Complex order van der Pol oscillator

In this paper a complex-order van der Pol oscillator is considered. The complex derivative Dα±ȷβ , with α,β∈R + is a generalization of the concept of integer derivative, where α=1, β=0. By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values of the periodic solutions of the two versions of the complex-order van der Pol oscillator are studied for variation of these parameters. Fourier transforms of the periodic solutions of the two oscillators are also analyzed.

Complex order biped rhythms

Animal locomotion is a complex process, involving the central pattern generators (neural networks, located in the spinal cord, that produce rhythmic patterns), the brainstem command systems, the steering and posture control systems and the top layer structures that decide which motor primitive is activated at a given time. Pinto and Golubitsky studied an integer CPG model for legs rhythms in bipeds. It is a four-coupled identical oscillators' network with dihedral symmetry. This paper considers a new complex order central pattern generator (CPG) model for locomotion in bipeds. A complex derivative Dα±jβ, with α, β ∈ ℜ+, j = √-1, is a generalization of the concept of an integer derivative, where α = 1, β = 0. Parameter regions where periodic solutions, identified with legs' rhythms in bipeds, occur, are analyzed. Also observed is the variation of the amplitude and period of periodic solutions with the complex order derivative.

Adaptive tackling of the swinging problem for a 2 DOF crane – payload system

The control of a crane carrying its payload by an elastic string corresponds to a task in which precise, indirect control of a subsystem dynamically coupled to a directly controllable subsystem is needed. This task is interesting since the coupled degree of freedom has little damping and it is apt to keep swinging accordingly. The traditional approaches apply the input shaping technology to assist the human operator responsible for the manipulation task. In the present paper a novel adaptive approach applying fixed point transformations based iterations having local basin of attraction is proposed to simultaneously tackle the problems originating from the imprecise dynamic model available for the system to be controlled and the swinging problem, too. The most important phenomenological properties of this approach are also discussed. The control considers the 4th time-derivative of the trajectory of the payload. The operation of the proposed control is illustrated via simulation results.

Fractional central pattern generators for bipedal locomotion

Locomotion has been a major research issue in the last few years. Many models for the locomotion rhythms of quadrupeds, hexapods, bipeds and other animals have been proposed. This study has also been extended to the control of rhythmic movements of adaptive legged robots. In this paper, we consider a fractional version of a central pattern generator (CPG) model for locomotion in bipeds. A fractional derivative D α f(x), with α non-integer, is a generalization of the concept of an integer derivative, where α=1. The integer CPG model has been proposed by Golubitsky, Stewart, Buono and Collins, and studied later by Pinto and Golubitsky. It is a network of four coupled identical oscillators which has dihedral symmetry. We study parameter regions where periodic solutions, identified with legs’ rhythms in bipeds, occur, for 0<α≤1. We find that the amplitude and the period of the periodic solutions, identified with biped rhythms, increase as α varies from near 0 to values close to unity.

Effect of fractional orders in the velocity control of a servo system

The application of fractional-order PID controllers is now an active field of research. This article investigates the effect of fractional (derivative and integral) orders upon system's performance in the velocity control of a servo system. The servo system consists of a digital servomechanism and an open-architecture software environment for real-time control experiments using MATLAB/Simulink tools. Experimental responses are presented and analyzed, showing the effectiveness of fractional controllers. Comparison with classical PID controllers is also investigated.

Fractional derivatives: probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.

Using fractional derivatives for the joint ontrol of hexapod robots

This article studies several Fractional Order Control algorithms used for joint control of a hexapod robot. Both Padé and series approximations to the fractional derivative are considered for the control algorithm. The walking performance is evaluated through two indices: The mean absolute density of energy used per unit distance travelled, and the control effort. A set of simulation experiments reveals the influence of the different approximations upon the proposed indices. The results show that the fractional proportional and derivative algorithm, implemented using the Padé approximation with a small number of terms, gives the best results.

Quantificação de polifosfatos no bacalhau. Validação de um método de análise

O bacalhau (Gadus morhua) faz parte da dieta alimentar dos portugueses há vários séculos, sendo atualmente, um dos maiores consumidores deste peixe a nível mundial. Após o processo de salga, esta espécie possui características únicas como a consistência, cheiro, paladar e cor amarela. É precisamente devido à coloração do peixe que alguns produtores da Islândia, Noruega e Dinamarca requisitaram às autoridades da União Europeia (UE) a aprovação da utilização de polifosfatos no processo de salga húmida do bacalhau. Os polifosfatos são aditivos alimentares bastante usados no processamento do pescado pois previnem a oxidação dos lípidos e proteínas do músculo do bacalhau, evitando assim a indesejada mudança de cor do peixe. Apesar dos esforços da Associação dos Industriais do Bacalhau (AIB) e do governo português para a rejeição da proposta nórdica, tal não se verificou. Deste modo, no início do próximo ano já será possível a venda na UE de bacalhau com fosfatos. A quantificação do teor de fosfatos no bacalhau é geralmente efetuada por Espetrofotometria de absorção molecular no ultravioleta-visível (UV-Visível). Esta quantificação é baseada no método de determinação do fósforo total, através da hidrólise dos fosfatos a ortofosfatos com posterior medição da cor amarela, gerada pela reação destes com uma solução de molibdato-vanadato. O objetivo desta dissertação foi a validação de um método de análise para a quantificação dos polifosfatos no bacalhau. O método validado foi o descrito na norma NP 4495 para produtos de pesca e aquicultura. O desenvolvimento deste trabalho foi realizado em laboratório acreditado para águas e produtos alimentares (Equilibrium - Laboratório de Controlo de Qualidade e de Processos Lda, L0312). Foi ainda determinada a influência do teor de cloreto de sódio na quantificação dos polifosfatos e o teor de humidade, uma vez que este pode afetar o produto durante a sua comercialização. No processo de validação do método foram estudados diversos parâmetros, tais como a seletividade, linearidade, sensibilidade, limite de quantificação e precisão. Pela análise dos resultados obtidos conclui-se que o método para determinação de fosfatos no bacalhau se encontra validado, uma vez que satisfaz todas as especificações determinadas para cada parâmetro de validação avaliado.

