Dissertations / Theses on the topic 'Fractal scaling'

This dissertation is focused on electrical conduction behaviour in granular systems with the purpose of acquiring a fundamental understanding towards applications of granular materials. Performance in a range of engineering systems can be largely influenced by complex multi-physics interactions arising from microstructures of granular materials. The bulk of this dissertation is built on six published or submitted papers. After project background and related previous work introduced in Chapters 1 and 2, respectively, Chapters 3 and 4 deal primarily with the contact properties between rough surfaces. The obtained information at the interfacial scale serves as an experimental and numerical basis for modelling inter-particle contacts in granular media. Chapter 5 with the fifth paper presents the effects of network configuration on macroscopic network responses focussing on the dielectric universal scaling behaviour. In Chapter 6, the final paper shows a physical picture illustrating experimentally observed alternating-current universal scaling in conductive granular systems under different stress states. An effective numerical approach incorporating inter-particle interaction has been provided to simulate electrical responses of granular materials. The combination of the studies from macro-scale phenomena, network topologies, and inter-particle properties is presented leading to new physics-based constitutive models that contain lower scale information. This dissertation presents a new comprehensive understanding of conduction behaviour in granular materials by means of a physics-based framework combining features containing both experimental and numerical information obtained across various length scales, guiding design and optimisation of various granular materials.

Carbon dioxide efflux rates (CER) of stems and roots of overstory and understory black cherry (<i>Prunus serotina</i> Ehrh., BC), red maple (<i>Acer rubrum</i> L., RM) and northern red oak (<i>Quercus rubra</i> L., RO) trees were monitored over two growing seasons at two contrasting sites in the Great Smoky Mountains to investigate diurnal and seasonal patterns in respiration and to develop prediction models based on environmental and plant parameters. CER of small roots (d<0-8 mm) was measured with a newly developed system which allows periodic <i>in situ</i> measurements by using permanently installed flexible cuvettes. Temperature-adjusted CER of roots showed no diel variation. The moderate long-term changes occurred simultaneously in all species and size classes, suggesting that they were driven mostly by environmental factors. Mean root CER ranged from 0.5 to 4.0 nmol g⁻¹ d.w. s⁻¹. Rates were up to six times higher for fine roots (d<2.0 mm) than for coarse roots. CER (per unit length) of boles (d>10 cm) and twigs (d<2 cm) was related to diameter by the function lnCER = a+<i>D</i>·lnd, with <i>D</i> between 1.2 and 1.8. A new, scale-invariant measure of CER, based on <i>D</i>, facilitated comparisons across diameters. Q₁₀ varied with the method of determination, and it was higher in spring (1.8-2.5) than in autumn (1.4-1.5) for all species. Daytime bole CER often fell below temperature-based predictions, likely due to transpiration. The reduction (usually <10%) was less pronounced at the drier site. Twig CER showed more substantial (often >±50%) deviations from the predictions. Deviations were higher in the canopy than in the understory. Mean bole maintenance respiration (at 20°C and d=20 cm) was 0.66, 0.43 and 0.50 μMol m⁻¹, while the volume-based growth coefficient was around 5, 6 and 8 mol cm⁻³ for BC, RM and RO, respectively. In a controlled study, BC and RM seedlings were fumigated in open-top chambers with sub-ambient, ambient and twice-ambient levels of ozone. The twice-ambient treatment reduced stem CER in BC by 50% (p=0.05) in July, but there was no treatment effect in September or in RM. Ozone reduced root/shoot ratio and diameter growth in BC, and P_max in both species.<br>Ph. D.

