Complex evolution of a multi-particle system

This paper studies a discrete dynamical system of interacting particles that evolve by interacting among them. The computational model is an abstraction of the natural world, and real systems can range from the huge cosmological scale down to the scale of biological cell, or even molecules. Different conditions for the system evolution are tested. The emerging patterns are analysed by means of fractal dimension and entropy measures. It is observed that the population of particles evolves towards geometrical objects with a fractal nature. Moreover, the time signature of the entropy can be interpreted at the light of complex dynamical systems.

Self-adaptive combination of global tabu search and local search for nonlinear equations

Solving systems of nonlinear equations is a very important task since the problems emerge mostly through the mathematical modelling of real problems that arise naturally in many branches of engineering and in the physical sciences. The problem can be naturally reformulated as a global optimization problem. In this paper, we show that a self-adaptive combination of a metaheuristic with a classical local search method is able to converge to some difficult problems that are not solved by Newton-type methods.

Double power laws, fractals and self-similarity

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.

Modelação Dinâmica de Sistemas de Drenagem Urbana. Aplicação a um caso de estudo

A crescente expansão urbana e o incremento das exigências ambientais e financeiras promovem a implementação de abordagens sustentáveis para a gestão das infraestruturas sanitárias. Assim, o recurso a instrumentos de monitorização e à modelação matemática surge como o caminho para a racionalização do investimento e a otimização dos sistemas existentes. Neste contexto, a modelação dinâmica de sistemas de drenagem urbana assume relevância para o controlo e redução dos caudais em excesso e das descargas de poluentes nos meios recetores, resultantes de um incremento significativo de afluências pluviais indevidas, de problemas de sub-dimensionamento ou falta de operação e manutenção. O objetivo da presente dissertação consiste na modelação, calibração e diagnóstico do sistema intercetor de Lordelo utilizando o software Storm Water Management Model, através dos dados recolhidos a partir do projeto de Reabilitação dos intercetores de Lordelo, elaborado pela Noraqua. A modelação considera a avaliação das afluências de tempo seco e as afluências pluviais pelo software Sanitary Sewer Overflow Analysis and Planning Toolbox. Com efeito, a simulação dinâmica, permitiu um conhecimento mais detalhado do sistema, avaliando a capacidade hidráulica e localizando os pontos propícios a inundações. Assim, foi possível testar soluções de beneficiação do sistema, englobando a problemática das afluências pluviais indevidas calibradas. Apesar das dificuldades sentidas face à qualidade dos dados existentes, verificou-se que o SSOAP e o SWMM são ferramentas úteis na deteção, diagnóstico e redução dos caudais em excesso e que o procedimento utilizado pode ser aplicado a sistemas semelhantes, como forma de definir a melhor solução técnica e económica ao nível do planeamento, operação e reabilitação do sistema.

Double power laws, fractals and self-similarity

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.

Fractional Order Description of DNA

This study addresses the deoxyribonucleic acid (DNA) and proposes a procedure based on the association of statistics, information theory, signal processing, Fourier analysis and fractional calculus for describing fundamental characteristics of the DNA. In a first phase the 24 chromosomes of the Human are evaluated. In a second phase, 10 chromosomes for different species are also processed and the results compared. The results reveal invariance in the description and close resemblances with fractional Brownian motion.

Modelling real solar cell using PSCAD/MATLAB

This paper presents the development of a solar photovoltaic (PV) model based on PSCAD/EMTDC - Power System Computer Aided Design – including a mathematical model study. An additional algorithm has been implemented in MATLAB software in order to calculate several parameters required by the PSCAD developed model. All the simulation study has been performed in PSCAD/MATLAB software simulation tool. A real data base concerning irradiance, cell temperature and PV power generation was used in order to support the evaluation of the implemented PV model.

A simple approach to numerical modelling of propane combustion in fluidized beds

A mathematical model is proposed for the evolution of temperature, chemical composition, and energy release in bubbles, clouds, and emulsion phase during combustion of gaseous premixtures of air and propane in a bubbling fluidized bed. The analysis begins as the bubbles are formed at the orifices of the distributor, until they explode inside the bed or emerge at the free surface of the bed. The model also considers the freeboard region of the fluidized bed until the propane is thoroughly burned. It is essentially built upon the quasi-global mechanism of Hautman et al. (1981) and the mass and heat transfer equations from the two-phase model of Davidson and Harrison (1963). The focus is not on a new modeling approach, but on combining the classical models of the kinetics and other diffusional aspects to obtain a better insight into the events occurring inside a fluidized bed reactor. Experimental data are obtained to validate the model by testing the combustion of commercial propane, in a laboratory-scale fluidized bed, using four sand particle sizes: 400–500, 315–400, 250–315, and 200–250 µm. The mole fractions of CO2, CO, and O2 in the flue gases and the temperature of the fluidized bed are measured and compared with the numerical results.

Fractional calculus: application in modelling and control

This contribution introduces the fractional calculus (FC) fundamental mathematical aspects and discuses some of their consequences. Based on the FC concepts, the chapter reviews the main approaches for implementing fractional operators and discusses the adoption of FC in control systems. Finally are presented some applications in the areas of modeling and control, namely fractional PID, heat diffusion systems, electromagnetism, fractional electrical impedances, evolutionary algorithms, robotics, and nonlinear system control.

