CONCENTRATION FIELDS NEAR AIR-WATER INTERFACES DURING INTERFACIAL MASS TRANSPORT: OXYGEN TRANSPORT AND RANDOM SQUARE WAVE ANALYSIS

Mass transfer across a gas-liquid interface was studied theoretically and experimentally, using transfer of oxygen into water as the gas-liquid system. The experimental results support the conclusions of a theoretical description of the concentration field that uses random square waves approximations. The effect of diffusion over the concentration records was quantified. It is shown that the peak of the normalized rills concentration fluctuation profiles must be lower than 0.5, and that the position of the peak of the rms value is an adequate measure of the thickness of the diffusive layer. The position of the peak is the boundary between the regions more subject to molecular diffusion or to turbulent transport of dissolved mass.

Implementación de instrumentación virtual con LaBVIEW

El objetivo del PFC es el diseño e implementación de una aplicación que funcione como osciloscopio, analizador de espectro y generador de funciones virtual, todo dentro de la misma aplicacion. Mediante una tarjeta de adquisición de datos tomaremos muestras de señales del mundo real (sistema analógico) para generar datos que puedan ser manipulados por un ordenador (sistema digital). Con esta misma tarjeta también se podrán generar señales básicas, tales como señales senoidales, cuadradas.... y además se ha añadido la funcionalidad de generar señales moduladas en frecuencia, señales tipo Chirp (usadas comúnmente tanto en aplicaciones sonar y radar, como en transmisión óptica) o PRN (ruido pseudo-aleatorio que consta de una secuencia determinista de pulsos que se repite cada periodo, usada comúnmente en receptores GPS), como también señales ampliamente conocidas como el ruido blanco Gaussiano o el ruido blanco uniforme. La aplicación mostrará con detalle las señales adquiridas y analizará de diversas maneras esas señales. Posee la función de enventanado de los tipos de ventana mas comunes, respuesta en frecuencia, transformada de Fourier, etc. La configuración es elegida por el usuario en un entorno amigable y de visualización atractiva. The objective of the PFC is the design and implementation of an application that works as oscilloscope, spectrum analyzer and virtual signal generator, all within the same application. Through a data acquisition card, the user can take samples of real-world signals (analog system) to generate data that can be manipulated by a computer (digital system). This same card can also generate basic signals, such as sine waves, square waves, sawtooth waves.... and further has added other functionalities as frequency modulated signals generation, Chirp signals type generation (commonly used in both sonar and radar applications, such as optical transmission) or PRN (pseudo-random noise sequence comprising a deterministic pulse that repeats every period, commonly used in GPS receivers). It also can generate widely known as Gaussian white noise signals or white noise uniform signals. The application will show in detail the acquired signals and will analyze these signals in different ways selected by the user. Windowing function has the most common window types, frequency response, Fourier transform are examples of what kind of analyzing that can be processed. The configuration is chosen by the user throught friendly and attractive displays and panels.

Random input problem for the nonlinear Schrödinger equation

We consider the random input problem for a nonlinear system modeled by the integrable one-dimensional self-focusing nonlinear Schrödinger equation (NLSE). We concentrate on the properties obtained from the direct scattering problem associated with the NLSE. We discuss some general issues regarding soliton creation from random input. We also study the averaged spectral density of random quasilinear waves generated in the NLSE channel for two models of the disordered input field profile. The first model is symmetric complex Gaussian white noise and the second one is a real dichotomous (telegraph) process. For the former model, the closed-form expression for the averaged spectral density is obtained, while for the dichotomous real input we present the small noise perturbative expansion for the same quantity. In the case of the dichotomous input, we also obtain the distribution of minimal pulse width required for a soliton generation. The obtained results can be applied to a multitude of problems including random nonlinear Fraunhoffer diffraction, transmission properties of randomly apodized long period Fiber Bragg gratings, and the propagation of incoherent pulses in optical fibers.

Evaluation of the detection and quantification limits in electroanalysis using two popular methods: application in the case study of paraquat determination

In this work, the reduction reaction of paraquat herbicide was used to obtain analytical signals using electrochemical techniques of differential pulse voltammetry, square wave voltammetry and multiple square wave voltammetry. Analytes were prepared with laboratory purified water and natural water samples (from Mogi-Guacu River, SP). The electrochemical techniques were applied to 1.0 mol L-1 Na2SO4 solutions, at pH 5.5, and containing different concentrations of paraquat, in the range of 1 to 10 mu mol L-1, using a gold ultramicroelectrode. 5 replicate experiments were conducted and in each the mean value for peak currents obtained -0.70 V vs. Ag/AgCl yielded excellent linear relationships with pesticide concentrations. The slope values for the calibration plots (method sensitivity) were 4.06 x 10(-3), 1.07 x 10(-2) and 2.95 x 10(-2) A mol(-1) L for purified water by differential pulse voltammetry, square wave voltammetry and multiple square wave voltammetry, respectively. For river water samples, the slope values were 2.60 x 10(-3), 1.06 x 10(-2) and 3.35 x 10(-2) A mol(-1) L, respectively, showing a small interference from the natural matrix components in paraquat determinations. The detection limits for paraquat determinations were calculated by two distinct methodologies, i.e., as proposed by IUPAC and a statistical method. The values obtained with multiple square waves voltammetry were 0.002 and 0.12 mu mol L-1, respectively, for pure water electrolytes. The detection limit from IUPAC recommendations, when inserted in the calibration curve equation, an analytical signal (oxidation current) is smaller than the one experimentally observed for the blank solution under the same experimental conditions. This is inconsistent with the definition of detection limit, thus the IUPAC methodology requires further discussion. The same conclusion can be drawn by the analyses of detection limits obtained with the other techniques studied.

