Development of fractional order capacitors based on electrolyte processes

In recent years, significant research in the field of electrochemistry was developed. The performance of electrical devices, depending on the processes of the electrolytes, was described and the physical origin of each parameter was established. However, the influence of the irregularity of the electrodes was not a subject of study and only recently this problem became relevant in the viewpoint of fractional calculus. This paper describes an electrolytic process in the perspective of fractional order capacitors. In this line of thought, are developed several experiments for measuring the electrical impedance of the devices. The results are analyzed through the frequency response, revealing capacitances of fractional order that can constitute an alternative to the classical integer order elements. Fractional order electric circuits are used to model and study the performance of the electrolyte processes.

Fractional control of heat diffusion systems

The concept of differentiation and integration to non-integer order has its origins in the seventeen century. However, only in the second-half of the twenty century appeared the first applications related to the area of control theory. In this paper we consider the study of a heat diffusion system based on the application of the fractional calculus concepts. In this perspective, several control methodologies are investigated and compared. Simulations are presented assessing the performance of the proposed fractional-order algorithms.

Fractional electrical impedances in botanical elements

Fractional calculus (FC) is no longer considered solely from a mathematical viewpoint, and is now applied in many emerging scientific areas, such as electricity, magnetism, mechanics, fluid dynamics, and medicine. In the field of dynamical systems, significant work has been carried out proving the importance of fractional order mathematical models. This article studies the electrical impedance of vegetables and fruits from a FC perspective. From this line of thought, several experiments are developed for measuring the impedance of botanical elements. The results are analyzed using Bode and polar diagrams, which lead to electrical circuit models revealing fractional-order behaviour.

Using fractional derivatives for the joint ontrol of hexapod robots

This article studies several Fractional Order Control algorithms used for joint control of a hexapod robot. Both Padé and series approximations to the fractional derivative are considered for the control algorithm. The walking performance is evaluated through two indices: The mean absolute density of energy used per unit distance travelled, and the control effort. A set of simulation experiments reveals the influence of the different approximations upon the proposed indices. The results show that the fractional proportional and derivative algorithm, implemented using the Padé approximation with a small number of terms, gives the best results.

Fractional dynamics in the trajectory control of redundant manipulators

Under the pseudoinverse control, robots with kinematical redundancy exhibit an undesirable chaotic joint motion which leads to an erratic behavior. This paper studies the complexity of fractional dynamics of the chaotic response. Fourier and wavelet analysis provides a deeper insight, helpful to know better the lack of repeatability problem of redundant manipulators. This perspective for the study of the chaotic phenomena will permit the development of superior trajectory control algorithms.

Performance of fractional PID algorithms controlling nonlinear systems with saturation and backlash phenomena

The development of fractional-order controllers is currently one of the most promising fields of research. However, most of the work in this area addresses the case of linear systems. This paper reports on the analysis of fractional-order control of nonlinear systems. The performance of discrete fractional-order PID controllers in the presence of several nonlinearities is discussed. Some results are provided that indicate the superior robustness of such algorithms.

Analysis of the Van der Pol oscillator containing derivatives of fractional order

In this paper a modified version of the classical Van der Pol oscillator is proposed, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, using phase portraits, spectral analysis and bifurcation diagrams. The fractional-order dynamics is illustrated through numerical simulations of the proposed schemes using approximations to fractional-order operators. Finally, the analysis is extended to the forced Van der Pol oscillator.

Fractional order electromagnetics

The Maxwell equations constitute a formalism for the development of models describing electromagnetic phenomena. The four Maxwell laws have been adopted successfully in many applications and involve only the integer order differential calculus. Recently, a closer look for the cases of transmission lines, electrical motors and transformers, that reveal the so-called skin effect, motivated a new perspective towards the replacement of classical models by fractional-order mathematical descriptions. Bearing these facts in mind this paper addresses the concept of static fractional electric potential. The fractional potential was suggested some years ago. However, the idea was not fully explored and practical methods of implementation were not proposed. In this line of thought, this paper develops a new approximation algorithm for establishing the fractional order electrical potential and analyzes its characteristics.

