ISEL - Matemática - Comunicações
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- Allee effect bifurcation in the γ-Ricker population model using the Lambert W functionPublication . Rocha, J. Leonel; Taha, Abdel-KaddousThe main purpose of this talk is to present the dynamical study and the bifurcation structures of the γ-Ricker population model. Resorting to the Lambert W function, the analytical solutions of the positive fixed point equation for the γ-Ricker population model are explicitly presented and conditions for the existence and stability of these fixed points are established. Another main focus of this work is the definition and characterization of the Allee effect bifurcation for the γ-Ricker population model, which is not a pitchfork bifurcation. Consequently, we prove that the phenomenon of Allee effect for the γ-Ricker population model is associated to the asymptotic behavior of the Lambert W function in a neighborhood of zero. Numerical studies are included.
- Allee's dynamics and bifurcation structures in von Bertalanffy's population size functionsPublication . Rocha, J. Leonel; Taha, Abdel-Kaddous; Fournier-Prunaret, D.The interest and the relevance of the study of the population dynamics and the extinction phenomenon are our main motivation to investigate the induction of Allee Effect in von Bertalanffy's population size functions. The adjustment or correction factor of rational type introduced allows us to analyze simultaneously strong and weak Allee's functions and functions with no Allee effect, whose classification is dependent on the stability of the fixed point x = 0. This classification is founded on the concepts of strong and weak Allee's effects to the population growth rates associated. The transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, is verified with the evolution of the rarefaction critical density or Allee's limit. The existence of cusp points on a fold bifurcation curve is related to this phenomenon of transition on Allee's dynamics. Moreover, the "foliated" structure of the parameter plane considered is also explained, with respect to the evolution of the Allee limit. The bifurcation analysis is based on the configurations of fold and flip bifurcation curves. The chaotic semistability and the nonadmissibility bifurcation curves are proposed to this family of 1D maps, which allow us to define and characterize the corresponding Allee effect region.
- Allee's dynamics and bifurcation structures in von Bertalanffy's population size functionsPublication . Rocha, J. Leonel; Taha, Abdel-Kaddous; Fournier-Prunaret, D.The interest and the relevance of the study of the population dynamics and the extinction phenomenon are our main motivation to investigate the induction of Allee Effect in von Bertalanffy's population size functions. The adjustment or correction factor of rational type introduced allows us to analyze simultaneously strong and weak Allee's functions and functions with no Allee effect, whose classification is dependent on the stability of the fixed point x = 0. This classification is founded on the concepts of strong and weak Allee's effects to the population growth rates associated. The transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, is verified with the evolution of the rarefaction critical density or Allee's limit. The existence of cusp points on a fold bifurcation curve is related to this phenomenon of transition on Allee's dynamics. Moreover, the "foliated" structure of the parameter plane considered is also explained, with respect to the evolution of the Allee limit. The bifurcation analysis is based on the configurations of fold and flip bifurcation curves. The chaotic semistability and the nonadmissibility bifurcation curves are proposed to this family of 1D maps, which allow us to define and characterize the corresponding Allee effect region.
- An algorithm for constrained optimization with applications to the design of mechanical structuresPublication . Barbarosie, Cristian; Lopes, Sérgio; Toader, Anca-MariaWe propose an algorithm for minimizing a functional under constraints. It uses _rst order derivatives of both the objective function and the constraints. The step is computed as a sum between a steepest descent step (which minimizes the objective functional) and a correction step related to the Newton method (which aims to solve the equality constraints). The linear combination between these two steps envolves coefficients similar to Lagrange multipliers which are computed in a natural way based on the Newton method. The algorithm uses no projection and thus the iterates are not feasible; the constraints are only satis_ed in the limit (after convergence). Although the algorithm can be used as a general-purpose optimization tool, it is designed speci_cally for problems where _rst order derivatives of both objective and constraint functionals are available but not second order derivatives (as is often the case in structural optimization).
- Application of multiobjective optimization based on differences of modal displacements and modal rotations for damage quantification in beamsPublication . Santos, J. V. Araújo dos; J.F.A. Madeira; Lopes, H.; Moreno-García, P.This paper presents an application of multiobjective optimization for the damage quantification in beams. The simulation of damage relies on the finite element analysis of Euler-Bernoulli beams and is carried out by considering a reduction in the Young`s modulus of specific elements. The damage is quantified by minimizing two objective functions. These two functions are based on the difference in the Frobenius norm of matrices containing the modal displacements and the modal rotations of a beam in the undamaged and damaged states. The solution of the optimization problem thus defined is solved by a direct multisearch algorithm, which is an extension of the direct search algorithm to multiobjective optimization. This algorithm does not need any derivatives information about the objective functions. The validity, robustness and efficiency of the present application is tested for different boundary conditions of the damaged beam and high levels of noise in the simulated measured data.
