The transient extensional rheology and the dynamics of elastocapillary thinning in aqueous solutions of polyethylene oxide (PEO) are studied with high-speed digital video microscopy. At long times, the evolution of the thread radius deviates from self-similar exponential decay and competition between elastic, capillary and inertial forces leads to the formation of a periodic array of beads connected by axially-uniform ligaments. This configuration is unstable and successive instabilities propagate from the necks connecting the beads and ligaments. This iterated process results in multiple generations of beads developing along the string in general agreement with predictions of Chang et al. [Phys Fluids, 11, 1717 (1999)] although the experiments yield a different recursion relation between the successive generations of beads. At long times, finite extensibility truncates the iterated instability, and slow axial translation of the bead arrays along the interconnecting threads leads to progressive coalescence before the ultimate rupture of the fluid column. Despite these dynamical complexities it is still possible to measure the steady growth in the transient extensional viscosity by monitoring the slow capillarydriven thinning in the cylindrical ligaments between beads. / Accepted for publication in JNNFM, December 2005. / NASA and the Portuguese Science Foundation

Estudos empíricos [1],[2] demonstraram que o trafego das redes Internet Protocol (IP) possui propriedades fractais tais como impulsividade, auto-similaridade e dependência de longa duração em diversas escalas de agregação temporal, na faixa de milissegundos a minutos. Essas características tem motivado o desenvolvimento de novos modelos fractais de teletráfego e de novos algoritmos de controle de trafego em redes convergentes. Este trabalho propõe um novo modelo de trafego no espaço de estados baseado numa aproximação finito-dimensional do processo AutoRegressive Fractionally Integrated Moving Average (ARFIMA). A modelagem por meio de processos auto-regressivos (AR) também é investigada. A analise estatística de series simuladas e de series reais de trafego mostra que a aplicação de modelos AR de ordem alta em esquemas de previsão de teletráfego é fortemente prejudicada pelo problema da identificação da ordem do modelo. Também demonstra-se que a modelagem da memória longa pode ser obtida as custas do posicionamento de um ou mais pólos nas proximidades do circulo de raio unitário. Portanto, a implementação do modelo AR ajustado pode ser instável devido a efeitos de quantização dos coeficientes do filtro digital. O modelo de memória longa proposto oferece as seguintes vantagens: a) possibilidade de implementação pratica, pois não requer memória infinita, b) modelagem (explícita) da região das baixas freqüências do espectro e c) viabilização da utilização do filtro de Kalman. O estudo de caso apresentado demonstra que é possível aplicar o modelo de memória longa proposto em trechos estacionários de sinais de teletráfego fractal. Os resultados obtidos mostram que a dinâmica do parâmetro de Hurst de sinais de teletráfego pode ser bastante lenta na pratica. Sendo assim, o novo modelo proposto é adequado para esquemas de previsão de trafego, tais como Controle de Admissão de Conexões (CAC) e alocação dinâmica de banda, dado que o parâmetro de Hurst pode ser estimado em tempo real por meio da aplicação da transformada wavelet discreta (Discrete Wavelet Transform (DWT)). / Empirical studies [1],[2] demonstrated that heterogeneous IP traffic has fractal properties such as impulsiveness, self-similarity, and long-range dependence over several time scales, from miliseconds to minutes. These features have motivated the development of new traffic models and traffic control algorithms. This work presents a new state-space model for teletraffic which is based on a finite-dimensional representation of the ARFIMA random process. The modeling via AutoRegressive (AR) processes is also investigated. The statistical analysis of simulated time series and real traffic traces show that the application of high-order AR models in schemes of teletraffic prediction can be highly impaired by the model identification problem. It is also demonstrated that the modeling of the long memory can be obtained at the cost of positioning one or more poles near the unit circle. Therefore, the implementation of the adjusted AR model can be unstable due to the quantization of the digital filter coefficients. The proposed long memory model has the following advantages: a) possibility of practical implementation, inasmuch it does not require infinite memory, b) explicit modeling of the low frequency region of the power spectrum, and c) forecasts can be performed via the Kalman predictor. The presented case study suggests one can apply the proposed model in periods where stationarity can be safely assumed. The results indicate that the dynamics of the Hurst parameter can be very slow in practice. Hence, the new proposed model is suitable for teletraffic prediction schemes, such as CAC and dynamic bandwidth allocation, given that the Hurst parameter can be estimated on-line via DWT.

