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1
Robinson, Sebastian Thomas. "Curvature-based surface fairing." Thesis, University of Bath, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.488895.
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In the computer aided engineering environment, exceptionally smooth but irregular surfaces are often required, such as car bonnets. It is often a lengthy process to design these surfaces to the degree of smoothness and aesthetic beauty that is required by the designer. Smoothing these surfaces is known as fairing and a variety of techniques exist to tackle the problem in different ways. A new method of surface fairing is proposed and demonstrated in this thesis. Many conventional fairing methods use an agreeable curvature plot across the surface as proof of fairness, the method documented here takes the more holistic approach of constructing the improved surface from an agreeable curvature plot.
2
Karkanis, Tasso. "Curvature dependent implicit surface tiling." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape7/PQDD_0003/MQ45948.pdf.
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Nunnery, Grady A. "The influence of surface curvature on polymer behavior at inorganic surfaces." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/33929.
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Nanoscale surfaces were examined in order to determine the influence of surface curvature on polymer behavior at polymer-ceramic interfaces, as well as the influence of nanoparticles in cellulosic media.
Poly(methyl methacrylate) and block copolymers thereof were adsorbed onto porous alumina substrates of various pore sizes in order to determine how polymer and copolymer adsorption behavior at nanoscale surfaces differs from adsorption onto flat surfaces. It was determined that chain density on concave surfaces dramatically decreases as curvature increases in much the same way that it does on convex surfaces (e.g. on the surface of nanoparticles), and physical models are provided to explain this similarity. Diblock copolymer adsorption is observed to vary dramatically with solvent quality and block asymmetry and can be correlated with the surface curvature very similarly to the adsorptive behavior of homopolymers on those same surfaces.
The addition of nanoparticles to cellulosic media was investigated as a means to significantly modify the properties of cellulosic composites with minimal additions of nanoparticles. Although cellulose is among the most abundant polymers on earth, its primary uses are limited to bulk commodity goods, such as paper and textiles. This work demonstrates a simple means to control cellulosic fluid viscosity, thereby increasing the versatility of these biopolymers in additional applications with higher value-added potential. The formation of iron-cellulosic nanocomposites by the in-situ thermolysis of metal carbonyls to form metallic nanoparticles was performed and was analyzed by viscometry among other techniques. It was determined that the nanocomposites that were formed exhibited significantly increased viscosity, up to the point of gelation.
Additionally, an introduction to the expansive field of nanocomposites is provided, including how and why composite properties change abruptly as filler size approaches the nanoscale. An extensive background on this diverse field as it relates to the current work is provided with an emphasis on cellulosic nanocomposites and the dependence of curvature on polymer-surface interactions. A detailed account of the experimental work relevant to this work is provided, including materials and characterization methods. Future work is proposed for both cellulosic nanocomposites as well as for curvature-dependent polymer adsorption. Finally, conclusions are drawn from the entire work and its implications to the greater field of nanocomposites.
4
McCoy, James A. (James Alexander) 1976. "The surface area preserving mean curvature flow." Monash University, Dept. of Mathematics, 2002. http://arrow.monash.edu.au/hdl/1959.1/8291.
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Sinha, Bhaskar. "Surface mesh generation using curvature-based refinement." Master's thesis, Mississippi State : Mississippi State University, 2002. http://library.msstate.edu/etd/show.asp?etd=etd-09252002-141359.
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Simon, Lentz, and Felix Erksell. "Deriving the shape of the surface from its Gaussian curvature." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-254698.
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A global statement about a compact surface with constant Gaussian curvature is derived by elementary differential geometry methods. Surfaces and curves embedded in three-dimensional Euclidian space are introduced, as well as several key properties such as the tangent plane, the first and second fundamental form, and the Weingarten map. Furthermore, intrinsic and extrinsic properties of surfaces are analyzed, and the Gaussian curvature, originally derived as an extrinsic property, is proven to be an intrinsic property in Gauss Theorema Egregium. Lastly, through the aid of umbilical points on a surface, the statement that a compact, connected surface with constant Gaussian curvature is a sphere is proven.
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Al-Barwani, Hamdi. "Propagation of fronts with gradient and curvature dependent velocities." Thesis, Loughborough University, 1996. https://dspace.lboro.ac.uk/2134/10341.