Mitochondria are the main source and one of the targets of Pb (lead)-induced oxidative stress in the yeast Saccharomyces cerevisiae

The yeast Saccharomyces cerevisiae is a useful model organism for studying lead (Pb) toxicity. Yeast cells of a laboratory S. cerevisiae strain (WT strain) were incubated with Pb concentrations up to 1,000 μmol/l for 3 h. Cells exposed to Pb lost proliferation capacity without damage to the cell membrane, and they accumulated intracellular superoxide anion (O2 .−) and hydrogen peroxide (H2O2). The involvement of the mitochondrial electron transport chain (ETC) in the generation of reactive oxygen species (ROS) induced by Pb was evaluated. For this purpose, an isogenic derivative ρ0 strain, lacking mitochondrial DNA, was used. The ρ0 strain, without respiratory competence, displayed a lower intracellular ROS accumulation and a higher resistance to Pb compared to the WT strain. The kinetic study of ROS generation in yeast cells exposed to Pb showed that the production of O2 .− precedes the accumulation of H2O2, which is compatible with the leakage of electrons from the mitochondrial ETC. Yeast cells exposed to Pb displayed mutations at the mitochondrial DNA level. This is most likely a consequence of oxidative stress. In conclusion, mitochondria are an important source of Pb-induced ROS and, simultaneously, one of the targets of its toxicity.

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.

New findings on the dynamics of HIV and TB coinfection models

In this paper we study a model for HIV and TB coinfection. We consider the integer order and the fractional order versions of the model. Let α∈[0.78,1.0] be the order of the fractional derivative, then the integer order model is obtained for α=1.0. The model includes vertical transmission for HIV and treatment for both diseases. We compute the reproduction number of the integer order model and HIV and TB submodels, and the stability of the disease free equilibrium. We sketch the bifurcation diagrams of the integer order model, for variation of the average number of sexual partners per person and per unit time, and the tuberculosis transmission rate. We analyze numerical results of the fractional order model for different values of α, including α=1. The results show distinct types of transients, for variation of α. Moreover, we speculate, from observation of the numerical results, that the order of the fractional derivative may behave as a bifurcation parameter for the model. We conclude that the dynamics of the integer and the fractional order versions of the model are very rich and that together these versions may provide a better understanding of the dynamics of HIV and TB coinfection.

Multiple Roots of Systems of Equations by Repulsion Merit Functions

In this paper we address the problem of computing multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function. The search procedure for a global minimizer of the merit function is carried out by a metaheuristic, known as harmony search, which does not require any derivative information. The multiple roots of the system are sequentially determined along several iterations of a single run, where the merit function is accordingly modified by penalty terms that aim to create repulsion areas around previously computed minimizers. A repulsion algorithm based on a multiplicative kind penalty function is proposed. Preliminary numerical experiments with a benchmark set of problems show the effectiveness of the proposed method.

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.

Certificação de filtros em fatores de transmissão e de cerâmicas em fatores de reflexão, em colorimetria

Mestrado em Engenharia Química - Tecnologias de Protecção Ambiental

New and low cost plastic membrane electrode with low detection limits for sulfadimethoxine determination in aquaculture waters

Sulfadimethoxine (SDM) is one of the drugs, often used in the aquaculture sector to prevent the spread of disease in freshwater fish aquaculture. Its spread through the soil and surface water can contribute to an increase in bacterial resistance. It is therefore important to control this product in the environment. This work proposes a simple and low-cost potentiometric device to monitor the levels of SDM in aquaculture waters, thus avoiding its unnecessary release throughout the environment. The device combines a micropipette tip with a PVC membrane selective to SDM, prepared from an appropriate cocktail, and an inner reference solution. The membrane includes 1% of a porphyrin derivative acting as ionophore and a small amount of a lipophilic cationic additive (corresponding to 0.2% in molar ratio). The composition of the inner solution was optimized with regard to the kind and/or concentration of primary ion, chelating agent and/or a specific interfering charged species, in different concentration ranges. Electrodes constructed with inner reference solutions of 1 × 10−8 mol/L SDM and 1 × 10−4 mol/L chromate ion showed the best analytical features. Near-Nernstian response was obtained with slopes of −54.1 mV/decade, an extraordinary detection limit of 7.5 ng/mL (2.4 × 10−8 mol/L) when compared with other electrodes of the same type. The reproducibility, stability and response time are good and even better than those obtained by liquid contact ISEs. Recovery values of 98.9% were obtained from the analysis of aquaculture water samples.