Fractional order calculus: basic concepts and engineering applications

The fractional order calculus (FOC) is as old as the integer one although up to recently its application was exclusively in mathematics. Many real systems are better described with FOC differential equations as it is a well-suited tool to analyze problems of fractal dimension, with long-term “memory” and chaotic behavior. Those characteristics have attracted the engineers' interest in the latter years, and now it is a tool used in almost every area of science. This paper introduces the fundamentals of the FOC and some applications in systems' identification, control, mechatronics, and robotics, where it is a promissory research field.

Lifestyle factors, direct and indirect costs for a Brazilian airline company

OBJECTIVE To analyze lifestyle risk factors related to direct healthcare costs and the indirect costs due to sick leave among workers of an airline company in Brazil. METHODS In this longitudinal 12-month study of 2,201 employees of a Brazilian airline company, the costs of sick leave and healthcare were the primary outcomes of interest. Information on the independent variables, such as gender, age, educational level, type of work, stress, and lifestyle-related factors (body mass index, physical activity, and smoking), was collected using a questionnaire on enrolment in the study. Data on sick leave days were available from the company register, and data on healthcare costs were obtained from insurance records. Multivariate linear regression analysis was used to investigate the association between direct and indirect healthcare costs with sociodemographic, work, and lifestyle-related factors. RESULTS Over the 12-month study period, the average direct healthcare expenditure per worker was US$505.00 and the average indirect cost because of sick leave was US$249.00 per worker. Direct costs were more than twice the indirect costs and both were higher in women. Body mass index was a determinant of direct costs and smoking was a determinant of indirect costs. CONCLUSIONS Obesity and smoking among workers in a Brazilian airline company were associated with increased health costs. Therefore, promoting a healthy diet, physical activity, and anti-tobacco campaigns are important targets for health promotion in this study population.

A fractional approach for the motion planning of redundant and hyper-redundant manipulators

The trajectory planning of redundant robots through the pseudoinverse control leads to undesirable drift in the joint space. This paper presents a new technique to solve the inverse kinematics problem of redundant manipulators, which uses a fractional differential of order α to control the joint positions. Two performance measures are defined to examine the strength and weakness of the proposed method. The positional error index measures the precision of the manipulator's end-effector at the target position. The repeatability performance index is adopted to evaluate if the joint positions are repetitive when the manipulator execute repetitive trajectories in the operational workspace. Redundant and hyper-redundant planar manipulators reveal that it is possible to choose in a large range of possible values of α in order to get repetitive trajectories in the joint space.

Recent history of fractional calculus

This survey intends to report some of the major documents and events in the area of fractional calculus that took place since 1974 up to the present date.

Particle swarm optimization: dynamical analysis through fractional calculus

This chapter considers the particle swarm optimization algorithm as a system, whose dynamics is studied from the point of view of fractional calculus. In this study some initial swarm particles are randomly changed, for the system stimulation, and its response is compared with a non-perturbed reference response. The perturbation effect in the PSO evolution is observed in the perspective of the fitness time behaviour of the best particle. The dynamics is represented through the median of a sample of experiments, while adopting the Fourier analysis for describing the phenomena. The influence upon the global dynamics is also analyzed. Two main issues are reported: the PSO dynamics when the system is subjected to random perturbations, and its modelling with fractional order transfer functions.

Fractional calculus: application in modelling and control

This contribution introduces the fractional calculus (FC) fundamental mathematical aspects and discuses some of their consequences. Based on the FC concepts, the chapter reviews the main approaches for implementing fractional operators and discusses the adoption of FC in control systems. Finally are presented some applications in the areas of modeling and control, namely fractional PID, heat diffusion systems, electromagnetism, fractional electrical impedances, evolutionary algorithms, robotics, and nonlinear system control.