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The thesis considers and examines methods of surface propagation, where the normal velocity of the surface depends on the local curvature and the gradient of the surface. Such fronts occur in many different physical situations from the growth of crystals to the spreading of flames. A number of different methods are considered to find solutions to these physical problems. First the motion is modelled by partial differential equations and numerical methods are developed for solving these equations. The numerical methods involve characteristic, finite differences and transformation of the equations. Stability of the solutions is also briefly considered. Secondly the fronts are modelled by using a cellular approach which subdivides space into regions of small cells. The fronts are assumed to propagate through the region according to stochastic rules. Monte-Carlo simulations are carried out using this approach. Results of the simulations are carried out in two-dimensions and three-dimensions for a number of interesting physical examples.
8
Monnoyer, F. "The effect of surface curvature on three-dimensional, laminar boundary layers." Doctoral thesis, Universite Libre de Bruxelles, 1985. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/213617.
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Ferreira, Thiago Lucas da Silva, and 92-99320-5663. "Superfícies de translação Weingarten lineares nos espaços euclidiano e Lorentz-Minkowski." Universidade Federal do Amazonas, 2016. https://tede.ufam.edu.br/handle/tede/6458.
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In this dissertation we will present a demonstration that a linear Weingarten translation surface in Euclidean space and Lorentz-Minkowski space should have constant mean curvature or constant Gaussian curvature. The work is based on the article "Translation surfaces of linear Weingarten type" Antonio Bueno and Rafael López.
Nesta dissertação apresentaremos uma demonstração de que uma superfície de translação Weingarten linear no espaço euclidiano e no espaço Lorentz- Minkowski deve ter curvatura média constante ou curvatura de Gauss constante. O trabalho é baseado no artigo "Translation surfaces of linear Weingarten type"de Antonio Bueno e Rafael López.
10
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.
11
Capil, Tyler George. "Flame Surface Density Measurements and Curvature Statistics for Turbulent Premixed Bunsen Flames." Thesis, Virginia Tech, 2017. http://hdl.handle.net/10919/75121.
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In this work, turbulent premixed combustion was analyzed through CH (methylidyne) planar laser induced fluorescence (PLIF). Flame topography measurements in terms of flame surface density and curvature were calculated based on the flame front detected by the CH PLIF signal. The goal of this work was to investigate turbulent flames with extremely high turbulence intensity using a recently developed HiPilot burner (a Bunsen-type burner). The studies were first conducted on a series of piloted jet flames to validate the methodology, and then conducted on the highly turbulent flames generated by the HiPilot burner. All flames were controlled by combusting methane and air under a fuel to air equivalence ratio of Φ=1.05, and the Reynolds number varied from 7,385 to 28,360. Flame surface density fields and profiles for the HiPilot burner are presented. These flame surface density measurements showed an overall decrease with height above the burner. In addition, curvature statistics for the HiPilot flames were calculated and probability density functions of the curvature samples were determined. The probability density functions of curvature for the flames showed Gaussian-shaped distributions centered near zero curvature. To conclude, flame topography measurements were verified on jet flames and were demonstrated on the new HiPilot flames.Master of Science
12
Sacchi, Rainer. "Primitive-based segmentation for triangulated surfaces." Thesis, Nottingham Trent University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.391003.
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Ronchi, Elena. "The notion of curvature in differential geometry." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021.
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In questo lavoro ci occupiamo di studiare la geometria differenziale delle superfici con un'attenzione particolare al concetto di curvatura.
Nel primo capitolo studieremo le superfici, in particolare, immerse in spazi Euclidei utilizzando un approccio più semplice e concreto.
Nel secondo capitolo introdurremo la nozione di forma differenziale e la applicheremo nello studio delle superfici all'interno degli spazi Euclidei attraverso il metodo dei moving frames. Presenteremo anche una generalizzazione del concetto di superficie, vale a dire ciò che chiameremo varietà differenziabile.
Infine nel terzo capitolo introdurremo un terzo approccio più astratto, quello della geometria riemanniana, focalizzandoci in particolare sulla nozione di curvatura.
