Soluções numéricas de Equações Diferenciais Fracionária e Ordinária para o cálculo da distribuição da concentração em um sistema de compartimento

The purpose of this work was the study of numerical methods for differential equations of fractional order and ordinary. These methods were applied to the problem of calculating the distribution of the concentration of a given substance over time in a given physical system. The two compartment model was used for representation of this system. Comparison between numerical solutions obtained were performed and, in particular, also compared with the analytical solution of this problem. Finally, estimates for the error between the solutions were calculated

Análise estrutural e fadiga em prótese implanto-suportada unitária através do método dos elementos finitos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Reducing the spurious oscillations in the lumped parameters model using low-pass filter

Voltages and currents in the transmission line are described by differential equations that are difficult to solve due soil and skin effect that has to be considered for accurate results, but it increases their complexity. Therefore there are some models to study the voltages and currents along in transmission line. The distributed parameters model that transforms the equations in time domain to the frequency domain and once the solutions are obtained, they are converted to time domain using the Inverse Laplace Transform using numerical methods. Another model is named lumped parameters model and it considers the transmission line represented by a pi-circuit cascade and the currents and voltages are described by state equations. In the simulations using the lumped parameters model, it can be observed the presence of spurious oscillations that are independent of the quantity of pi-circuits used and do not represent the real value of the transient. In this work will be projected a passive low-pass filter directly inserted in the lumped parameters model to reduce the spurious oscillations in the simulations, making this model more accurate and reliable for studying the electromagnetic transients in power systems.

Yang-Lee zeros of the two- and three-state Potts model defined on π3 Feynman diagrams

We present both analytical and numerical results on the position of partition function zeros on the complex magnetic field plane of the q=2 state (Ising) and the q=3 state Potts model defined on phi(3) Feynman diagrams (thin random graphs). Our analytic results are based on the ideas of destructive interference of coexisting phases and low temperature expansions. For the case of the Ising model, an argument based on a symmetry of the saddle point equations leads us to a nonperturbative proof that the Yang-Lee zeros are located on the unit circle, although no circle theorem is known in this case of random graphs. For the q=3 state Potts model, our perturbative results indicate that the Yang-Lee zeros lie outside the unit circle. Both analytic results are confirmed by finite lattice numerical calculations.

Métodos numéricos para equações diferencias ordinárias

Pós-graduação em Matemática Universitária - IGCE

An introductory informatics theoretical framework, based on an integrable lattice model using quantized function algebras, for studying DNA-ionized gas interaction system

Usually we observe that Bio-physical systems or Bio-chemical systems are many a time based on nanoscale phenomenon in different host environments, which involve many particles can often not be solved explicitly. Instead a physicist, biologist or a chemist has to rely either on approximate or numerical methods. For a certain type of systems, called integrable in nature, there exist particular mathematical structures and symmetries which facilitate the exact and explicit description. Most integrable systems, we come across are low-dimensional, for instance, a one-dimensional chain of coupled atoms in DNA molecular system with a particular direction or exist as a vector in the environment. This theoretical research paper aims at bringing one of the pioneering ‘Reaction-Diffusion’ aspects of the DNA-plasma material system based on an integrable lattice model approach utilizing quantized functional algebras, to disseminate the new developments, initiate novel computational and design paradigms.

Análise matemática e estatística da produtividade de lavouras cafeeiras agroquímica e orgânica na região da alta paulista

Studies with organic systems have shown the feasibility and ecological and social sustainability of these agroecosystems, unlike the systems agrochemicals (conventional) production. Some studies have concluded that for the model agrochemical exists less interaction between the flow of internal energy, basically the crop receives all inputs to production with no increase in "energy quality" within the system, while in the organic model of production has increased interaction between different resources in the system. The current economic and ecological crisis, exposed no sustainability of the production pattern of industrialized agriculture developed in a way, showing the dependence of developed countries on imports of agricultural commodities produced in the third world, among there coffee. Given these facts, developed a survey to identify problems in the Alta Paulista region, west of São Paulo State, in relation to coffee production systems. Actually, the fundamental problem, according to the research, farmers in this region, is to choose a viable production system correctly (environmental, social and economic); agrochemical or organic. The objectives of this study were to analyze the yield of production systems and agro-chemical and organic coffee in the period from 2003 to 2007, in 30 producing properties, located in this region, in order to point the production system to produce the highest yield. According to the methodology of CONAB, data collected were recorded on spreadsheets to be used as variables in statistical analysis models and mathematics. We performed a descriptive analysis of productivity data and were used for statistical analysis tests for parametric and nonparametric analysis of variance. The mathematical analyses of the curves were prepared with Origin for Windows 6.0 software, which uses numerical methods to fit the data supplied to a function of variable parameters. Unlike conventional systems of production, the organic system showed greater viability of the production model. Furthermore, with the quantitative modeling proposal, it is possible to perform the evaluation of these types of investments, providing more security to the farmer at the time of decision.