Application of fractional calculus in engineering

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades. It has been recognized the advantageous use of this mathematical tool in the modelling and control of many dynamical systems. Having these ideas in mind, this paper discusses a FC perspective in the study of the dynamics and control of several systems. The paper investigates the use of FC in the fields of controller tuning, legged robots, electrical systems and digital circuit synthesis.

Internal structure of the nanogratings generated inside bulk fused sílica by ultrafast laser direct writing

The aim of the present work was to characterize the internal structure of nanogratings generated inside bulk fused silica by ultrafast laser processing and to study the influence of diluted hydrofluoric acid etching on their structure. The nanogratings were inscribed at a depth of 100 mu m within fused silica wafers by a direct writing method, using 1030 nm radiation wavelength and the following processing parameters: E = 5 mu J, tau = 560 fs, f = 10 kHz, and v = 100 mu m/s. The results achieved show that the laser-affected regions are elongated ellipsoids with a typical major diameter of about 30 mu m and a minor diameter of about 6 mu m. The nanogratings within these regions are composed of alternating nanoplanes of damaged and undamaged material, with an average periodicity of 351 +/- 21 nm. The damaged nanoplanes contain nanopores randomly dispersed in a material containing a large density of defects. These nanopores present a roughly bimodal size distribution with average dimensions for each class of pores 65 +/- 20 x 16 +/- 8 x 69 +/- 16 nm(3) and 367 +/- 239 x 16 +/- 8 x 360 +/- 194 nm(3), respectively. The number and size of the nanopores increases drastically when an hydrofluoric acid treatment is performed, leading to the coalescence of these voids into large planar discontinuities parallel to the nanoplanes. The preferential etching of the damaged material by the hydrofluoric acid solution, which is responsible for the pores growth and coalescence, confirms its high defect density. (C) 2014 AIP Publishing LLC.

Node adaptation for global collocation with radial basis functions using direct multisearch for multiobjective optimization

Meshless methods are used for their capability of producing excellent solutions without requiring a mesh, avoiding mesh related problems encountered in other numerical methods, such as finite elements. However, node placement is still an open question, specially in strong form collocation meshless methods. The number of used nodes can have a big influence on matrix size and therefore produce ill-conditioned matrices. In order to optimize node position and number, a direct multisearch technique for multiobjective optimization is used to optimize node distribution in the global collocation method using radial basis functions. The optimization method is applied to the bending of isotropic simply supported plates. Using as a starting condition a uniformly distributed grid, results show that the method is capable of reducing the number of nodes in the grid without compromising the accuracy of the solution. (C) 2013 Elsevier Ltd. All rights reserved.

Some applications of fractional calculus in engineering

Fractional Calculus FC goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses FC in the study of system dynamics and control. In this perspective, this paper investigates the use of FC in the fields of controller tuning, legged robots, redundant robots, heat diffusion, and digital circuit synthesis.

Electrical skin phenomena: a fractional calculus analysis

The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects of the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal.

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.

Evidences for direct magnetic patterning via diffusive transformations using femtosecond laser interferometry

The application of femtosecond laser interferometry to direct patterning of thin-film magnetic alloys is demonstrated. The formation of stripe gratings with submicron periodicities is achieved in Fe1-xVx (x=18-34wt. %) layers, with a difference in magnetic moments up to Delta mu/mu similar to 20 between adjacent stripes but without any significant development of the topographical relief (<1% of the film thickness). The produced gratings exhibit a robust effect of their anisotropy shape on magnetization curves in the film plane. The obtained data witness ultrafast diffusive transformations associated with the process of spinodal decomposition and demonstrate an opportunity for producing magnetic nanostructures with engineered properties upon this basis.

Chaînes opératoires and resource-exploitation strategies in chimpanzee (Pan troglodytes) nut cracking

Journal of Human Evolution, V. 55, pp. 148-163

The influence of sludge characteristics from fullscale MBR in membrane filterability

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para a obtenção do grau de Mestre em Engenharia do Ambiente,perfil Sanitária