14
Kim, Man-Woong. "Effect of transverse convex surface curvature on turbulent fluid flow and heat transfer." Thesis, University of Ottawa (Canada), 1996. http://hdl.handle.net/10393/10183.
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The effect of transverse convex surface curvature on turbulent boundary layer flow and heat transfer over circular cylinders, and on fully developed turbulent flow and heat transfer in concentric annular ducts with smooth surfaces are studied both analytically and experimentally. The analytical results are obtained through a turbulence model based on the variable von Karman's constants, $\rm\kappa\sb{i}$, proposed for the first time in the present study. A computer program is developed for calculation of the desired momentum and thermal characteristics. A numerical calculation using the standard k-$\varepsilon$ turbulence model, with a modified procedure is also carried out. It is assumed that the thermodynamic fluid properties are independent of temperature. An experimental study is conducted to study the effect of the transverse convex surface curvature of the core tubes both on fully developed turbulent flows and heat transfer in concentric annular ducts. Air is used as the working fluid. Three annuli having different radii of the inner cores, R$\rm\sb{i}$ = 3.98 mm, 8.57 mm, and 16.7 mm, with a fixed radius ratio of $\alpha$ = 0.3, are used over a range of the Reynolds number between about 20,000 and 60,000. The inner cores are heated electrically to provide constant heat fluxes throughout the test sections and are instrumented for the temperature and power measurements. The outer tubes are insulated to minimize the leakage of heat. In the case of the experimental study for turbulent boundary layer flows and heat transfer on circular cylinders, the experimental data of Willmarth et al. (31) and Kim and Lee (45, 46) are recompiled for the present study. It is seen that both the friction coefficient and heat transfer increase with decreasing value of the inner core radius of concentric annuli and the radius of circular cylinders, R$\rm\sb{i}$ It is concluded that, while the effect of transverse concave curvature on fluid flow and heat transfer is negligible, that of transverse convex curvature is rather significant.
15
Servat-Djoo, Kambiz. "The effects of surface curvature on heat transfer through a turbulent boundary layer." Thesis, Imperial College London, 1987. http://hdl.handle.net/10044/1/46516.
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Wang, Xijun. "Geometric Trimming and Curvature Continuous Surface Blending for Aircraft Fuselage and Wing Shapes." Thesis, Virginia Tech, 2001. http://hdl.handle.net/10919/31664.
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Most of the work accomplished on surface blending is based on visual trimming. In the process of visual trimming, the unwanted portion of a surface is only hidden but not removed. Geometric trimming provides a complete mathematical description of the wanted portion of the trimming surface, and generates a new mathematical surface or sets of surface patches. The new surface is intended to resemble closely the corresponding portion of the original surface. A robust procedure is developed to geometrically trim the intersecting surfaces and blend the trimmed surface patches into one new surface. This research generates a filleting algorithm for surface blending of an aircraft fuselage shape and a wing shape at a closed trimming intersection curve, and verifies the properties of the newly created surface. In order to distinguish how well the new surface approximates the original, an error comparison tool developed in MATLAB has been employed.Master of Science
17
Diomedi, II Kevin Paul. "A Curvature-Corrected Rough Surface Scattering Theory Through The Single-Scatter Subtraction Method." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/88512.
