper addresses the calculation of derivatives of fractional order for non-smooth data. The noise is avoided by adopting an optimization formulation using genetic algorithms (GA). Given the flexibility of the evolutionary schemes, a hierarchical GA composed by a series of two GAs, each one with a distinct fitness function, is established.

A fractional calculus perspective in the evolutionary design of combinational circuits

This paper analyses the performance of a genetic algorithm (GA) in the synthesis of digital circuits using two novel approaches. The first concept consists in improving the static fitness function by including a discontinuity evaluation. The measure of variability in the error of the Boolean table has similarities with the function continuity issue in classical calculus. The second concept extends the static fitness by introducing a fractional-order dynamical evaluation.

Dynamical modelling of a genetic algorithm

This work addresses the signal propagation and the fractional-order dynamics during the evolution of a genetic algorithm (GA). In order to investigate the phenomena involved in the GA population evolution, the mutation is exposed to excitation perturbations during some generations and the corresponding fitness variations are evaluated. Three distinct fitness functions are used to study their influence in the GA dynamics. The input and output signals are studied revealing a fractional-order dynamic evolution, characteristic of a long-term system memory.

Optimal fuzzy PID control tuned with genetic algorithms

Fuzzy logic controllers (FLC) are intelligent systems, based on heuristic knowledge, that have been largely applied in numerous areas of everyday life. They can be used to describe a linear or nonlinear system and are suitable when a real system is not known or too difficult to find their model. FLC provide a formal methodology for representing, manipulating and implementing a human heuristic knowledge on how to control a system. These controllers can be seen as artificial decision makers that operate in a closed-loop system, in real time. The main aim of this work was to develop a single optimal fuzzy controller, easily adaptable to a wide range of systems – simple to complex, linear to nonlinear – and able to control all these systems. Due to their efficiency in searching and finding optimal solution for high complexity problems, GAs were used to perform the FLC tuning by finding the best parameters to obtain the best responses. The work was performed using the MATLAB/SIMULINK software. This is a very useful tool that provides an easy way to test and analyse the FLC, the PID and the GAs in the same environment. Therefore, it was proposed a Fuzzy PID controller (FL-PID) type namely, the Fuzzy PD+I. For that, the controller was compared with the classical PID controller tuned with, the heuristic Ziegler-Nichols tuning method, the optimal Zhuang-Atherton tuning method and the GA method itself. The IAE, ISE, ITAE and ITSE criteria, used as the GA fitness functions, were applied to compare the controllers performance used in this work. Overall, and for most systems, the FL-PID results tuned with GAs were very satisfactory. Moreover, in some cases the results were substantially better than for the other PID controllers. The best system responses were obtained with the IAE and ITAE criteria used to tune the FL-PID and PID controllers.

New modified electrochemical conductive paper support for BSA detection

Chemical sensors and biosensors are widely used to detect various kinds of protein target biomolecules. Molecularly Imprinted Polymers (MIPs) have raised great interest in this area, because these act as antibody-like recognition materials, with high affinity to the template molecule. Compared to natural antibodies, these are also of lower cost and higher stability. There are different types of supports used to carry MIP materials, mostly of these made of gold, favourably assembled on a Screen Printed Electrode (SPE) strategy. For this work a new kind of support for the sensing layer was developed: conductive paper. This support was made by modifying first cellulose paper with paraffin wax (to make it waterproof), and casting a carbon-ink on it afterwards, to turn it conductive. The SPAM approach previously reported in1 was employed herein to assemble to MIP sensing material on the conductive paper. The selected charged monomers were (vinylbenzyl) trimethlammonium chloride (positive charge) or vinylbenzoic acid (negative charge), used to generate binding positions with single-type charge (positive or negative). The non-specific binding area of the MIP layer was assembled by chronoamperometry-assisted polymerization (at 1 V, for 60, 120 or 180 seconds) of vinylbenzoate, cross-linked with ethylene glycol vinyl ether. The BSA biomolecules lying within the polymeric matrix were removed by Proteinase K action. All preparation stages of the MIP assembly were followed by FTIR, Raman spectroscopy and, electrochemical analysis. In general, the best results were obtained for longer polymerization times and positively charged binding sites (which was consistent with a negatively-charged protein under physiological pH, as BSA). Linear responses against BSA concentration ranged from 0.005 to 100 mg/mL, in PBS buffer standard solutions. The sensor was further calibrated in standard solutions that were prepared in synthetic or real urine, and the analytical response became more sensitive and stable. Compared to the literature, the detection capability of the developed device is better than most of the reported electrodes. Overall, the simplicity, low cost and good analytical performance of the BSA SPE device, prepared with positively charged binding positions, seems a suitable approach for practical application in clinical context. Further studies with real samples are required, as well as gathering with electronic-supporting devices to allow on-site readings.