La description aux échelles macroscopiques et gigascopiques des feux de forêts permet l'établissement de modèles physiques aptes à représenter l'évolution d'un feu avec une meilleure précision que les modèles empiriques de type Rothermel développés jusqu'alors. Cependant ces modèles nécessitent l'ajustement de paramètres dont la mesure directe est impossible, car les équations associées à ces modèles ne sont pas relatives à l'air et à la matière végétale mais aux milieux équivalents à la végétation pour l'échelle considérée. Les propriétés des milieux équivalents sont alors liées aux propriétés des milieux les constituant, mais la connaissance des propriétés des milieux constitutifs ne permet pas de connaître directement les propriétés du milieu équivalent. Ce travail consistera tout d'abord en la reconstruction du milieu végétal à l'aide d'outils issus de la géométrie fractale. Des méthodes de mesures de paramètres géométriques venant de la foresterie ont ensuite été utilisées pour valider nos modèles de végétation. Enfin, des expériences numériques ont été menées sur nos structures reconstruites afin d'identifier les paramètres macroscopiques qui nous intéressent. Ces expériences permettent également de valider ou non les hypothèses effectuées lors de l'établissement des équations du milieu équivalent. Les paramètres ajustés sont la viscosité du milieu équivalent, le coefficient d'échange convectif et le coefficient d'extinction<br>The macroscopic and gigascopic scale description of forest fires allows physical modelings of the propagation which can predict the fire evolution with a better accuracy than usually developed empirical Rothermel-like models. However, those models need fitting for their parameters which cannot be measured directly as the models equations are related to the equivalent media at the considered scale and not related to the air and the vegetal material. The equivalent media properties are related to the inner media properties, but the inner media properties knowledge does not allow directly the equivalent media properties knowledge. This work is then aiming on the vegetal medium reconstruction using fractal geometry. Geometrical parameters measurement methods used in forestry sciences are applied for the vegetal modeling validation. Numerical studies are finally done on the reconstructed structures to fit the relevant macroscopic scale parameters. Those studies also allow us to validate or invalidate the assumptions which have been done for the equivalent medium equation development. Those parameters are: the equivalent medium viscosity, the convective heat transfer coefficient and the extinction coefficient

We investigate dynamical processes on random and regular fractals. The (static) problem of percolation in the semi-infinite plane introduces many pertinent ideas including real space renormalisation group (RSRG) fugacity transformations and scaling forms. We study the percolation probability to determine the surface critical behaviour and to establish exponent relations. The fugacity approach is generalised to study random walks on diffusion-limited aggregates (DLA). Using regular and random models, we calculate the walk dimensionality and demonstrate that it is consistent with a conjecture by Aharony and Stauffer. It is shown that the kinetically grown DLA is in a distinct dynamic universality class to lattice animals. Similarly, the speculation of Helman-Coniglio-Tsallis regarding diffusion on self-avoiding walks (SAWs) is shown to be incorrect. The results are corroborated by an exact enumeration analysis of the internal structure of SAWs. A 'spin' and field theoretic Hamiltonian formulation for the conformational and resistance properties of random walks is presented. We consider Gaussian random walks, SAWs, spiral SAWs and valence walks. We express resistive susceptibilities as correlation functions and hence e-expansions are calculated for the resistance exponents. For SAWs, the local crosslinks are shown to be irrelevant and we calculate corrections to scaling. A scaling description is introduced into an equation-of-motion method in order to study spin wave damping in d-dimensional isotropic Heisenberg ferro-, antiferro- and ferri- magnets near pc . Dynamic scaling is shown to be obeyed by the Lorentzian spin wave response function and lifetime. The ensemble of finite clusters and multicritical behaviour is also treated. In contrast, the relaxational dynamics of the dilute Anisotropic Heisenberg model is shown to violate conventional dynamic scaling near the percolation bicritical point but satisfies instead a singular scaling behaviour arising from activation of Bloch walls over percolation cluster energy barriers.

