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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
221

High-order discontinuous Galerkin discretization for flows with strong moving shocks

Κοντζιάλης, Κωνσταντίνος 04 February 2013 (has links)
Supersonic flows over both simple and complex geometries involve features over a wide spectrum of spatial and temporal scales, whose resolution in a numerical solution is of significant importance for accurate predictions in engineering applications. While CFD has been greatly developed in the last 30 years, the desire and necessity to perform more complex, high fidelity simulations still remains. The present thesis has introduced two major innovations regarding the fidelity of numerical solutions of the compressible \ns equations. The first one is the development of new a priori mesh quality measures for the Finite Volume (FV) method on mixed-type (quadrilateral/triangular) element meshes. Elementary types of mesh distortion were identified expressing grid distortion in terms of stretching, skewness, shearing and non-alignment of the mesh. Through a rigorous truncation error analysis, novel grid quality measures were derived by emphasizing on the direct relation between mesh distortion and the quality indicators. They were applied over several meshes and their ability was observed to identify faithfully irregularly-shaped small or large distortions in any direction. It was concluded that accuracy degradation occurs even for small mesh distortions and especially at mixed-type element mesh interfaces the formal order of the FV method is degraded no matter of the mesh geometry and local mesh size. Therefore, in the present work, the high-order Discontinuous Galerkin (DG) discretization of the compressible flow equations was adopted as a means of achieving and attaining high resolution of flow features on irregular mixed-type meshes for flows with strong moving shocks. During the course of the thesis a code was developed and named HoAc (standing for High Order Accuracy), which can perform via the domain decomposition method parallel $p$-adaptive computations for flows with strong shocks on mixed-type element meshes over arbitrary geometries at a predefined arbitrary order of accuracy. In HoAc in contrast to other DG developments, all the numerical operations are performed in the computational space, for all element types. This choice constitutes the key element for the ability to perform $p$-adaptive computations along with modal hierarchical basis for the solution expansion. The time marching of the DG discretized Navier-Stokes system is performed with the aid of explicit Runge-Kutta methods or with a matrix-free implicit approach. The second innovation of the present thesis, which is also based on the choice of implementing the DG method on the regular computational space, is the development of a new $p$-adaptive limiting procedure for shock capturing of the implemented DG discretization. The new limiting approach along with positivity preserving limiters is suitable for computations of high speed flows with strong shocks around complex geometries. The unified approach for $p$-adaptive limiting on mixed-type meshes is achieved by applying the limiters on the transformed canonical elements, and it is fully automated without the need of ad hoc specification of parameters as it has been done with standard limiting approaches and in the artificial dissipation method for shock capturing. Verification and validation studies have been performed, which prove the correctness of the implemented discretization method in cases where the linear elements are adequate for the tessellation of the computational domain both for subsonic and supersonic flows. At present HoAc can handle only linear elements since most grid generators do not provide meshes with curved elements. Furthermore, p-adaptive computations with the implemented DG method were performed for a number of standard test cases for shock capturing schemes to illustrate the outstanding performance of the proposed $p$-adaptive limiting approach. The obtained results are in excellent agreement with analytical solutions and with experimental data, proving the excellent efficiency of the developed shock capturing method for the DG discretization of the equations of gas dynamics. / -
222

Um modelo constitutivo de dano composto para simular o comportamento de materiais quase-frágeis

