Many problems in fluid mechanics and material sciences deal with liquid-vapour flows. In these flows, the ideal gas assumption is not accurate and the van der Waals equation of state is usually used. This equation of state is non-convex and causes the solution domain to have two hyperbolic regions separated by an elliptic region. Therefore, the governing equations of these flows have a mixed elliptic-hyperbolic nature. Numerical oscillations usually appear with standard finite-difference space discretization schemes, and they persist when the order of accuracy of the semi-discrete scheme is increased. In this study, we propose to use a Chebyshev pseudospectral method for solving the governing equations. A comparison of the results of this method with very high-order (up to tenth-order accurate) finite difference schemes is presented, which shows that the proposed method leads to a lower level of numerical oscillations than other high-order finite difference schemes, and also does not exhibit fast-traveling packages of short waves which are usually observed in high-order finite difference methods. The proposed method can thus successfully capture various complex regimes of waves and phase transitions in both elliptic and hyperbolic regimes

Ingeniero Civil Eléctrico / La creciente competitividad de las Energías Renovables No Convencionales (ERNC) y la preocupación por el medio ambiente han cambiado el paradigma energético, han permitido que en los últimos años este tipo de energías jueguen un rol cada vez más relevante en los Sistemas Eléctricos de Potencia (SEP), donde las tecnologías eólicas y solar fotovoltaica han aumentado explosivamente, particularmente en Chile. Sin embargo, por naturaleza estas energías tienen características de variabilidad e incertidumbre, lo que plantea desafíos adicionales en la operación de los SEP, que deben adaptarse a los cambios rápidos e intempestivos de generación, producto de las ráfagas de viento y/o del ciclo solar diario, mediante la toma de carga o descarga por parte de otras unidades de generación en el sistema. La capacidad de un SEP de adaptarse a estos cambios se denomina flexibilidad. Este trabajo aborda principalmente al estudio de la flexibilidad como un atributo sistémico y al desafío correspondiente a los procesos de toma de carga y descarga de las máquinas térmicas del sistema, especialmente críticos en los períodos de amanecer y atardecer por los importantes cambios de energía solar disponible. El proceso se vuelve cada vez más crítico en la medida que se aumenta la participación solar fotovoltaica, tecnología muy relevante para el futuro energético de Chile, pues se estima que para el año 2035 alcance cerca de 13 GW de capacidad instalada, lo que será aproximadamente el 30% del parque generador para aquel año. La propuesta metodológica de este trabajo consiste en la simulación de la operación horaria del sistema en el corto y largo plazo, para el cálculo de índices de flexibilidad que cuantifiquen la capacidad del sistema de adaptarse a cambios rápidos en generación. Para ello se considera como caso base de estudio el Plan de Expansión de Largo Plazo , en su Escenario B, publicado por el Ministerio de Energía, y se simula la operación horaria del sistema durante 4 años específicos (2018, 2025, 2035 y 2050), considerando la estocasticidad de diferentes escenarios hidrológicos futuros. El análisis de resultados de los índices de flexibilidad obtenidos permite identificar una situación crítica en los procesos de toma de carga para el año 2035, específicamente en las horas de atardecer, año donde la penetración de energía solar fotovoltaica es máxima. Para resolver el problema de falta de flexibilidad sistémica, se proponen y evalúan dos medidas claves que deben ser tomadas en conjunto; (i) adelantar parte de la inversión en tecnología solar térmica (CSP) que propone el plan de expansión y (ii) el reemplazo de centrales de carbón lentas por un equivalente de Gas Natural Licuado flexible. Una vez tomadas, las medidas indicadas permiten mejorar la situación crítica identificada. / Este trabajo ha sido parcialmente financiado por Acciona Energía Chile

A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge-Kutta- Chebyshev (RKC) scheme is adjusted to integrate diffusion. Spatial operator is de- scretised by second-order finite differences on a uniform grid. The overall solution is advanced over S fractional stiff integrations, where S corresponds to the number of RKC stages. The behavior of the scheme is analyzed by applying it to three simple problems. The results show that it achieves second-order accuracy, thus, preserving the formal accuracy of the original RKC. The presented development sets the stage for future extensions, particularly, to multidimensional reacting flows with detailed chemistry.

