Dissertations / Theses on the topic 'Minimal surface'
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Dalpé, Denis. "Schwarz's surface and the theory of minimal surfaces." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0023/MQ39958.pdf.
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Hao, Shuai. "An Introduction to Discrete Minimal Surfaces via the Enneper Surface." Thesis, Southern Illinois University at Edwardsville, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=1543912.
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In this paper, we are exploring how to construct a discrete minimal surface. We map the conformal curvature lines of a parameterized continuous minimal surface to a unit sphere by the Gauss map. Then, based on a circle patterns we create, the Koebe polyhedron can be obtained. By dualizing the Koebe polyhedron, we are able to get the discrete minimal surface. Moreover, instead of only developing the method theoretically, we also show concrete procedures visually by Mathematica for Enneper with arbitrary domain. This is an expository project mainly based on the paper "Minimal surface from circle patterns: geometry from combinatorics" by Alexander I. Bobenko, Tim Hoffmann and Boris A. Springborn.
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Zolotareva, Tatiana. "Construction de surfaces à courbure moyenne constante et surfaces minimales par des méthodes perturbatives." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX003/document.
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Cette thèse s'inscrit dans l'étude des sous-variétés minimales et à courbure moyenne constante et de l'influence de la géométrie de la variété ambiante sur les solutions de ce problème.Dans le premier chapitre, en suivant les idées de F. Almgren, on propose une généralisation de la notion d'hypersurface de courbure moyenne constante à toutes codimensions. En dimension n-k on définie les sous-variétés à courbure moyenne constante comme les points critiques de la fonctionnelle de k-volume des bords des variétés minimales de dimension k+1. On prouve l'existence dans une variété riemannienne compacte de dimension n de sous-variétés à courbure moyenne constante de codimension n-k pour tout k < n qui sont des perturbations des sphères géodésiques de petit volume.Dans le deuxième chapitre, on s'intéresse aux surfaces minimales à bords libres dans la boule unité de l'espace euclidien de dimension 3, c'est-à-dire aux surfaces minimales plongées dans la boule unité dont le bord rencontre la sphère unité orthogonalement. On démontre l'existence de deux famille géométriquement distinctes de telles surfaces qui sont indexées par un entier n assez grand, qui représente le nombre de composantes connexes du bord de ces surfaces. Nous donnons en particulier une deuxième preuve d'un résultat de A. Fraser et R. Schoen concernant l'existence de telles surfaces.Un des résultats fondamentaux de la théorie des surfaces à courbure moyenne constante est le théorème de Hopf qui affirme que les seules sphères topologiques à courbure moyenne constante dans l'espace euclidien de dimension 3 sont les sphères rondes. Dans le troisième chapitre, on propose une construction dans une variété riemannienne de dimension 3 d'une famille de sphères topologiques à courbure moyenne constante qui ne sont pas convexes et dont la courbure moyenne est très grandeThe subject of this thesis is the study of minimal and constant mean curvature submanifolds and of the influence of the geometry of the ambient manifold on the solutions of this problem.In the first chapter, following the ideas of F. Almgren, we propose a generalization of the notion of hypersurface with constant mean curvature to all codimensions. In codimension n-k we define constant mean curvature submanifolds as the critical points of the functional of the k - dimensional volume of the boundaries of k+1 - dimensional minimal submanifolds. We prove the existence in compact n-dimensional manifolds of n-k codimensional submanifolds with constant mean curvature for all k
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Aman, Ronald L. "A Minimal Surface Perturbation Method for Global Surface Registration of Unstructured Point Cloud Data." NCSU, 2004. http://www.lib.ncsu.edu/theses/available/etd-04192004-145303/.
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This thesis presents a minimal surface perturbation method for the surface registration of unstructured point cloud data. The registration problem is applicable to many disciplines. Computer vision (stereo vision), computer graphics, image processing, and reverse engineering and quality inspection are examples of areas currently implementing surface registration techniques. The surface registration problem is defined as: Given the unstructured point cloud data sets, find the rotation and translation of one data set such that the two sets are properly aligned in a single coordinate frame. Current techniques fail to find global alignment in instances where the initial starting points are not favorable. In this paper, the proposed method generates a ?geometric handler? to approximate the unstructured data sets using a small number of points capturing the global shape of the data while reducing local variations or features. An iterative searching method is proposed to minimize both the surface perturbation of point cloud data and the orientation variation by using a self-organizing neural network. The transformation of the geometric handlers is found using orientation invariant methods and is applied to the original point cloud. Once the global registration is accomplished, a local registration method is invoked requiring a search in local neighborhoods only. The proposed method can be used for the global surface registration of overlapped unstructured point cloud data sets. The presented techniques can be used in reverse engineering and CAD/CAM systems for product development and surface generation from scanned data.
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Krust, Romain. "Le problème de Dirichlet pour l' équation des surfaces minimales." Paris 7, 2005. http://www.theses.fr/1992PA077323.
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Coutant, Antoine. "Déformation et construction de surfaces minimales." Phd thesis, Université Paris-Est, 2012. http://tel.archives-ouvertes.fr/tel-00802379.
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L'objet de cette thèse consiste en la construction de nouveaux exemples de surfaces (ou hypersurfaces) minimales dans les espaces euclidiens R^3, R^n x R avec n>2 ou dans l'espace homogène S^2 x R. Nous prouvons l'existence de surfaces minimales dans R^3 arbitrairement proches d'un polygone convexe. Nous prouvons également l'existence d'hypersurfaces minimales de type Riemann dans R^n x R, n>2. Celles-ci peuvent être interprétées comme étant une famille d'hyperplans horizontaux (des bouts) reliés les uns aux autres par des morceaux de caténoïdes déformés (des cous). Nous donnons un résultat général pour ce type d'objet quand il est périodique ou bien quand il a un nombre fini de bouts horizontaux. Cela se fait sous certaines hypothèses de contraintes sur les forces intervenant dans la construction. Nous finissons en donnant plusieurs exemples, notamment l'existence d'une hypersurface de type Wei verticale qui n'existe pas en dimension 3. Nous donnons aussi la preuve de l'existence d'une surface minimale de type Riemann dans S^2 x R telle que deux bouts sphériques sont reliés entre eux alternativement par 1 cou et 2 cous. Là aussi, nous mettons en évidence le rôle joué par les forces lors de la construction. De même que dans le chapitre précédent, la méthode repose sur un processus de recollement. Nous donnons une description très précise de la caténoïde et la surface de Riemann dans S^2 x R. Enfin, nous établissons l'existence dans R^n x R d'hypersurfaces de type Scherk lorsque n>2
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Makki, Ali. "Morphismes harmoniques et déformation de surfaces minimales dans des variétés de dimension 4." Thesis, Tours, 2014. http://www.theses.fr/2014TOUR4013/document.
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Dans cette thèse, nous étudions la structure d’un morphisme harmonique F d’une variété riemannienne M4 dans une surface N2 au voisinage d’un point critique mO. Si mO est un point I critique isolé ou si M4 est compact sans bord, nous montrons que F est pseudo-Holomorphe par rapport à une structure presque hermitienne definie dans un voisinage de mO. Si M4 est compact sans bord, les fibres singuliers de F sont des surfaces minimales avec points de branchement. Ensuite, nous étudions des exemples de morphismes harmoniques due a Burel de (S4, gk,l) dans S2 où (gk,I) est une famille de métriques conforme à la métrique canonique. Nous construisons tout d’abord une application semi-Conforme Φk,l de S4 dans S2 en composant deux applications semi-Conformes régulières, F de S4 dans S3 et Φk,i, de S3 dans S2. II résulte de Baird-Eells que le fibres régulier de øk,l pour tout k, I sont minimales. Si [k] = [l] = 1, l’ensemble des points critiques est donnée par l’image réciproque du pâle nord: il consiste en deux 2-Sphères ayant deux points d’intersection. Si k, I 6= 1 l’ensemble des points critiques sont les images réciproques du pôle nord (de la même façon que pour k = t = 1 deux sphères, mais avec une multiplicité I) ainsi que la pré-Image du pôle sud (un tore) avec multiplicité k. Enfin, nous étudions une construction due à Baird-Ou de morphismes harmoniques d’une ensembles ouverts de (S2×S2, can) dans S2. Nous vérifions qu’ils sont holomorphe par rapport à une des quatre structures complexes canoniques hermitiennesIn this thesis, we are interested in harmonic morphisms between Riemannian manifolds (Mm, g) and (Nn, h) for m > n. Such a smooth map is a harmonic morphism if it pulls back local harmonic functions to local harmonic functions: if ƒ : V → ℝ is a harmonic function on an open subset V on N and Φ-1(V) is non-Empty, then the composition ƒ ∘ Φ : Φ-1(V) → ℝ is harmonic. The conformal transformations of the complex plane are harmonic morphisms. In the late 1970's Fuglede and Ishihara published two papers ([Fu]) and ([Is]), where they discuss their results on harmonic morphisms or mappings preserving harmonic functions. They characterize non-Constant harmonic morphisms F : (M,g) → (N,h) between Riemannian manifolds as those harmonic maps, which are horizontally conformal, where F horizontally conformal means : for any x ∈ M with dF(x) ≠ 0, the restriction of dF(x) to the orthogonal complement of kerdF(x) in TxM is conformal and surjective. This means that we are dealing with a special class of harmonic maps
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Robakiewicz, Stefania. "Minimal structural glyco-epitope for antibody recognition." Thesis, Lille 1, 2020. http://www.theses.fr/2020LIL1S101.