In this thesis, we develop a physical understanding of the effects of viscosity and geometry on the dynamics of interfacial flows in drops and bubbles. We first consider the coalescence of pairs of conical water droplets surrounded by air. Droplet pairs can form cones under the influence of an electric field and have been observed to coalesce or recoil depending on the angle of this cone. With high resolution numerical simulations we show the coalescence and non-coalescence of these drop pairs is negligibly affected by the electric field and can be understood through a purely hydrodynamic process. The coalescence and recoil dynamics are shown to be self similar, demonstrating that for these conical droplet pairs viscosity has a negligible effect on the observed behavior. We generalize this result to the coalescence and recoil of droplets with different cone angles, and focus on droplets coalescing with a liquid bath and flat substrate. From the simulations of these droplets with different cone angles, an equivalent angle is found that describes the coalescence and recoil behavior for all water cones of any cone angle. While viscosity is found to negligibly affect the coalescence of conical water drops, it plays a key role in regulating the coalescence process of bursting gas bubbles. When these gas bubbles burst, a narrow liquid jet is formed that can break up into tiny liquid jet drops. Through consideration of the effects of viscosity, we show that these jet drops can be over an order of magnitude smaller than previously thought. Here, viscosity plays a key role in balancing surface tension and inertial forces and determining the size of the jet drops. Finally, we investigate the drainage of surfactant free, ultra-viscous bubbles where surface tension serves only to set the initial shape of the bubble. We use interferometry to find the thickness profiles of draining bubble films up to the point the of rupture. A theoretical film drainage model considering the balance of viscous and gravitational stresses is developed and numerically computed. The numerical results are found to be consistent with the experimentally obtained thickness profiles. In this work we provide insight into the role of viscosity in the outlined interfacial flows. The results of this thesis will advance the understanding of drop production in clouds, the marine climate, and the degassing of glass melts.

This paper will examine analogues of Cantor sets, called fractal squares, and some of the geometric ways in which fractal squares raise issues not raised by Cantor sets. Also discussed will be a technique using directed graphs to prove bilipschitz equivalence of two fractal squares. / Ph. D.

<div>A strongly implicit, nonlinear Crank-Nicolson-based finite-difference scheme was constructed for the numerical study of the self-similar behavior of viscous gravity currents. Viscous gravity currents are low Reynolds number flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. Under the lubrication approximation, the mathematical description of the spreading of these fluids is reduced to solving a nonlinear parabolic partial differential equation for the shape of the fluid interface. This thesis focuses on the finite-speed propagation of a power-law non-Newtonian current in a variable width channel-like geometry (a "Hele-Shaw cell'') subject to a given mass conservation/balance constraint. The proposed numerical scheme was implemented on a uniform but staggered grid. It is shown to be strongly stable, while possessing formal truncation error that is of second-order in space and it time. The accuracy of the scheme was verified by benchmarking it against established analytical solutions, which were obtained via a first-kind self-similarity transformation. A series of numerical simulations confirmed that the proposed scheme accurately respects the mass conservation/balance constraint. Next, the numerical scheme was used to study the second-kind self-similar behaviour of Newtonian viscous gravity currents flowing towards the end of a converging channel. Second-kind self-similar transformations are not fully specified without further information from simulation or experiment. Thus, using the proposed numerical scheme, the self-similar spreading and leveling leveling of the current was definitively addressed. The numerical results showed favorable comparison with experimental data.</div>

