Neste trabalho mostramos uma caracterização para os espaços de potência fracionária associados ao operador 1 - Δp, em que Δp representa o fecho do operador laplaciano em Lp(Rn), usando o fato de que o mesmo pode ser visto como um operador pseudodiferencial com símbolo a(ξ) = 1+4π2|ξ|2. No processo para obter essa caracterização representamos de maneira concreta a solução abstrata u : [0;+ ∞) → Lp(Rn), obtida através da teoria de operadores setoriais e semigrupos analíticos, da equação u - Δpu = 0 em (0;+∞) com condição inicial u(0) = f ∈ Lp(Rn). / In this work we show a characterization for the fractional power spaces associated with the operator 1 - Δp, where Δp, represents the closure of the Laplacian operator in Lp(Rn), using the fact that the operator may be seen as a pseudo-differential operator with symbol a(ξ) = 1+4π2|ξ|2. In the process for this characterization we represent of concrete way the abstract solution u : [0;+∞) Lp(Rn), obtained through the theory of sector operators and analytic semigroups, of the equation u - Δpu = 0 in (0;+∞) with initial condition u(0) = f ∈ Lp(Rn).

In this thesis, a novel framework for dynamic congestion control has been proposed. The study is about the congestion control in broadband communication networks. Congestion results when demand temporarily exceeds capacity and leads to severe degradation of Quality of Service (QoS) and possibly loss of traffic. Since traffic is stochastic in nature, high demand may arise anywhere in a network and possibly causing congestion. There are different ways to mitigate the effects of congestion, by rerouting, by aggregation to take advantage of statistical multiplexing, and by discarding too demanding traffic, which is known as admission control. This thesis will try to accommodate as much traffic as possible, and study the effect of routing and aggregation on a rather general mix of traffic types. Software Defined Networking (SDN) and Network Function Virtualization (NFV) are concepts that allow for dynamic configuration of network resources by decoupling control from payload data and allocation of network functions to the most suitable physical node. This allows implementation of a centralised control that takes the state of the entire network into account and configures nodes dynamically to avoid congestion. Assumes that node controls can be expressed in commands supported by OpenFlow v1.3. Due to state dependencies in space and time, the network dynamics are very complex, and resort to a simulation approach. The load in the network depends on many factors, such as traffic characteristics and the traffic matrix, topology and node capacities. To be able to study the impact of control functions, some parts of the environment is fixed, such as the topology and the node capacities, and statistically average the traffic distribution in the network by randomly generated traffic matrices. The traffic consists of approximately equal intensity of smooth, bursty and long memory traffic. By designing an algorithm that route traffic and configure queue resources so that delay is minimised, this thesis chooses the delay to be the optimisation parameter because it is additive and real-time applications are delay sensitive. The optimisation being studied both with respect to total end-to-end delay and maximum end-to-end delay. The delay is used as link weights and paths are determined by Dijkstra's algorithm. Furthermore, nodes are configured to serve the traffic optimally which in turn depends on the routing. The proposed algorithm is a fixed-point system of equations that iteratively evaluates routing - aggregation - delay until an equilibrium point is found. Three strategies are compared: static node configuration where each queue is allocated 1/3 of the node resources and no aggregation, aggregation of real-time (taken as smooth and bursty) traffic onto the same queue, and dynamic aggregation based on the entropy of the traffic streams and their aggregates. The results of the simulation study show good results, with gains of 10-40% in the QoS parameters. By simulation, the positive effects of the proposed routing and aggregation strategy and the usefulness of the algorithm. The proposed algorithm constitutes the central control logic, and the resulting control actions are realisable through the SDN/NFV architecture.

Maintaining the pH of a fluid or a solution at a specific value is a concern in many industrial processes, wastewater management, and food and pharmaceutical production. Given the importance of controlling pH in many processes, the objective of this thesis is to study and compare the effectiveness of some controller algorithms to control the pH of a process. In this study, the performance of three controller algorithms, namely PID, fractional PID and LA controllers, is evaluated for the control of a simple neutralization process using conventional controller performance metrics. Performance metrics used are the response time, the Integral of the Time weighted Absolute Error (ITAE), the Integral of the Squared Error (ISE), and the Integral of the Squares of the changes (ΔU) in the manipulated variable (ISDU). The three controllers were therefore tuned to minimize one or a combination of the controller performance metrics. Results show that PID, fractional PID and LA controllers implemented and tested in this research are all worthy controllers for maintaining pH of the neutralization process. Simulation results show that the three controllers can be used with confidence to cope with the high nonlinearity of a pH neutralization process provided that the process is properly designed. The relative small gain in performance obtained with the fractional PID controller, compared to a linear PID controller, suggests that it is not worth resorting to a fractional PID controller given its complexity and higher computation effort. Results show that PID and LA controllers are easy to implement with short response time and low ITAE and ISDU performance metrics.