MATHEMATICAL ANALYSIS OF MAXIMUM POWER GENERATED BY PHOTOVOLTAIC SYSTEMS AND FITTING CURVES FOR STANDARD TEST CONDITIONS

The rural electrification is characterized by geographical dispersion of the population, low consumption, high investment by consumers and high cost. Moreover, solar radiation constitutes an inexhaustible source of energy and in its conversion into electricity photovoltaic panels are used. In this study, equations were adjusted to field conditions presented by the manufacturer for current and power of small photovoltaic systems. The mathematical analysis was performed on the photovoltaic rural system I- 100 from ISOFOTON, with power 300 Wp, located at the Experimental Farm Lageado of FCA/UNESP. For the development of such equations, the circuitry of photovoltaic cells has been studied to apply iterative numerical methods for the determination of electrical parameters and possible errors in the appropriate equations in the literature to reality. Therefore, a simulation of a photovoltaic panel was proposed through mathematical equations that were adjusted according to the data of local radiation. The results have presented equations that provide real answers to the user and may assist in the design of these systems, once calculated that the maximum power limit ensures a supply of energy generated. This real sizing helps establishing the possible applications of solar energy to the rural producer and informing the real possibilities of generating electricity from the sun.

Application of the log-conformation tensor to three-dimensional time-dependent free surface flows

The numerical simulation of flows of highly elastic fluids has been the subject of intense research over the past decades with important industrial applications. Therefore, many efforts have been made to improve the convergence capabilities of the numerical methods employed to simulate viscoelastic fluid flows. An important contribution for the solution of the High-Weissenberg Number Problem has been presented by Fattal and Kupferman [J. Non-Newton. Fluid. Mech. 123 (2004) 281-285] who developed the matrix-logarithm of the conformation tensor technique, henceforth called log-conformation tensor. Its advantage is a better approximation of the large growth of the stress tensor that occur in some regions of the flow and it is doubly beneficial in that it ensures physically correct stress fields, allowing converged computations at high Weissenberg number flows. In this work we investigate the application of the log-conformation tensor to three-dimensional unsteady free surface flows. The log-conformation tensor formulation was applied to solve the Upper-Convected Maxwell (UCM) constitutive equation while the momentum equation was solved using a finite difference Marker-and-Cell type method. The resulting developed code is validated by comparing the log-conformation results with the analytic solution for fully developed pipe flows. To illustrate the stability of the log-conformation tensor approach in solving three-dimensional free surface flows, results from the simulation of the extrudate swell and jet buckling phenomena of UCM fluids at high Weissenberg numbers are presented. (C) 2012 Elsevier B.V. All rights reserved.

A marker-and-cell approach to free surface 2-D multiphase flows

This work describes a methodology to simulate free surface incompressible multiphase flows. This novel methodology allows the simulation of multiphase flows with an arbitrary number of phases, each of them having different densities and viscosities. Surface and interfacial tension effects are also included. The numerical technique is based on the GENSMAC front-tracking method. The velocity field is computed using a finite-difference discretization of a modification of the NavierStokes equations. These equations together with the continuity equation are solved for the two-dimensional multiphase flows, with different densities and viscosities in the different phases. The governing equations are solved on a regular Eulerian grid, and a Lagrangian mesh is employed to track free surfaces and interfaces. The method is validated by comparing numerical with analytic results for a number of simple problems; it was also employed to simulate complex problems for which no analytic solutions are available. The method presented in this paper has been shown to be robust and computationally efficient. Copyright (c) 2012 John Wiley & Sons, Ltd.

The concept of quasi-integrability for modified non-linear Schrodinger models

We consider modifications of the nonlinear Schrodinger model (NLS) to look at the recently introduced concept of quasi-integrability. We show that such models possess an in finite number of quasi-conserved charges which present intriguing properties in relation to very specific space-time parity transformations. For the case of two-soliton solutions where the fields are eigenstates of this parity, those charges are asymptotically conserved in the scattering process of the solitons. Even though the charges vary in time their values in the far past and the far future are the same. Such results are obtained through analytical and numerical methods, and employ adaptations of algebraic techniques used in integrable field theories. Our findings may have important consequences on the applications of these models in several areas of non-linear science. We make a detailed numerical study of the modified NLS potential of the form V similar to (vertical bar psi vertical bar(2))(2+epsilon), with epsilon being a perturbation parameter. We perform numerical simulations of the scattering of solitons for this model and find a good agreement with the results predicted by the analytical considerations. Our paper shows that the quasi-integrability concepts recently proposed in the context of modifications of the sine-Gordon model remain valid for perturbations of the NLS model.