Ce travail de thèse interroge la structure fondamentale du langage. Il s’inscrit dans la tradition greimassienne en ce sens qu’elle assume son affiliation avec les théories de Hjelmslev, Jakobson, Lévi-Strauss et Propp. Mais au-delà, il cherche ce que ces théories ont en commun et qu’elles n’avaient peut-être pas encore suffisamment abordé, notamment certaines relations avec la théorie thomienne/petitotienne. Nous postulons dans cette étude que le discours subit la contrainte d’un ordre sémantico-syntaxique sous-jacent et structurant. Plus précisément, nous postulons que le discours tend à s’organiser à partir, et/ou autour, d’une même chaîne sous-jacente, hiérarchique, contraignante, non aléatoire, transphrastique et restreinte de catégories sémantiques fondamentales. Nous nous inscrivons de fait dans le champ morphodynamique. A partir d’une double approche sémasiologique et distributionnelle, puis par des méthodes statistiques et mathématiques, nous montrons que certains sèmes, assimilables à des universaux et aux propriétés topologiques sous-jacentes, s’incrémentent naturellement dans le corps des énoncés. Ainsi, ce ne sont plus principalement des sèmes isolés que nous étudions mais des séries, des chaînes, des agencements syntagmatiques qui débouchent sur une forme de « proto-raisonnement » associant des sèmes. Enfin, nous montrons par l’expérimentation qu’il existe vraisemblablement aussi d’autres régularités à l’intérieur de cette structure continue ; régularités qui permettent de conforter l’hypothèse d’un principe autosimilaire entre structure profonde et structure superficielle. Notre thèse s’attache en principal à décrire, et à justifier l’existence d’un tel phénomène structural. / This thesis questions the fundamental structure of language. It belongs to the Greimas tradition in the sense that it assumes its affiliation with the theories of Hjelmslev, Jakobson , Levi-Strauss, and Propp. This work tries to go beyond by defining connections with Thom and Petitot theory. In this study, we postulate that discourse is constrained by an underlying semantic and syntactic structural order. More specifically, our assumption is that the discourse tends to be organized from and/or around a same underlying chain, involving non-random hierarchy, going beyond the sentences and being constrained to semantic fundamental categories. Our analysis is also included in a morphodynamic framework.From a double semasiologic and distributional approach, and from statistical and mathematical methods, we show that various semes, linked to universals and topological underlying properties, are naturally incremented in the discourse.As a consequence, what we are studying is not a collection of isolated semes but series, chains, syntagmatic arrangements that yield to a form of "proto-reasoning" associating semes. Finally, we show by experimentation, as there are likely other regularity patterns within the continuous structure. These regularities allow us to support the hypothesis of a self-similar principle between deep structure and surface structure. This thesis work is mainly focused on the description and the justification of the existence of such a structural phenomenon.

ABSTRACT Beach and nearshore surveys are conducted in a variety of ways, the most commonly used being the level-and-transit method; because it is inexpensive, time conducive and highly accurate. Specifically, beach surveys are conducted to better understand cross-shore, long-shore sediment transport processes, as well as to quantify volume changes, which are used to evaluate beach performance. In this study, a section of the beach on Sand Key, FL was surveyed using rod-and-transit. In addition to the commonly used linear data analysis, a non-linear analysis was conducted using NURBS (Non-Uniform Rational B-Splines). Survey data was collected within a short time window to ensure minimal environmental changes associated with waves and anthropological factors. Beach profiles were surveyed using two spatial resolutions, including 1) a typical variable resolution determined by the rodman based on observed morphology changes, and 2) a uniform, high resolution of 25 centimeters per point. The results indicate that variable resolution survey with careful observation by the rodman provided adequate accuracy as compared to the very high-resolution survey. The goal of this study is to create a realistic surface between the beach profiles that are spaced relatively far apart. The commonly used contouring method (a linear method) may create mismatch among major morphology units, .e.g., bar crest, if they have different elevations alongshore. Here a non-linear method is developed by 1) identifying major morphological units, in this case dune top, berm crest, trough bottom, and bar crest 2) linking the units using a cubic spline, and 3) generating a surface using a NURBS sweep2 function. Bisector profiles are sliced from the surface generated using linear and non-linear methods, and compared with surveyed profiles at the same location. The profiles generated using the non-linear method matched more closely to the measured profile than that from the linear method. The non-linear NURBS surface resulted in a consistently greater beach volume between the surveyed profiles than the linear method of volume calculation.

This thesis documents the design and fabrication of an experimental facility that was built to produce a turbulent plane wall jet. The target flow was two-dimensional with a uniform profile of the mean streamwise velocity and a low turbulence level at the slot exit. The design requirements for a flow conditioning apparatus that could produce this flow were determined. The apparatus was then designed and constructed, and measurements of the fluid flow were obtained using particle image velocimetry (PIV). The first series of measurements was along the slot width, the second series was along the slot centerline and the third was at 46 slot heights off the centerline. The Reynolds number, based on the slot height and jet exit velocity, of the wall jet varied from 7594 to 8121. Data for the streamwise and transverse components of velocity and the three associated Reynolds stress components were analyzed and used to determine the characteristics of the wall jet.<p> This experimental facility was able to produce a profile of the mean streamwise velocity near the slot exit that was uniform over 71% of the slot height with a streamwise turbulence that was equal to 1.45% of the mean velocity. This initial velocity was maintained to 6 slot heights. The fully developed region for the centerline and the off-centerline measurements was determined to extend from 50 to 100 slot heights and 40 to 100 slot heights, respectively. This was based on self-similarity of the mean streamwise velocity profiles when scaled using the maximum streamwise velocity and the jet half-width. The off-centerline Reynolds stress profiles achieved a greater degree of collapse than did the centerline profiles.<p> The rate of spread of the wall jet along the centerline was 0.080 in the self-similar region from 50 to 100 slot heights, and the off-centerline growth rate was 0.077 in the self-similar region from 40 to 100 slot heights. The decay rate of the maximum streamwise velocity was -0.624 within the centerline self-similar region, and -0.562 within the off-centerline self-similar region. These results for the spread and decay of the wall jet compared well with recent similar studies.<p> The two-dimensionality was initially assessed by measuring the mean streamwise velocity at 1 slot height along the entire slot width. The two-dimensionality of this wall jet was further analyzed by comparing the centerline and off-centerline profiles of the mean streamwise velocity at 2/3, 4, 50, 80, and 100 slot heights, and by comparing the growth rates and decay rates. Although this facility was able to produce a wall jet that was initially two-dimensional, the two-dimensionality was compromised downstream of the slot, most likely due to the presence of return flow and spanwise spreading. Without further measurements, it is not yet clear exactly how the lack of complete two-dimensionality affects the flow characteristics noted above.