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A new technique is presented to study radio propagation and rough surface scattering problems based on a reformulation of the Magnetic Field Integration Equation (MFIE) called the Single-Scatter Subtraction (S^3) method. This technique amounts to a physical preconditioning by separating the single- and multiple-scatter currents and removing the single-scattering contribution from the integral term that is present in the MFIE. This requires the calculation of a new quantity that is the kernel of the MFIE integral call the kernel integral or Gbar. In this work, 1-dimensional deterministically rough surfaces are simulated by surfaces consisting of single and multiple cosines. In order to truncate the problem domain, a beam illumination is used as the source term and it is shown that this also causes the kernel integral to have a finite support. Using the Single Scatter Subtraction method on these surfaces, closed-form expressions are found for the kernel integral and thus the single-scatter current for a well defined region of validity of surface parameters which may then be efficiently radiated into the far field numerically. Both the closed-form expressions, and the computed radiated fields are studied for their physical significance. This provides a clear physical intuition for the technique as an augmentation to existing ones as a bent-plane approximation as shown analytically and also validated by numeric results. Further analysis resolves a controversy on the nature of Bragg scatter which is found to be a multiple-scatter phenomenon. Error terms present in the kernel integral also raise new questions on the effect of truncation for any MFIE-based solution. Additionally, a dramatic enhancement of backscatter predicted by this new approach versus the Kirchhoff method is observed as the angle of incidence increases due to the error terms.Doctor of Philosophy
A new technique is presented to study the interaction of electromagnetic waves with rough surfaces. Building on the technique called the Magnetic Field Integral Equation (MFIE) which allows the solution for the electromagnetic fields scattered from the surface by considering only the induced electric and magnetic currents on the surface, the Single-Scatter Substraction (S 3 ) method separates the surface currents into those that interact with the surface only once or single-scatter, and those that interact multiple times called multiple-scatter. Since this is the introduction of this technique, only the former is investigated. In this study, a new quantity which is an integral of one of the components of the standard MFIE is studied and closed-form approximations are presented along with bounds of validity. This provides closed form solutions for the single-scattering currents, from which the radiated fields may be efficiently found numerically. Since they are closed form, the expressions provide insight into the nature of the physical scattering process. Numerical results of these expressions are compared to the standard approximate technique as well as the ”exact” solution found by numerically solving the MFIE. Compared to the standard approximate technique which approximates the surface by a tangent plane at each point on the surface, the single-scatter currents approximate the surface with a bent-plane at each point. This shifts the scattered fields from certain directions to others, and highlights where single- and multiple-scattering have an effect.
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Tellioglu, Zafer Hasim. "Real Time 3d Surface Feature Extraction On Fpga." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612200/index.pdf.
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Three dimensional (3D) surface feature extractions based on mean (H) and
Gaussian (K) curvature analysis of range maps, also known as depth maps, is an
important tool for machine vision applications such as object detection,
registration and recognition. Mean and Gaussian curvature calculation algorithms
have already been implemented and examined as software. In this thesis,
hardware based digital curvature processors are designed. Two types of real time
surface feature extraction and classification hardware are developed which
perform mean and Gaussian curvature analysis at different scale levels. The
techniques use different gradient approximations. A fast square root algorithm
using both LUT (look up table) and linear fitting technique is developed to
calculate H and K values of the surface described by the 3D Range Map formed
by fixed point numbers. The proposed methods are simulated in MatLab software
and implemented on different FPGAs using VHDL hardware language.
Calculation times, outputs and power analysis of these techniques are compared to
CPU based 64 bit float data type calculations.
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Yang, Xiaoyu. "Numerical investigation of turbulent channel flow subject to surface roughness, acceleration, and streamline curvature." Thesis, University of Cambridge, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708441.
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Sousa, F. Raquel R. F. de. "Exploratory spatial analysis of topographic surface metrics for the prediction of water table occurrence." Master's thesis, Universidade de Évora, 2014. http://hdl.handle.net/10174/12215.
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Starting from the premise that water table in aquifers follows topographic surface as
well as underground flow direction tends to be consistent with the surface streams
flow directions, the present work presents the essays of the research to define a model
that predicts, through a piecewise multiple regression, groundwater level in the
Estremoz-Cano Aquifer System and in the surrounding igneous and metamorphic rocks
of the OMZ as a function of topography, namely a set of terrain metrics like curvature
and structural curvature to be related with the static water level (SWL) measured on
dug wells of farms and cottages.
The spatial analysis of the topographic surface draining water to the sampled aquifer
systems is based on a DEM at different resolutions to acquire and infer information
about the surface shape and processes, namely the hydrologic characteristics of the
basins and its relation with infiltration process and the prediction of water table; Análise exploratória da métrica da superfície topográfica para previsão do nível
freático da água subterrânea
### Resumo:
O presente trabalho parte da premissa de que não só o nível freático acompanha a
linha topográfica do terreno, mas também a direcção de escorrência das bacias
subterrâneas tende a coincidir com a direcção predominante de escorrência das bacias
hidrográficas à superfície, principalmente em aquíferos fraturados.