The Miocene rhyolites of the Spor Mountain Formation hosts the world's largest beryllium deposit which produced 85% of the world's beryllium in 2010. The fresh lava is extremely enriched in Be (up to 75 ppm in matrix glass). We have examined the rhyolite to understand the Be enrichment. The Spor Mountain rhyolite contains ~40% quartz, ~40% sanidine, ~10% biotite, and ~10% plagioclase, along with accessory fluorite, columbite, euxenite, fergusonite, monazite, thorite, and zircon. Two types of rhyolite erupted within the Spor Mountain Formation, a less evolved magma (1150 ppm Rb, 42 ppm Be, 0.68 wt% F in matrix glass) and an evolved magma (1710 ppm Rb, 75 ppm Be, 1.56 wt% F in matrix glass). Eruption temperatures estimated using zircon saturation, feldspar-liquid, two feldspar, and Ti-in-quartz geothermometers converge on 718 °C for the less evolved magma and 682 °C for the evolved magma. Using the Ti-in-Qz equation of Huang and Audetat (2012), the pressure of the Spor Mountain rhyolite system is estimated to be around 2 kbar at 700°C. Water content of the rhyolite melt was less than <5 wt%, based on the presence of all four major mineral phases at 700°C and the magma was water undersaturated (Webster et al., 1987). Viscosity of the rhyolite was about 6.2 log Pa·s for the less evolved rhyolite and 5.8 log Pa·s for the evolved rhyolite. Magma viscosities calculated using the Einstein-Roscoe question suggest the evolved magma has a slightly higher viscosity than the less evolved magma (7.0 log Pa·s in the evolved magma vs 6.7 log Pa·s in the less evolved magma) because of higher phenocryst content. Fluorine lowered the melt viscosity, though not by a significant amount (less than 0.5 log units at 1.7 wt% F). Partition coefficients for 32 elements have been calculated for biotite, for 21 elements for sanidine and plagioclase, and for 6 elements for quartz, using data acquired by laser ablation inductively coupled plasma mass spectrometry. Partition coefficients for feldspars in the Spor Mountain rhyolite are generally higher than other silicic magmas, and lower for biotite. Beryllium is one of the most incompatible trace elements in the Spor Mountain rhyolite, with a bulk partition coefficient <0.1. Volatile content of the melt (specifically F), melt composition, and the low temperature of crystallization act as the major controls of trace element partitioning. Trace element models using these partition coefficients suggests that crystal fractionation is the dominant magmatic enrichment process within the rhyolite, requiring ~45% crystallization (f = 55%) of the observed phenocrysts to get compositions from the less evolved to evolved rhyolite. Accumulation of batches of melt formed by different degrees of partial melting cannot explain the great depletion of compatible elements.

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The classical Fickian model for solute transport in porous media cannot correctly predict the spreading (the dispersion) of contaminant plumes in a heterogeneous subsoil unless its structure is completely characterized. Although the required precision is outside the reach of current field characterization methods, the classical Fickian model remains the most widely used model among practitioners. Two approaches can be adopted to solve the effect of physical heterogeneity on transport. First, upscaling methods allow one to compute “apparent” scale-dependent parameters to be used in the classical Fickian model. In the second approach, upscaled (non-Fickian) transport equations with scale-independent parameters are used. This research aims at comparing upscaling methods for Fickian transport parameters with non-Fickian upscaled transport equations, and evaluate their capabilities to predict solute transport in heterogeneous media. The models were tested using simplified numerical examples (perfectly stratified aquifers and bidimensional heterogeneous media). Hypothetical lognormal permeability fields were investigated, for different values of variance, correlation length and anisotropy ratio. Examples exhibiting discrete and multimodal permeability distributions were also investigated using both numerical examples and a physical laboratory experiment. It was found that non-Fickian transport equations involving fractional derivatives have higher upscaling capabilities regarding the prediction of contaminant plume migration and spreading, although their key parameters can only be inferred from inverse modelling of test data.

The prospect of rapid changes to the climate due to global warming is subject of public concern. The need to reduce the emissions of atmospheric green house gases and in particular carbon dioxide is greater than ever. Extensive research is performed to find new solutions and new materials, which tackles this problem in economically benign way. This thesis dealt with two potential adsorbents for post combustion  carbon capture, namely, amine modified silica and calcium carbonates. We modified porous silica with large surface area by propyl-amine groups to enhance the carbon dioxide adsorption capacity and selectivity. Experimental parameters, such as reaction time, temperature, water content, acid and heat treatment of silica substrate were optimized using a fractional factorial design. Adsorption properties and the nature of formed species upon reaction of CO2 and amine-modified silica were studied by sorption and infrared spectroscopy. Physisorbed and chemisorbed amount of adsorbed CO2 were, for the first time, estimated directly in an accurate way. The effects of temperature and moisture on the CO2 adsorption properties were also studied. Crystallization of calcium carbonate as a precursor to calcium oxide, which can be used as carbon dioxide absorbent, was studied in the second part of this thesis. Structure of different amorphous phases of calcium carbonate was studied in detail. Crystallization of calcium carbonate with and without additives was studied. Parameters like stirring rate, temperature, pH and polymer concentration showed to be important in selection of phase and morphology. An aggregation mediated crystallization was postulated to explain the observed morphologies. / At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 3: Accepted.

