Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.

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.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.

The Persistence of Memory

This paper analyzes several natural and man-made complex phenomena in the perspective of dynamical systems. Such phenomena are often characterized by the absence of a characteristic length-scale, long range correlations and persistent memory, which are features also associated to fractional order systems. For each system, the output, interpreted as a manifestation of the system dynamics, is analyzed by means of the Fourier transform. The amplitude spectrum is approximated by a power law function and the parameters are interpreted as an underlying signature of the system dynamics. The complex systems under analysis are then compared in a global perspective in order to unveil and visualize hidden relationships among them.

Dynamical Analysis and Visualization of Tornadoes Time Series

In this paper we analyze the behavior of tornado time-series in the U.S. from the perspective of dynamical systems. A tornado is a violently rotating column of air extending from a cumulonimbus cloud down to the ground. Such phenomena reveal features that are well described by power law functions and unveil characteristics found in systems with long range memory effects. Tornado time series are viewed as the output of a complex system and are interpreted as a manifestation of its dynamics. Tornadoes are modeled as sequences of Dirac impulses with amplitude proportional to the events size. First, a collection of time series involving 64 years is analyzed in the frequency domain by means of the Fourier transform. The amplitude spectra are approximated by power law functions and their parameters are read as an underlying signature of the system dynamics. Second, it is adopted the concept of circular time and the collective behavior of tornadoes analyzed. Clustering techniques are then adopted to identify and visualize the emerging patterns.

Gait Selection for Quadruped Legged Robots

This paper studies periodic gaits of quadruped locomotion systems. The purpose is to determine the best set of gait and locomotion variables for different robot velocities based on the system dynamics during walking. In this perspective, several performance measures are formulated and a set of experiments reveals the influence of the gait and locomotion variables upon those proposed indices. The results show that the locomotion parameters (β, LS and HB) should be adapted to the walking velocity in order to optimize the robot performance. Furthermore, for the case of a quadruped robot, we concluded that the gait should be adapted to VF .

Cascade Control of a Hexapod Robot

6th International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines, Catania, Italy, 17-19 September

Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus

In this paper we study several natural and man-made complex phenomena in the perspective of dynamical systems. For each class of phenomena, the system outputs are time-series records obtained in identical conditions. The time-series are viewed as manifestations of the system behavior and are processed for analyzing the system dynamics. First, we use the Fourier transform to process the data and we approximate the amplitude spectra by means of power law functions. We interpret the power law parameters as a phenomenological signature of the system dynamics. Second, we adopt the techniques of non-hierarchical clustering and multidimensional scaling to visualize hidden relationships between the complex phenomena. Third, we propose a vector field based analogy to interpret the patterns unveiled by the PL parameters.

Fractional State Space Analysis of Temperature Time Series

Atmospheric temperatures characterize Earth as a slow dynamics spatiotemporal system, revealing long-memory and complex behavior. Temperature time series of 54 worldwide geographic locations are considered as representative of the Earth weather dynamics. These data are then interpreted as the time evolution of a set of state space variables describing a complex system. The data are analyzed by means of multidimensional scaling (MDS), and the fractional state space portrait (fSSP). A centennial perspective covering the period from 1910 to 2012 allows MDS to identify similarities among different Earth’s locations. The multivariate mutual information is proposed to determine the “optimal” order of the time derivative for the fSSP representation. The fSSP emerges as a valuable alternative for visualizing system dynamics.

Assessing self-organization and emergence in Evolvable Assembly Systems (EAS)

Dissertação para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores

Analysis of a controversial decision process: the case of the pumped hydro storage power plant Atdorf in Germany

Based on the report for the unit “Métodos Interactivos de Participação e Decisão A” (Interactive methods of participation and decision A), coordinated by Prof. Lia Maldonado Teles de Vasconcelos and Prof. Nuno Miguel Ribeiro Videira Costa. This unit was provided for the PhD Program in Technology Assessment in 2015/2016.

Modern piracy

A definição de pirataria ou a desmistificação da sua origem, no tempo e espaço, revela maiores dificuldades do que atualmente. Com este trabalho propusemo-nos a estudar como é que a pirataria era perpetrada e entendida no passado, bem como no presente. Também nos propomos a identificar limitações legais e as medidas operativas no combate à pirataria, como por exemplo: limites conceptuais, lacunas, estratégias, entre outros. Por outro lado, atendemos as soluções encontradas no combate à pirataria sem deixar de observar fraqueza da lei e conflitos entre jurisdições. Por fim, o curso da história dá-nos a seguinte percepção: a pirataria era tida como crime se fosse contra os interesses das nações. O desinteresse dos Estados para reprimir a pirataria possibilitou o seu aumento, proliferação, domínio e sofisticação em certas regiões do Mundo. O presente trabalho tem como objetivo trazer para o centro da discussão os direitos humanos numa perspetiva tripla: proibição da pirataria, supressão e raízes, aliando o estudo de possíveis respostas a dar a esta epidemia.

Pure elastic contact force models

"Series: Solid mechanics and its applications, vol. 226"

Multibody systems formulation

"Series: Solid mechanics and its applications, vol. 226"

Improving the effort concept: a revision of the traditional approach in the context of controlled Dynamic Stochastic Environments

The objective of this paper is to re-evaluate the attitude to effort of a risk-averse decision-maker in an evolving environment. In the classic analysis, the space of efforts is generally discretized. More realistic, this new approach emploies a continuum of effort levels. The presence of multiple possible efforts and performance levels provides a better basis for explaining real economic phenomena. The traditional approach (see, Laffont, J. J. & Tirole, J., 1993, Salanie, B., 1997, Laffont, J.J. and Martimort, D, 2002, among others) does not take into account the potential effect of the system dynamics on the agent's behavior to effort over time. In the context of a Principal-agent relationship, not only the incentives of the Principal can determine the private agent to allocate a good effort, but also the evolution of the dynamic system. The incentives can be ineffective when the environment does not incite the agent to invest a good effort. This explains why, some effici