Rodrigues, Eduardo Alexandre [UNESP] 21 March 2011 (has links) (PDF)
Made available in DSpace on 2014-06-11T19:28:35Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-03-21Bitstream added on 2014-06-13T20:37:41Z : No. of bitstreams: 1 rodrigues_ea_me_bauru.pdf: 1602991 bytes, checksum: 7f755b87b5be84900b2d054f02413197 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / No presente trabalho desenvolve-se um modelo constitutivo baseado na mecânica do dano contínuo para representar o comportamento de materiais que apresentam diferentes respostas quando solicitados à tração ou à compreensão. obtem-se uma representação constitutiva através da composição de modelos simples e específicos para tratar cada tipo de solicitação. Este modelo combinado é capaz inclusive de lidar com carregamentos alternados (tração e compreensão), envolvendo fechamento e reabertura de fissuras existentes. Para modelar o comportamento em compreensão emprega-se o modelo constitutivo que tem como critério de degradação o segundo invariante do tensor de tensão desviador (critério de Von Mises ou J2). Para simular o aparecimento de fissuras de tração, usa-se o modelo de dano com critério de degradação baseado na energia de deformação da parte positiva do tensor efetivas. A integração dos modelos é feita com base em tensões efetivas associadas a duas escalas distintas (escala grosseira e refinada). O modelo é apto para representar a formação de descontinuidades no campo de deslocamento (descontinuidades fortes) em materiais quase-frágeis. Nesse caso, a região de localização de deformação (zona de processo da fatura) pode ser descrita pelo modelo de dano combinado, com lei de abrandamento de tensões (softening) exponencial, que estabelece dissipação compatível com a energia de fratura. A região contínua pode ser descrita pelo modelo de dano J2, com parâmetros ajustados com base no comportamento não linear à compreensão. Valida-se o modelo proposto mediante testes básicos, focando a capacidade do modelo em representar os principais aspectos do comportamento de materiais quase-frágeis. A aplicabilidade do modelo é demonstrada através do estudo da capacidade de rotação plástica de vigas de concreto armado, confrontando-se os resultados numéricos com os experimentais / A combined constitutive model based on the Continuum Damage Mechanics (CDM) is presented to represent the nonlinear behavior of quasi-brittle materials, which present different response when subjected to tension or compreession. The constitutive model is a composition of two simple and specific models designed to treat each type of behavior. The combined model is able to deal with alternating load (tension-compression), involving formation, closure and reopening cracks. To model the compressive behavior, a degradation criterion based on the second invariant of the deviatoric part of the effective stress tensor (Von Miser or J2 criterion) is used. To simulate cracking, a damage model with degradation criterion based on the strain energy associated to the positive part the effective stress tensor is adopted. The combination of the models is made on the basis of the effective stresses associated to two distinct scales (coarse and fine scales) The model is able to represented the formation of discontinuities in the displacement field (strong discontinuities) for quasi-brittle materials. The region of strain localization (fracture process zone) is described by a softening law which establishes dissipation energy compatible with the fracture energy. The continuous region is described by the J2 damage model, with parameters ajusted to describle the compressive nonlinear behavior in compression. Some basic tests are performed to asses the ability of the model to represent the main aspects of the behavior of quasi-brittle materials. The applicability of the model is demonstrated by the study of the plastic rotation capacity of reinforced concrete beams, comparing the numerical responses with the experimental ones
223

Variations temporelles et spatiales des paramètres du mouvement fort du terrain de séismes de subduction / Time and Space Variation of Strong Motions Parameters for Subduction Interface Earthquakes

