Academic literature on the topic 'Lagrangian surfaces'

We deal with several problems on the surfaces obtained as second symmetric products of smooth projective curves. In particular, we treat both some attempts at extending the notion of gonality for curves and some classical problems, as the study of the ample cone in the Néron-Severi group. Moreover, we develop a family of examples of Lagrangian surfaces having particular topological properties.

Cette thèse est constituée de quatre chapitres. Le premier contient les notions de base qui permettent d'aborder les divers thèmes qui y sont étudiés. Le second est consacré à l'étude des sous-variétés lagrangiennes d'une variété presque kählérienne. J'y présente les résultats obtenus en collaboration avec Burcu Bektas, Joeri Van der Veken et Luc Vrancken. Dans le troisième, je m'intéresse à un problème de géométrie différentielle affine et je donne une classification des hypersphères affines qui sont isotropiques. Ce résultat a été obtenu en collaboration avec Luc Vrancken. Et enfin dans le dernier chapitre, je présente quelques résultats sur les surfaces de translation et les surfaces homothétiques, objet d'un travail en commun avec Rafael López<br>Abstract in English not available

In this thesis we study the properties of Lagrangian matroids of dessins d'enfants (also known as maps on orientable surfaces) and their behaviour under the action of the absolute Galois group Gal(Q). We show that while the Lagrangian matroid of a dessin itself is not invariant under this action, some of its properties, namely its width and parity, are. We also study the partial duals of a dessin and their Lagrangian matroids and show that certain partial duals can always be defined over their field of moduli. We prove some results on the representations of Lagrangian matroids as well. A relationship between dessins, their partial duals and tropical curves arising from monodromy groups of dessins is observed.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-04-18T13:51:58Z No. of bitstreams: 1 marcusviniciusdesouzaferraz.pdf: 4103901 bytes, checksum: e4adcd64380c6ba8941b29bcc9d0abfd (MD5)<br>Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-04-19T17:48:41Z (GMT) No. of bitstreams: 1 marcusviniciusdesouzaferraz.pdf: 4103901 bytes, checksum: e4adcd64380c6ba8941b29bcc9d0abfd (MD5)<br>Made available in DSpace on 2018-04-19T17:48:41Z (GMT). No. of bitstreams: 1 marcusviniciusdesouzaferraz.pdf: 4103901 bytes, checksum: e4adcd64380c6ba8941b29bcc9d0abfd (MD5) Previous issue date: 2018-02-27<br>CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>O conhecimento da topografia das superfícies e uma compreensão da interação entre elas é essencial para qualquer estudo que envolva os fenômenos de atrito, desgaste e lubrificação. O estudo da relação entre o atrito e os parâmetros de rugosidade é um problema difícil e de interesse tanto industrial como acadêmico e trabalhos experimentais e teóricos têm mostrado que uma película de fluido entre duas superfícies rugosas em movimento relativo impede o contato sólido - sólido e pode proporcionar atrito muito baixo e desgaste desprezível. A modelagem matemática utilizada neste trabalho é baseada em modelos clássicos, tais como a equação de Reynolds para a descrição dos fenômenos hidrodinâmicos e as formulações de Hertz (1896) e Greenwood e Williamson (1966) para a modelagem do contato das asperezas entre as superfícies rugosas. Para tratar a complexidade das interações entre o fluido e os pares sólidos contactados, a descrição Lagrangiana-Euleriana Arbitrária é apresentada nesta pesquisa. Através do Método dos Elementos Finitos um modelo tridimensional é gerado no Abaqus ®, a fim de identificar as pressões de contato, as tensões tangenciais e normais resultantes e os coeficientes de atrito decorrrentes do deslizamento entre uma superfície texturizada e lubrificada e um plano rígido (em analogia aos modelos de contato clássicos), cujos perfis de rugosidade são construídos a partir de informações da rugosidade média quadrática de superfícies dentárias. São avaliados também a sensibilidade de alguns parâmetros do lubrificante na determinação do coeficiente de atrito e são propostos modelos com condições de contorno distintas. Entretanto, para a verificação destes últimos busca-se reproduzir qualitativamente o resultado encontrado por Lorentz (2013) na investigação numérica de sistemas tribológicos no regime misto de lubrificação. A metodologia aqui proposta emerge como uma alternativa eficaz no campo da Tribologia, na predição do coeficiente de atrito e outras variáveis pertinentes a um fenômeno ainda pouco compreendido. Realiza-se uma análise de sensibilidade dos parâmetros de modelagem, a fim de identificar como os mesmos afetam consideravelmente o comportamento mecânico na interface de contato.<br>The knowledge of the topography of surfaces and an understanding of the interaction between them is essential for any study involving the phenomena of friction, wear and lubrication. The study of the relationship between friction and roughness parameters is a difficult problem of both industrial and academic interest and experimental and theoretical works have shown that a fluid film between two rough surfaces in relative motion prevents solid - solid contact and can provide very low friction and negligible wear. The mathematical modeling used in this paper is based on classical models, such as the Reynolds equation for the description of the hydrodynamic phenomena and the formulations of Hertz (1896) and Greenwood e Williamson (1966) of the contact between the asperities of rough surfaces. To address the complexity of the interactions between the fluid and the contacted solid pairs, the Lagrangian-Eulerian Arbitrary description is presented in this research. Through the Finite Element Method, a three-dimensional model is generated in Abaqus ®R to identify contact pressures, resulting tangential and normal stresses, and friction coefficients resulting from sliding between a textured and lubricated surface and a rigid plane (in analogy to classic contact models), whose roughness profiles are constructed from information on the quadratic roughness of dental surfaces. The sensitivity of some lubricant parameters in the determination of the coefficient of friction is also evaluated and models with different boundary conditions are proposed. However, for the vefrification of the latter, it is sought to qualitatively reproduce the result found by Lorentz (2013) in the numerical investigation of tribological systems without mixed lubrication regime. A methodology proposed here emerges as an effective alternative in the field of Tribology, in the prediction of the coefficient of friction and other relevant variables to a phenomenon still little understood. A sensitivity analysis of the modeling parameters is performed, in order to identify how they considerably affect the mechanical behavior at the contact interface.

Thesis (Master of Engineering in Ocean Engineering)--University of California at Berkeley, 2004.<br>"January 2005." Description based on title screen as viewed on May 25, 2010. DTIC Descriptor(s): Fluid Dynamics, Lagrangian Functions, Equations Of Motion, Acceleration, Formulations, Grids, Continuum Mechanics, Gaussian Quadrature, Derivatives (Mathematics), Compact Disks, Boundary Value Problems, Polynomials, Interpolation, Pressure, Operators (Mathematics). DTIC Identifier(s): Multimedia (CD-Rom), Moving Grids, Meshless Discretization, Lifs (Lagrange Implicit Fraction Step), Lagrangian Dynamics, Meshless Operators, Mlip (Multidimensional Lagrange Interpolating Polynomials), Flux Boundary Conditions, Radial Basis Functions Includes bibliographical references (58-59).