O presente trabalho apresenta o estudo realizado na investigação de um modelo que
explique o nível freático no sistema aquífero Estremoz-Cano e na área circundante a
este, nas rochas ígneas e metamórficas da ZOM, em função da curvatura e das
características métricas do terreno. Na base dos modelos desenvolvidos estiveram os
dados de elevação do terreno a diferentes resoluções, a curvatura e a convexidade
deste, assim como as características hidrológicas e a influência destas nos processos de
infiltração.
21
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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Diewald, Udo. "Anisotrope Krümmungsflüsse parametrischer Flächen sowie deren Anwendung in der Flächenverarbeitung / Anisotropic Curvature Motion of Parametric Surfaces and Applications in Surface Processing." Gerhard-Mercator-Universitaet Duisburg, 2005. http://www.ub.uni-duisburg.de/ETD-db/theses/available/duett-08142005-194705/.
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The presented dissertation is concerned with anisotropic curvature motion of two-dimensional parametric surfaces as well as their application in surface fairing and surface restauration. Mainly the so called anisotropic mean curvature motion (AMCM) and the anisotropic Willmore-flow are being treated. These flows are generalizations of the classical mean curvature flow and the classical Willmore-flow, respectively. The anisotropies are induced by positive, 1-homogenous and convex functions, which can be regarded as support functions of convex bodies, so called Wulff-shapes. Being a method of fourth order of differentiation in the surface coordinates, the anisotropic Willmore-flow allows the prescription of boundary values for the position of the boundary itself as well as for the surface normals on the boundary of a surface patch under consideration. Hence it is an appropriate method for the reconstruction of partially destroyed surfaces. In this work a numerical scheme for the anisotropic Willmore-flow is presented, which is based on an operator splitting of the fourth order evolution equation into two weak equations of first order of differentiation, which is discretized using linear finite elements in space. In particular the discretization of the AMCM turns out to be one of these equations. Based on the AMCM a method for the fairing of surfaces with crystalline edges is developed. Modifications of the discrete AMCM are also used for surface modeling purposes. Schemes for the artificial aging and for virtual engraving of surfaces are presented. Further on a subdivision scheme based on the isotropic mean curvature motion is introduced. Finally, the isotropic as well as the anisotropic Willmore-flow is employed for the restauration of partially destroyed triangulated surfaces.
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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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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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Rodrigues, Débora Santos. "Projetivo de curvatura em pontos de uma 3-variedade." Universidade Federal de Viçosa, 2013. http://locus.ufv.br/handle/123456789/4926.
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In this work we study of the curvature projective plane at a point of a 3-manifold immersed in Rn n ≥ 4, based one the thesis of R. R. Binotto [1]. We analyzed the different types of surfaces that describe the projective. We show that it can to be described as an isomorphism of the Veronese s surface of order 2 followed by a linear transformation and a translation. We also relate the types of a point on a 3-manifold with the degenericity of projective in the normal space. We conclude this study by analyzing the curvature locus of points in a n-manifold immersed in codimension 2, according to [14]. We present some examples, analyzing a few geometric properties of the curvature locus and comment on some results related to the geometry of a 3-manifold in codimension 2.
Neste trabalho fazemos um estudo do projetivo de curvatura em um ponto de uma 3-variedade imersa em Rn , n ≥ 4, tendo como base a tese de de R. R. Binotto [1]. Analisamos os diferentes tipos de superfícies que descrevem o projetivo, mostramos que este pode ser descrito como um isomorfismo da superfície de Veronese de ordem 2 seguido de uma transformação linear e de uma translação. Também relacionamos os tipos de pontos da 3-variedade com a degenericidade do projetivo no espaço normal. Finalizamos o estudo analisando o locus de curvatura em pontos de uma n-variedade imersa em codimenso 2, de acordo com [14], apresentamos alguns exemplos, analisando algumas propriedades geométricas do locus de curvatura e comentamos alguns resultados relacionados à geometria de uma 3-variedade em codimensão 2.
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Cenanovic, Mirza. "Finite element methods for surface problems." Doctoral thesis, Tekniska Högskolan, Högskolan i Jönköping, JTH, Produktutveckling, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-35369.