Dynamic stabilization of Rayleigh-Taylor instability of ablation fronts in inertial confinement fusion

One of the most important problems in inertial confinement fusion is how to find a way to mitigate the onset of the Rayleigh-Taylor instability which arises in the ablation front during the compression. In this thesis it is studied in detail the possibility of using for such a purpose the well-known mechanism of dynamic stabilization, already applied to other dynamical systems such as the inverted pendulum. In this context, a periodic acceleration superposed to the background gravity generates a vertical vibration of the ablation front itself. The effects of different driving modulations (Dirac deltas and square waves) are analyzed from a theoretical point of view, with a focus on stabilization of ion beam driven ablation fronts, and a comparison is made, in order to look for optimization.

Evolution of classifiers for pitch estimation of piano music using cartesian genetic programming

Pitch Estimation, also known as Fundamental Frequency (F0) estimation, has been a popular research topic for many years, and is still investigated nowadays. The goal of Pitch Estimation is to find the pitch or fundamental frequency of a digital recording of a speech or musical notes. It plays an important role, because it is the key to identify which notes are being played and at what time. Pitch Estimation of real instruments is a very hard task to address. Each instrument has its own physical characteristics, which reflects in different spectral characteristics. Furthermore, the recording conditions can vary from studio to studio and background noises must be considered. This dissertation presents a novel approach to the problem of Pitch Estimation, using Cartesian Genetic Programming (CGP).We take advantage of evolutionary algorithms, in particular CGP, to explore and evolve complex mathematical functions that act as classifiers. These classifiers are used to identify piano notes pitches in an audio signal. To help us with the codification of the problem, we built a highly flexible CGP Toolbox, generic enough to encode different kind of programs. The encoded evolutionary algorithm is the one known as 1 + , and we can choose the value for . The toolbox is very simple to use. Settings such as the mutation probability, number of runs and generations are configurable. The cartesian representation of CGP can take multiple forms and it is able to encode function parameters. It is prepared to handle with different type of fitness functions: minimization of f(x) and maximization of f(x) and has a useful system of callbacks. We trained 61 classifiers corresponding to 61 piano notes. A training set of audio signals was used for each of the classifiers: half were signals with the same pitch as the classifier (true positive signals) and the other half were signals with different pitches (true negative signals). F-measure was used for the fitness function. Signals with the same pitch of the classifier that were correctly identified by the classifier, count as a true positives. Signals with the same pitch of the classifier that were not correctly identified by the classifier, count as a false negatives. Signals with different pitch of the classifier that were not identified by the classifier, count as a true negatives. Signals with different pitch of the classifier that were identified by the classifier, count as a false positives. Our first approach was to evolve classifiers for identifying artifical signals, created by mathematical functions: sine, sawtooth and square waves. Our function set is basically composed by filtering operations on vectors and by arithmetic operations with constants and vectors. All the classifiers correctly identified true positive signals and did not identify true negative signals. We then moved to real audio recordings. For testing the classifiers, we picked different audio signals from the ones used during the training phase. For a first approach, the obtained results were very promising, but could be improved. We have made slight changes to our approach and the number of false positives reduced 33%, compared to the first approach. We then applied the evolved classifiers to polyphonic audio signals, and the results indicate that our approach is a good starting point for addressing the problem of Pitch Estimation.

Branching random motions, nonlinear hyperbolic systems and traveling waves

A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independient of random motion, and intensities of reverses are defined by a particle's current direction. A soluton of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) have a so-called McKean representation via such processes. Commonly this system possesses traveling-wave solutions. The convergence of solutions with Heaviside terminal data to the travelling waves is discussed.This Paper realizes the McKean programme for the Kolmogorov-Petrovskii-Piskunov equation in this case. The Feynman-Kac formula plays a key role.

Advances in sequential data assimilation and numerical weather forecasting: an Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic Ensemble Square Root Filters, and a test of a new time stepping scheme in an atmospheric model

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.

Propagation of spherical waves in a weak random medium.

"NsG 24-59. Sponsored by National Aeronautics and Space Administration."

From rogue waves to random walks:nonlinear instabilities in supercontinuum generation

The noise properties of supercontinuum generation continue to be a subject of wide interest within both pure and applied physics. Aside from immediate applications in supercontinuum source development, detailed studies of supercontinuum noise mechanisms have attracted interdisciplinary attention because of links with extreme instabilities in other physical systems, especially the infamous and destructive oceanic rogue waves. But the instabilities inherent in supercontinuum generation can also be interpreted in terms of natural links with the general field of random processes, and this raises new possibilities for applications in areas such as random number generation. In this contribution we will describe recent work where we interpret supercontinuum intensity and phase fluctuations in this way.

Surface Waves and Roughness in Self-Aerated Supercritical Flow

In high-velocity open channel flows, free-surface aeration is commonly observed. The effects of surface waves on the air-water flow properties are tested herein. The study simulates the air-water flow past a fixed-location phase-detection probe by introducing random fluctuations of the flow depth. The present model yields results that are close to experimental observations in terms of void fraction, bubble count rate and bubble/droplet chord size distributions. The results show that the surface waves have relatively little impact on the void fraction profiles, but that the bubble count rate profiles and the distributions of bubble and chord sizes are affected by the presence of surface waves.

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

Error and complexity of random walk Monte Carlo radiosity

The author studies the error and complexity of the discrete random walk Monte Carlo technique for radiosity, using both the shooting and gathering methods. The author shows that the shooting method exhibits a lower complexity than the gathering one, and under some constraints, it has a linear complexity. This is an improvement over a previous result that pointed to an O(n log n) complexity. The author gives and compares three unbiased estimators for each method, and obtains closed forms and bounds for their variances. The author also bounds the expected value of the mean square error (MSE). Some of the results obtained are also shown