L'invariance d'échelle repose sur l'intuition que les dynamiques temporelles ne sont pas gouvernées par une (ou quelques) échelle(s) caratéristique(s). Cette propriété est massivement utilisée dans la modélisation et l'analyse de données univariées issues d'applications réelles. Son utilisation pratique se heurte pourtant à deux difficultés dans les applications modernes : les propriétés d'invariance d'échelle ne sont plus nécessairement homogènes en temps ou espace ; le caractère multivarié des données rend fortement non linéaires et non convexes les fonctionnelles à minimiser pour l'estimation des paramètres d'invariance d'échelle. La première originalité de ce travail est d'envisager l'étude de l'invariance d'échelle inhomogène comme un problème conjoint de détection/segmentation et estimation et d'en proposer une formulation par minimisation de fonctionnelles vectorielles, construites autour de pénalisation par variation totale, afin d'estimer à la fois les frontières délimitant les changements et les propriétés d'invariance d'échelle de chaque région. La construction d'un algorithme de débruitage par variation totale vectorielle à la volée est proposée. La seconde originalité réside dans la conception d'une procédure de minimisation de fonctionnelle non convexe type « branch and bound » pour l'identification complète de l'extension bivariée, du mouvement brownien fractionnaire, considéré comme référence pour la modélisation de l'invariance d'échelle univariée. Cette procédure est mise en œuvre en pratique sur des données de trafic Internet dans le contexte de la détection d'anomalies. Dans un troisième temps, nous proposons des contributions spécifiques au débruitage par variation totale : modèle poissonnien d'attache aux données en relation avec un problème de détection d'états pour la fluorescence intermittente ; sélection automatique du paramètre de régularisation<br>Scale invariance relies on the intuition that temporal dynamics are not driven by one (or a few) characteristic scale(s). This property is massively used in the modeling and analysis of univariate data stemming from real-world applications. However, its use in practice encounters two difficulties when dealing with modern applications: scaling properties are not necessarily homogenous in time or space ; the multivariate nature of data leads to the minimization of highly non-linear and non-convex functionals in order to estimate the scaling parameters.The first originality of this work is to investigate the study of non-homogenous scale invariance as a joint problem of detection/segmentation and estimation, and to propose its formulation by the minimization of vectorial functionals constructed around a total variation penalization, in order to estimate both the boundaries delimiting the changes and the scaling properties within each region.The second originality lies in the design of a branch and bound minimization procedure of non-convex functional for the full identification of the bivariate extension of fractional Brownian motion, considered as the reference for modeling univariate scale invariance. Such procedure is applied in practice on Internet traffic data in the context of anomaly detection.Thirdly, we propose some contributions specific to total variation denoising: Poisson data-fidelity model related to a state detection problem in intermittent fluorescence ; automatic selection of the regularization parameter

The aesthetic response is a multifaceted and subtle behavior that ranges in magnitude from sublime to mundane. Few studies have investigated the more subtle, weak aesthetic responses to mundane scenes. But all aesthetic responses rely upon sensory-perceptual processes, which serve as a crucial first step in contemporary models of the aesthetic response. As such, understanding the roles of perceptual processes in aesthetic responses to the mundane provides insights into all aesthetic responses. Variation in the physical properties of aesthetic objects must cause such responses, but to understand the relationship, such physical properties must be quantified. Then, the mechanism can be determined. Here, I present the theoretical basis and reason for interest in such a test of mundane aesthetic responses in Chapter I. In Chapter II, I present metrics that quantify the physical properties of natural scenes, using computer-generated images that model the complexity of natural scenes to validate these measurement techniques. The methods presented in Chapter II are adapted to analyze the physical properties of natural scenes in Chapter III, extending the analysis to photographs and clarifying the relationship between the properties fractal dimension and spectral scaling decay rate. A behavioral study is presented in Chapter IV that investigates the extent that perceptual responses about complexity serve as an intermediary between aesthetic ratings and the physical properties of the images described in Chapters II and III. Chapter V summarizes the results of these studies and explores future directions. This dissertation includes previously published and unpublished coauthored material.

In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. A more intricate approach drawing from renormalization theory as well as a short consideration of some of the topological properties will also be presented. I was furthermore trying to put great emphasis on diagrams throughout the text to make the contents more comprehensible and intuitive.

