Application of real and functional analysis to solve boundary value problems

This thesis is about using appropriate tools in functional analysis arid classical analysis to tackle the problem of existence and uniqueness of nonlinear partial differential equations. There being no unified strategy to deal with these equations, one approaches each equation with an appropriate method, depending on the characteristics of the equation. The correct setting of the problem in appropriate function spaces is the first important part on the road to the solution. Here, we choose the setting of Sobolev spaces. The second essential part is to choose the correct tool for each equation. In the first part of this thesis (Chapters 3 and 4) we consider a variety of nonlinear hyperbolic partial differential equations with mixed boundary and initial conditions. The methods of compactness and monotonicity are used to prove existence and uniqueness of the solution (Chapter 3). Finding a priori estimates is the main task in this analysis. For some types of nonlinearity, these estimates cannot be easily obtained, arid so these two methods cannot be applied directly. In this case, we first linearise the equation, using linear recurrence (Chapter 4). In the second part of the thesis (Chapter 5), by using an appropriate tool in functional analysis (the Sobolev Imbedding Theorem), we are able to improve previous results on a posteriori error estimates for the finite element method of lines applied to nonlinear parabolic equations. These estimates are crucial in the design of adaptive algorithms for the method, and previous analysis relies on, what we show to be, unnecessary assumptions which limit the application of the algorithms. Our analysis does not require these assumptions. In the last part of the thesis (Chapter 6), staying with the theme of choosing the most suitable tools, we show that using classical analysis in a proper way is in some cases sufficient to obtain considerable results. We study in this chapter nonexistence of positive solutions to Laplace's equation with nonlinear Neumann boundary condition. This problem arises when one wants to study the blow-up at finite time of the solution of the corresponding parabolic problem, which models the heating of a substance by radiation. We generalise known results which were obtained by using more abstract methods.

DSP-based sliding-mode control for electromagnetic-levitation precise position system

This paper investigates the robust tracking control problem for a bipolar electromagnetic-levitation precise-position system. The dynamic model of the precise-position device is derived by conducting a thorough analysis on the nonlinear electromagnetic forces. Conventional sliding-mode control and terminal sliding-mode control strategies are developed to guarantee asymptotic and finite-time tracking capabilities of the closed-loop system. A lumped uncertainty estimator is proposed to estimate the system uncertainties. The estimated information is then used to construct a smooth uniformly ultimately bounded sliding-mode control. An exact estimator is also proposed to exactly estimate the unknown uncertainties in finite time. The output of the exact estimator is used to design a continuous chattering free terminal sliding-mode control. The time taken for the closed-loop system to reach zero tracking error is proven to be finite. Experiment results are presented, using a real time digital-signal-processor (DSP) based electromagnetic-levitation system to validate the analysis.

Exact-estimator-based terminal sliding mode control system design

This paper investigates an estimator-based terminal sliding mode control system. An exact estimator is proposed to exactly estimate the unknown uncertainties in finite time. The output of the exact estimator is used to design a continuous chattering free terminal sliding mode control. The time taken for the closed-loop system to reach zero tracking error is proven to be finite. Experiment results are presented, using a real time digital-signal-processor (DSP) based electromagnetic levitation system to implement the control performance.

Placing sensors for area coverage in a complex environment by a team of robots

Existing solutions to carrier-based sensor placement by a single robot in a bounded unknown Region of Interest (ROI) do not guarantee full area coverage or termination. We propose a novel localized algorithm, named Back-Tracking Deployment (BTD). To construct a full coverage solution over the ROI, mobile robots (carriers) carry static sensors as payloads and drop them at the visited empty vertices of a virtual square, triangular, or hexagonal grid. A single robot will move in a predefined order of directional preference until a dead end is reached. Then it back-tracks to the nearest sensor adjacent to an empty vertex (an "entrance" to an unexplored/uncovered area) and resumes regular forward movement and sensor dropping from there. To save movement steps, the back-tracking is carried out along a locally identified shortcut. We extend the algorithm to support multiple robots that move independently and asynchronously. Once a robot reaches a dead end, it will back-track, giving preference to its own path. Otherwise, it will take over the back-track path of another robot by consulting with neighboring sensors. We prove that BTD terminates within finite time and produces full coverage when no (sensor or robot) failures occur. We also describe an approach to tolerate failures and an approach to balance workload among robots. We then evaluate BTD in comparison with the only competing algorithms SLD [Chang et al. 2009a] and LRV [Batalin and Sukhatme 2004] through simulation. In a specific failure-free scenario, SLD covers only 40-50% of the ROI, whereas BTD covers it in full. BTD involves significantly (80%) less robot moves and messages than LRV.