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The purpose of this thesis is to further develop numerical methods for solving surface problems by utilizing tangential calculus and the trace finite element method. Direct computation on the surface is possible by the use of tangential calculus, in contrast to the classical approach of mapping 2D parametric surfaces to 3D surfaces by means of differential geometry operators. Using tangential calculus, the problem formulation is only dependent on the position and normal vectors of the 3D surface. Tangential calculus thus enables a clean, simple and inexpensive formulation and implementation of finite element methods for surface problems. Meshing techniques are greatly simplified from the end-user perspective by utilizing an unfitted finite element method called the Trace Finite Element Method, in which the basic idea is to embed the surface in a higher dimensional mesh and use the shape functions of this background mesh for the discretization of the partial differential equation. This method makes it possible to model surfaces implicitly and solve surface problems without the need for expensive meshing/re-meshing techniques especially for moving surfaces or surfaces embedded in 3D solids, so called embedded interface problems. Using these two approaches, numerical methods for solving three surface problems are proposed: 1) minimal surface problems, in which the form that minimizes the mean curvature was computed by iterative update of a level-set function discretized using TraceFEM and driven by advection, for which the velocity field was given by the mean curvature flow, 2) elastic membrane problems discretized using linear and higher order TraceFEM, which makes it straightforward to embed complex geometries of membrane models into an elastic bulk for reinforcement and 3) stabilized, accurate vertex normal and mean curvature estimation with local refinement on triangulated surfaces. In this thesis the basics of the two main approaches are presented, some aspects such as stabilization and surface reconstruction are further developed, evaluated and numerically analyzed, details on implementations are provided and the current state of work is presented.
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Niaki, Mossadeg Saadat. "Effect of transverse convex curvature on heat transfer from uniformly heated surface with backward-facing steps." Thesis, University of Ottawa (Canada), 1995. http://hdl.handle.net/10393/10269.
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Local heat transfer coefficients have been obtained through measuring the temperature distribution along the separating, reattaching, and redeveloping regions of axisymmetric turbulent boundary layers on the wall of cylinders with constant heat flux. Measurements have been made with different configuration of three cylinders and five ellipsoidal steps on the leading face. The velocity of the turbulent flow was changed stepwise from 5 to 30 $m/s.$ The range of Reynolds number, based on either the step height or diameter of convex curvature, is between 4,000 and 100,000. In addition, a surface-streamline flow visualization technique was tried to identify the reattachment loci, as well as the axisymmetry of the temperature distribution. It was found that the points of maximum heat transfer and reattachment are coincident within an uncertainty of $\pm$0.5 inch. As a common feature, the rate of heat transfer undergoes a drop within a short length distance right after separation, followed by a rise leading to a sharp maximum at the reattachment neighborhood. The study demonstrates that the maximum Nusselt number and heat transfer rate increase with either decreasing cylinder radius, or increasing step diameter. The effect of step height is similar to that of the step diameter. An empirical equation, correlated as a function of Reynolds number and aspect ratio of cylinder-step diameters, is proposed for the maximum Nusselt number.
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Miyasaka, Keiichi. "A structural study into the boundary surface and associated curvature of three-dimensional mesoporous silica crystals /." Stockholm : Department of Physical, Inorganic and Structural Chemistry, Stockholm University, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-7651.
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Goul, Jawher El. "Surfaces algébriques hyperboliques : propriétés de négativité de la courbure." Université Joseph Fourier (Grenoble ; 1971-2015), 1997. http://www.theses.fr/1997GRE10195.