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L'importance biologique de la glycosylation pour la santé et la maladie est largement reconnue. Les structures tronquées à terminaison mannose consistant en 1 à 3 résidus de mannose, deux N-acétylglucosamines et un nombre variable de fragments fucose sont appelées paucimannose. Les N-glycanes paucimannosidiques sont abondamment exprimés dans les plantes et les invertébrés. Cependant, chez les vertébrés, leur présence est limitée à certaines conditions pathophysiologiques, telles que le cancer, les troubles immunitaires, les infections et l'inflammation, et chez les individus en bonne santé, ils ne sont détectables qu'en quantités infimes. Il a été démontré que le Mannitou, un anticorps monoclonal murin, reconnaît spécifiquement les glycoépitopes de paucimannose.Une tentative de caractérisation de la structure de Mannitou IgM a été faite en appliquant des techniques de modélisation d'homologie, de microscopie cryoélectronique et de cristallisation. L'anticorps complet de Mannitou a été généré en utilisant la technologie des hybridomes. Le Fab recombinant de Mannitou a été exprimé avec succès de manière transitoire dans des cellules HEK293T. La spécificité de liaison de Mannitou envers différents N-glycanes de paucimannose ont été élucidées par une combinaison de méthodes expérimentales. Le criblage par microréseau a révélé que le glyco-épitope minimal était Man2GlcNAc2. À son tour, Man3GlcNAc2 a manifesté l'une des interactions les plus fortes avec l'anticorps Mannitou. Des études de reconnaissance moléculaire, utilisant des mesures de résonance plasmonique de surface et une calorimétrie de titrage isotherme, ont établi une affinité de liaison micromolaire de l'anticorps Mannitou envers le glycane Man3GlcNAc2. La cartographie de l'épitope de liaison par résonance magnétique nucléaire de transfert de saturation a démontré que Manα1-3 est le principal résidu impliqué dans la reconnaissance des anticorps de Mannitou. La régulation positive des N-glycanes paucimannosidiques dans des conditions physiopathologiques fait de l'anticorps Mannitou un outil diagnostique et thérapeutique prometteur.Pour déterminer la structure minimale des glycanes requise pour mimer l'activité antigénique du polysaccharide MenX natif, des études de résonance plasmonique de surface ont été réalisées. Les expériences ont consisté à étudier les interactions de liaison entre un anticorps anti-MenX et des oligosaccharides capsulaires du sérogroupe X de Neisseria meningitides de différentes longueurs. Les résultats suggèrent que la portion minimale de saccharide capable d'assurer une protection contre les infections à MenX pourrait être DP5, ce qui en fait un candidat prometteur pour le développement de vaccinsThe biological importance of glycosylation in health and disease is broadly acknowledged. The truncated, mannose-terminating structures consisting of 1–3 mannose residues, two N-acetylglucosamines, and a variable number of fucose moieties are termed paucimannose. Paucimannosidic N-glycans are abundantly expressed in plants and invertebrates. However, in vertebrates their presence is restricted to some pathophysiological conditions, such as cancer, immune disorders, infections, and inflammation, and in healthy individuals, they are detectable only in trace amounts. Mannitou, a murine monoclonal antibody, has been demonstrated to specifically recognise paucimannose glycoepitopes. An attempt to characterise Mannitou IgM structure was made by applying homology modelling, cryo-electron microscopy, and crystallisation techniques. Full-length Mannitou antibody has been generated using hybridoma technology. Recombinant Mannitou Fab has been successfully transiently expressed in HEK293T cells. The binding specificity of Mannitou towards different paucimannose N-glycans have been unravelled by a combination of experimental methods. The microarray screening revealed the minimal glyco-epitope to be Man2GlcNAc2. In turn, Man3GlcNAc2 manifested one of the strongest interactions with Mannitou antibody. Molecular recognition studies, employing surface plasmon resonance measurements and isothermal titration calorimetry, established a micromolar binding affinity of Manniotu antibody towards Man3GlcNAc2 glycan (Kd = ~50 μM). The mapping of the binding epitope by saturation transfer difference nuclear magnetic resonance demonstrated Manα1-3 as the main residue involved in Mannitou antibody recognition. The upregulation of paucimannosidic N-glycans in pathophysiological conditions makes Mannitou antibody a promising diagnostic and therapeutic tool.For determining the minimal carbohydrate structure required for mimicking the antigenic activity of the native MenX polysaccharide, surface plasmon resonance studies were performed. The experiments involved studying the binding interactions between an anti-MenX antibody and Neisseria meningitides serogroup X capsular oligosaccharides of different length. The results suggest that the minimal saccharide portion capable of ensuring protection against MenX infections may be DP5, making it a promising candidate for vaccine development
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Truong, David Hien. "Single-Step Factor Screening and Response Surface Optimization Using Optimal Designs with Minimal Aliasing." VCU Scholars Compass, 2010. http://scholarscompass.vcu.edu/etd/64.
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Cheng and Wu (2001) introduced a method for response surface exploration using only one design by using a 3-level design to first screen a large number of factors and then project onto the significant factors to perform response surface exploration. Previous work generally involved selecting designs based on projection properties first and aliasing structure second. However, having good projection properties is of little concern if the correct factors cannot be identified. We apply Jones and Nachtsheim’s (2009) method for finding optimal designs with minimal aliasing to find 18, 27, and 30-run designs to use for single-step screening and optimization. Our designs have better factor screening capabilities than the designs of Cheng and Wu (2001) and Xu et al. (2004), while maintaining similar D-efficiencies and allowing all projections to fit a full second order model.
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Xiao, Changhong. "A structural investigation into the complexity of mesoporous silica crystals : From a view of curvature and micellar interaction to quasicrystallinity." Doctoral thesis, Stockholms universitet, Institutionen för material- och miljökemi (MMK), 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-82382.
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Mesoporous silica crystals have a large variety of structures mainly due to the versatility of their structure template. The configuration and the chemical state of the templating micellar surfactants, together with the kinetic process of silica will determine the final outcome of the synthesis. Increasing the understanding of the complex formation processes involved will enable a possibilityto fine tune the material for specific uses, today focused into the fields of photoniccrystals, drug delivery, catalysis and separation technology. In this thesis emphasis is put on (1) increasing the understanding the formation mechanism yielding the different species of mesoporous silica crystals through an in depth study of quasicrystallinity (2) Characterization and description of the structural complexity through various characterization techniquesand also by studying the kinetic structural transformation phenomenon related to the minimal G- and D-surfaces. (3) The structural studies of the versatile surfactant liquid crystals for establishing a thermodynamically stable basis to evaluate the kinetic mesoporous silica growth processes. Furthermorethe thesis both enlightens the possibilities of and contributes to the developmentof electron microscopy characterization techniques. In these studies, electron microscopy is largely employed in the characterization to give a thorough picture of the mesoporous structures. This is combined with the sample preparation techniques cross-section polishing and ionslicing. Low voltage scanning electron microscopy is utilized for studying the surfaces and cross-sections of various materials at the limit of the resolution. Here, a deep understanding of the electron beam-material interaction is used for a better interpretation of the detected signals. Transmission electron microscopyis combined with electron crystallographic reconstruction to yield a three dimensional structural model. For determination of the quasicrystallinity level for a structure of dodecagonal tiling, revealed in the scope of this study,a phason strain analysis was made.At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 7: Manuscript.
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Palmer, Fleur. "Using emergent technologies to develop sustainable architectural composites." AUT University, 2009. http://hdl.handle.net/10292/933.
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The intention of this project is to research the potential of emergent technologies for developing sustainable composites for the building industry. It is divided into three parts: Part 1 Identifies emergent practices which are being applied to the development of new sustainable building prototypes such as developments using nanotechnologies, the influence of biomimetics, the development of intelligent interactive systems and the use of digital technologies to generate complex cellular structural systems. Part 2 Outlines existing processes involved in selecting and manufacturing prototypes, as many existing processes have been opportunistically applied to emergent practices to generate innovative sustainable prototypes. Part 3 By synthesising the research gathered in the previous parts of this thesis, this section documents the design process for developing a sustainable building system. The design is based on a minimal surface structure to reduce materiality and to optimise strength and its manufacturing process exploits emergent and existing technologies for its generation.
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Zang, Yiming. "Les surfaces de Ricci et les surfaces minimales dans les groupes de Lie métriques." Electronic Thesis or Diss., Université de Lorraine, 2022. https://docnum.univ-lorraine.fr/ulprive/DDOC_T_2022_0115_ZANG.pdf.
