Approximating fractional derivatives in the perspective of system control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.

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 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.

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.

New insights into pseudo-fractional ARMA modelling

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

Internet Geography: Spaces of Innovation

Information Society plays an important role in all kinds of human activity, inducing new forms of economic and social organization and creating knowledge. Over the last twenty years of the 20th century, large investments in telecommunication networks were made to approach economies and put an end to the asymmetries. The most isolated regions were the beneficiaries of this new technological investment’s wave disseminating trough the territories. The new economic scenarios created by globalisation make high capacity backbones and coherent information society polity, two instruments that could change regions fate and launch them in to an economic development context. Technology could bring international projection to services, products and could be the differentiating element between a national and an international economic strategy. So, the networks and its fluxes are becoming two of the most important variables to the economies. Measuring and representing this new informational accessibility, mapping new communities, finding new patterns and localisation models, could be today’s challenge. In the physical/real space, location is defined by two or three geographical co-ordinates. In the network/virtual space or in cyberspace, geography seems incapable to define location, because it doesn’t have a good model. Trying to solve the problem and based on geographical theories and concepts, new fields of study came to light. Internet Geography is one example. In this paper and using Internet Geography and informational cartography, it was possible to observe and analyse the spacialisation of the Internet phenomenon trough the distribution of the IP addresses in the Portuguese territory. This work shows the great potential and applicability of this indicator to regional development studies, and at the same time. The IP address distribution of Country Code Top Level Domains (.pt for Portugal) could show the same economic patterns, reflecting territorial inflexibility or, by opposition, new regional hierarchies. The spatial concentration or dispersion of top level domains seems to be a good instrument to analyse the info-structural dynamic and economic development of a territory, especially at regional level. At the same time it shows that information technologies are essential to innovation and competitive advantage.

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.

Laser-induced diffusion decomposition in Fe-V thin-film alloys

We investigate the origin of ferromagnetism induced in thin-film (similar to 20 nm) Fe-V alloys by their irradiation with subpicosecond laser pulses. We find with Rutherford backscattering that the magnetic modifications follow a thermally stimulated process of diffusion decomposition, with formation of a-few-nm-thick Fe enriched layer inside the film. Surprisingly, similar transformations in the samples were also found after their long-time (similar to 10(3) s) thermal annealing. However, the laser action provides much higher diffusion coefficients (similar to 4 orders of magnitude) than those obtained under standard heat treatments. We get a hint that this ultrafast diffusion decomposition occurs in the metallic glassy state achievable in laser-quenched samples. This vitrification is thought to be a prerequisite for the laser-induced onset of ferromagnetism that we observe. 2014 Elsevier B.V. All rights reserved.

Real-time scheduling with resource sharing on heterogeneous multiprocessors

Consider the problem of scheduling a task set τ of implicit-deadline sporadic tasks to meet all deadlines on a t-type heterogeneous multiprocessor platform where tasks may access multiple shared resources. The multiprocessor platform has m k processors of type-k, where k∈{1,2,…,t}. The execution time of a task depends on the type of processor on which it executes. The set of shared resources is denoted by R. For each task τ i , there is a resource set R i ⊆R such that for each job of τ i , during one phase of its execution, the job requests to hold the resource set R i exclusively with the interpretation that (i) the job makes a single request to hold all the resources in the resource set R i and (ii) at all times, when a job of τ i holds R i , no other job holds any resource in R i . Each job of task τ i may request the resource set R i at most once during its execution. A job is allowed to migrate when it requests a resource set and when it releases the resource set but a job is not allowed to migrate at other times. Our goal is to design a scheduling algorithm for this problem and prove its performance. We propose an algorithm, LP-EE-vpr, which offers the guarantee that if an implicit-deadline sporadic task set is schedulable on a t-type heterogeneous multiprocessor platform by an optimal scheduling algorithm that allows a job to migrate only when it requests or releases a resource set, then our algorithm also meets the deadlines with the same restriction on job migration, if given processors 4×(1+MAXP×⌈|P|×MAXPmin{m1,m2,…,mt}⌉) times as fast. (Here MAXP and |P| are computed based on the resource sets that tasks request.) For the special case that each task requests at most one resource, the bound of LP-EE-vpr collapses to 4×(1+⌈|R|min{m1,m2,…,mt}⌉). To the best of our knowledge, LP-EE-vpr is the first algorithm with proven performance guarantee for real-time scheduling of sporadic tasks with resource sharing on t-type heterogeneous multiprocessors.

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.

Rhapsody in fractional

This paper studies several topics related with the concept of “fractional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabilities, fractional delay discrete-time linear systems, and fractional Fourier transform.

Riesz potential versus fractional Laplacian

This paper starts by introducing the Grünwald–Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied. It is presented as a fractional version of the Cauchy–Riemann conditions and, finally, it is discussed with the n-dimensional Laplacian.

Delay approximation of fractional integrals

This paper explores the calculation of fractional integrals by means of the time delay operator. The study starts by reviewing the memory properties of fractional operators and their relationship with time delay. Based on the time response of the Mittag-Leffler function an approximation of fractional integrals consisting of time delayed samples is proposed. The tuning of the approximation is optimized by means of a genetic algorithm. The results demonstrate the feasibility of the new perspective and the limits of their application.

Simulation of wave action on a moored container carrier inside Sines’ Harbour

The integrated numerical tool SWAMS (Simulation of Wave Action on Moored Ships) is used to simulate the behavior of a moored container carrier inside Sines’ Harbour. Wave, wind, currents, floating ship and moorings interaction is discussed. Several case scenarios are compared differing in the layout of the harbour and wind and wave conditions. The several harbour layouts correspond to proposed alternatives for the future expansion of Sines’ terminal XXI that include the extension of the East breakwater and of the quay. Additionally, the influence of wind on the behavior of the ship moored and the introduction of pre tensioning the mooring lines was analyzed. Hydrodynamic forces acting on the ship are determined using a modified version of the WAMIT model. This modified model utilizes the Haskind relations and the non-linear wave field inside the harbour obtained with finite element numerical model, BOUSS-WMH (Boussinesq Wave Model for Harbors) to get the wave forces on the ship. The time series of the moored ship motions and forces on moorings are obtained using BAS solver. © 2015 Taylor & Francis Group, London.

Evaluation of the double diffusion, enzyme immunoassay and immunoblotting techniques, for the diagnosis of human hydatid disease in tropical areas

Hydatid disease in tropical areas poses a serious diagnostic problem due to the high frequence of cross-reactivity with other endemic helminthic infections. The enzyme-linked-immunosorbent assay (ELISA) and the double diffusion arc 5 showed respectively a sensitivity of 73% and 57% and a specificity of 84-95% and 100%. However, the specificity of ELISA was greatly increased by using ovine serum and phosphorylcholine in the diluent buffer. The hydatic antigen obtained from ovine cyst fluid showed three main protein bands of 64,58 and 30 KDa using SDS PAGE and immunoblotting. Sera from patients with onchocerciasis, cysticercosis, toxocariasis and Strongyloides infection cross-reacted with the 64 and 58 KDa bands by immunoblotting. However, none of the analyzed sera recognized the 30 KDa band, that seems to be specific in this assay. The immunoblotting showed a sensitivity of 80% and a specificity of 100% when used to recognize the 30 KDa band.