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Le theme central de cette these est l'etude de certaines proprietes de negativite de courbure des surfaces algebriques hyperboliques au sens de kobayashi. L'etude que nous avons faite est divisee en deux parties : dans un premier temps, nous introduisons la notion de connexion projective partielle a coefficients meromorphes, et montrons comment de telles connexions peuvent servir a construire des operateurs wronskiens globaux agissant sur les jets de courbes holomorphes (un type tres particulier de jets de differentielles invariantes). Grace a un theoreme d'annulation du wronskien reposant sur des hypotheses de negativite de la courbure de ricci et generalisant des resultats anterieurs de green-griffiths, siu et nadel, nous donnons des exemples explicites de familles algebriques de surfaces hyperboliques dans l'espace projectif, de degre quelconque superieur ou egal a onze. Ceci illustre une (toute petite) partie d'une conjecture celebre de s. Kobayashi, qui prevoit qu'une hypersurface generique de l'espace projectif de degre assez grand (par rapport a la dimension) est hyperbolique. Dans un deuxieme temps, nous montrons la presque amplitude au sens de miyaoka du fibre cotangent a toute surface de type general fibree sur une courbe de genre superieur ou egal a deux, et qui admet au moins une fibre singuliere. Comme application, nous obtenons une reponse positive a une conjecture de demailly (qui relie l'hyperbolicite a une propriete de negativite de courbure au sens des jets) dans le cas d'une surface fibree hyperbolique stable sur une courbe de genre au moins deux. Ces resultats sont obtenus grace a une etude algebro-geometrique qui nous permet de construire des sections globales des fibres en droites tautologiques associes aux espaces des jets. Les techniques que nous utilisons sont assez variees, et combinent des outils algebriques tels que des theoremes de rigidite et d'additivite des dimensions de kodaira-iitaka, et des outils analytiques de geometrie differentielle complexe : metriques hermitiennes singulieres et techniques de recollement de metriques.
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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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Zheng, Shu. "Effect of pore curvature and surface chemistry of model silica hosts on biocatalytic activity of immoibilized lipase PS." Cincinnati, Ohio : University of Cincinnati, 2005. http://www.ohiolink.edu/etd/view.cgi?acc%5Fnum=ucin1132251762.
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ZHENG, SHU `. "EFFECT OF PORE CURVATURE AND SURFACE CHEMISTRY OF MODEL SILICA HOSTS ON BIOCATALYTIC ACTIVITY OF IMMOBILIZED LIPASE PS." University of Cincinnati / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1132251762.
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COLOMBO, GIULIO. "GLOBAL GRADIENT BOUNDS FOR SOLUTIONS OF PRESCRIBED MEAN CURVATURE EQUATIONS ON RIEMANNIAN MANIFOLDS." Doctoral thesis, Università degli Studi di Milano, 2021. http://hdl.handle.net/2434/813095.
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This thesis is concerned with the study of qualitative properties of solutions of the minimal surface equation and of a class of prescribed mean curvature equations on complete Riemannian manifolds. We derive global gradient bounds for non-negative solutions of such equations on manifolds satisfying a uniform Ricci lower bound and we obtain Liouville-type theorems and other rigidity results on Riemannian manifolds with non-negative Ricci curvature.
The proof of the aforementioned global gradient bounds for non-negative solutions u is based on the application of the maximum principle to an elliptic differential inequality satisfied by a suitable auxiliary function z=f(u,|Du|), in the spirit of Bernstein’s method of a priori estimates for nonlinear PDEs and of Yau’s proof of global gradient bounds for harmonic functions on complete Riemannian manifolds. The particular choice of the auxiliary function z parallels the one in Korevaar’s proof of a priori gradient estimates for the prescribed mean curvature equation in Euclidean space.
The rigidity results obtained in the last part of the thesis include a Liouville theorem for positive solutions of the minimal surface equation on complete Riemannian manifolds with non-negative Ricci curvature, a splitting theorem for complete parabolic manifolds of non-negative sectional curvature supporting non-constant solutions with linear growth of the minimal surface equation, and a splitting theorem for domains of complete parabolic manifolds with non-negative Ricci curvature supporting non-constant solutions of overdetermined problems involving the mean curvature operator.
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Santos, Alexandre Jesus dos. "Hipersuperfícies estáveis com curvatura média constante e fronteira livre." Pós-Graduação em Matemática, 2018. http://ri.ufs.br/jspui/handle/riufs/8036.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESA hypersurface in a manifold, both with nonempty boundary, is called free boundary hypersurface if it is a critical point of the area functional restricted to all admissible variations which preserve volume. A variation is admissible if the boundary and the interior of the manifold contains the boundary and the interior of the hypersurfaces of the variation, respectively. It is well known that free boundary hypersurface has constant mean curvature. In this work we study free boundary hypersurfaces in bounded convex domains in the euclidean space. More precisely, we prove the results obtained by A. Ros and E. Vergasta [18] and I. nunes [15]. As the main result we prove that a stable free boundary surface in the unit ball of the three-dimensional euclidian space has to be either the totally geodesic disc or a spherical cap.