A new perspective on the PPP hypothesis

This paper the stastistical properties of the real exchange rates of G-5 countries for the Bretton-Woods peiod, and draw implications on the purchasing power parity (PPP) hypothesis. In contrast to most previous studies that consider only unit root and stationary process to describe the real exchange tae, this paper also considers two in-between processes, the locally persistent process ans the fractionally integrated process, to complement past studies. Seeking to be consistent with tha ample evidence of near unit in the real exchange rate movements very well. This finding implies that: 1) the real exchange movement is more persistent than the stationary case but less persistent than the unit root case; 2) the real exchange rate is non-stationary but the PPP reversion occurs and the PPP holds in the long run; 3) the real exchange rate does not exhibit the secular dependence of the fractional integration; 4) the real exchange rate evolves over time in a way that there is persistence over a range of time, but the effect of shocks will eventually disappear over time horizon longer than order O (nd), that is, at finite time horizon; 5) shocks dissipation is fasters than predicted by the fractional integracion, and the total sum of the effects of a unit innovation is finite, implying that a full PPP reversion occurs at finite horizons. These results may explain why pasrt empirical estudies could not provide a clear- conclusion on the real exchange rate processes and the PPP hypothesis.

A comment on "Rational learning lead to nash equilibrium" by professors Ehud Kalai and Ehud Lehrer

Kalai and Lebrer (93a, b) have recently show that for the case of infinitely repeated games, a coordination assumption on beliefs and optimal strategies ensures convergence to Nash equilibrium. In this paper, we show that for the case of repeated games with long (but finite) horizon, their condition does not imply approximate Nash equilibrium play. Recently Kalai and Lehrer (93a, b) proved that a coordination assumption on beliefs and optimal strategies, ensures that pIayers of an infinitely repeated game eventually pIay 'E-close" to an E-Nash equilibrium. Their coordination assumption requires that if players believes that certain set of outcomes have positive probability then it must be the case that this set of outcomes have, in fact, positive probability. This coordination assumption is called absolute continuity. For the case of finitely repeated games, the absolute continuity assumption is a quite innocuous assumption that just ensures that pIayers' can revise their priors by Bayes' Law. However, for the case of infinitely repeated games, the absolute continuity assumption is a stronger requirement because it also refers to events that can never be observed in finite time.

Influência da vermiculita expandida na resistência à compressão e reologia de pastas cimentantes de poços de petróleo

Several problems related to the loss of hydraulic seal in oilwells, causing gas migration and/or contamination of the production zone by water, have been reported. The loss of the hydraulic seal is a consequence of cracks which can be occasioned either by the invasion of gas during the wait on cement or by the expansion of the casing causing the fracture of the cement sheath. In case of the pressure of the formation is higher than the pressure in the annulus, gas can migrate into the slurry and form microannulus, which are channels where gas migrates after the cement is set. Cracks can be also occasioned by the fracture of the cement sheath when it does not withstand the thermal and dynamic loads. In reservoirs where the oil is heavy, steam water injection operation is required in order to get the oil flowing. This operation increases the temperature of the casing, and then it expands and causes the fracture of the cement sheath in the annulus. When the failures on the cement are detected, remedial cementing is required, which raise costs caused by the interventions. Once the use of cement in the construction civil sector is older than its use in the petroleum sector, it is common to bring technologies and solutions from the civil construction and apply them on the petroleum area. In this context, vermiculite, a mineral-clay widely encountered in Brazil, has been used, on its exfoliated form, in the civil construction, especially on the manufacture of lights and fireproof concretes with excellent thermal and acoustical properties. It has already been reported in scientific journals, studies of the addition of exfoliated vermiculite in Portland cements revealing good properties related to oilwell cementing operations. Thus, this study aimed to study the rheological behavior, thickening time, stability and compressive strength of the slurries made of Portland cement and exfoliated vermiculite in 5 different compositions, at room temperature and heated. The results showed that the compressive strength decreased with the addition of exfoliated vermiculite, however the values are still allowed for oiwell cementing operations. The thickening time of the slurry with no exfoliated vermiculite was 120 min and the thickening time of the slurry with 12 % of exfoliated vermiculite was 98 min. The stability and the rheological behavior of the slurries revealed that the exfoliated vermiculite absorbed water and therefore increased the viscosity of the slurries, even though increasing the factor cement-water. The stability experiment carried out at 133 ºF showed that, there was neither sedimentation nor reduction of the volume of the cement for the slurry with 12 % of exfoliated vermiculite. Thus, the addition of exfoliated vermiculite accelerates the set time of the cement and gives it a small shrinkage during the wait on cement, which are important to prevent gas migration