<p>Integralne nejednakosti Jensena i Čebiševa<br />uopštene su za integrale bazirane na neaditivnim<br />merama. Prvo uopštenje dokazano je za<br />pseudo-integral skupovno-vrednosne&nbsp; funkcije, a<br />drugo za pseudo-integral realno-vrednosne funkcije<br />u odnosu na intervalno-vrednosnu -meru.<br />Dokazana je i uopštena nejednakost Čebiševa<br />za pseudo-integral realno-vrednosne&nbsp; funkcije i<br />njena dva intervalno-vrednosna oblika. Nejednakost<br />Jensena je primenjena u principu premije, a<br />nejednakost Čebiševa na procenu verovatnoće.</p> / <p>Integral inequalities of Jensen and Chebyshev type are<br />generalized for integrals based on nonadditive measures.<br />The first generalization is proven for the pseudointegral<br />of a set valued function and the second one<br />for the pseudo-integral of a real-valued function with<br />respect to the interval-valued -measure. Generalized<br />Chebyshev inequality for the pseudo-integral of a realvalued<br />function and its two interval-valued forms are<br />proven. Jensen inequality is applied in the premium<br />principle and Chebyshev inequality is applied to the<br />probability estimation.</p>

The emphasis on higher data rates, spectral efficiency and cost reduction has driven the field towards linear modulation techniques such as quadrature phase shift keying (QPSK), quadrature amplitude modulation (QAM), wideband code division multiple access (WCDMA), and orthogonal frequency division multiplexing (OFDM). The result is a complex signal with a non-constant envelope and a high peak-to-average power ratio. This characteristic makes these signals particularly sensitive to the intrinsic nonlinearity of the RF power amplifier (PA) in the transmitter. The nonlinearity will generate intermodulation (IMD) components, also referred to as out-of-band emission or spectral re-growth, which interfere with adjacent channels. Such distortion, or so called Adjacent Channel Interference (ACI), is strictly limited by FCC and ETSI regulations. Meanwhile, the nonlinearity also causes in-band distortion which degrades the bit error rate performance. Typically, the required linearity can be achieved either by reducing power efficiency or by using linearization techniques. For a Class-A PA, simply “backing off” the input power level can improve linearity; however, for high peak to average power ration (PAPR) signals, this normally reduces the power efficiency down to 10% while increasing heat dissipation up to 90%.When considering the vast number of base stations that wireless operators need to account for, increasing power consumption, or in other words, power back-off is not a viable tradeoff. Therefore, amplifier linearization has become an important technology and a desirable alternative to backing-off an amplifier in modern communications systems. In this work, a novel adaptive algorithm is presented for predistorter linearization of power amplifiers. This algorithm uses Pade-Chebyshev polynomials and a QR decomposition followed by back substitution to find the pre-distorter coefficients.This algorithm is implemented on a Field Programmable Gate Array (Stratix 1S80).The implementation provides improved linearization and also runs the algorithm fast enough so that the adaptive part can be done quickly. Yet another challenge was the integration of a transmitter, receiver and this adaptive algorithm into a single FPGA chip and its communication with a base station. The work thus presents a novel pre-distortion implementation technique using an FPGA and a soft processor (Nios 2) which provides significant intermodulation distortion suppression.

We consider the problem of optimizing the choice of interpolation nodes such that the interpolation error is minimized, given the constraint that none of the nodes may be placed inside a forbidden region. Restricting the problem to using one-dimensional polynomial interpolants, we explore different ways of quantifying the interpolation error; such as the integral of the absolute/squared difference between the interpolated function and the interpolant, or the Lebesgue constant, which compares the interpolant with the best possible approximating polynomial of a given degree. The interpolation error then serves as a cost function that we intend to minimize using gradient-based optimization algorithms. The results are compared with existing theory about the optimal choice of interpolation nodes in the absence of a forbidden region (mainly due to Chebyshev) and indicate that the Chebyshev points of the second kind are near-optimal as interpolation nodes for optimizing the Lebesgue constant, whereas placing the points as close as possible to the forbidden region seems optimal for minimizing the integral of the difference between the interpolated function and the interpolant. We conclude that the Chebyshev points of the second kind serve as a great choice of interpolation nodes, even with the constraint on the placement of the nodes explored in this paper, and that the interpolation nodes should be placed as close as possible to the forbidden region in order to minimize the interpolation error.