Compte tenu de la forte hétérogénéité spatio-temporelle des surfaces continentales, la télédétection spatiale s’est avérée être un moyen indispensable pour réaliser un suivi à la fois régulier, local et global des processus qui régissent ces surfaces. Les facteurs dont ils dépendent, tels que l’humidité du sol ou la végétation sont variables sur de larges gammes d’échelles auxquelles seuls les satellites peuvent accéder. En raison du nombre grandissant d’observations satellitaires présentes à plusieurs échelles spatiales et fondées sur de multiples technologies, diverses méthodes ont alors été développées pour permettre d’analyser et d’extraire au mieux l’information riche et conséquente acquise par satellite. Les méthodes basées sur l’analyse multi-échelle fournissent un moyen efficace pour décrire l’hétérogénéité de ces observations et ainsi mieux comprendre la complexité des processus de surface. En particulier, une possibilité consiste à s’intéresser à l’existence de lois d’échelles statistiques qui offrent un outil conceptuel générique applicable à la caractérisation de tout type de géométrie. Cela peut contribuer à caractériser les processus de surface selon une approche multi-échelle rarement prise en compte dans les modèles actuels de surface.Dans ce contexte, l’objectif de cette thèse est de montrer le potentiel d’une méthode permettant de caractériser sur plusieurs échelles spatiales les comportements de variables géophysiques de surface. Pour cela, différentes observations satellitaires complémentaires ont été analysées au moyen du modèle des Multifractales Universelles (Schertzer and Lovejoy, 1987). Deux cas d’étude ont permis de répondre à cet objectif. La première application porte sur l’analyse multifractale des produits intervenant dans l’algorithme de désagrégation spatiale d’humidité du sol DisPATCh (Disaggregation based on Physical And Theoretical scale Change; Merlin et al., 2008; Molero et al., 2016), sur la partie Sud-Est de l’Australie. Dans le deuxième cas d’étude, nous avons étudié le comportement multi-échelle de réflectances de surface et indices optiques acquis par le satellite Sentinel-2 sur la région Sud-Ouest de la France, et corrigés des effets atmosphériques par la chaine MAJA (MACCS-ATCOR Joint Algorithm; Hagolle et al., 2010, 2015; Rouquié et al., 2017). Dans ces deux cas d’étude, l’analyse de séries temporelles d’images nous a permis de mettre en relation l’évolution temporelle des propriétés d’échelle avec les variations saisonnières de la région d’étude (conditions météorologiques, cycles de cultures).Ce travail a révélé dans les produits de surface la présence de lois d’échelles qui diffèrent en fonction de la gamme d’échelles considérée. Ces comportements différents mettent en évidence des régimes d’échelles spécifiques qui, selon le produit étudié, peuvent s’expliquer de deux manières. D’une part, les régimes observés peuvent traduire la présence de processus de surface non-linéaires tels que les précipitations, le ruissellement ou l’évapotranspiration, agissant à différentes échelles spatiales et modulés par divers facteurs tels que la composition et la structure du sol (distribution de la végétation, présence de parcelles agricoles, etc.). D’autre part, ces comportements d’échelle peuvent également refléter l’impact sur les variables de surface des méthodes d’acquisition (fonction de transfert des capteurs) ou de traitement (combinaison de produits au sein des modèles) qui sont couramment utilisées en télédétection. De cette manière, cette étude a montré le potentiel de l’analyse multifractale pour décrire l’hétérogénéité des surfaces continentales, mais également pour évaluer la fiabilité de produits ou modèles de surface. Cette méthode pourrait être utile à la préparation de futures missions spatiales afin de déterminer les limites des capteurs en termes de propriétés multi-échelles, et ainsi mieux estimer la résolution effective de différents produits satellitaires<br>Considering the strong spatial and temporal heterogeneity of continental surfaces, remote sensing has proved to be an indispensable means for conducting regular, local and global monitoring of the physical and biophysical processes governing these surfaces. The factors on which they depend, such as soil moisture, surface temperature, vegetation, or topography, are variable over wide ranges of scales that only satellites can access. Thus, over the last fifty years, we have seen a growing number of satellite observations defined at multiple spatial scales and based on multiple technologies. Various methods were then developed to analyze and extract the rich and consistent information acquired by satellites. Methods based on multi-scale analysis can provide an effective means to describe the heterogeneity of these observations and thus better understand the complexity of surface processes. In particular, one possibility is to focus on the existence of statistical scaling laws offering a generic tool applicable to the characterization of any type of geometry. The demonstration of specific scaling behaviors can help to characterize surface processes using a multi-scale approach that is rarely taken into account in current surface models.In this context, the objective of this thesis is to demonstrate the potential of a method dedicated to the characterization of the behaviors of surface geophysical variables on several spatial scales. For this, different complementary satellite observations were analyzed using the Universal Multifractal model (Schertzer and Lovejoy, 1987). Two case studies helped to meet this objective. The first