Estudo da formulação de pré-misturas secas para a cimentação de poços em terra

An economical solution for cementing oil wells is the use of pre-prepared dry mixtures containing cement and additives. The mixtures may be formulated, prepared and transported to the well where is added water to be pumped.Using this method, becomes dispensable to prepare the cement mixes containing additives in the cementing operation, reducing the possibility of error. In this way, the aim of this work is to study formulations of cement slurries containing solid additives for primary cementing of oil wells onshore for typical depths of 400, 800 and 1,200 meters. The formulations are comprised of Special Class Portland cement, mineral additions and solids chemical additives.The formulated mixtures have density of 1.67 g / cm ³ (14.0 lb / gal). Their optimization were made through the analysis of the rheological parameters, fluid loss results, free water, thickening time, stability test and mechanical properties.The results showed that mixtures are in conformity the specifications for cementing oil wells onshore studied depths

A teoria da ruína aplicada em um modelo de empresa financeira com risco de crédito

In this work we study a new risk model for a firm which is sensitive to its credit quality, proposed by Yang(2003): Are obtained recursive equations for finite time ruin probability and distribution of ruin time and Volterra type integral equation systems for ultimate ruin probability, severity of ruin and distribution of surplus before and after ruin

Expansion effects on back-to-back correlations

The back-to-back correlations (BBC) of particle-antiparticle pairs, signalling in-medium mass modification, are studied in a finite size thermalized medium. The width of BBC function is explicitly evaluated in the case of a nonrelativistic spherically symmetric expanding fireball. The effect of the flow is to reduce the BBC signal as compared to the case of non flow. Nevertheless, a significant signal survives finite-time emission plus expansion effects.

Incorporating memory effects in phase separation processes

We consider the modification of the Cahn-Hilliard equation when a time delay process through a memory function is taken into account. We then study the process of spinodal decomposition in fast phase transitions associated with a conserved order parameter. Finite-time memory effects are seen to affect the dynamics of phase transition at short times and have the effect of delaying, in a significant way, the process of rapid growth of the order parameter that follows a quench into the spinodal region. These effects are important in several systems characterized by fast processes, like non-equilibrium dynamics in the early universe and in relativistic heavy-ion collisions. (C) 2006 Elsevier B.V. All rights reserved.

Chaotic thermalization in Yang-Mills-Higgs theory on a spacial lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Shielding quantum discord through continuous dynamical decoupling

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonmodal energetics of resistive drift waves

The modal and nonmodal linear properties of the Hasegawa-Wakatani system are examined. This linear model for plasma drift waves is nonnormal in the sense of not having a complete set of orthogonal eigenvectors. A consequence of nonnormality is that finite-time nonmodal growth rates can be larger than modal growth rates. In this system, the nonmodal time-dependent behavior depends strongly on the adiabatic parameter and the time scale of interest. For small values of the adiabatic parameter and short time scales, the nonmodal growth rates, wave number, and phase shifts (between the density and potential fluctuations) are time dependent and differ from those obtained by normal mode analysis. On a given time scale, when the adiabatic parameter is less than a critical value, the drift waves are dominated by nonmodal effects while for values of the adiabatic parameter greater than the critical value, the behavior is that given by normal mode analysis. The critical adiabatic parameter decreases with time and modal behavior eventually dominates. The nonmodal linear properties of the Hasegawa-Wakatani system may help to explain features of the full system previously attributed to nonlinearity.