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Nous étudions dans cette thèse des sujets liés aux surfaces minimales dans les variétés homogènes de dimension trois. La première partie est consacrée à l'étude des surfaces de Ricci à courbure négative ou nulle avec des bouts caténoïdaux. L'idée principale de cette recherche vient d'un célèbre théorème d'Huber. Nous commençons par introduire la définition des bouts caténoïdaux pour les surfaces de Ricci complètes à courbure négative ou nulle avec la courbure totale finie. Ensuite, nous développons un outil analogue à des données de Weierstrass. En utilisant cet outil, nous avons trouvé quelques résultats de classification et de non-existence pour les surfaces de Ricci à courbure négative ou nulle de genre zéro avec des bouts caténoïdaux. À la fin du deuxième chapitre, nous prouvons aussi un théorème d'existence pour les surfaces de Ricci à courbure négative ou nulle de genre arbitraire avec un nombre fini de bouts caténoïdaux. Dans la deuxième partie de cette thèse, nous nous concentrons sur les surfaces minimales dans un groupe de Lie métrique de dimension trois widetilde{E(2)}, qui est le revêtement universel du groupe des isométries affines directes du plan euclidien muni d'une métrique riemannianne invariante à gauche. Premièrement, un résultat de Patrangenaru affirme que les métriques riemanniennes invariantes à gauche de widetilde{E(2)} peuvent être décrites comme une famille de métriques à deux paramètres. Nous appliquons ensuite une representation de type Weierstrass due à Meeks, Mira, Pérez et Ros pour construire une famille à un paramètre des surfaces minimales hélicoïdales, ainsi qu'une famille à un paramètre des surfaces minimales annulaires qui sont proprement plongées dans widetilde{E(2)}. Pour conclure, nous étudions le cas limite de la famille des surfaces minimales annulaires, et nous obtenons une nouvelle preuve d'un théorème de demi-espace pour les surfaces minimales dans widetilde{E(2)}In this thesis, we will study some topics related to minimal surfaces in three-dimensional homogeneous manifolds. The first part is devoted to the study of non-positively curved Ricci surfaces with catenodial ends. The idea comes from a famous theorem of Huber. In the first place, we give a definition of catenoidal end for non-positively curved Ricci surfaces with finite total curvature. Secondly, we develop a tool which can be regarded as an analogue of the Weierstrass data. By using this tool, we get some classification results and some non-existence results for non-positively curved Ricci surfaces of genus zero with catenoidal ends. In the end of Chapter 2, we also prove an existence result for non-positively curved Ricci surfaces of arbitrary positive genus with finite many catenoidal ends.In the second part of this thesis, we concern about minimal surfaces in a three-dimensional metric Lie group widetilde{E(2)}, which is the universal covering of the group of rigid motions of Euclidean plane endowed with a left-invariant Riemannian metric. Firstly, a result of Patrangenaru describes the left-invariant metrics as a two-parameter family of metrics. Then we take advantage of a Weierstrass-type representation due to Meeks, Mira, Pérez and Ros to construct a one-parameter family of helicoidal minimal surfaces in widetilde{E(2)} as well as a one-parameter family of minimal annuli which are properly embedded in widetilde{E(2)}. In the end, by a discussion of the limit case of the second family of surfaces, we obtain a new proof of a half-space theorem for minimal surfaces in widetilde{E(2)}
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Tcherniavski, Leonid [Verfasser], and Peer [Akademischer Betreuer] Stelldinger. "Minimal Sampling Criteria and Method for Nonmanifold Surface Reconstruction from Unorganized Points / Leonid Tcherniavski. Betreuer: Peer Stelldinger." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2014. http://d-nb.info/1051435536/34.
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Welch, Stephen William. "C¹,α regularity for boundaries with prescribed mean curvature." Diss., University of Iowa, 2012. https://ir.uiowa.edu/etd/3551.
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In this study we provide a new proof of C¹,α boundary regularity for finite perimeter sets with flat boundary which are local minimizers of a variational mean curvature formula. Our proof is provided for curvature term H∈LΩ. The proof is a generalization of Cafarelli and C#243;rdoba's method, and combines techniques from geometric measure theory and the theory of viscosity solutions which have been developed in the last 50 years. We rely on the delicate interplay between the global nature of sets which are variational minimizers of a given functional, and the pointwise local nature of comparison surfaces which satisfy certain PDE. As a heuristic, in our proof we can consider the curvature as an error term which is estimated and controlled at each point of the calculation.
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Giovannardi, Gianmarco. "Geometric properties of 2-dimensional minimal surfaces in a sub-Riemannian manifold which models the Visual Cortex." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/11473/.
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In this paper we study the notion of degree forsubmanifolds embedded in an equiregular sub-Riemannian manifold and we provide the definition of their associated area functional. In this setting we prove that the Hausdorff dimension of a submanifold coincides with its degree, as stated by Gromov. Using these general definitions we compute the first variation for surfaces embedded in low dimensional manifolds and we obtain the partial differential equation associated to minimal surfaces. These minimal surfaces have several applications in the neurogeometry of the visual cortex.
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Berthiere, Clément. "Entanglement, boundaries and holography." Thesis, Tours, 2017. http://www.theses.fr/2017TOUR4017.
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La notion d’entropie d’intrication a eu un profond impact sur la physique théorique, particulièrement depuis ces dix dernières années. D’abord introduite afin expliquer l’entropie des trous noirs, son champ d’application s’est par la suite ouvert à une grande variété de domaines de recherche, de la matière condensée à la gravitation quantique, de l’information quantique à la théorie quantique des champs. Dans ce contexte scientifique effervescent, l’entropie d’intrication apparait comme un outil central et doit donc intensivement être étudiée. A l’origine de cette thèse se trouve le désir de mieux comprendre cette entropie. D’intéressants développements concernant les effets de bord sur l’entropie d’intrication ont vu le jour récemment. Nous proposons donc d’explorer comment le bord d’un espace affecte l’entropie, en particulier dans la situation où la surface d’intrication intersecte ce bord. Nous présentons des calculs explicites de l’entropie d’intrication en espace plat avec bords. Nous montrons que des termes induits par ces bords apparaissent dans l’entropie et nous soulignons le rôle prépondérant que jouent les conditions aux bords. Nous étudions ensuite la contribution de bord dans le terme logarithmique de l’entropie d’intrication en dimensions trois et quatre. Nous calculons en premier lieu ce terme en théorie des champs pour la théorie N = 4 de Yang-Mills, puis nous répétons ce calcul de manière holographique. Nous montrons que ces deux méthodes de calcul donnent le même résultat, si du côté théorie des champs les conditions aux bords préservent la moitié de la supersymétrie et que du côté gravité l’extension du bord dans le bulk est une surface minimaleThe entanglement entropy has had a tremendous and profound impact on theoretical physics, particularly since the last decade. First introduced in an attempt to explain black holes entropy, it has then found applications in a wide range of research areas, from condensed matter physics to quantum gravity, from quantum information to quantum field theory. In this exciting scientific context, the entanglement entropy has thus emerged as a useful and pivotal tool, and as such justifies the need to be intensively studied. At the heart of this thesis therefore lies the desire to better understand the entanglement entropy. Interesting developments during the recent years concern the boundary effects on the entanglement entropy. This dissertation proposes to explore the question of how the presence of spacetime boundaries affects the entropy, specifically in situations where the entangling surface intersects these boundaries. We present explicit calculations of entanglement entropy in flat spacetime with plane boundaries. We show that boundary induced terms appear in the entropy and we emphasize the prominent role of the boundary conditions. We then study the boundary contribution to the logarithmic term in the entanglement entropy in three and four dimensions. We perform the field theoretic computation of this boundary term for the free N = 4 super-gauge multiplet and then repeat the same calculation holographically. We show that these two calculations are in agreement provided that on the field theory side one chooses the boundary conditions which preserve half of the full supersymmetry and that on the gravity side the extension of the boundary in the bulk is minimal
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Alvino, Christopher Vincent. "Multiscale Active Contour Methods in Computer Vision with Applications in Tomography." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/6896.
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Most applications in computer vision suffer from two major difficulties. The first is they are notoriously ridden with sub-optimal local minima. The second is that they typically require high
computational cost to be solved robustly. The reason for these two drawbacks is that most problems in computer vision, even when
well-defined, typically require finding a solution in a very large high-dimensional space.
It is for these two reasons that multiscale methods are particularly well-suited to problems in computer vision. Multiscale methods, by
way of looking at the coarse scale nature of a problem before considering the fine scale nature, often have the ability to avoid sub-optimal local minima and obtain a more globally optimal solution. In addition, multiscale methods typically enjoy reduced computational
cost.
This thesis applies novel multiscale active contour methods to several problems in computer vision, especially in simultaneous segmentation
and reconstruction of tomography images. In addition, novel multiscale methods are applied to contour registration using minimal surfaces and to the computation of non-linear rotationally invariant optical flow. Finally, a methodology for fast robust image segmentation is presented that relies on a lower dimensional image
basis derived from an image scale space.