application concerns the multifractal analysis of the products involved in the soil moisture disaggregation algorithm called DisPATCh (Disaggregation based on Physical And Theoretical scale Change; Merlin et al., 2008; Molero et al., 2016), on the southeastern part of Australia. In the second case study, we studied the multi-scale behavior of surface reflectances and optical indices acquired by Sentinel-2 satellite over the South-West region of France, and corrected from atmosphere effects by the processing chain MAJA (MACCS-ATCOR Joint Algorithm; Hagolle et al., 2010, 2015; Rouquié et al., 2017). In both case studies, time series of images were analyzed. Thus, for each variable studied, we were able to relate the temporal evolution of scaling properties to the seasonal variations specific to the study area (meteorological conditions, crop cycles).During this work, different scaling laws were observed on different scale ranges. Two arguments were given to explain these different scaling behaviors, depending on the case study and the product. On the one hand, the observed regimes can reflect the presence of non-linear surface processes such as precipitation, runoff or evapotranspiration, acting at different spatial scales and modulated by various factors such as soil composition and structure (distribution of vegetation, presence of agricultural parcels, etc.). On the other hand, these scaling behaviors may also reflect the impact on surface variables of acquisition techniques (sensor transfer function) or processing methods (combination of products within surface models) that are commonly used in remote sensing. In this way, this study showed the potential of multifractal analysis to describe the heterogeneity of continental surfaces, but also to evaluate the reliability of geophysical products and surface models. This method could be useful for the preparation of future space missions in order to determine the limits of satellite sensors in terms of multi-scale properties, and thus to better estimate the effective resolution of different products derived from satellite acquisitions

A map combines scientific facts with aesthetic perceptions. This study argues that scaling is universal in mapping reality and evoking a sense of beauty. Scaling laws are used to reveal the underlying structures and dynamics of spatial features. Complex systems, such as living cities involve various interacting entities at all scales. Each individual coherently interacts and overlaps with others to create an unbreakable entity. Scaling structures are also known as fractals. Fractal geometry is used to depict a complex system. Natural objects, such as trees, contain a similar geometry (branches) at all scales. This study attempts to effectively visualize the scaling pattern of geographic space. In this regard, the head/tail breaks classification is applied to visualize the scaling pattern of spatial features. A scaling pattern underlies a geographic space. Visualizing the scaling structure using the head/tail breaks classification can further evoke a sense of beauty. This kind of beauty is on the structural level and was identified by Christopher Alexander, who asserted that beauty is not a personal experience but objectively exists in any space. Alexander developed the theory of centers to broaden the concepts of life and beauty.  A structure with a scaling property (with recursive centers) has high quality of life, and a scaling pattern has positive effects on individual’s psychological and physical well-being. To verify the concept of objective beauty, human beings are used as measuring instruments to examine the assumptions. This study adopts the mirror-of-the-self test to examine human reactions to 23 pairs of images, including photographs of buildings and two types of map. The idea is that participants sense the quality of life by comparing a pair of objects and selecting the object that presents a better picture of themselves. Once individuals feel the self in a picture, they are able to detect real beauty. In this manner, individuals can detect real beauty and life that deeply connect to their inner hearts. The tests were conducted through personal interviews and Internet surveys with the public and with professionals, and 392 samples were collected. The study results show that more than 60% of the individuals selected images with a scaling pattern. These results are in accordance with Alexander’s assumption. In particular, more than 65% individuals selected maps that depict scaling forms. Moreover, this study conducted a training test with a particular group of individuals, after which more than 70% of individuals selected scaling maps. The results reveal that scaling laws are applicable for creating maps and evoking a sense of beauty.

Introduzimos uma familia de trajetorias aleatorias coalescentes com certo tipo de comportamento radial a qual chamaremos de Teia Poissoniana radial discreta. Mostramos que o limite fraco na escala difusiva desta familia e uma familia de trajetorias aleatorias coalescentes que chamaremos de Teia Browniana radial. Por m, caraterizamos o objeto limite como um mapeamento continuo da Teia Browniana restrita num subconjunto de R2.<br>We introduce a family of coalescing random paths with certain kind of radial behavior. We call them the discrete radial Poisson Web. We show that under diusive scaling this family converges in distribution to a family of coalescing random paths which we call radial Brownian Web. Finally, we characterize the limiting object as a continuous mapping of the Brownian Web restricted to a subset of R2.