Wind power is a rapidly increasing resource of electrical power world-wide. With the increasing number of wind turbines installed one major concern is the noise they generate. Sometimes already built wind turbines have to be put down or down-regulated, when certain noise levels are exceeded, resulting in economical and environmental losses. Therefore, accurate sound propagation calculations would be beneficial already in a planning stage of a wind farm. A model that can account for varying wind speeds and complex terrains could therefore be of great importance when future wind farms are planned. In this report an extended version of the classical wave equation that allows for variations in wind speed and terrain is derived which can be used to solve complex terrain and wind settings. The equation are solved with the use of Fourier transforms and Chebyshev polynomials and a numerical code is developed. The numerical code is evaluated against test cases where analytical and simple solutions exist. Tests with no wind for both totally free propagation and with a ground surface is evaluated in both 2D and 3D settings. For these simple cases the developed code shows good agreement to analytical solutions if the computational domain is sufficiently large. More advanced test cases with wind and terrain is not evaluated in this report and needs further validation. If the sound pressure needs to be calculated for a large area, and if the frequency is high, the developed model has problems regarding computational time and memory. These problems could be solved by further development of the numerical code or by using other solution methods.

Air Quality Models are defined for prediction and simulation of air pollutant concentrations over a certain period of time. The predictions can be used in setting limits for the emission levels of industrial facilities. The input data for the air quality models are very large and encompass various environmental conditions like wind speed, turbulence, temperature and cloud density. Most air quality models are based on advection-diffusion equations. These differential equations are moderately stiff and require appropriate techniques for fast integration over large intervals of time. Implicit time stepping techniques for solving differential equations being unconditionally stable are considered suitable for the solution. However, implicit time stepping techniques impose certain data dependencies that can cause the parallelization of air quality models to be inefficient. The current approach uses Runge Kutta Chebyshev explicit method for solution of advection diffusion equations. It is found that even if the explicit method used is computationally more expensive in the serial execution, it takes lesser execution time when parallelized because of less complicated data dependencies presented by the explicit time-stepping. The implicit time-stepping on the other hand cannot be parallelized efficiently because of the inherent complicated data dependencies. / Master of Science

A risk-based approach for addressing several non-structural stream quality management objectives is presented. To estimate risk, the input process, the stream contaminant transport, and the consequence of contamination are modeled mathematically. The transport of soluble contaminant introduced at a point into a turbulent stream medium is modeled as a boundary value problem in which the contaminant satisfies the Kolmogorov forward equation within the medium. Observed properties of turbulence are used to justify the adoption of this equation. The fundamental solution, as the probabilistic response of the stream to an instantaneous unit flux input, is derived and used as the kernel in a stochastic integral representation of the transport problem. The bulk input is used as the forcing function in the integral equation. It is modeled as a sequence of independent pulses with random magnitude and duration and also with random interval between the incidence of adjacent pulses ,. Stochastic simulation is used to construct the moments and the probability distribution of stream concentration and those of several variables associated with the exceedance of the concentration above a specified threshold. The variables include the dosage and the time to the first exceedance. The probability that an observed stream concentration exceeds the threshold within a given interval of time is also constructed. Generalizations of the Chebyshev inequality are extended to the case of a stochastic process. Upper bounds on the constructed probability distributions are calculated using these extensions. Based on previous studies, a rectangular hyperbolic relationship is assumed between dosage and consequence. The relationship is combined with the empirical dosage density function to obtain estimates of value risk of stream concentration for various thresholds. Given an acceptable risk, the corresponding threshold may be used as the stream standard. The reliability function, defined as the complementary density function of exceedance times, may be used as a gauge of the effectiveness of pollution abatement measures. Other illustrated areas of application include the construction of a minimum cost contaminant discharge policy and the determination of the optimal sampling interval for stream surveillance.

Nous introduisons les variables génériques dans une algèbre amassée acyclique $\mathcal A(Q)$. Nous explicitons ces variables en termes de théorie AR de l'algèbre des chemins $kQ$ et montrons qu'elles forment une $\mathbb Z$-base pour une certaine classe d'algèbres amassées comprenant les algèbres amassées affines de type $\tilde A$. <br /><br />Nous introduisons des polynômes de Chebyshev généralisés grâce auxquels nous pouvons montrer des formules de multiplications de type Caldero-Keller pour les variables associées aux $kQ$-modules réguliers.<br /><br />Nous donnons une démonstration simplifiée d'un résultat de Buan, Marsh et Reiten interprétant les dénominateurs des variables d'amas en termes de théorie de basculement dans la catégorie amassée. Nous étudions aussi la compatibilité entre application Caldero-Chapoton et foncteurs BGP étendus.<br /><br />Enfin, nous réalisons les algèbres amassées non simplement lacées comme sous-algèbres de quotients d'algèbres simplement lacées munies d'un groupe d'automorphismes.