Fractional Dynamics and Control of Distributed Parameter Systems

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 a FC perspective in the study of the dynamics and control of some distributed parameter systems.

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

Fractional Dynamics in Forest Fires

Every year forest fires consume large areas, being a major concern in many countries like Australia, United States and Mediterranean Basin European Countries (e.g., Portugal, Spain, Italy and Greece). Understanding patterns of such events, in terms of size and spatiotemporal distributions, may help to take measures beforehand in view of possible hazards and decide strategies of fire prevention, detection and suppression. Traditional statistical tools have been used to study forest fires. Nevertheless, those tools might not be able to capture the main features of fires complex dynamics and to model fire behaviour [1]. Forest fires size-frequency distributions unveil long range correlations and long memory characteristics, which are typical of fractional order systems [2]. Those complex correlations are characterized by self-similarity and absence of characteristic length-scale, meaning that forest fires exhibit power-law (PL) behaviour. Forest fires have also been proved to exhibit time-clustering phenomena, with timescales of the order of few days [3]. In this paper, we study forest fires in the perspective of dynamical systems and fractional calculus (FC). Public domain forest fires catalogues, containing data of events occurred in Portugal, in the period 1980 up to 2011, are considered. The data is analysed in an annual basis, modelling the occurrences as sequences of Dirac impulses. The frequency spectra of such signals are determined using Fourier transforms, and approximated through PL trendlines. The PL parameters are then used to unveil the fractional-order dynamics characteristics of the data. To complement the analysis, correlation indices are used to compare and find possible relationships among the data. It is shown that the used approach can be useful to expose hidden patterns not captured by traditional tools.

Symmetry and order parameter dynamics of the human odometer

Bipedal gaits have been classified on the basis of the group symmetry of the minimal network of identical differential equations (alias cells) required to model them. Primary bipedal gaits (e.g., walk, run) are characterized by dihedral symmetry, whereas secondary bipedal gaits (e.g., gallop-walk, gallop- run) are characterized by a lower, cyclic symmetry. This fact has been used in tests of human odometry (e.g., Turvey et al. in P Roy Soc Lond B Biol 276:4309–4314, 2009, J Exp Psychol Hum Percept Perform 38:1014–1025, 2012). Results suggest that when distance is measured and reported by gaits from the same symmetry class, primary and secondary gaits are comparable. Switching symmetry classes at report compresses (primary to secondary) or inflates (secondary to primary) measured distance, with the compression and inflation equal in magnitude. The present research (a) extends these findings from overground locomotion to treadmill locomotion and (b) assesses a dynamics of sequentially coupled measure and report phases, with relative velocity as an order parameter, or equilibrium state, and difference in symmetry class as an imperfection parameter, or detuning, of those dynamics. The results suggest that the symmetries and dynamics of distance measurement by the human odometer are the same whether the odometer is in motion relative to a stationary ground or stationary relative to a moving ground.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

The effect of adhesive thickness on the mechanical behavior of a structural polyurethane adhesive

One parameter that influences the adhesively bonded joints performance is the adhesive layer thickness. Hence, its effect has to be investigated experimentally and should be taken into consideration in the design of adhesive joints. Most of the results from literature are for typical structural epoxy adhesives which are generally formulated to perform in thin sections. However, polyurethane adhesives are designed to perform in thicker sections and might have a different behavior as a function of adhesive thickness. In this study, the effect of adhesive thickness on the mechanical behavior of a structural polyurethane adhesive was investigated. The mode I fracture toughness of the adhesive was measured using double-cantilever beam (DCB) tests with various thicknesses of the adhesive layer ranging from 0.2 to 2 mm. In addition, single lap joints (SLJs) were fabricated and tested to assess the influence of adhesive thickness on the lap-shear strength of the adhesive. An increasing fracture toughness with increasing adhesive thickness was found. The lap-shear strength decreases as the adhesive layer gets thicker, but in contrast to joints with brittle adhesives the decrease trend was less pronounced.

Structural adhesives modified with thermally expandable particles

In this study, the behaviour of two structural adhesives modified with thermally expandable particles (TEPs) was investigated as a preliminary study for further investigations on the potential of TEPs in adhesive joints. Tensile bulk tests were performed to get the tensile properties of the adhesives and TEPs-modified adhesives. In order to determine the expansion temperature of the particles while encapsulated in these particular adhesive systems, the variation of the volume of adhesive samples modified with different TEPs concentration as a function of temperature was measured. Further, the possibility of any chemical interactions between TEPs and adhesives matrix in the TEPs-modified specimens was verified by a Fourier transform infrared spectroscopy analysis. Finally, the fracture surfaces of the unmodified and TEPs-modified specimens, as well as the dispersion and the morphology of the particles, were examined by a scanning electron microscopy analysis. It was found that the stiffness of the TEPs-modified adhesives is not affected by incorporation of TEPs in the adhesives matrix, while the tensile yield strength decreased by increasing the wt% TEPs content. In applications of such particular materials (TEPs-modified adhesives), the temperature should be controlled to stay between 90°C and 120°C in order to obtain the highest expansion ratio. At a lower temperature, not all the particles will expand, and above, the TEPs will deteriorate and as a result the TEPs-modified adhesives will deteriorate.