Pina Valdes, Jesus Vladimir 25 September 2017 (has links)
Les mouvements forts du sol générés par les séismes peuvent être reliés aux caractéristiques de la source sismique (chute de contrainte, vitesse de rupture, etc.), et aux conditions frictionnelles des failles. Ces caractéristiques sont généralement étudiées via l’analyse des enregistrements accélérométriques des grands séismes à basses fréquences (≤ 1 Hz). L'amélioration des réseaux accélérométriques a permis l’enregistrement de nombreux séismes de magnitudes faibles et modérées (Mw ≤ 6,0). Ces enregistrements contiennent des informations dans la bande de hautes fréquences (1 Hz - 50 Hz), qui ne peuvent pas être exploitées avec les méthodes sismologiques classiques.Pour exploiter ces données de mouvements forts des séismes de faible intensité dans l’objectif d’étudier étudier les conditions frictionnelles de l'interface de subduction, nous explorons deux méthodes pour comparer le contenu fréquentiel des séismes: la première basée sur les rapports spectraux et la deuxième basée sur les équations de prédiction du mouvement du terrain (GMPE). Ces méthodes ont été utilisées pour étudier la variabilité spatiale et temporelle du contenu fréquentiel des séismes rompant l'interface de subduction au nord du Chili et au Japon. Leurs avantages et limitations respectifs ont été analysés. Ces comparaisons méthodologiques nous ont a permis de confronter et de valider les résultats, et ainsi de proposer une nouvelle méthodologie fiable basée sur l'analyse des résidus de GMPE pour analyser le contenu fréquentiel des séismes.L'analyse des résultats obtenus a montré une dépendance avec la profondeur du contenu en fréquence des séismes de l’interface de subduction, concordant avec les observations de grandes ruptures de subduction [Lay et al., 2012]. En même temps, des variations du contenu fréquentiel des séismes ont été détectées le long de la fosse de subduction, ce qui nous a conduit à décrire une segmentation latérale de l'interface de subduction. Cette segmentation a été comparée avec la distribution spatiale de la sismicité, à la géométrie de l'interface de subduction et à ses conditions de glissement. Finalement, avant le séisme d’Iquique de 2014 (Mw 8.1) au nord du Chili, nous avons détecté une évolution temporelle du contenu en fréquence des séismes associée à l’occurrence d'un glissement lent précurseur au choc principal. / The strong ground motions generated by earthquakes can be related to the characteristics of the earthquakes source (stress drop, rupture velocity etc..), and therefore to the frictional conditions of the faults. These characteristics are usually studied by analyzing the low frequency band (≤ 1Hz) of the strong motion records of large earthquakes. The improvement of strong motion networks has generated large datasets of records of moderate and low magnitude earthquakes (Mw ≤ 6.0). These records contain informations in the high frequency band (1 Hz – 50 Hz), which cannot be exploited using classical seismological methods.In order exploit the strong motion records of low magnitude earthquakes to study the subduction interface’s frictional conditions, we explore two methods for comparing the earthquakes frequency content: the first one based on spectral ratios, and the second one based on the Ground Motion Prediction Equations (GMPEs). These methods have been used to investigate the spatial and temporal variability of the frequency content of subduction interface earthquakes in North Chile and Japan. Their respective benefits and limitations have been analyzed. These methodological comparisons allowed us to cross compare and validate the results, and to propose a new, reliable methodology based on the analysis of GMPEs residuals to compare the earthquakes frequency content.The analysis of the results showed a depth dependency of the frequency content of subduction earthquakes in agreement with the one derived from large megathrust ruptures [Lay et al., 2012]. Additionally, variations of the earthquake frequency content along trench have been detected, which may drive to a lateral segmentation of the subduction interface. This segmentation has been compared to the spatial distribution of the seismicity, the geometry of the subduction interface and its slippage conditions. Finally, before the occurrence of 2014 Iquique Earthquake Mw 8.1 in North Chile, a temporal evolution of the frequency content of the foreshocks has been detected, associated to a precursory slow slip of the subduction interface.
224

Ett starkt och heligt landskap : Centralplats och kosmologi under järnåldern

Nordström, Karl- Erik January 2018 (has links)
Karl- Erik Nordström 2018. A strong and sacred Landscape. Central Places and Cosmology during the Iron Age   This study intends to address a specific aspect of the landscape, not only as something that can be linked to economic, political and legal factors but also spiritual and cosmological. Much of these thoughts have been taken from certain studies of "the strong landscape" that shape the beliefs and identities. Such ethnoarchaeological approach has grown to a great extent in recent decades and is represented internationally by several authors from the 70s and 80s, who in their Bronze Age studies highlight the importance of contemporary world of imagination.   Something that characterized much of the research tradition in the period after 1945 is building history and research around central places. The central site concept, which includes "a place of specific qualities", was not developed until the 1970s.   One thing that can not be avoided in this case is the adaptation to the harsh climate and the environmental problems that develop during the Iron Age, which in many cases have been devastating but can also involve reorganization, better use of resources and a more centralized structure. The emerging economic, political, legal and religious centers that the central places make up can be seen as an expression of this. Here, spiritual and cosmological performances about landscapes, towns, farms and houses have also been developed.   This aspect of the landscape as a cosmological unit I intend to study closer to the rich iron age community in Sundhede outside Hudiksvall. Here, a number of villages and smaller regions are grouped around a high-rise city center and here we also find outfields, which extract the substance that had an important significance during this time and also gave a spiritual cosmological significance, namely the iron. With this I hope to contribute to further knowledge of the role played by the landscape during the Iron Age, not least metaphysical.
225