The specific advantages of using multiscale methods in each of these problems is highlighted in the various simulations throughout the
thesis, particularly their ability to avoid sub-optimal local minima and their ability to solve the problems at a lower overall
computational cost.
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Antico, Alessandro. "Computer aided design and finite element modeling to predict bulk mechanical properties of bone scaffolds using triply periodic minimal surfaces (progettazione assistita al calcolatore ed analisi con il metodo degli elementi finiti per predire il comportamento meccanico di scaffolds ossei creati con l'uso di superfici minime periodiche in tre direzioni)." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/6864/.
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The aim of Tissue Engineering is to develop biological substitutes that will restore lost morphological and functional features of diseased or damaged portions of organs. Recently computer-aided technology has received considerable attention in the area of tissue engineering and the advance of additive manufacture (AM) techniques has significantly improved control over the pore network architecture of tissue engineering scaffolds. To regenerate tissues more efficiently, an ideal scaffold should have appropriate porosity and pore structure. More sophisticated porous configurations with higher architectures of the pore network and scaffolding structures that mimic the intricate architecture and complexity of native organs and tissues are then required. This study adopts a macro-structural shape design approach to the production of open porous materials (Titanium foams), which utilizes spatial periodicity as a simple way to generate the models. From among various pore architectures which have been studied, this work simulated pore structure by triply-periodic minimal surfaces (TPMS) for the construction of tissue engineering scaffolds. TPMS are shown to be a versatile source of biomorphic scaffold design. A set of tissue scaffolds using the TPMS-based unit cell libraries was designed. TPMS-based Titanium foams were meant to be printed three dimensional with the relative predicted geometry, microstructure and consequently mechanical properties. Trough a finite element analysis (FEA) the mechanical properties of the designed scaffolds were determined in compression and analyzed in terms of their porosity and assemblies of unit cells. The purpose of this work was to investigate the mechanical performance of TPMS models trying to understand the best compromise between mechanical and geometrical requirements of the scaffolds. The intention was to predict the structural modulus in open porous materials via structural design of interconnected three-dimensional lattices, hence optimising geometrical properties. With the aid of FEA results, it is expected that the effective mechanical properties for the TPMS-based scaffold units can be used to design optimized scaffolds for tissue engineering applications. Regardless of the influence of fabrication method, it is desirable to calculate scaffold properties so that the effect of these properties on tissue regeneration may be better understood.
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Ha, Pham Hoang. "On unicity problems of meromorphic mappings of Cn into PN(C) and the ramification of the Gauss maps of complete minimal surfaces." Phd thesis, Université de Bretagne occidentale - Brest, 2013. http://tel.archives-ouvertes.fr/tel-00871320.
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In 1975, H. Fujimoto generalized Nevanlinna's known results for meromorphic fonctions to the case of meromorphic mappings of Cn into PN(C). He proved that for two linearly nondegenerate meromorphic mappings f and g of C into PN(C). if they have the saine inverse images counted with multiplicities for 3N + 2 hyperplanes in general position in PN(C) then f = g. After that, this problem has been studied intensively by a number of mathematicans as H. Fujimoto, W. Stoll, L. Smiley, M. Ru, G. Dethloff - T. V. Tan, D. D. Thai - S. D. Quang, Chen-Yan and so on. Parallel to the development of Nevanlinna theory, the value distribution theory of the Gauss map of minimal surfaces immersed in Rm vas studied by many mathematicans as R. Osserman, S.S. Chern, F. Xavier, H. Fujimoto, S. J. Kao, M. Ru and many other mathematicans. In this thesis, we continuous studing some problems on these directions. The main goals of the thesis are followings. * Unicity theorems with truncated multiplicities of meromorphic mappings of Cn into PN(C) sharing 2N + 2 fixed hyperplanes.* Unicity theorems with truncated multiplicities of meromorphic mappings of Cn into PN(C) for moving targets, and a small set of identity.
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Campos, Geovan Carlos Mendonça. "Rigidez de planos projetivos minimizantes de área em 3-Variedades." Universidade Federal do Maranhão, 2016. http://tedebc.ufma.br:8080/jspui/handle/tede/1615.
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In this work, we talk about the article "Area-Minimizing Projective Planes in 3- Manifolds" due to Hubert Bray, Simon Brendle, Michael Eichmair and Andr´e Neves. In this article they consider a compact Riemannian 3-manifold (M; g) with positive scalar curvature and an embedded projective plane. In these conditions they prove a higher estimate of curvature, in term of infimum of the scalar curvature of (M; g), for the area of the projective plane that has the smallest area within the class of all surfaces Σ ⊂ M homeomorphic to projective plane. Furthermore, they prove that this inequality is great. More precisely, they get that if this equality hold in (M 3; g), so M is isometric to the three-dimensional projective space RP3 with constant sectional curvature.
Neste trabalho, dissertamos sobre o artigo "Area-minimizing Projective Planes in 3-Manifolds" devido a Hubert Bray, Simon Brendle, Michael Eichmair e André Neves. Neste artigo eles consideram uma 3-variedades Riemannianas compactas (M³, g) com curvatura escalar positiva e que admitem planos projetivos mergulhados. Nestas condições eles provam uma estimativa superior, em termo do ínfimo da curvatura escalar de (M; g), para a área do plano projetivo que possui a menor área dentro da classe de todas as superfícies Σ ⊂ M homeomorfas ao plano projetivo. Além disso, eles provam que esta desigualdade é ótima. Mais precisamente, eles obtém que se a igualdade ocorre então a variedade Riemanniana (M³, g) é isométrica ao espaço projetivo tridimensional RP3 coma métrica de curvatura seccional constante.
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Bedel, Sophie. "Conception de nouvelles surfaces à propriétés antibactériennes." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112358.
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La biocontamination des surfaces et les risques associés sont des enjeux majeurs économiques et de santé publique. Afin de limiter ou empêcher l’adhésion bactérienne, une des solutions possible consiste en la modification des propriétés des surfaces, afin de leur conférer les fonctions voulues. Dans ce contexte, l’objectif de cette étude est de modifier des surfaces de types métallique (acier) ou polymère : poly(téréphtalate d’éthylène) par des glycomonomères ou des monomères bioactifs. La stratégie de modification des surfaces s’effectue en plusieurs étapes.La première étape permet d’incorporer des fonctions réactives sur les surfaces par traitement acide puis réaction avec la dopamine, ou par traitement plasma ammoniaque. Des fonctions hydroxyle et amine sont introduites. Par la suite un amorceur de polymérisation par transfert d’atome est greffé sur les surfaces. Les monomères sont synthétisés et leur polymérisation étudiée en solution, dans un premier temps dans les conditions de polymérisation radicalaire classique, puis par polymérisation par transfert d’atome. Les conditions optimales sont déterminées, puis les polymérisations sur surfaces effectuées. La dernière étape concerne l’étude des propriétés microbiologiques des surfaces synthétisées.Les glycopolymères protégés et déprotégés de galactose ainsi que les polymères de méthacrylate de gaïacyle et de méthacrylate de thymyle ont été synthétisés. Les monomères ont été polymérisés par polymérisation par transfert d’atome à partir de la surface, sur les surfaces d’acier et de poly(téréphtalate d’éthylène). Après chaque étape de modification de surface, les matériaux ont été systématiquement caractérisés par goniométrie et spectroscopie à photoélectrons X. Les surfaces d’acier fonctionnalisées par le glycopolymère présentent des propriétés anti-adhésives vis-à-vis de Bacillus subtilis, un effet plus marqué est observé après greffage du glycopolymère déprotégé. Les surfaces de poly(téréphtalate d’éthylène) quant à elles, possèdent des propriétés anti-adhésives leur du greffage du poly(méthacrylate de thymyle) vis-à-vis de Listeria monocytogenes, Staphilococcus aureus et Pseudomonas aeruginosa. Un effet anti-biofilm a également été mis en évidence vis-à-vis de Staphilococcus aureus.En parallèle des homopolymères d’ammonium quaternaire et des copolymères obtenus en incorporant les monomères bioactifs ont été synthétisés. Les propriétés antibactériennes sont testées en milieu planctonique vis-à-vis de Bacillus subtilis. Un degré de polymérisation égal à 78 et les groupements halogénoalcane : iodométhane ou bromoéthane permettent l’obtention de la concentration minimale inhibitrice la plus faible. La présence des monomères bioactifs permettent la diminution de la concentration minimale inhibitrice. Le résultat le plus intéressant est obtenu lors de l’incorporation d’un pourcent de N-(4-hydroxy-3-méthoxy-benzyl)-acrylamideBio-contamination of surfaces and related risks are very important economically and for public health. To prevent this phenomenon, one solution is to modify the properties of the surfaces, in order to give them the wanted functionalities. The goal of this study is the modification of metallic surfaces (steel) or polymer surfaces: poly(ethylene terephtalate) with glycomonomers or bioactives monomers. To reach this objective, a multi-step strategy is applied.The first step enabled the incorporation of reactive species on the surfaces by an acid treatment followed by a reaction with dopamine, or by ammonia plasma treatment. Hydroxyl or amine functional groups are added. Then, an initiator of atom transfer radical polymerization is grafted on surfaces. Monomers are synthesized and conventional polymerization and atom transfer radical polymerization are studied. Optimal conditions are determined and polymerization on surfaces achieved. The last step is the study of the microbiological properties of the synthesized surfaces.Protected and unprotected galactose glycopolymers as well as gaiacyl methacrylate and thymyl methacrylate have been synthesized. Monomers have been polymerized by atom transfer radical polymerization directly to the steel or poly(ethylene therephtalate) surfaces. After each step, materials are analyzed by contact angle measurements and X-ray photoelectron spectrometry.Steel surfaces which are functionalized by a glycopolymer and tested in presence of Bacillus subtilis are found to have antiadhesive properties. A most important effect is observed with the unprotected glycopolymer. Poly(ethylene terephtalate) surfaces have antiadhesive properties in presence of Listeria monocytogenes, Staphilococcus aureus and Pseudomonas aeruginosa when poly(thymyl methacrylate) is grafted. An antibiofilm effect is observed with Staphilococcus aureus.Simultaneously, quaternary ammonium homopolymers and copolymers by integration of bioactive monomers have been obtained. Their antibacterial properties are tested in planctonik conditions in presence of Bacillus subtilis. A degree of polymerization equal to 78 and alkyl halide groups: iodomethane and bromoethane enabled to obtain the lowest minimal inhibitory concentration. Bioactive monomers contributed to emphasize this decrease. The most decreasing effect is obtained when one per cent of N-(4-hydroxy-3-méthoxy-benzyl)-acrylamide is integrated
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Chaparro, Maria Guadalupe. "Minimal surfaces." CSUSB ScholarWorks, 2007. https://scholarworks.lib.csusb.edu/etd-project/3118.