La nécessaire représentation en échelle du monde nous amène à expliquer pourquoi la théorie des ondelettes en constitue le formalisme le mieux adapté. Ses performances sont comparées à d'autres outils : la méthode des étendues normalisées (R/S) et la méthode par décomposition empirique modale (EMD).La grande diversité des bases analysantes de la théorie des ondelettes nous conduit à proposer une approche à caractère morphologique de l'analyse. L'exposé est organisé en trois parties.Le premier chapitre est dédié aux éléments constitutifs de la théorie des ondelettes. Un lien surprenant est établi entre la notion de récurrence et l'analyse en échelle (polynômes de Daubechies) via le triangle de Pascal. Une expression analytique générale des coefficients des filtres de Daubechies à partir des racines des polynômes est ensuite proposée.Le deuxième chapitre constitue le premier domaine d'application. Il concerne les plasmas de bord des réacteurs de fusion de type tokamak. Nous exposons comment, pour la première fois sur des signaux expérimentaux, le coefficient de Hurst a pu être mesuré à partir d'un estimateur des moindres carrés à ondelettes. Nous détaillons ensuite, à partir de processus de type mouvement brownien fractionnaire (fBm), la manière dont nous avons établi un modèle (de synthèse) original reproduisant parfaitement la statistique mixte fBm et fGn qui caractérise un plasma de bord. Enfin, nous explicitons les raisons nous ayant amené à constater l'absence de lien existant entre des valeurs élevées du coefficient d'Hurst et de supposées longues corrélations.Le troisième chapitre est relatif au second domaine d'application. Il a été l'occasion de mettre en évidence comment le bien-fondé d'une approche morphologique couplée à une analyse en échelle nous ont permis d'extraire l'information relative à la taille, dans un écho rétrodiffusé d'une cible immergée et insonifiée par une onde ultrasonore<br>The necessary scale-based representation of the world leads us to explain why the wavelet theory is the best suited formalism. Its performances are compared to other tools: R/S analysis and empirical modal decomposition method (EMD). The great diversity of analyzing bases of wavelet theory leads us to propose a morphological approach of the analysis. The study is organized into three parts. The first chapter is dedicated to the constituent elements of wavelet theory. Then we will show the surprising link existing between recurrence concept and scale analysis (Daubechies polynomials) by using Pascal's triangle. A general analytical expression of Daubechies' filter coefficients is then proposed from the polynomial roots. The second chapter is the first application domain. It involves edge plasmas of tokamak fusion reactors. We will describe how, for the first time on experimental signals, the Hurst coefficient has been measured by a wavelet-based estimator. We will detail from fbm-like processes (fractional Brownian motion), how we have established an original model perfectly reproducing fBm and fGn joint statistics that characterizes magnetized plasmas. Finally, we will point out the reasons that show the lack of link between high values of the Hurst coefficient and possible long correlations. The third chapter is dedicated to the second application domain which is relative to the backscattered echo analysis of an immersed target insonified by an ultrasonic plane wave. We will explain how a morphological approach associated to a scale analysis can extract the diameter information

Une nouvelle technique basée sur la diffusion des rayons X et un montage adapté ont été conçus et implémentés sur la ligne de lumière BM5 de l'ESRF. L'instrument permet l'étude in-situ et en temps réel de la rugosité d'une surface par diffusion en incidence rasante. L'interaction des rayons X avec la surface, analysée dans le cadre de la théorie des perturbations scalaire du premier ordre, permet d'exprimer les paramètres caractérisant une surface par sa densité spectrale de puissance. En final les valeurs de rugosité, de longueur de corrélation, de conformité de la rugosité, et les exposants propres aux processus de synthèse ont été obtenus. Les potentiels d'un tel instrument ont été vérifiés dans deux cas particuliers : le dépôt de couches minces par pulvérisation magnétron et le décapage par bombardement ionique. Les résultats expérimentaux obtenus ont été discutés par rapport aux modèles actuels décrivan la croissance des films minces et l'interaction des ions avec un solide<br>A novel X-ray scattering technique and a dedicated apparatus have been conceived and realized at the optics beamline BM5 at the ESRF. The apparatus permits to study the surface roughness in-situ and in-real time via grazing incidence X-ray scattering. The interaction of X-rays with the surface was analyzed in the framework of the first order scalar perturbation theory expressing the surface's attributes through the power spectral density function. Information on the rms roughness, the correlation length, the roughness conformi and the scaling exponents characterizing the synthesis process could be extracted. The potential of the method was demonstrated for two particular cases : thin film deposition by magnetron sputtering and surface etching by ion beam bombardment. Finally, the obtained experimental results were discussed in the light of the present models of film growth an ion interaction with solids