Energy-momentum tensor from Wilson flow in lattice φ4-theory

Ehret, Susanne January 2017 (has links)
The energy-momentum tensor (EMT) is the Noether current associated with translations. It is of interest because, first of all, it has physical meaning as it contains the energy density and the momentum density. Moreover, its trace can be related to the beta function so that the scaling behaviour of the theory at hand can be studied. We are particularly interested in the scaling behaviour of strongly coupled theories. To explore the strong coupling regime it is necessary to compute the EMT non-perturbatively, i.e. on the lattice. This complicates matters greatly. On the lattice translation invariance is broken which leads to additional terms in the translation Ward identity from which the EMT is derived. This results in turn in the need to renormalise the EMT on the lattice. In this thesis we extend recent studies on the renormalisation of the EMT in four-dimensional gauge theory to the case of a three-dimensional scalar theory to investigate its divergence structure and the numerical feasibility of the suggested procedure on a more basic level. Furthermore, scalar φ4-theory in three dimensions exhibits an infrared fixed point and can thus serve as a toy model to examine mechanisms for building theories beyond the standard model. Our strategy to renormalise the EMT on the lattice is to identify all possible terms that can mix with both sides of the translation Ward identity. The renormalised EMT is a combination of operators of the same or lower dimension obeying the symmetries of the theory. The mixing is determined by requiring that the renormalised EMT satisfies the correct Ward identities. Using different probes in the translation Ward identity one can compute the coefficients of the EMT by solving a linear system of equations. However, contact terms can arise. One solution is the recently introduced Wilson flow. Its renormalisation properties allow for expectation values free of contact terms. That way the Wilson flow provides for a meaningful theoretical formulation of the EMT on the lattice that can be used in practice. In this thesis we review the renormalisation properties and the phase diagram of scalar φ4-theory in three dimensions, the translation Ward identity and the EMT in the continuum, as well as the gradient flow for scalar theory. A large part is dedicated to the perturbative renormalisation of the EMT on the lattice. Finally, our strategy to compute the renormalisation constants of the EMT in scalar theory non-perturbatively is discussed in detail, and our results for the renormalisation constants are presented.
226

Modeling Recurrent Gap Times Through Conditional GEE

Liu, Hai Yan 16 August 2018 (has links)
We present a theoretical approach to the statistical analysis of the dependence of the gap time length between consecutive recurrent events, on a set of explanatory random variables and in the presence of right censoring. The dependence is expressed through regression-like and overdispersion parameters, estimated via estimating functions and equations. The mean and variance of the length of each gap time, conditioned on the observed history of prior events and other covariates, are known functions of parameters and covariates, and are part of the estimating functions. Under certain conditions on censoring, we construct normalized estimating functions that are asymptotically unbiased and contain only observed data. We then use modern mathematical techniques to prove the existence, consistency and asymptotic normality of a sequence of estimators of the parameters. Simulations support our theoretical results.
227

Sur l'étude du processus de filamentation laser dans les gaz rares en modèle de champ fort : des influences de la génération de troisième harmonique et de la proximité de résonances dans l'ultraviolet / On the study of the laser filamentation process in rare gases under the strong field model : impacts of third harmonic generation and of the vicinity of resonances in the ultraviolet

Doussot, Julien 19 December 2017 (has links)
Le processus de filamentation découle de la balance dynamique de plusieurs effets linéaires et non-linéaires, permettant l'auto-stabilisation du faisceau laser sur des distances de propagation significativement supérieures à celles prédites par la théorie des faisceaux gaussiens. Cette thèse s'attache à décrire ce phénomène dans les gaz rares en modèle dit de champ fort, par opposition au modèle usuel, utilisé dans le cadre de la théorie des perturbations et s'appuyant sur l'approximation du champ faible. L'influence des harmoniques, jusqu'ici négligée, est alors revisitée tant au niveau microscopique qu'à l'échelle d'une propagation. Il est montré, expérimentalement et par l'appui de simulations numériques, qu'il suffit d'une faible proportion de troisième harmonique pour que la dynamique de la filamentation soit fortement impactée, notamment à travers le processus d'ionisation. Egalement, la proximité d'une résonance peut mener à de fortes modifications du mécanisme d'auto-guidage: lorsqu'un champ fondamental centré à 400nm et sa troisième harmonique interagissent avec du krypton, il est montré que le processus de modulation de phase croisée est renforcé et qu'il peut alors endosser un rôle défocalisant de manière non-négligeable. Une autre situation - à 300nm dans le krypton - amène à un renforcement résonant de la filamentation, se traduisant par l'allongement de la longueur du filament par rapport au cas hors-résonance. / Filamentation originates from the dynamic balance between linear and nonlinear effects, allowing the laser beam autostabilization over distances significantly greater than those predicted by linear optics laws. The aim of this thesis is to describe this phenomenon on rare gases under the strong field model, contrary to the commonly used perturbation model based on the weak field approximation. The influence of harmonics, so far neglected, is then revisited both at the microscopic level and at a propagation scale. It is shown, experimentally and with the support of numerical simulations, that a weak proportion of third harmonic is sufficient to strongly impact the filamentation dynamics, especially through the ionization process. Also, the vicinity of a resonance can lead to strong modifications of the self-guiding mechanism: when a fundamental field centered at 400nm and its third harmonic interact together with krypton, it is shown that the cross-phase modulation process is enhanced and can participate to the beam defocusing. Another situation - at 300nm in krypton - leads to resonantly enhanced filamentation, i.e. to longer filaments compared to the non-resonant case.
228