Assessing and comparing the total antioxidant capacity of commercial beverages: application to beers, wines, waters and soft drinks using TRAP, TEAC and FRAP methods.

This work measures and tries to compare the Antioxidant Capacity (AC) of 50 commercial beverages of different kinds: 6 wines, 12 beers, 18 soft drinks and 14 flavoured waters. Because there is no reference procedure established for this purpose, three different optical methods were used to analyse these samples: Total Radical trapping Antioxidant Parameter (TRAP), Trolox Equivalent Antioxidant Capacity (TEAC) and Ferric ion Reducing Antioxidant Parameter (FRAP). These methods differ on the chemical background and nature of redox system. The TRAP method involves the transfer of hydrogen atoms while TEAC and FRAP involves electron transfer reactions. The AC was also assessed against three antioxidants of reference, Ascorbic acid (AA), Gallic acid (GA) and 6-hydroxy-2,5,7,8-tetramethyl- 2-carboxylic acid (Trolox). The results obtained were analyzed statistically. Anova one-way tests were applied to all results and suggested that methods and standards exhibited significant statistical differences. The possible effect of sample features in the AC, such as gas, flavours, food colouring, sweeteners, acidity regulators, preservatives, stabilizers, vitamins, juice percentage, alcohol percentage, antioxidants and the colour was also investigated. The AC levels seemed to change with brand, kind of antioxidants added, and kind of flavour, depending on the sample. In general, higher ACs were obtained for FRAP as method, and beer for kind of sample, and the standard expressing the smaller AC values was GA.

A Fractional Calculus Perspective in the Evolutionary Design of Combinational Circuits

This paper analyses the performance of a genetic algorithm (GA) in the synthesis of digital circuits using two novel approaches. The first concept consists in improving the static fitness function by including a discontinuity evaluation. The measure of variability in the error of the Boolean table has similarities with the function continuity issue in classical calculus. The second concept extends the static fitness by introducing a fractional-order dynamical evaluation.

A comparison between thin film solar cells made from co-evaporated CuIn1-xGaxSe2using a one-stage process versus a three-stage process

Until this day, the most efficient Cu(In,Ga)Se2 thin film solar cells have been prepared using a rather complex growth process often referred to as three-stage or multistage. This family of processes is mainly characterized by a first step deposited with only In, Ga and Se flux to form a first layer. Cu is added in a second step until the film becomes slightly Cu-rich, where-after the film is converted to its final Cu-poor composition by a third stage, again with no or very little addition of Cu. In this paper, a comparison between solar cells prepared with the three-stage process and a one-stage/in-line process with the same composition, thickness, and solar cell stack is made. The one-stage process is easier to be used in an industrial scale and do not have Cu-rich transitions. The samples were analyzed using glow discharge optical emission spectroscopy, scanning electron microscopy, X-ray diffraction, current–voltage-temperature, capacitance-voltage, external quantum efficiency, transmission/reflection, and photoluminescence. It was concluded that in spite of differences in the texturing, morphology and Ga gradient, the electrical performance of the two types of samples is quite similar as demonstrated by the similar J–V behavior, quantum spectral response, and the estimated recombination losses.