Time domain design of fractional differintegrators using least-squares

In this paper we propose the use of the least-squares based methods for obtaining digital rational approximations (IIR filters) to fractional-order integrators and differentiators of type sα, α∈R. Adoption of the Padé, Prony and Shanks techniques is suggested. These techniques are usually applied in the signal modeling of deterministic signals. These methods yield suboptimal solutions to the problem which only requires finding the solution of a set of linear equations. The results reveal that the least-squares approach gives similar or superior approximations in comparison with other widely used methods. Their effectiveness is illustrated, both in the time and frequency domains, as well in the fractional differintegration of some standard time domain functions.

Immunofluorescent antibody to rotavirus and antigen excretion in infantile acute diarrhoea

A serological study was carried out to evaluate the causal relationship of acute diarrhoea and rotavirus in children under five years of age. The rotaviral infection was demonstrated in paired sera by determining the antibody titers by immunofluorescence test (IF). Bovine rotavirus-infected MA-104 cell culture was used as substratum for IF. Out of 80 paired sera it was shown that 23 (28.75%) presented seroconversion, 19 (23.75%) samples showed a twofold increase in their titers and 38 (47.5%) had no increase in rotavirus antibody. This result is discussed on the light of previously obtained results on viral antigen detection by counterimmunoelectrosmophoresis (CIEOP).

New insights into pseudo-fractional ARMA modelling

Proceedings of the International Conference on Computational Cybernetics, Vienna University of Technology, August 30 - September 1, 2004

Fractional central differences and derivatives

Journal of Vibration and Control, 14(9–10): 1255–1266, 2008

Fractional Dynamics of Computer Virus Propagation

We propose a fractional model for computer virus propagation. The model includes the interaction between computers and removable devices. We simulate numerically the model for distinct values of the order of the fractional derivative and for two sets of initial conditions adopted in the literature. We conclude that fractional order systems reveal richer dynamics than the classical integer order counterpart. Therefore, fractional dynamics leads to time responses with super-fast transients and super-slow evolutions towards the steady-state, effects not easily captured by the integer order models.

Herpes simplex virus type 2 infection in pregnancy: asymptomatic viral excretion at delivery and seroepidemiologic survey of two socioeconomically distinct populations in São Paulo, Brazil

The objective of the present study was to estimate the prevalence of herpes simplex virus type 2 (HSV 2) antibodies in child bearing women of 2 Brazilian populations with different socioeconomic status and to determine the risk of neonatal HSV exposure by means of maternal cultures at the onset of labor. The study was conducted at 2 hospitals: A, serving very low income patients and B, serving middle socioeconomic class. 173 participants from group A and 127 from B answered a questionnaire which showed that the patients had similar ages (27.7 and 26.8 years, respectively) but differed with regard to socioeconomic status, age at first intercourse (18.6 vs 20.6 years), number of sex partners (1.5 vs 1.2) and previous sexually transmitted diseases (15% vs. 1.5%). History of genital herpes was given by 11% of group A participants and by a similar number, 7%, of patients from group B. In addition, 200 serum samples from population A and 455 from B were tested by ELISA for and HSV antibodies and 92% and 86%, respectively, were found to be positive. Sixty seropositive samples from group A and 90 from B were further analyzed by Western blot, which showed the presence of type 2 specific antibodies in 46% and 36%, respectively, suggesting an overall HSV 2 prevalence of 42% in group A and 31% in B. Cervical specimens were obtained for culture from 299 asymptomatic patients of population A and 313 of B. HSV was isolated from one specimen in each group, indicating a 0.3% incidence of asymptomatic viral excretion in both populations. In conclusion, the prevalence of type 2 antibodies in childbearing women was very high, but it did not differ with the socioeconomic status. The risk of HSV perinatal transmission was also similar in the 2 study populations and it was comparable with the data from developed countries. Our findings do not indicate the need of special screening programs for asymptomatic HSV excretion in Brazilian pregnant women.

A fractional perspective to financial indices

The application of mathematical methods and computer algorithms in the analysis of economic and financial data series aims to give empirical descriptions of the hidden relations between many complex or unknown variables and systems. This strategy overcomes the requirement for building models based on a set of ‘fundamental laws’, which is the paradigm for studying phenomena usual in physics and engineering. In spite of this shortcut, the fact is that financial series demonstrate to be hard to tackle, involving complex memory effects and a apparently chaotic behaviour. Several measures for describing these objects were adopted by market agents, but, due to their simplicity, they are not capable to cope with the diversity and complexity embedded in the data. Therefore, it is important to propose new measures that, on one hand, are highly interpretable by standard personal but, on the other hand, are capable of capturing a significant part of the dynamical effects.