INTERESTS, PERSONAL STYLES, VALUES, SPECIALTY CHOICE, AND MAJOR SATISFACTION AMONG MASTER OF SOCIAL WORK STUDENTS

KATO, YUKA 01 December 2015 (has links)
This study examined how vocational interests, vocational personal styles and work values impact on major satisfaction and specialization choice of 256 students in Master of Social Work programs from several regions of the United States. Participants completed the General Occupational Themes (GOTs) and the Personal Style Scales (PSSs) of the Strong Interest Inventory (SII; Donnay et al., 2005), the Values Scale (VS; Super & Nevill, 1989), and the modified Academic Major Satisfaction Scale (AMSS; Nauta, 2007). A series of logistic regression analyses were conducted to examine factors predicting major satisfaction, and a series of discriminant function analyses were conducted to investigate factors involved in distinguishing the three specialization groups (clinical social work-health/mental health/special population; clinical social work-children/youth/family; and non-profit organization administration/management, policy, community development). The results supported the importance of person-environment fit (P-E fit) in the membership of the MSW programs, the MSW students’ major satisfaction, and their specialization choices. The results also showed the validity and the utility of the GOTs, the PSSs, and the VS. Beyond three-letter Holland codes, further utilization of the GOTs and integration of the PSSs and the VS seem to be essential. Significant roles of work values of the VS were also noted. Implications for future research and career counseling are discussed. Recommendations for administrators of MSW programs are offered to more effectively recruit students, support their process of selecting a specialization, train them during the program, and provide additional training to professional social workers.
229

Promoting social emotional competency through quality teaching practices: The impact of consultation on a multidimensional treatment integrity model of the "Strong Kids" program / Impact of consultation on a multidimensional treatment integrity model of the "Strong Kids" program

Levitt, Verity Helaine, 1979- 09 1900 (has links)
xiv, 131 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / This dissertation study investigated the impact of brief teacher consultation on teachers' implementation fidelity, quality of implementation, and student responsiveness during the Strong Kids social-emotional learning curriculum. Additional outcome measures included teachers' self-efficacy and teachers' perceptions of social validity of the Strong Kids program. Participants included six teachers, three of whom were randomly assigned to the treatment group and three of whom were randomly assigned to the control group. Teachers in the treatment group received brief performance feedback consultation for six out of the twelve Strong Kids lessons; whereas, teachers in the control group did not receive consultation, but instead were given a frequently asked questions sheet that provided them with general information about the curriculum. Results of the study indicated an increase in implementation fidelity for the teachers receiving performance feedback consultation and a decrease in implementation fidelity for the teachers who did not receive performance feedback. The data did not indicate any substantial effects for the consultation group teachers with respect to quality of implementation or student responsiveness. Overall, teachers in both the treatment and control groups had positive attitudes toward social-emotional learning and the curriculum. Both groups of teachers also reported similar negative attitudes regarding the curriculum. For example, both groups of teachers felt that the lessons took too long to implement within a given class period. Implications of this study for future research and practice are discussed. / Committee in charge: Kenneth Merrell, Chairperson, Special Education and Clinical Sciences; Jeffrey Sprague, Member, Special Education and Clinical Sciences; Terry Scott, Member, Special Education and Clinical Sciences; John Seeley, Member, Not from U of 0; Lynn Kahle, Outside Member, Marketing
230

Surfaces quantile : propriétés, convergences et applications / Quantile surfaces : properties, convergence and applications