The first part of this thesis studies tail probabilities forelliptical distributions and probabilities of extreme eventsfor multivariate stochastic processes. It is assumed that thetails of the probability distributions satisfy a regularvariation condition. This means, roughly speaking, that thereis a non-negligible probability for very large or extremeoutcomes to occur. Such models are useful in applicationsincluding insurance, finance and telecommunications networks.It is shown how regular variation of the marginals, or theincrements, of a stochastic process implies regular variationof functionals of the process. Moreover, the associated tailbehavior in terms of a limit measure is derived. The second part of the thesis studies problems related toparameter estimation in stochastic models with long memory.Emphasis is on the estimation of the drift parameter in somestochastic differential equations driven by the fractionalBrownian motion or more generally Volterra-type processes.Observing the process continuously, the maximum likelihoodestimator is derived using a Girsanov transformation. In thecase of discrete observations the study is carried out for theparticular case of the fractional Ornstein-Uhlenbeck process.For this model Whittle’s approach is applied to derive anestimator for all unknown parameters.

The demand for efficient and reliable high rate communication is ever increasing. In this thesis we study different challenges in such systems, and their possible solutions. A goal for many years has been to implement as much as possible of a radio system in the digital domain, the ultimate goal being so called software defined radio (SDR) where the inner workings of a radio standard can be changed completely by changing the software. One important part of an SDR receiver is the high speed analog-to-digital converter (ADC) and one path to reach this high speed is to use a number of parallel, time-interleaved, ADCs. Such ADCs are, however, sensitive to sampling instant offsets, DC level offsets and gain offsets. This thesis discusses estimators based on fractional-delay filters and one application of these estimmators is to estimate and calibrate the relative delay, gain, and DC level offset between the ADCs comprising the time interleaved ADC. In this thesis we also present a technique for carrier frequency offset (CFO) estimation in orthogonal frequency division multiplexing (OFDM) systems. OFDM has gone from a promising digital radio transmission technique to become a mainstream technique used in several current and future standards. The main attractive property of OFDM is that it is inherently resilient to multipath reflections because of its long symbol time. However, this comes at the cost of a relatively high sensitivity to CFO. The proposed estimator is based on locating the spectral minimas within so-called null or virtual subcarriers embedded in the spectrum.~The spectral minimas are found iteratively over a number of symbols and is therefore mainly useful for frequency offset tracking or in systems where an estimate is not immediately required, such as in TV or radio broadcasting systems. However, complexity-wise the estimator is relatively easy to implement and it does not need any extra redundancy beside a nonmodulated subcarrier. The estimator performance is studied both in a channel with additive white Gaussian noise and in a multipath frequency selective channel environment. Interpolators and decimators are an important part of many systems, e.g. radio systems, audio systems etc. Such interpolation (decimation) is often performed using cascaded interpolators (decimators) to reduce the speed requirements in different parts of the system. In a fixed-point implementation, scaling is needed to maximize the use of the available word lengths and to prevent overflow. In the final part of the thesis, we present a method for scaling of multistage interpolators/decimators using multirate signal processing techniques. We also present a technique to estimate the output roundoff noise caused by the internal quantization.

In this thesis we develop and analyze the performance ofadaptive finite element methods for multiphysics problems. Inparticular, we propose a methodology for deriving computable errorestimates when solving unidirectionally coupled multiphysics problemsusing segregated finite element solvers.  The error estimates are of a posteriori type and are derived using the standard frameworkof dual weighted residual estimates.  A main feature of themethodology is its capability of automatically estimating thepropagation of error between the involved solvers with respect to anoverall computational goal. The a posteriori estimates are used todrive local mesh refinement, which concentrates the computationalpower to where it is most needed.  We have applied and numericallystudied the methodology to several common multiphysics problems usingvarious types of finite elements in both two and three spatialdimensions. Multiphysics problems often involve convection-diffusion equations for whichstandard finite elements can be unstable. For such equations we formulatea robust discontinuous Galerkin method of optimal order with piecewiseconstant approximation. Sharp a priori and a posteriori error estimatesare proved and verified numerically. Fractional step methods are popular for simulating incompressiblefluid flow. However, since they are not genuine Galerkin methods, butrather based on operator splitting, they do not fit into the standardframework for a posteriori error analysis. We formally derive an aposteriori error estimate for a prototype fractional step method byseparating the error in a functional describing the computational goalinto a finite element discretization residual, a time steppingresidual, and an algebraic residual.