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The focus of this project consists of investigating when a ruled surface is a minimal surface. A minimal surface is a surface with zero mean curvature. In this project the basic terminology of differential geometry will be discussed including examples where the terminology will be applied to the different subjects of differential geometry. In addition the focus will be on a classical theorem of minimal surfaces referred to as the Plateau's Problem.
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Morabito, Filippo. "Minimal surfaces derived from the Costa-Hoffman-Meeks examples." Phd thesis, Université Paris-Est, 2008. http://tel.archives-ouvertes.fr/tel-00469114.
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Cette thèse porte sur la construction de nouveaux exemples de surfaces minimales dérivées de la famille de surfaces de Costa-Hoffman-Meeks. Il s'agit d'une famille de surfaces minimales complètes plongées avec trois bouts et genre k > 0. Soit M_k la surface de Costa_Hoffman_Meeks de genre k. Dans le chapitre 1, j'ai démontré que M_k est non dégénérée pour k > 37. J'ai donc étendu les résultats de S. Nayatani qui assuraient que la surface M_k est non dégénérée seulement pour k=1,...,37. Ce résultat permet de montrer dans les chapitres 2 et 3 l'existence de nouveaux exemples de surfaces minimales de genre g arbitraire à l'aide d'une procédure de collage d'autres surfaces déjà connues (parmi lesquelles y figure la surface M_k). Sans ceci, ces résultats ne seraient valables que pour k < 38. En particulier dans le chapitre 2, j'ai démontré l'existence, dans H^2 x R, (H^2 étant le plan hyperbolique) d'une famille de surfaces minimales plongées inspirées de M_k, pour tout k > 0. Ce résultat peut être censé un cas particulier d'un théorème générale de désingularisation de l'intersection de deux surfaces minimales annoncé par N. Kapouleas et jamais publié. Le chapitre 3 est consacré à la construction de trois familles de surfaces minimales simplement périodiques plongées dans R^3 dont le quotient a genre arbitraire. Les résultats présentés dans ce chapitre (obtenus en collaborations avec L. Hauswirth et M. Rodríguez) généralisent plusieurs anciennes constructions
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Melin, Jaron Patric. "Examples of discontinuity for the variational solution of the minimal surface equation with Dirichlet data on a domain with a nonconvex corner and locally negative mean curvature." Thesis, Wichita State University, 2013. http://hdl.handle.net/10057/10639.
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The purpose of this thesis is to investigate the role of smoothness, specifically the smoothness of the boundary ∂Ω, in the behavior of the variational solution f on a domain Ω to the Dirichlet problem for the Minimal Surface Equation at a point O ∈ ∂Ω when the (generalized) curvature of ∂Ω has a negative upper bound in a neighborhood of O. We give examples which show that the assumption of boundary-regularity which Simon made in [12] or at least some weaker boundary-regularity assumption which excludes nonconvex corners in the boundary of the domain is necessary in order to guarantee that the variational solution of the Dirichlet problem for the Minimal Surface Equation is continuous in the closure of the domain for every Lipschitz-continuous boundary-data function ϕ : ∂Ω → R. This is independent of whether or not f equals ϕ on ∂Ω. Furthermore, these examples give credence to the Concus-Finn Conjecture, which still awaits to be proven in the case that the contact-angle is 0 or π at nonconvex corners.Thesis (M.S.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics
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Passeggi, Alejandro Verfasser], Gerhard [Akademischer Betreuer] Keller, and Andreas [Akademischer Betreuer] [Knauf. "Contributions in Surface Dynamics : a classification of minimal sets of homeomorphisms and aspects of the rotation theory on the torus / Alejandro Passeggi. Gutachter: Gerhard Keller ; Andreas Knauf." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2014. http://d-nb.info/1064996493/34.
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Passeggi, Alejandro [Verfasser], Gerhard [Akademischer Betreuer] Keller, and Andreas [Akademischer Betreuer] Knauf. "Contributions in Surface Dynamics : a classification of minimal sets of homeomorphisms and aspects of the rotation theory on the torus / Alejandro Passeggi. Gutachter: Gerhard Keller ; Andreas Knauf." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2014. http://nbn-resolving.de/urn:nbn:de:bvb:29-opus4-50012.
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Passeggi, Alejandro [Verfasser], Gerhard Akademischer Betreuer] Keller, and Andreas [Akademischer Betreuer] [Knauf. "Contributions in Surface Dynamics : a classification of minimal sets of homeomorphisms and aspects of the rotation theory on the torus / Alejandro Passeggi. Gutachter: Gerhard Keller ; Andreas Knauf." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2014. http://d-nb.info/1064996493/34.
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Nguyen, Minh Hoang. "Surfaces minimales dans des variétés homogènes de dimension 3 minimal surfaces in three dimensional homogeneous manifolds." Toulouse 3, 2016. http://www.theses.fr/2016TOU30173.
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Cette thèse est consacrée aux surfaces minimales dans certains espaces homogènes riemanniens de dimension 3. Dans une première partie, nous considérons la variété homogène riemannienne PSL2(IR. , T) qui peut encore être considéré comme IHI2 x IR = {(x, y, z) E JR3 : :r2 + y2 < 4} munie de lametrique. \2 (d:c2 + dy 2) + (x. \(ydx- xdy) + dz) 2 où,\= 4 (oc}+y')" Nous construisons des anneaux plongés complets dont le bord se compose de 4 droites verticales sur le bord à nnfinide IHI2 x IR. . De plus, ces anneaux sont asymptotiques à deux surfaces minimales verticales de PSL2 (1R, T). Ces anneaux sont construits en prenant la limite d'une suite d'anneaux minimaux compacts. L'ingredient principal de cette démonstration est d'estimer la courbure des suites d'anneaux minimaux compacts, basé sur le controle l'espace tangent en utilisant les feuilletages minimaux do PSL2(1R, x). Dans une seconde partie, nous étudions le problème de Dirichlet pour réquation des surfaces minimales dans Sol3 avec des données à bord peut être infinies1 où Sol3 est un groupe de Lie non-abélien résoluble de dimension 3 muni d'une métrique invariante à gauche qui en fait un modèle de l'une des huit géometries de Thurston. Notre résultat est un théorème de type Jenkins-Scrrin qni établit les conditions nécessaires et suffisantes pour l'existence et l'unicité de certains graphes de Killing dans Sol;3, où le champ de vecteur de Killing est non-unitaireThis thesis deals with minimal surfaces in some homogencous Riemannian 3-manifolds. In a first part, we consider the homogeneous Riemannian 3-manifolrl PSL2(1H:, r) which can be vicwed as IHI2 x IR= {(:r,y,z) E IR. 3 : :r2 +y2 < 4} endowcd with the Ricmannian metric>. 2 (dx 2+dy2 )+(r À(ydx- xdy) + dz)2 where À= 4 (x~+y'), we construct complete, embedded minimal annuli whose boundary consists of 4 vertical lines on the boundary at infinity of PSL_2(R, t):. J\. 'forcover, these minimal annuli arc asymptotic ta two vertical minimal surfaces ofPSL2(R r). The annuli arc constructcrl by taldng the limit of a sequence of compact minimalannuli. The main idca of this proof is to cstimatc curvaturc of sequences of compact minimalannuli bascd on controlling their tangent spaccs by using minimal foliations of PSL2 (IR, T). In a second part, \VC study the Dirichlet problem for the minimal surface equation in Sol3\'Vith possible infinite bounda. Ry data, whcrc Sol;~ is the non-Abclian solvable 3-climcnsionalLie group cquippcd \vith its usual !cft-invariant metric that makcs it into a madel spacc forone of the eight Thurston geometries. Our main result is a JcnkinsScrrin type theorcm \Vhichestablishes neccssary and sufficient conditions for the existence and uniqucness of certainminimal Killing graphs \Vith a non-unitary Killing vcctor field in So l3
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Magnapera, Claudia. "Minimal surfaces, a study." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13490/.
