Fractional order inductive phenomena based on the skin effect

The Maxwell equations play a fundamental role in the electromagnetic theory and lead to models useful in physics and engineering. This formalism involves integer-order differential calculus, but the electromagnetic diffusion points towards the adoption of a fractional calculus approach. This study addresses the skin effect and develops a new method for implementing fractional-order inductive elements. Two genetic algorithms are adopted, one for the system numerical evaluation and another for the parameter identification, both with good results.

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.

Filtering method in backlash phenomena analysis

The behavior of robotic manipulators with backlash is analyzed. Based on the pseudo-phase plane two indices are proposed to evaluate the backlash effect upon the robotic system: the root mean square error and the fractal dimension. For the dynamical analysis the noisy signals captured from the system are filtered through wavelets. Several tests are developed that demonstrate the coherence of the results.

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.

Characterization of middle-ear condition of Oporto daycare children up-to 3 years-old: A cross sectional study

Objective The aim of this study was to determine tympanometric values of children who attend Oporto daycare centers and further analyze any relations with host and environmental factors. Methods Cross sectional study in a randomly selected sample of 117 daycare children up-to 3-years old from Oporto. Tympanometric measures were collected. Results Children presented in left ear (LE) a mean peak pressure (PP) of −156.53 daPa and a mean compliance of 0.16 cm3. Right ear (RE) revealed a PP of −145.61 daPa and a compliance of 0.19 cm3. Normal tympanograms (type A) had a lower frequency than abnormal tympanograms (type B and type C). There was a positive association between age and compliance (LE: p = 0.016; RE: p = 0.013) and between the presence of rhinorrhea and PP (LE: p = 0.002; RE: p < 0.05). Abnormal tympanograms were more frequent in Spring (RE: p = 0.009), in younger children (LE: p = 0.03) and in children that had rhinorrhea (LE: p = 0.002; RE: p = 0.044). Healthy children had a mean PP of −125.19 daPa and a mean compliance of 0.21 cm3 in LE and a mean PP of −144.27 daPa and a mean compliance of 0.22 cm3 in RE. Conclusion Tympanometric measures presented in this paper may be applicable to Oporto daycare children up-to 3 years-old. Most of daycare children revealed abnormal tympanograms. Age, rhinorrhea and season influenced children's middle-ear condition.

Analysis of Forest Fires by means of Pseudo Phase Plane and Multidimensional Scaling Methods

Forest fires dynamics is often characterized by the absence of a characteristic length-scale, long range correlations in space and time, and long memory, which are features also associated with fractional order systems. In this paper a public domain forest fires catalogue, containing information of events for Portugal, covering the period from 1980 up to 2012, is tackled. The events are modelled as time series of Dirac impulses with amplitude proportional to the burnt area. The time series are viewed as the system output and are interpreted as a manifestation of the system dynamics. In the first phase we use the pseudo phase plane (PPP) technique to describe forest fires dynamics. In the second phase we use multidimensional scaling (MDS) visualization tools. The PPP allows the representation of forest fires dynamics in two-dimensional space, by taking time series representative of the phenomena. The MDS approach generates maps where objects that are perceived to be similar to each other are placed on the map forming clusters. The results are analysed in order to extract relationships among the data and to better understand forest fires behaviour.

Distributed Sensing of Fluid Dynamic Phenomena with the XDense Sensor Grid Network

IEEE International Conference on Cyber Physical Systems, Networks and Applications (CPSNA'15), Hong Kong, China.

Fractional Order Junctions

Gottfried Leibniz generalized the derivation and integration, extending the operators from integer up to real, or even complex, orders. It is presently recognized that the resulting models capture long term memory effects difficult to describe by classical tools. Leon Chua generalized the set of lumped electrical elements that provide the building blocks in mathematical models. His proposal of the memristor and of higher order elements broadened the scope of variables and relationships embedded in the development of models. This paper follows the two directions and proposes a new logical step, by generalizing the concept of junction. Classical junctions interconnect system elements using simple algebraic restrictions. Nevertheless, this simplistic approach may be misleading in the presence of unexpected dynamical phenomena and requires including additional “parasitic” elements. The novel γ-junction includes, as special cases, the standard series and parallel connections and allows a new degree of freedom when building models. The proposal motivates the search for experimental and real world manifestations of the abstract conjectures.