La nécessaire représentation en échelle du monde nous amène à expliquer pourquoi la théorie des ondelettes en constitue le formalisme le mieux adapté. Ses performances sont comparées à d'autres outils : la méthode des étendues normalisées (R/S) et la méthode par décomposition empirique modale (EMD).La grande diversité des bases analysantes de la théorie des ondelettes nous conduit à proposer une approche à caractère morphologique de l'analyse. L'exposé est organisé en trois parties.Le premier chapitre est dédié aux éléments constitutifs de la théorie des ondelettes. Un lien surprenant est établi entre la notion de récurrence et l'analyse en échelle (polynômes de Daubechies) via le triangle de Pascal. Une expression analytique générale des coefficients des filtres de Daubechies à partir des racines des polynômes est ensuite proposée.Le deuxième chapitre constitue le premier domaine d'application. Il concerne les plasmas de bord des réacteurs de fusion de type tokamak. Nous exposons comment, pour la première fois sur des signaux expérimentaux, le coefficient de Hurst a pu être mesuré à partir d'un estimateur des moindres carrés à ondelettes. Nous détaillons ensuite, à partir de processus de type mouvement brownien fractionnaire (fBm), la manière dont nous avons établi un modèle (de synthèse) original reproduisant parfaitement la statistique mixte fBm et fGn qui caractérise un plasma de bord. Enfin, nous explicitons les raisons nous ayant amené à constater l'absence de lien existant entre des valeurs élevées du coefficient d'Hurst et de supposées longues corrélations.Le troisième chapitre est relatif au second domaine d'application. Il a été l'occasion de mettre en évidence comment le bien-fondé d'une approche morphologique couplée à une analyse en échelle nous ont permis d'extraire l'information relative à la taille, dans un écho rétrodiffusé d'une cible immergée et insonifiée par une onde ultrasonore<br>The necessary scale-based representation of the world leads us to explain why the wavelet theory is the best suited formalism. Its performances are compared to other tools: R/S analysis and empirical modal decomposition method (EMD). The great diversity of analyzing bases of wavelet theory leads us to propose a morphological approach of the analysis. The study is organized into three parts. The first chapter is dedicated to the constituent elements of wavelet theory. Then we will show the surprising link existing between recurrence concept and scale analysis (Daubechies polynomials) by using Pascal's triangle. A general analytical expression of Daubechies' filter coefficients is then proposed from the polynomial roots. The second chapter is the first application domain. It involves edge plasmas of tokamak fusion reactors. We will describe how, for the first time on experimental signals, the Hurst coefficient has been measured by a wavelet-based estimator. We will detail from fbm-like processes (fractional Brownian motion), how we have established an original model perfectly reproducing fBm and fGn joint statistics that characterizes magnetized plasmas. Finally, we will point out the reasons that show the lack of link between high values of the Hurst coefficient and possible long correlations. The third chapter is dedicated to the second application domain which is relative to the backscattered echo analysis of an immersed target insonified by an ultrasonic plane wave. We will explain how a morphological approach associated to a scale analysis can extract the diameter information

The use of grading scales is common in clinical practice and research settings. A number of grading scales are available to the practitioner, however, despite their frequent use, they are only poorly understood and may be criticised for a number of things such as the variability of the assessments or the inequality of scale steps within or between scales. Hence, the global aim of this thesis was to study the McMonnies/Chapman-Davies (MC-D), Institute for Eye Research (IER), Efron, and validated bulbar redness (VBR) grading scales in order to (1) get a better understanding and (2) attempt a cross-calibration of the scales. After verifying the accuracy and precision of the objective and subjective techniques to be used (chapter 3), a series of experiments was conducted. The specific aims of this thesis were as follows: • Chapter 4: To use physical attributes of redness to determine the accuracy of the four bulbar redness grading scales. • Chapter 5: To use psychophysical scaling to estimate the perceived redness of the four bulbar redness grading scales. • Chapter 6: To investigate the effect of using reference anchors when scaling the grading scale images, and to convert grades between scales. • Chapter 7: To grade bulbar redness using cross-calibrated versions of the MC-D, IER, Efron, and VBR grading scales. Methods: • Chapter 4: Two image processing metrics, fractal