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Le superfici minime, sono di grande interesse in vari campi della matematica, e parecchie sono le applicazioni in architettura e in biologia, ad esempio. È possibile elencare diverse definizioni equivalenti per tali superfici, che corrispondono ad altrettanti approcci. Nella seguente tesi ne affronteremo alcuni, riguardanti: la curvatura media, l'equazione differenziale parziale di Lagrange, la proprietà di una funzione di essere armonica, i punti critici del funzionale di area, le superfici di area minima con bordo fissato e la soluzione del problema di Plateau.
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PEREIRA, FELIPE DE ALBUQUERQUE MELLO. "MINIMAL SURFACES IN R3." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2013. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=22141@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
FUNDAÇÃO DE APOIO À PESQUISA DO ESTADO DO RIO DE JANEIRO
PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO
Neste trabalho estudamos a teoria clássica das superfícies mínimas em R3, focando na representação de Enneper-Weierstrass e suas consequências. São exibidos vários exemplos, incluindo as superfícies de Jorge-Meeks e de Jorge-Xavier. Também mostramos princípios do máximo para superfícies mínimas e várias aplicações como, por exemplo, o teorema do semi-espaço. Em seguida, nos concentramos na teoria das superfícies mínimas completas de curvatura total finita e, com esta, podemos analisar o desenvolvimento assintótico de fins mínimos completos mergulhados de curvatura total finita. Por fim, a dissertação culmina com o teorema de Schoen, que afirma que as únicas superfícies mínimas completas, conexas, de curvatura total finita e apenas dois fins - ambos mergulhados - são um par de planos e o catenoide.
In this work we study the classical theory of minimal surfaces in R3, with special focus on the Enneper-Weierstrass representation and its consequences. We exhibit many examples, including the Jorge-Meeks and Jorge-Xavier surfaces. We also show maximum principles for minimal surfaces and many applications as, for instance, the half-space theorem. Afterwards, we focus on the theory of complete minimal surfaces with finite total curvature, with which we can analyse the asymptotic development of complete minimal embedded ends with finite total curvature. This dissertation culminates with the Schoen s theorem, which states that the only complete, connected minimal surfaces with finite total curvature and exactly two ends - both embedded - are a pair of planes or a catenoid.
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MORALES, DANIA GONZALEZ. "STABILITY OF MINIMAL SURFACES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2014. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=24800@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
Este trabalho tem como propósito o estudo da estabilidade de hipersuperfícies mínimas imersas em R n mais 1. Apresentamos algumas caracterizações de hipersuperfícies mínimas deduzindo as fórmulas da primeira e segunda variação do funcional da área. Em seguida, a partir do cálculo de variações, estabelecemos a relação entre a teoria espectral e a estabilidade. Em particular, estudamos a caraterização variacional do primeiro autovalor do operador de estabilidade. Com base nesta relação mostramos alguns critérios de estabilidade para hipersuperfícies mínimas imersas em R n mais 1. Em especial, exibimos em detalhes o critério de estabilidade de Barbosa-Do Carmo para a estabilidade de superfícies mínimas em R3. Assim como o critério de Fischer-Colbrie-Shoen para superfícies mínimas completas, não compactas, usando a teoria elíptica. Concluímos com a análise da estabilidade do catenoide em R3 e em R n mais 1. Obtemos os domínios de estabilidade do catenoide em R3 a partir da teoria de Sturm Liouville. Exibimos o teorema de estabilidade de Lindelof em R3 e em R n mais 1 e a propriedade do catenoide ter índice 1.
This work aims to study the stability of minimally immersed hypersurfaces in R n more 1. We present some characterizations of minimal hypersurfaces deducting the formulas of the first and second variation of area. Afterwards, from the variational calculus, we establish the relationship between spectral theory and stability. Particulary, we study a variational characterization of the first eigenvalue associated to the stability operator. Based in this relationship we show some stability criteria for minimally immersed hypersurfaces in R n more 1. In particular, we exhibit in details the Barbosa-Do Carmo criterion for the stability of minimal surfaces in R3. We also establish the Fischer- Colbrie-Shoen criterion for complete, non compact, minimal surfaces using the elliptic theory. We conclude with the analysis of the stability of the catenoid in R3 and in Rn more 1. This is done by studying the stability domains of the catenoid in R3 using the Sturm-Liouville theory. We explain the Lindelof stability theorem in R3 and in R n more 1 and the property of the catenoids have index 1.
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Karst, Maxime. "Mesure et discrimination de rayonnements bêta et gamma dans une ambiance gamma élevée et fluctuante : conception, développement et caractérisation d'un contaminamètre haute sensibilité." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0358.
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Dans le cadre des activités de maintenance des centrales nucléaires, les personnes intervenant sur des chantiers en zone contrôlée doivent effectuer des mesures de contamination surfacique sur leurs outils, gants, sur tenue de travail et sur les parties de leur corps susceptible d’être contaminées (cou et tête par exemple). Or, les mesures de contamination surfacique bêta ne peuvent pas toujours être réalisées au plus près des chantiers. Le bruit de fond gamma présent à ces endroits étant élevé et fluctuant, ce dernier perturbe les appareils utilisés habituellement pour la mesure de contamination surfacique. L’objectif principal de ce travail était de concevoir un appareil de mesure adapté à la détection de contamination surfacique bêta de quelques Bq/cm2 (typiquement < 4 Bq/cm2), dans une ambiance gamma de quelques dizaines de µSv/h (typiquement < 100 µSv/h) et fluctuante (typiquement de l’ordre de 30% en 1 seconde)In the framework of the nuclear power plants maintenance, the onsite workers incontrolled areas must performed some surface contamination controls of their tools, gloves, workingsuits and over their body parts which may be contaminated (neck and head for instance). However,surface beta contamination measurements can’t always been done as close as possible of the working location. The onsite ambient gamma background, being high and fluctuating, may disturb the radiation protection devices commonly used for surface contamination measurements.The main goal of this work was to conceive a radiation protection device adapted to the betasurface contamination of about a few Bq/cm2 (< 4Bq/cm2 typicaly) in a fluctuating (typicaly 30%variation per second) ambient gamma background of a few μSv/h (typicaly <100 μSv/h)
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Lopes, Lauriclecio Figueiredo. "Superficies minimas folheadas por circunferencias." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306661.
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Orientador: Valerio Ramos BatistaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Entende-se por superfícies mínimas aquelas cuja curvatura média é nula. Têm-se como exemplos clássicos o catenóide, o helicóide e a superfície de Scherk. Historicamente, elas estão relacionadas com minimização de área, porém quando realiza-se uma variação normal incluindo os bordos, a superfície original com curvatura média nula pode representar uma área localmente máxima. Em certos casos de variação com bordo fixo, tem-se realmente a minimização do funcional área. No espaço euclidiano tridimensional, o Teorema da Representação de Weierstrass expressa uma superfície mínima em termos de integrais envolvendo uma função holomorfa e uma meromorfa. A partir desta meromorfa pode-se deduzir a aplicação normal de Gauss. Conceitos como curvatura Gaussiana, curvatura total, superfícies completas e regularidade também são utilizados para deduzir propriedades das superfícies mínimas. Quando estudamos as superfícies mínimas para as quais o bordo consiste de duas circunferências disjuntas, os Teoremas de Enneper e Shiffman, o Princípio de Reflexão de Schwarz e a unicidade do Problema de Bjõrling são ferramentas importantes para a dedução das soluções, a saber, o catenóide e as superfícies de Riemann. Estas apresentam simetrias por reflexão a um plano e invariância por rotação de 180 graus em torno de uma reta. A função "P de Weierstrass" simétrica é de grande utilidade no estudo destas propriedades
Abstract: Minimal surfaces are known to be the ones with mean curvature zero. Classical exampIes are the catenoid, helicoid and the Scherk surface. Historically, they were associated with the property of minimizing area. However, they can even maximize it localIy for cases of normal variation which include the boundary. For fixed boundary, we shalI analyse when they realIy minimize the area functional. In the three-dimensional Euclidean space, the Weierstrass Representation Theorem expresses any minimal surface S by means of integraIs with a holomorphic and a meromorphic functions, usualIy denoted by f and g, respectively. The unitary normal N of S is fulIy determined by g. Concepts like "Gaussian curvature", "total curvature", "com pleteness" and "regularity" are also employed in order to read off some properties of minimal surfaces. Concerning the case for which the boundary of S consists of two disjoint circumferences, Enneper's and Shiffman's Theorems, The Schwarz's Reflection PrincipIe and the B6rling's Problem are fundamental tools to characterize the solutions, namely the catenoid and the Riemann's examples. AlI these are invariant by a reflectional symmetry in a plane, and also by a rotation of 180-degree around a straight line. The symmetric Weierstrass-Pfunction is very useful to deduce these properties
Mestrado
Matematica
Mestre em Matemática
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Duran, James Joseph. "Differential geometry of surfaces and minimal surfaces." CSUSB ScholarWorks, 1997. https://scholarworks.lib.csusb.edu/etd-project/1542.