Ahidar-Coutrix, Adil 03 July 2015 (has links)
Dans la thèse on introduit et on étudie une généralisation spatiale sur $\R^d$ du quantile réel usuel sous la forme d'une surface quantile via des formes $\phi$ et d'un point d'observation $O$. Notre point de départ est de simplement admettre la subjectivité due à l'absence de relation d'ordre totale dans $\R^d$ et donc de développer une vision locale et directionnelle des données. Ainsi, les observations seront ordonnées du point de vue d'un observateur se trouvant à un point $O \in \R^d$. Dans le chapitre 2, on introduit la notion du quantile vue d'un observateur $O$ dans la direction $u \in \Sd$ et de niveau $\alpha$ via des des demi-espaces orthogonaux à chaque direction d'observation. Ce choix de classe implique que les résultats de convergence ne dépendent pas du choix de $O$. Sous des hypothèses minimales de régularité, l'ensemble des points quantile vue de $O$ définit une surface fermée. Sous hypothèses minimales, on établit pour les surfaces quantile empiriques associées les théorèmes limites uniformément en le niveau de quantile et la direction d'observation, avec vitesses asymptotiques et bornes d'approximation non-asymptotiques. Principalement la LGNU, la LLI, le TCLU, le principe d'invariance fort uniforme puis enfin l'approximation du type Bahadur-Kiefer uniforme, et avec vitesse d'approximation. Dans le chapitre 3, on étend les résultats du chapitre précédent au cas où les formes $\phi$ sont prises dans une classe plus générale (fonctions, surfaces, projections géodésiques, etc) que des demi-espaces qui correspondent à des projections orthogonales par direction. Dans ce cadre plus général, les résultats dépendent fortement du choix de $O$, et c'est ce qui permet de tirer des interprétations statistiques. Dans le chapitre 4, des conséquences méthodologiques en statistique inférentielle sont tirées. Tout d'abord on introduit une nouvelle notion de champ de profondeurs directionnelles baptisée champ d'altitude. Ensuite, on définit une notion de distance entre lois de probabilité, basée sur la comparaison des deux collections de surfaces quantile du type Gini-Lorrentz. La convergence avec vitesse des mesures empiriques pour cette distance quantile, permet de construire différents tests en contrôlant leurs niveaux et leurs puissances. Enfin, on donne une version des résultats dans le cas où une information auxiliaire est disponible sur une ou plusieurs coordonnées sous la forme de la connaissance exacte de la loi sur une partition finie. / The main issue of the thesis is the development of spatial generalizations on $\R^d$ of the usual real quantile. Facing the usual fact that $\R^d$ is not naturally ordered, our idea is to simply admit subjectivity and thus to define a local viewpoint rather than a global one, anchored at some point of reference $O$ and arbitrary shape $\phi$ with the motivation of crossing information gathered by changing viewpoint $O$, shape $\phi$ and $\alpha$-th order of quantile. In Chapter 2, we study the spatial quantile points seen from an observer $O$ in a direction $u \in \Sd$ of level $\alpha$ through the class of the half-spaces orthogonal to the direction $u$. This choice implies that the convergence theorems do not depend on the choice of $O$. Under minimal regularity assumptions, the set of all quantile points seen from $O$ is a closed surface. Under minimal assumptions, we establish for the associated empirical quantile surfaces the convergence theorems uniformly on the quantile level and the observation direction with the asymptotic speed and non-asymptotic bounds of approximation. Mainly, we establish the ULLN, the ULIL, the UCLT, the uniform strong invariance principle and finally the Bahadur-Kiefer type embedding, with the approximation speed rate. In Chapter 3, all the results of the previous chapter are extended to the case where the shapes $ \phi $ are taken in a class more general (functions, surfaces, geodesic projections, etc) than orthogonal projections (half-spaces). In this general setting, the results depend strongly on the choice of $ O $. It is this dependence which permit to draw statistical interpretations: modes detection, mass localization, etc. In Chapter 4, some methodological consequences in inferential statistics are drawn. First we introduce a new concept of directional depth fields called altitude fields. In a second application is defined a new distances between probability distributions, based on the comparison of two collections of quantile surfaces, which are indexes of the type Gini-Lorrentz. The convergence with speed of the empirical quantile measures for these distances, can build different tests with control of their level and their power. A third use of the quantile surfaces is for the case where $ \alpha = 1/2$. Finally, we give a version of our theorems in the case where auxiliary information is available on one or more coordinates of the random variable. By assuming known the probability of the elements of a finite partition, the asymptotic variance of the limiting process decreases and the simulations with few points clearly shows the reframe of the estimated surfaces to the real ones.

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