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.

Exciting dynamical behavior in a network of two coupled rings of Chen oscillators

We study exotic patterns appearing in a network of coupled Chen oscillators. Namely, we consider a network of two rings coupled through a “buffer” cell, with Z3×Z5 symmetry group. Numerical simulations of the network reveal steady states, rotating waves in one ring and quasiperiodic behavior in the other, and chaotic states in the two rings, to name a few. The different patterns seem to arise through a sequence of Hopf bifurcations, period-doubling, and halving-period bifurcations. The network architecture seems to explain certain observed features, such as equilibria and the rotating waves, whereas the properties of the chaotic oscillator may explain others, such as the quasiperiodic and chaotic states. We use XPPAUT and MATLAB to compute numerically the relevant states.

Entropy analysis of integer and fractional dynamical systems

This paper investigates the adoption of entropy for analyzing the dynamics of a multiple independent particles system. Several entropy definitions and types of particle dynamics with integer and fractional behavior are studied. The results reveal the adequacy of the entropy concept in the analysis of complex dynamical systems.

Foraging at the Edge of Chaos: Internal Clock versus External Forcing

Activity rhythms in animal groups arise both from external changes in the environment, as well as from internal group dynamics. These cycles are reminiscent of physical and chemical systems with quasiperiodic and even chaotic behavior resulting from “autocatalytic” mechanisms. We use nonlinear differential equations to model how the coupling between the self-excitatory interactions of individuals and external forcing can produce four different types of activity rhythms: quasiperiodic, chaotic, phase locked, and displaying over or under shooting. At the transition between quasiperiodic and chaotic regimes, activity cycles are asymmetrical, with rapid activity increases and slower decreases and a phase shift between external forcing and activity. We find similar activity patterns in ant colonies in response to varying temperature during the day. Thus foraging ants operate in a region of quasiperiodicity close to a cascade of transitions leading to chaos. The model suggests that a wide range of temporal structures and irregularities seen in the activity of animal and human groups might be accounted for by the coupling between collectively generated internal clocks and external forcings.

The Past, Polish politics of memory, and stereotyping: an intercultural perspective

The main idea of the article is to consider the interdependence between Politics of Memory (as a type of narrating the Past) and Stereotyping. The author suggests that, in a time of information revolution, we are still constructing images of others on the basis of simplification, overestimation of association between features, and illusory correlations, instead of basing them on knowledge and personal contact. The Politics of Memory, national remembrance, and the historical consciousness play a significant role in these processes, because – as the author argues – they transform historically based 'symbolic analogies' into 'illusory correlations' between national identity and the behavior of its members. To support his theoretical investigation, the author presents results of his draft experiment and two case studies: (a) a social construction of images of neighbors based on Polish narrations about the Past; and (b) various processes of stereotyping based on the Remembrance of the Holocaust. All these considerations lead him to state that the Politics of Memory should be recognized as an influential source of commonly shared stereotypes on other cultures and nations.

Intrinsic fractal dynamics in the respiratory system by means of pressure-volume loops

This contribution presents novel concepts for analysis of pressure–volume curves, which offer information about the time domain dynamics of the respiratory system. The aim is to verify whether a mapping of the respiratory diseases can be obtained, allowing analysis of (dis)similarities between the dynamical pattern in the breathing in children. The groups investigated here are children, diagnosed as healthy, asthmatic, and cystic fibrosis. The pressure–volume curves have been measured by means of the noninvasive forced oscillation technique during breathing at rest. The geometrical fractal dimension is extracted from the pressure–volume curves and a power-law behavior is observed in the data. The power-law model coefficients are identified from the three sets and the results show that significant differences are present between the groups. This conclusion supports the idea that the respiratory system changes with disease in terms of airway geometry, tissue parameters, leading in turn to variations in the fractal dimension of the respiratory tree and its dynamics.

Reusability assessment of thermoset polymeric composite wastes as reinforcement and filler replacement for polymer concrete materials

The development and applications of thermoset polymeric composites, namely fiber reinforced polymers (FRP), have shifted in the last decades more and more into the mass market [1]. Production and consume have increased tremendously mainly for the construction, transportation and automobile sectors [2, 3]. Although the many successful uses of thermoset composite materials, recycling process of byproducts and end of lifecycle products constitutes a more difficult issue. The perceived lack of recyclability of composite materials is now increasingly important and seen as a key barrier to the development or even continued used of these materials in some markets.

An experimental study on recycling and reuse of pultruded composite material wastes

Glass fibre-reinforced plastics (GFRP) have been considered inherently difficult to recycle due to both: cross-linked nature of thermoset resins, which cannot be remoulded, and complex composition of the composite itself. Presently, most of the GFRP waste is landfilled leading to negative environmental impacts and supplementary added costs. With an increasing awareness of environmental matters and the subsequent desire to save resources, recycling would convert an expensive waste disposal into a profitable reusable material. In this study, efforts were made in order to recycle grinded GFRP waste, proceeding from pultrusion production scrap, into new and sustainable composite materials. For this purpose, GFRP waste recyclates, were incorporated into polyester based mortars as fine aggregate and filler replacements at different load contents and particle size distributions. Potential recycling solution was assessed by mechanical behaviour of resultant GFRP waste modified polymer mortars. Results revealed that GFRP waste filled polymer mortars present improved flexural and compressive behavior over unmodified polyester based mortars, thus indicating the feasibility of the GFRP industrial waste reuse into concrete-polymer composite materials.

Chaos Dynamics in the Trajectory Conjtrol of Redundant Manipulators

Nonlinear Dynamics, chaos, Control, and Their Applications to Engineering Sciences: Vol. 6 - Applications of nonlinear phenomena