- Assessing parametric uncertainty on fibre reinforced composite laminatesPublication . Carvalho, A.; Silva, T. A. N.; Loja, AméliaWhen modeling a composite structure it is important to take into account its greater exposition to parametric variability, when compared to other types of materials more traditionally used. The possibility to tailor composite materials according to specific requisites is simultaneously a source of additional variability, which origin may be associated to material and to geometrical characteristics. Regardless the origin of this variability, they will produce its effect in the structure response, thus it is very important to anticipate them and to quantify them as much as possible. With the present work, it is intended to assess and quantify the influence of geometrical parameters variabilities on the composite structural response. Behind this characterization, linear static analyses were performed, considering that the layers’ thicknesses and fibre orientation angles will be affected by uncertainty. A set of simulations and numerical results are presented and discussed.
- Clustering stability and ground truth: numerical experimentsPublication . Amorim, Maria José; Cardoso, Maria MargaridaStability has been considered an important property for evaluating clustering solutions. Nevertheless, there are no conclusive studies on the relationship between this property and the capacity to recover clusters inherent to data ("ground truth"). This study focuses on this relationship resorting to synthetic data generated under diverse scenarios (controlling relevant factors). Stability is evaluated using a weighted cross-validation procedure. Indices of agreement (corrected for agreement by chance) are used both to assess stability and external validation. The results obtained reveal a new perspective so far not mentioned in the literature. Despite the clear relationship between stability and external validity when a broad range of scenarios is considered, within-scenarios conclusions deserve our special attention: faced with a specific clustering problem (as we do in practice), there is no significant relationship between stability and the ability to recover data clusters.
- Damping optimization of viscoelastic laminated sandwich structures using the direct multisearch methodPublication . J.F.A. Madeira; Araújo, A. L.; Soares, C. M. Mota; Soares, C. A. MotaA multiobjective approach for optimization of passive damping for vibration reduction in sandwich structures is presented in this paper. A layerwise finite element model for sandwich plates with viscoelastic core and anisotropic laminated face layers is used along with the complex modulus approach and the dynamic problem is solved in the frequency domain. Constrained optimization is conducted for maximisation of modal loss factors and minimisation of weight of sandwich beams and plates with elastic laminated constraining layers and a viscoelastic core, with layer thickness and laminate layer ply orientation angles as design variables. The problem is solved using the Direct MultiSearch (DMS) solver for derivative-free multiobjective optimization and solutions are compared with alternative ones obtained using genetic algorithms. DMS is a solver for multiobjective optimization problems which does not use any derivatives of the objective functions. It is based on a novel technique called direct multisearch, developed by extending direct search from single to multiobjective optimisation.
- Detection and adsorption of Triclosan on sensors based on PAH/PVS thin-filmsPublication . Pereira-da-Silva, J.; Zagalo, P. M..; Magro, Cátia; Pinto, Iola; Ribeiro, P. A.; Raposo, MariaGiven the vital role of water in life it is paramount to thrive and succeed in areas that look to clean and prevent further contamination in water bodies. Triclosan (TCS) is present in most of our day-to-day products and if left unchecked it can lead to long-term significant problems due to its many inauspicious effects in both human and animal health. Thus arose the need to develop sensors to detect and possibly remove TCS for aqueous solutions. This work was rooted on this premise and sensors based on LbL polyectrolyte thin-films were developed, such as poly(allylamine hydrochloride) (PAH) and poly(vinylsulfonic acid, sodium salt) (PVS), namely (PAH/PVS)(10) and (PAH/PVS)/PAH(10). The goal of this work was to analyze the amount of TCS adsorbed onto reused (PAH/PVS)(10) and (PAH/PVS)/PAH(10) LbL thin-films when immersed in TCS aqueous solutions with decreasing pH. It was demonstrated that sensors with an outer layer of PAH led to a significantly better TCS molecules adsorption (removal). Additionally, sensors composed of (PAH/PVS)(10) presented higher sensibility in discriminating TCS solutions with concentrations between 10(-5) M and 10(-8) M, using impedance spectroscopy.
- Electricity spot prices structural changes in the Iberian electricity marketPublication . Bolas, João; Sousa, Jorge A. M.; Martins, Ana Alexandra; Lagarto, JoãoIn recent years, the power sector has undergone a restructuring process in many economies in the world. This movement towards liberalization led to the establishment of electricity markets that promote the competitiveness of the production and trading segments of the power sector. In these markets, the agents have to deal with frequent electricity price changes leading to different strategies in their daily bidding behavior. There are a set of variables that can have an impact in the electricity price definition, such as: fuel prices, CO 2 emissions prices, electricity production and demand. This paper proposes to analyze structural changes in the Iberian electricity market price between two periods of time: 2007/2008 and 2010/2011. For this purpose, three quantitative analysis methods were used: correlation, causality and Principal Components. Results suggest that the electricity price had a structural change between the analyzed periods, in particular the increasing importance of special regime production.