This thesis has two related goals: the first involves the concept of self-similarity of images. Image self-similarity is important because it forms the basis for many imaging techniques such as non-local means denoising and fractal image coding. Research so far has been focused largely on self-similarity in the pixel domain. That is, examining how well different regions in an image mimic each other. Also, most works so far concerning self-similarity have utilized only the mean squared error (MSE). In this thesis, self-similarity is examined in terms of the pixel and wavelet representations of images. In each of these domains, two ways of measuring similarity are considered: the MSE and a relatively new measurement of image fidelity called the Structural Similarity (SSIM) Index. We show that the MSE and SSIM Index give very different answers to the question of how self-similar images really are. The second goal of this thesis involves non-local image processing. First, a generalization of the well known non-local means denoising algorithm is proposed and examined. The groundwork for this generalization is set by the aforementioned results on image self-similarity with respect to the MSE. This new method is then extended to the wavelet representation of images. Experimental results are given to illustrate the applications of these new ideas.

This thesis documents the design and fabrication of an experimental facility that was built to produce a turbulent plane wall jet. The target flow was two-dimensional with a uniform profile of the mean streamwise velocity and a low turbulence level at the slot exit. The design requirements for a flow conditioning apparatus that could produce this flow were determined. The apparatus was then designed and constructed, and measurements of the fluid flow were obtained using particle image velocimetry (PIV). The first series of measurements was along the slot width, the second series was along the slot centerline and the third was at 46 slot heights off the centerline. The Reynolds number, based on the slot height and jet exit velocity, of the wall jet varied from 7594 to 8121. Data for the streamwise and transverse components of velocity and the three associated Reynolds stress components were analyzed and used to determine the characteristics of the wall jet.<p> This experimental facility was able to produce a profile of the mean streamwise velocity near the slot exit that was uniform over 71% of the slot height with a streamwise turbulence that was equal to 1.45% of the mean velocity. This initial velocity was maintained to 6 slot heights. The fully developed region for the centerline and the off-centerline measurements was determined to extend from 50 to 100 slot heights and 40 to 100 slot heights, respectively. This was based on self-similarity of the mean streamwise velocity profiles when scaled using the maximum streamwise velocity and the jet half-width. The off-centerline Reynolds stress profiles achieved a greater degree of collapse than did the centerline profiles.<p> The rate of spread of the wall jet along the centerline was 0.080 in the self-similar region from 50 to 100 slot heights, and the off-centerline growth rate was 0.077 in the self-similar region from 40 to 100 slot heights. The decay rate of the maximum streamwise velocity was -0.624 within the centerline self-similar region, and -0.562 within the off-centerline self-similar region. These results for the spread and decay of the wall jet compared well with recent similar studies.<p> The two-dimensionality was initially assessed by measuring the mean streamwise velocity at 1 slot height along the entire slot width. The two-dimensionality of this wall jet was further analyzed by comparing the centerline and off-centerline profiles of the mean streamwise velocity at 2/3, 4, 50, 80, and 100 slot heights, and by comparing the growth rates and decay rates. Although this facility was able to produce a wall jet that was initially two-dimensional, the two-dimensionality was compromised downstream of the slot, most likely due to the presence of return flow and spanwise spreading. Without further measurements, it is not yet clear exactly how the lack of complete two-dimensionality affects the flow characteristics noted above.