dimension (D) and % pixel coverage (% PC), as well as photometric chromaticity (u’) were selected as physical measures to describe and compare redness in the four bulbar redness grading scales. Pearson correlation coefficients were calculated between each set of image metrics and the reference image grades to determine the accuracy of the scales. • Chapter 5: Ten naïve observers were asked to arrange printed copies of modified versions of the reference images (showing vascular detail only) across a distance of 1.5m for which only start and end point were indicated by 0 and 100, respectively (non-anchored scaling). After completion of scaling, the position of each image was hypothesised to reflect its perceived bulbar redness. The averaged perceived redness (across observers) for each image was used for comparison to the physical attributes of redness as determined in chapter 4. • Chapter 6: The experimental setup from chapter 5 was modified by providing the reference images of the VBR scale as additional, unlabelled anchors for psychophysical scaling (anchored scaling). Averaged perceived redness from anchored scaling was compared to non-anchored scaling, and perceived redness from anchored scaling was used to cross-calibrate grades between scales. • Chapter 7: The modified reference images of each grading scale were positioned within the 0 to 100 range according to their averaged perceived redness from anchored scaling, one scale at a time. The same 10 observers who had participated in the scaling experiments were asked to represent perceived bulbar redness of 16 sample images by placing them, one at a time, relative to the reference images of each scale. Perceived redness was taken as the measured position of the placed image from 0 and was averaged across observers. Results: • Chapter 4: Correlations were high between reference image grades and all sets of objective metrics (all Pearson’s r’s≥0.88, p≤0.05); each physical attribute pointed to a different scale as being most accurate. Independent of the physical attribute used, there were wide discrepancies between scale grades, with sometimes little overlap of equivalent levels when comparing the scales. • Chapter 5: The perceived redness of the reference images within each scale was ordered as expected, but not all consecutive within-scale levels were rated as having different redness. Perceived redness of the reference images varied between scales, with different ranges of severity being covered by the images. The perceived redness was strongly associated with the physical attributes of the reference images. • Chapter 6: There were differences in perceived redness range and when comparing reference levels between scales. Anchored scaling resulted in an apparent shift to lower perceived redness for all but one reference image compared to non-anchored scaling, with the rank order of the 20 images for both procedures remaining fairly constant (Spearman’s ρ=0.99). • Chapter 7: Overall, perceived redness depended on the sample image and the reference scale used (RM ANOVA; p=0.0008); 6 of the 16 images had a perceived redness that was significantly different between at least two of the scales. Between-scale correlation coefficients of concordance (CCC) ranged from 0.93 (IER vs. Efron) to 0.98 (VBR vs. Efron). Between-scale coefficients of repeatability (COR) ranged from 5 units (IER vs. VBR) to 8 units (IER vs. Efron) for the 0 to 100 range. Conclusions: • Chapter 4: Despite the generally strong linear associations between the physical characteristics of reference images in each scale, the scales themselves are not inherently accurate and are too different to allow for cross-calibration based on physical redness attributes. • Chapter 5: Subjective estimates of redness are based on a combination of chromaticity and vessel-based components. Psychophysical scaling of perceived redness lends itself to being used to cross calibrate the four clinical scales. • Chapter 6: The re-scaling of the reference images with anchored scaling suggests that redness was assessed based on within-scale characteristics and not using absolute redness scores, a mechanism that may be referred to as clinical scale constancy. The perceived redness data allow practitioners to modify the grades of the scale they commonly use so that comparisons of grading estimates between calibrated scales may be made. • Chapter 7: The use of the newly calibrated reference grades showed close agreement between grading estimates of all scales. The between-scale variability was similar to the variability typically observed when a single scale is repeatedly used. Perceived redness appears to be dependent upon the dynamic range of the reference images of the scale. In conclusion, this research showed that there are physical and perceptual differences between the reference images of all scales. A cross-calibration of the scales based on the perceived redness of the reference images provides practitioners with an opportunity to compare grades across scales, which is of particular value in research settings or if the same patient is seen by multiple practitioners who are familiar with using different scales.