Mathematical modeling and simulation of heat flow through pultrusion die assembly system for thermoset composites

Pultrusion is an industrial process used to produce glass fibers reinforced polymers profiles. These materials are worldwide used when performing characteristics, such as great electrical and magnetic insulation, high strength to weight ratio, corrosion and weather resistance, long service life and minimal maintenance are required. In this study, we present the results of the modelling and simulation of heat flow through a pultrusion die by means of Finite Element Analysis (FEA). The numerical simulation was calibrated based on temperature profiles computed from thermographic measurements carried out during pultrusion manufacturing process. Obtained results have shown a maximum deviation of 7%, which is considered to be acceptable for this type of analysis, and is below to the 10% value, previously specified as maximum deviation. © 2011, Advanced Engineering Solutions.

Pseudo Phase Plane and Fractional Calculus Modelling of Western Global Economic Downturn

This paper applies Pseudo Phase Plane (PPP) and Fractional Calculus (FC) mathematical tools for modeling world economies. A challenging global rivalry among the largest international economies began in the early 1970s, when the post-war prosperity declined. It went on, up to now. If some worrying threatens may exist actually in terms of possible ambitious military aggression, invasion, or hegemony, countries’ PPP relative positions can tell something on the current global peaceful equilibrium. A global political downturn of the USA on global hegemony in favor of Asian partners is possible, but can still be not accomplished in the next decades. If the 1973 oil chock has represented the beginning of a long-run recession, the PPP analysis of the last four decades (1972–2012) does not conclude for other partners’ global dominance (Russian, Brazil, Japan, and Germany) in reaching high degrees of similarity with the most developed world countries. The synergies of the proposed mathematical tools lead to a better understanding of the dynamics underlying world economies and point towards the estimation of future states based on the memory of each time series.

A novel framework for modeling value for the customer, an essay on negotiation

This paper proposes a novel framework for modelling the Value for the Customer, the so-called the Conceptual Model for Decomposing Value for the Customer (CMDVC). This conceptual model is first validated through an exploratory case study where the authors validate both the proposed constructs of the model and their relations. In a second step the authors propose a mathematical formulation for the CMDVC as well as a computational method. This has enabled the final quantitative discussion of how the CMDVC can be applied and used in the enterprise environment, and the final validation by the people in the enterprise. Along this research, we were able to confirm that the results of this novel quantitative approach to model the Value for the Customer is consistent with the company's empirical experience. The paper further discusses the merits and limitations of this approach, proposing that the model is likely to bring value to support not only the contract preparation at an Ex-Ante Negotiation Phase, as demonstrated, but also along the actual negotiation process, as finally confirmed by an enterprise testimonial.

Fuzzy Monte Carlo mathematical model for load curtailment minimization in transmission power systems

This paper presents a methodology which is based on statistical failure and repair data of the transmission power system components and uses fuzzyprobabilistic modeling for system component outage parameters. Using statistical records allows developing the fuzzy membership functions of system component outage parameters. The proposed hybrid method of fuzzy set and Monte Carlo simulation based on the fuzzy-probabilistic models allows catching both randomness and fuzziness of component outage parameters. A network contingency analysis to identify any overloading or voltage violation in the network is performed once obtained the system states by Monte Carlo simulation. This is followed by a remedial action algorithm, based on optimal power flow, to reschedule generations and alleviate constraint violations and, at the same time, to avoid any load curtailment, if possible, or, otherwise, to minimize the total load curtailment, for the states identified by the contingency analysis. In order to illustrate the application of the proposed methodology to a practical case, the paper will include a case study for the Reliability Test System (RTS) 1996 IEEE 24 BUS.

Modelling group decision simulation through argumentation

Group decision making plays an important role in today’s organisations. The impact of decision making is so high and complex, that rarely the decision making process is made individually. In Group Decision Argumentation, there is a set of participants, with different profiles and expertise levels, that exchange ideas or engage in a process of argumentation and counter-argumentation, negotiate, cooperate, collaborate or even discuss techniques and/or methodologies for problem solving. In this paper, it is proposed a Multi-Agent simulator for the behaviour representation of group members in a decision making process. Agents behave depending on rational and emotional intelligence and use persuasive argumentation to convince and make alternative choices.

Inexact restoration approaches to solve mathematical program with complementarity constraints

Mathematical Program with Complementarity Constraints (MPCC) finds applica- tion in many fields. As the complementarity constraints fail the standard Linear In- dependence Constraint Qualification (LICQ) or the Mangasarian-Fromovitz constraint qualification (MFCQ), at any feasible point, the nonlinear programming theory may not be directly applied to MPCC. However, the MPCC can be reformulated as NLP problem and solved by nonlinear programming techniques. One of them, the Inexact Restoration (IR) approach, performs two independent phases in each iteration - the feasibility and the optimality phases. This work presents two versions of an IR algorithm to solve MPCC. In the feasibility phase two strategies were implemented, depending on the constraints features. One gives more importance to the complementarity constraints, while the other considers the priority of equality and inequality constraints neglecting the complementarity ones. The optimality phase uses the same approach for both algorithm versions. The algorithms were implemented in MATLAB and the test problems are from MACMPEC collection.