Biosynthesis-Assisted Structural Elucidation of the Bartolosides, Chlorinated Aromatic Glycolipids from Cyanobacteria

The isolation of the bartolosides, unprecedented cyanobacterial glycolipids featuring aliphatic chains with chlorine substituents and C-glycosyl moieties, is reported. Their chlorinated dialkylresorcinol (DAR) core presented a major structural-elucidation challenge. To overcome this, we discovered the bartoloside (brt) biosynthetic gene cluster and linked it to the natural products through in vitro characterization of the DAR-forming ketosynthase and aromatase. Bioinformatic analysis also revealed a novel potential halogenase. Knowledge of the bartoloside biosynthesis constrained the DAR core structure by defining key pathway intermediates, ultimately allowing us to determine the full structures of the bartolosides. This work illustrates the power of genomics to enable the use of biosynthetic information for structure elucidation.

Structural change: a brief review

This is a short summary of some aspects of structural change models, and is not intended to be comprehensive survey or review. Many important works have been left out. Also, the presentation was not intended to be rigorous nor general. It’s main purpose is only to focus on some recent developments in this area and motivate the reader to learn more.

Projecto de estruturas de uma passagem superior em madeira

Este projecto visa um estudo de uma solução para uma ponte pedonal de Madeira Lamelada Colada (MLC) entre o Hospital Pedro Hispano e o Norte-Shopping, localizada na Senhor da Hora. Inicialmente foram analisadas diversas variantes, com vários tipos de sistemas, sendo adoptada uma ponte formada por dois arcos, que se aproximam à medida que se afastam dos encontros unidos por contraventamentos em cruz. O tabuleiro encontra-se suspenso por tirantes e apoiados dos dois lados nos encontros. Foi realizado uma pequena introdução histórica da utilização da madeira enquanto material de construção, a sua fabricação e os vários tipos de pontes pedonais em MLC. O uso da madeira em estruturas fez com que a abordagem do Eurocódigo 5 (EC5) tivesse uma maior importância. A estrutura é modelada no programa de cálculo “DLUBAL ” através de um modelo de barras tridimensional de modo a efectuar uma análise estática e dinâmica global, recorrendo-se para tal a normas e princípios gerais de verificação de segurança dos regulamentos Europeus, nomeadamente os Eurocódigos das várias especialidades. Apresentam-se em anexo vários desenhos da ponte, desenhos das peças de ligação, o mapa de trabalhos e quantidades, ideias preliminares, dimensionamento e a escolha dos ligadores e por fim os diagramas de esforços dos elementos aos Estados-limite Último.

In situ measured cross section geometry of old timber structures and its influence on structural safety

Old timber structures may show significant variation in the cross section geometry along the same element, as a result of both construction methods and deterioration. As consequence, the definition of the geometric parameters in situ may be both time consuming and costly. This work presents the results of inspections carried out in different timber structures. Based on the obtained results, different simplified geometric models are proposed in order to efficiently model the geometry variations found. Probabilistic modelling techniques are also used to define safety parameters of existing timber structures, when subjected to dead and live loads, namely self-weight and wind actions. The parameters of the models have been defined as probabilistic variables, and safety of a selected case study was assessed using the Monte Carlo simulation technique. Assuming a target reliability index, a model was defined for both the residual cross section and the time dependent deterioration evolution. As a consequence, it was possible to compute probabilities of failure and reliability indices, as well as, time evolution deterioration curves for this structure. The results obtained provide a proposal for definition of the cross section geometric parameters of existing timber structures with different levels of decay, using a simplified probabilistic geometry model and considering a remaining capacity factor for the decayed areas. This model can be used for assessing the safety of the structure at present and for predicting future performance.

Active bionanoconjugates of laccase and gold nanoparticles: kinetic and structural studies

Thesis for the master degree in Structural and Functional Biochemistry

Land cover dynamics in Savanna Ecosystem of Borena Ethiopia

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Urban land cover change detection analysis and modeling spatio-temporal Growth dynamics using Remote Sensing and GIS Techniques: A case study of Dhaka, Bangladesh

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Analysis of the EEG Dynamics of Epileptic Activity in Gelastic Seizures Using Decomposition in Independent Components

Objective: Gelastic seizures are a frequent and well established manifestation of the epilepsy associated with hypothalamic hamartomas. The scalp EEG recordings very seldom demonstrate clear spike activity and the information about the ictal epilepsy dynamics is limited. In this work, we try to isolate epileptic rhythms in gelastic seizures and study their generators. Methods: We extracted rhythmic activity from EEG scalp recordings of gelastic seizures using decomposition in independent components (ICA) in three patients, two with hypothalamic hamartomas and one with no hypothalamic lesion. Time analysis of these rhythms and inverse source analysis was done to recover their foci of origin and temporal dynamics. Results: In the two patients with hypothalamic hamartomas consistent ictal delta (2–3 Hz) rhythms were present, with subcortical generators in both and a superficial one in a single patient. The latter pattern was observed in the patient with no hypothalamic hamartoma visible in MRI. The deep generators activated earlier than the superficial ones, suggesting a consistent sub-cortical origin of the rhythmical activity. Conclusions: Our data is compatible with early and brief epileptic generators in deep sub-cortical regions and more superficial ones activating later. Significance: Gelastic seizures express rhythms on scalp EEG compatible with epileptic activity originating in sub-cortical generators and secondarily involving cortical ones.