1,720,976 research outputs found
Stationary solutions of the Einstein-Vlasov system
No full textCette thèse est consacrée à la construction des solutions stationnaires de type trou noir pour le système Einstein-Vlasov. Nous obtenons en premier lieu une famille de solutions stationnaires à symétrie sphérique à partir d’un argument de bifurcation de la solution dite de Schwarzschild, une des solutions de type trou noir de référence. La construction est basée sur l’analyse de l’ensemble des géodésiques piégées et de l’énergie effective potentielle associés aux espaces-temps statiques à symétrie sphérique proches de Schwarzschild. Plus précisément, le résultat de stabilité des géodésique piégées constitue le point central de cette thèse. Les solutions construites sont arbitrairement proches de la solution de Schwarzschild et montrent en particulier que la métrique de Schwarzschild n’est pas asymptotiquement stable pour le système Einstein-Vlasov. Par ailleurs, le champ de matière est à support compact en espace et il est situé en dehors du trou noir. Ensuite, nous généralisons cette méthode à un cas plus complexe. Plus précisément, nous construisons une famille à un paramètre de solutions stationnaires à symétrie axiale par un argument de bifurcation autour la solution de Kerr, une autre solution de type trou noir de référence. On obtient également un résultat d’instabilité pour la métrique de Kerr.This thesis is devoted to the construction of stationary black hole solutions to the Einstein-Vlasov system. In a first part, we obtain a one-parameter family of static and spherically symmetric solutions to the Einstein-Vlasov system by perturbing the Schwarzschild spacetime. The constructed solutions have the property that the spatial support of the matter is a finite, spherically symmetric shell located away from the black hole. In a second part, we generalise the method of construction to the challenging case of axial symmetry in order to prove the existence of a one-parameter family of stationary and axisymmetric solutions which bifurcate from a Kerr spacetime. The common features to these two constructions are the bifurcation argument from a reference black hole solution and the analysis of trapped geodesics and the associated effective potential energy in spacetimes close to Schwarzschild and close to Kerr. More precisely, the stability results for trapped geodesics in static spherically symmetric spaces and in stationary axisymmetric spaces are the key idea for our construction. The results obtained in our thesis show in particular that Schwarzschild spacetime and Kerr spacetime are not asymptomatically stable as solutions to the Einstein-Vlasov system
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
A review of the initial boundary problem in GR and geometric uniqueness
No full textIn the absence of time-like boundary, the classical initial
value problem in GR verifies a geometric uniqueness property. In
particular, isometric Cauchy data leads to (maximal globally hyperbolic)
developments which are isometric. While there exists several well-posed
formulation of the initial boundary value problem in GR, no such
geometric uniqueness is known. This important issue was put forward by
Helmut Friedrich. It is relevant not only for the local initial boundary
value problem, but also for more global aspects, due to the possible
breakdown of gauge choices. I will review the mathematical analysis of
the initial boundary value problem in GR, with an emphasis on various
aspects relevant to the geometric uniqueness problem. If time (and
progress) permits, I will present work in progress with Grigorios
Fournodavlos concerning an approach to the initial boundary value
problem based on the wave equation satisfied by the second fundamental
form of a foliation with prescribed mean curvature.Non UBCUnreviewedAuthor affiliation: Sorbonne UniversitéFacult
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Get PDFThe study of the stability of Minkowksi space has had a tremendous influence on the mathematical analysis of General Relativity and in a wider context, on geometric hyperbolic partial differential equations. This article proposes an overview of the context, ideas and part of the legacy surrounding this subject, focusing particularly on the original proof of Christodoulou–Klainerman
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
Asymptotic properties of the small data solutions of the Vlasov-Maxwell system
No full textL'objectif de cette thèse est de décrire le comportement asymptotique des solutions à données petites du système de Vlasov-Maxwell. En particulier, on s'attachera à étudier tant le champ électromagnétique que le champ de Vlasov par des méthodes de champs de vecteurs, nous permettant ainsi d'éviter toute contrainte de support sur les données initiales. La structure isotrope du système de Vlasov-Maxwell est d'une importance capitale pour compenser le phénomène de résonance causé par les particules approchant la vitesse de propagation du champ électromagnétique. De ce fait, plusieurs parties de ce manuscrit sont dédiées à sa description. Ajoutons également que les méthodes de champs de vecteurs sont connues pour être robustes et s'adapter relativement bien à d'autres situations telles que l'étude des solutions de l'équation des ondes sur un espace-temps courbé. Cette souplesse nous a notamment permis, contrairement aux travaux précédents sur ce sujet, de considérer des plasmas avec des particules sans masse.Notre étude débute par le cas des grandes dimensions d ≥ 4 où les effets dispersifs sont plus importants et permettent ainsi d'obtenir de meilleurs taux de décroissance sur les solutions du système et leurs dérivées. Une nouvelle inégalité de décroissance pour les solutions d'une équation de transport relativiste constitue d'ailleurs un élément central de la démonstration. Afin d'établir un résultat analogue dans le cas où les particules sont sans masse, nous avons dû imposer que le champ de Vlasov s'annule initialement pour les petites vitesses puis nous avons ensuite montré que cette hypothèse était nécessaire. Dans un second temps, nous nous intéressons au cas tridimensionnel avec des particules sans masse, où une étude plus poussée de la structure des équations sera nécessaire afin d'obtenir les taux de décroissance optimaux pour les composantes isotropes du champ électromagnétique, les moyennes en vitesse de la fonction de distribution et leurs dérivées. Nous nous concentrons ensuite sur l'étude du comportement asymptotique des solutions à données petites du système de Vlasov-Maxwell massif en dimension 3. Des difficultés spécifiques nous forcent à modifier les champs de vecteurs utilisés précédemment pour l'équation de transport dans le but de compenser les pires termes d'erreurs des équations commutées. Enfin, on considère le même problème en se restreignant à l'étude des solutions à l'extérieur d'un cône de lumière. Les fortes propriétés de décroissance vérifiées par la moyenne en vitesse de la densité de particules dans cette région nous permettent d'affaiblir les hypothèses sur les données initiales et d'avoir une démonstration considérablement plus simple.The purpose of this thesis is to study the asymptotic properties of the small data solutions of the Vlasov-Maxwell system using vector field methods for both the electromagnetic field and the particle density. No compact support asumption is required on the initial data. Instead, we make crucial use of the null structure of the equations in order to deal with a resonant phenomenon caused by the particles approaching the speed of propagation of the Maxwell equations. Due to the robustness of vector field methods and contrary to previous works on this topic, we also study plasmas with massless particles.We start by investigating the high dimensional cases d ≥ 4 where dispersive effects allow us to derive strong decay rate on the solutions of the system and their derivatives. For that purpose, we proved a new decay estimate for solutions to massive relativistic transport equations. In order to obtain an analogous result for massless particles, we required the velocity support of the distribution function to be initially bounded away from 0 and we then proved that this assumption is actually necessary. The second part of this thesis is devoted to the three dimensional massless case, where a stronger understanding of the null structure of the Vlasov-Maxwell system is essential in order to derive the optimal decay rate of the null components of the electromagnetic field, the velocity average of the particle density and their derivatives. We then focus on the asymptotic behavior of the small data solutions of the massive Vlasov-Maxwell system in 3d. Specific problems force us to modify the vector fields used previously to study the Vlasov field in order to compensate the worst error terms in the commuted transport equations. Finally, still for the massive system in 3d, we restrict our study of the solutions to the exterior of a light cone. The strong decay properties satisfied by the velocity average of the particle density in such a region permit us to relax the hypothesis on the initial data and lead to a much simpler proof
- …