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Xavier, Bruno Marino. "W-congruences for minimal surfaces in Nil3 and Laguerre minimal surfaces in space forms." reponame:Repositório Institucional da UnB, 2018. http://repositorio.unb.br/handle/10482/33036.
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Tese (doutorado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2018.Submitted by Raquel Viana (raquelviana@bce.unb.br) on 2018-10-30T21:20:30Z No. of bitstreams: 1 2018_BrunoMarinoXavier.pdf: 1783146 bytes, checksum: 58567e91e514f4dced7a3ca18f00354c (MD5)
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) e Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq).
Obtemos uma transformação de Bäcklund entre superfı́cies mı́nimas em Nil3 aplicando uma correspondência de Calabi entre uma superfı́cie CMC-1/2 em L3 e sua superfı́cie associada em Nil3 e fazendo uma transformação de Ribaucour na superfı́cie original relacionamos a geometria dessas duas superfı em L3. Em seguida, ́cies usando a segunda forma de Abresch- Rosenberg. Adiante, estendemos a definição de superfı́cies mı́nimas de Laguerre a formas espaciais enquanto relacionamos estas às superfı́cies mı́nimas em L3 e mı́nimas em outros espaços produto M2(k) × R e M2 (k) × R1 , com k = ±1.
We obtain a Bäcklund transformation between minimal surfaces in Nil3 by performing a Calabi correspondence between a CMC-1/2 surface in L3 and its associated minimal surface in Nil3 and sau Rrfiabcaeusc ouusrin tgra tnhsef oArmbr eosnc hth-eR oosreigninbaelr gs usrefaccoen din foLr3m .. NFeuxrtth, ewrem orerela,t ew eth ee xgteenodm ethtrey doef fbinoittiho nth oefs ea Laguerre minimal surface to space forms whilst relating these to the minimal immersions on L3 and minimal surfaces on other product spaces M2(k) × R and M2 (k) × R1 , with k = ±1.
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Bäck, Per. "Bäcklund transformations for minimal surfaces." Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-119914.
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In this thesis, we study a Bäcklund transformation for minimal surfaces - surfaces with vanishing mean curvature - transforming a given minimal surface into a possible infinity of new ones. The transformation, also carrying with it mappings between solutions to the elliptic Liouville equation, is first derived by using geometrical concepts, and then by using algebraic methods alone - the latter we have not been able to find elsewhere. We end by exploiting the transformation in an example, transforming the catenoid into a family of new minimal surfaces.
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HUAMANI, EDISON FAUSTO CUBA. "AFFINE MINIMAL SURFACES WITH SINGULARITIES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32452@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE EXCELENCIA ACADEMICA
Neste trabalho, estudamos superfícies com curvatura média afim zero. Elas são chamadas de superfícies mínimas afins e para superfícies convexas, também são chamadas de superfícies máximas afins. Provamos que uma superfície mínima euclidiana também é uma superfície mínima afim se, e somente se, as linhas de curvatura da superfície mínima euclidiana conjugada são planas. Para uma superfície máxima afim, descrevemos como recuperá-la do campo de vetor conormal ao longo de uma determinada curva. Para algumas escolhas do vector conormal, a superfície máxima é singular e descrevemos as condições sob as quais as singularidades são arestas cuspidais ou swallowtails.
In this work we study surfaces with zero affine mean curvature. They are called affine minimal surfaces and for convex surfaces, they are also called affine maximal surfaces. We prove that an euclidean minimal surface is also an affine minimal surface if and only if the curvature lines of the conjugate euclidean minimal surface are planar. For an affine maximal surface, we describe how to recover it from the conormal vector field along a given curve. For some choices of the conormal vector, the maximal surface is singular and we describe conditions under which the singularities are cuspidal edges or swallowtails.
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Melo, Édypo Ribeiro de [UNESP]. "Estruturas geômetro-diferenciais na superfície da corda bosônica." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/92033.
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melo_er_me_ift.pdf: 447081 bytes, checksum: de98930c32fa22dc471387d087c799b1 (MD5)Historicamente, as superfícies mínimas foram inicialmente estudadas por Lagrange e Euler no século XVIII. Fisicamente, uma superfície é mínima se ela não pode ser modificada sem consequente aumento de sua área. Tais superfícies desempenham papel fundamental na moderna pesquisa em geometria diferencial. Em física relativística e na teoria de cordas, elas são usadas a fim de descrever a formulação matem´atica de buracos negros e para o estudo de loops de quarks na fronteira do espaço Anti-de-Sitter, sendo estes denominados Wilson loops. Neste trabalho, pretendemos estudar o formalismo necessário para a análise destas superfícies nos espaços Euclideano, Lorentziano e Anti-de-Sitter sob à ótica da teoria de cordas bosônicas
Historically, minimal surfaces were first studied by Lagrange and Euler in the eighteenth century. Physically, a surface is minimal if it cannot be modified without consequent increase in your area. Such surfaces play a fundamental role in the modern research in differential geometry. In relativistic physics and string theory, they are used to describe the mathematical formulation of black holes and for the study of quark loops on the boundary of the Anti-de-Sitter space, called Wilson loops. In this work, we intend to study the necessary formalism for the analysis of surfaces in Euclidean, Lorentzian and Anti-de-Sitter spaces from the perspective of bosonic string theory
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Gosling, Peter David. "Numerical modelling of stable minimal surfaces." Thesis, University of Warwick, 1992. http://wrap.warwick.ac.uk/57526/.
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This thesis examines the numerical representation of stable minimal surfaces. In particular, the work presented concentrates on the formulation of a finite element, suitable for the analysis of systems subjected to large strains and large displacements. In order to obtain an understanding of the physical properties of a minimal surface, and to verify the proposed numerical solution algorithms, the surfaces developed by several soap-film models are given. The mechanisms involved in the formation of a soap-film (minimal) surface is summarised. Several types of minimal surfaces are investigated, including general surfaces between rigid boundaries, single minimal surfaces between two frames, and those with internal and external flexible boundaries. In addition, the question of the stability of minimal surfaces is discussed, in terms of a finite and an infinitesimal perturbation. The numerical modelling of minimal surfaces is presented, based initially on the discretisation of the form using plane linear (line) and triangular elements. The application of the matrix-based element formulations to the vector-based Dynamic Relaxation solution algorithm is described. The formulations of the elements are assessed in the context of large strains and large displacements. Subsequently, the effects of the violations of the assumptions inherent in the derivation of the element stiffness matrices on the accuracy of the numerical solution are demonstrated, and measures proposed to maintain the stability of the solution algorithm. The numerical solutions to several minimal surfaces are provided, based on the linear and triangular element discretisations respectively. An intended improvement on the plane linear and triangular element formulations is proposed by the derivation of a higher order finite element. A 24 degrees-of-freedom finite element is formulated, representing a general curved elastic (or inelastic) geometrically non-linear continuum, and modelling the condition of plane stress. The element equations are derived with special consideration of the simulation of the effects of large strains and large displacements. An appraisal of the quality of the element formulation is made through the application of the Patch test and the Eigenvalue test. The solutions to several minimal surfaces are presented, from which the effects of the assumptions in the element formulation on the accuracy of the proposed numerical solution algorithm are demonstrated.
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Merlino, Enzo Maria. "Fractional Perimeter and Nonlocal Minimal Surfaces." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021.
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This work aims to present a study of the principal results about the fractional perimeter and the regularity theory of nonlocal minimal surfaces. The fractional perimeter is a variation of the classical notion of Caccioppoli perimeter, recently introduced by L. Caffarelli, J.-M. Roquejoffre and O. Savin, that takes into account also long-range point-wise interactions between sets, modulated by a kernel with polynomial decay. That type of nonlocal minimal surfaces arises naturally, for instance, in the study of fractals and phase transitions models. First of all, we de�fine the fractional perimeter, and applying classical direct methods of Calculus of Variations we prove existence and compactness results for the corresponding minimizers. Then we deal with the regularity properties of such objects. Finally, we study a calibration result concerning nonlocal perimeters within Carnot groups.