Design of laminated piezocomposite shell transducers with arbitrary fiber orientation using topology optimization approach

Sensor and actuator based on laminated piezocomposite shells have shown increasing demand in the field of smart structures. The distribution of piezoelectric material within material layers affects the performance of these structures; therefore, its amount, shape, size, placement, and polarization should be simultaneously considered in an optimization problem. In addition, previous works suggest the concept of laminated piezocomposite structure that includes fiber-reinforced composite layer can increase the performance of these piezoelectric transducers; however, the design optimization of these devices has not been fully explored yet. Thus, this work aims the development of a methodology using topology optimization techniques for static design of laminated piezocomposite shell structures by considering the optimization of piezoelectric material and polarization distributions together with the optimization of the fiber angle of the composite orthotropic layers, which is free to assume different values along the same composite layer. The finite element model is based on the laminated piezoelectric shell theory, using the degenerate three-dimensional solid approach and first-order shell theory kinematics that accounts for the transverse shear deformation and rotary inertia effects. The topology optimization formulation is implemented by combining the piezoelectric material with penalization and polarization model and the discrete material optimization, where the design variables describe the amount of piezoelectric material and polarization sign at each finite element, with the fiber angles, respectively. Three different objective functions are formulated for the design of actuators, sensors, and energy harvesters. Results of laminated piezocomposite shell transducers are presented to illustrate the method. Copyright (C) 2012 John Wiley & Sons, Ltd.

A new enrichment space for the treatment of discontinuous pressures in multi-fluid flows

In this work, a new enrichment space to accommodate jumps in the pressure field at immersed interfaces in finite element formulations, is proposed. The new enrichment adds two degrees of freedom per element that can be eliminated by means of static condensation. The new space is tested and compared with the classical P1 space and to the space proposed by Ausas et al (Comp. Meth. Appl. Mech. Eng., Vol. 199, 10191031, 2010) in several problems involving jumps in the viscosity and/or the presence of singular forces at interfaces not conforming with the element edges. The combination of this enrichment space with another enrichment that accommodates discontinuities in the pressure gradient has also been explored, exhibiting excellent results in problems involving jumps in the density or the volume forces. Copyright (c) 2011 John Wiley & Sons, Ltd.

Contributions to underwater glider path planning

[ES] La Planificación de Rutas o Caminos es un disciplina de Robótica que trata la búsqueda de caminos factibles u óptimos. Para la mayoría de vehículos y entornos, no es un problema trivial y por tanto nos encontramos con un gran diversidad de algoritmos para resolverlo, no sólo en Robótica e Inteligencia Artificial, sino también como parte de la literatura de Optimización, con Métodos Numéricos y Algoritmos Bio-inspirados, como Algoritmos Genéticos y el Algoritmo de la Colonia de Hormigas. El caso particular de escenarios de costes variables es considerablemente difícil de abordar porque el entorno en el que se mueve el vehículo cambia con el tiempo. El presente trabajo de tesis estudia este problema y propone varias soluciones prácticas para aplicaciones de Robótica Submarina.

Longitudinal bar buckling behavior

Reinforced concrete columns might fail because of buckling of the longitudinal reinforcing bar when exposed to earthquake motions. Depending on the hoop stiffness and the length-over-diameter ratio, the instability can be local (in between two subsequent hoops) or global (the buckling length comprises several hoop spacings). To get insight into the topic, an extensive literary research of 19 existing models has been carried out including different approaches and assumptions which yield different results. Finite element fiberanalysis was carried out to study the local buckling behavior with varying length-over-diameter and initial imperfection-over-diameter ratios. The comparison of the analytical results with some experimental results shows good agreement before the post buckling behavior undergoes large deformation. Furthermore, different global buckling analysis cases were run considering the influence of different parameters; for certain hoop stiffnesses and length-over-diameter ratios local buckling was encountered. A parametric study yields an adimensional critical stress in function of a stiffness ratio characterized by the reinforcement configuration. Colonne in cemento armato possono collassare per via dell’instabilità dell’armatura longitudinale se sottoposte all’azione di un sisma. In funzione della rigidezza dei ferri trasversali e del rapporto lunghezza d’inflessione-diametro, l’instabilità può essere locale (fra due staffe adiacenti) o globale (la lunghezza d’instabilità comprende alcune staffe). Per introdurre alla materia, è proposta un’esauriente ricerca bibliografica di 19 modelli esistenti che include approcci e ipotesi differenti che portano a risultati distinti. Tramite un’analisi a fibre e elementi finiti si è studiata l’instabilità locale con vari rapporti lunghezza d’inflessione-diametro e imperfezione iniziale-diametro. Il confronto dei risultati analitici con quelli sperimentali mostra una buona coincidenza fino al raggiungimento di grandi spostamenti. Inoltre, il caso d’instabilità globale è stato simulato valutando l’influenza di vari parametri; per certe configurazioni di rigidezza delle staffe e lunghezza d’inflessione-diametro si hanno ottenuto casi di instabilità locale. Uno studio parametrico ha permesso di ottenere un carico critico adimensionale in funzione del rapporto di rigidezza dato dalle caratteristiche dell’armatura.