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Neto, Guilherme Luiz de Oliveira. "Superfícies Invariantes no Espaço Homogêneo Sol com Curvatura Constante." Universidade Federal da Paraíba, 2012. http://tede.biblioteca.ufpb.br:8080/handle/tede/7372.
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Previous issue date: 2012-07-27Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
In this paper we studied surfaces with constant mean curvature and surfaces with constant Gaussian curvature in the Sol space which are invariant under the action of two one-parameter subgroups of isometries of the ambient space. Furthermore, we classify the surfaces that satisfy a relationship of type k1 = mk2, where k1 and k2 are the principal curvatures of the surface and m ∈ R.
O presente trabalho aborda um estudo das superfícies com curvatura média constante e das superfícies com curvatura Gaussiana constante no espaço Sol que são invariantes sob a ação de dois grupos a 1-parâmetro de isometrias do espaço ambiente. Além disso, classificamos as superfícies que satisfazem uma relação do tipo k1 = mk2, onde k1 e k2 são as curvaturas principais da superfície e m ∈ R.
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Cvijovic, Djurdje. "Chemical applications of triply periodic minimal surfaces." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338025.
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Gandy, P. J. F. "Triply periodic minimal surfaces in chemical physics." Thesis, University of Cambridge, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.599299.
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Mathematically triply periodic minimal surfaces (TPMS) are easy to define but extremely hard to calculate. We have described the exact computation of three surfaces most commonly found in nature, designated P, D and G. We give analytical equations for their coordinates in terms of special functions, as well as for their metric properties such as surface to volume ratios. Nodal surfaces are simply surfaces over which any function f(x, y, z) = 0, for example Cos(x) + Cos(y) + Cos(z) = 0. We have obtained extremely accurate and far more practicable models for TPMS by fitting exact surfaces to a Fourier expansion in non-orthogonal basis sets of the nodal surfaces of crystallographic structure factor expressions. These have been compared with existing models in the literature by a novel technique of colouring their surface curvatures, and found to be far superior. The contours of zero electrostatic potential within an arrangement of positive and negative electric charges in ionic crystals, as for example in the lattice of CsCl, can be plotted as a surface which separates space into domains of positive and negative potential. These surfaces correspond topologically to TPMS. We give new analytical expressions for 11 zero equipotential surfaces (ZEPS) in terms of Jacobi theta functions. The numerical integration of these now standard expressions is extremely slow, taking several hours to obtain a surface. We give nodal expressions for the most important electrostatic surfaces reducing the computation time to mere seconds. Using this technique we have analysed the scalar curvature and vector field properties for a large range of crystal structures, producing the most comprehensive quantitative comparison of triply periodic surfaces to date. By considering the purely classical motion of a charged particle over the zero equipotential surfaces of CsCl, we have proved that quantization of field and energy is solely a function of the metric defined by charge, and not a function of scale. We have further proved that triply periodic minimal surfaces define this metric. This work shows the importance and relevance of TPMS as potential universal descriptors of all charge and matter.
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Nedita, Elisabeta. "Isotropicity of minimal surfaces and holomorphic curves." Thesis, University of Warwick, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.397213.
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Ketover, Daniel. "Min-max minimal surfaces in 3-manifolds." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/90188.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.35
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 51-54).
A Heegaard splitting of a 3-manifold gives rise to a natural set of sweepouts which by the Almgren-Pitts and Simon-Smith min-max theory generates a min-max sequence converging as varifolds to a smooth minimal surface (possibly disconnected, and with multiplicities). We prove a conjecture of Pitts-Rubinstein about how such a min-max sequence can degenerate; namely we show that after doing finitely many disk surgeries and isotopies on the sequence, and discarding some components, the remaining components are each isotopic to one component (or a double cover of one component) of the min-max limit. This convergence immediately gives rise to new genus bounds for min-max limits. Our results can be thought of as a min-max analog to the theorem of Meeks-Simon-Yau on convergence of a minimizing sequence of surfaces in an isotopy class.
by Daniel Ketover.
Ph. D.
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Turowski, Gudrun. "Nichtparametrische Minimalflächen vom Typ des Kreisrings und ihr Verhalten längs Kanten der Stützfläche." Bonn : [s.n.], 1998. http://catalog.hathitrust.org/api/volumes/oclc/41464677.html.
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Appleton, Benjamin C. "Globally minimal contours and surfaces for image segmentation /." [St. Lucia, Qld.], 2004. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe18429.pdf.
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Polthier, Konrad. "Geometric a priori estimates for hyperbolic minimal surfaces." Bonn : [s.n.], 1994. http://catalog.hathitrust.org/api/volumes/oclc/31760536.html.
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Mather, Kevin. "Regularity of minimal surfaces : a self-contained proof." Thesis, University of British Columbia, 2015. http://hdl.handle.net/2429/52820.
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In this thesis, a self-contained proof is given of the regularity of minimal surfaces via viscosity
solutions, following the ideas of L.Caffarelli,X.Cabré [2], O.Savin[11][12], E.Giusti[7] and J.Roquejoffre[8], where we expand upon the ideas and give full details on the approach. Basically the proof of the program consists of four parts: 1) Density and measure estimates, 2) Viscosity solution methods of elliptic equations , 3) a geometric Harnack inequality and 4) iteration of the De Giorgi flatness result.Science, Faculty of
Mathematics, Department of
Graduate
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Arezzo, Claudio. "Holomorphic curves and minimal surfaces in Kähler manifolds." Thesis, University of Warwick, 1996. http://wrap.warwick.ac.uk/37004/.
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Our work is concerned with the relation between a complex differential geometric property, namely holomorphicity, and a metric one, namely to be conformal and minimal, of immersions (possibly branched) of Riemann surfaces into Kahler manifolds. A well known theorem (Wirtinger's Inequality) states that every holomorphic surface inside a Kahler manifold is area minimizing w.r.t. variations with compact support. Of course, the converse is not true in general. However, there are important situations, as in the resolution of the Frankel Conjecture by Siu and Yau, when it is. A first motivation for our research is to understand to which extent is the converse true. In Chapter 1 we discuss this problem after having briefly recalled the basic notions and background material that will be needed in the sequel. We first tried to prove some general existence result for immersions into riemannian manifolds, which are area minimizing among classes of maps sharing some topological properties. Following the line of the proof of the existence theorem for minimal surfaces incompressible on the fundamental group, due to Sacks-Dhlenbeck and Schoen-Yau, in Chapter 2 we prove existence of minimal surfaces incompressible on the first homology group. We apply this result to the theory of Abelian Varieties, and we present here a new proof, completely based on riemannian techniques, of a classical result about the Schottky Problem, i.e. the characterization of the jacobian locus inside the space of principally polarized abelian varieties of complex dimension 2 and 3. A crucial step in the proof of this result is the fact, proved by Micallef, that a converse of Wirtinger's Inequality holds for immersions of closed surfaces of genus 2 and 3 into flat T4 or T6, respectively. As for the Schottky problem, also for minimal surface theory, the situation becomes more difficult as the dimension of the target torus increases. In Chapter 3 we give a unified presentation of an unpublished theorem of Micallef (Theorem 3.4.1) with our research work. In particular we give a very explicit way to construct stable minimal immersions of surfaces of genus r ≥ 4 into flat tori of dimension 2r and of genus r ≥ 7 into flat tori of dimension 2( r - 1). The existence of such examples represents a major difficulty in the attempt to apply minimal surface theory to the theory of abelian varieties. In his thesis Micallef proved a converse of Wirtinger's Inequality for isometric stable minimal immersions of complete oriented surfaces into R4, with the euclidean metric, provided that the Kahler angle of the immersion omits an open set of [0,π]. In Chapter 4 we show that this result does not depend on the linear structure of R4, but on a riemannian property of its flat metric, namely the fact that it is hyperkähler. We prove in fact the same theorem replacing R4 with any hyperkähler 4-manifold. In the same Chapter we give also a description of known results about the relation between the Kähler angle and the Gauss lift (or the Gauss map, in the case of euclidean space) associated to an immersion. In the last Chapter we go back to the study of periodic minimal surfaces. The results we proved in Chapter 2 and 3 pointed out many natural questions about uniqueness and rigidity of periodic minimal surfaces with some topological constraints. In Chapter 5 we describe a framework for the study of this kind of problems that we believe to be very promising in many different situations, and we study in detail this setting for immersions of surfaces of genus r into flat T2r. Our approach makes transparent a deep connection between algebraic properties of an algebraic curve and riemannian properties of the conformal minimal immersions into some flat torus of a fixed closed Riemann surface. Using previous results of Pirola and classical theorems about algebraic curves, such as the Torelli and the Infinitesimal Torelli Theorems, we give fairly complete answers to the problems about uniqueness and rigidity of minimal maps. In particular we see that these minimal immersions do not share the same rigidity properties as holomorphic and harmonic maps, but nevertheless they generically do not come in families. We are convinced that a deeper study of periodic minimal surfaces in fiat tori from the riemmanian point of view could give some new results in the theory of algebraic curves, especially about the structure of the singular locus of the theta divisors. We believe that our approach gives already some new insight on known phenomena.