Uma hipersupefície de uma variedade, ambas com fronteira não vazia, é chamada de hipersupefície com fronteira livre se é ponto crítico do funcional área restrito a todas as variações admissíveis que preservam volume. Uma variação é dita admissível se a fronteira e o interior da variedade contém as fronteiras e os inteiores das hipersupefícies da variação, respectivamente. É bem conhecido que hipersupefícies com fronteira livre possuem curvatura média constante. Neste trabalho estudamos hipersuperfíce com fronteira livre em domínios convexos limitados do espaço euclidiano. Mais especificamente, expomos com detalhes os resultados obtidos por A. Ros-E. Vergasta e I. Nunes. Provamos como resultado principal que toda superfícies de fronteira livre estável na bola unitária do espaço euclidiano tridimensional é um disco totalmente geodésico ou uma calota esférica.
São Cristóvão, SE
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Moruz, Marilena. "Étude des sous-variétés dans les variétés kählériennes, presque kählériennes et les variétés produit." Thesis, Valenciennes, 2017. http://www.theses.fr/2017VALE0003/document.
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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 LópezAbstract in English not available
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Sendova, Tsvetanka Bozhidarova. "A new approach to the modeling and analysis of fracture through an extension of continuum mechanics to the nanoscale." [College Station, Tex. : Texas A&M University, 2008. http://hdl.handle.net/1969.1/ETD-TAMU-2995.
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Lee, Sang Hun. "Effect of transverse convex surface curvature on turbulent fluid flow and heat transfer in concentric annuli with moving cores." Thesis, University of Ottawa (Canada), 2001. http://hdl.handle.net/10393/9088.
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This study investigates the effect of Transverse Convex Surface Curvature of the inner core (T.C.S.C) on the fully developed fluid flows in a concentric annulus with a moving core, by analytically predicting friction forces, velocity profiles, temperature profiles and heat transfer in terms of convex surface curvature, radius ratio, Prandtl number, Reynolds number and relative velocity. The analytical predictions are produced by a mathematical model based on the variable von Karman constant, kappai, proposed by Kim and Lee [1] and the variable van Driest damping parameter, Ai+, proposed in previous research by Suk [2]. The computer program developed for this study employs a numerical process to match velocity and temperature profiles with force and energy balances and calculates the desired momentum and thermal characteristics. The solutions are found in the case of the heat transfer where the inner core surface is uniformly heated and the outer insulated. It is assumed that the fluid flow is turbulent everywhere and the thermodynamic fluid properties are independent of temperature. It is concluded that in the fully developed turbulent flow in a concentric annulus with a moving core, the effects of Transverse Convex Surface Curvature (T.C.S.C), core velocity and turbulent motion on the momentum and heat transfer characteristics of the flow seem significant.
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Suk, Eugene. "Effect of transverse convex surface curvature on fluid flow and heat transfer in the entrance region of concentric annuli." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape17/PQDD_0006/MQ36743.pdf.
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Wei, Yu-Chen. "Pct1 regulates phosphatidylcholine synthesis in response to changes in surface curvature elastic stress sensed on the inner nuclear membrane." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/287931.
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Cell and organelle membranes consist of a complex mixture of phospholipids that determine their size, shape, and function. Among the distinct types of phospholipids found in membranes of living organisms, phosphatidylcholine (PC) is the most abundant. The rate-limiting step of the predominant pathway for PC synthesis in eukaryotic cells is catalysed by the enzyme, CTP: phosphocholine cytidylyltransferase α (CCTα or PCYT1A). CCTα has a critical role in lipid metabolism and also has direct clinical relevance as mutations in CCTα result in an interesting spectrum of human diseases, such as lipodystrophy with fatty liver, growth plate dysplasia and cone-rod related dystrophy. Numerous biochemical and structural studies on purified CCTα have revealed its membrane-bound activation and suggested that it acts as a lipid compositional sensor, yet the in vivo mechanism of how CCTα senses and regulates PC levels in membranes remains unclear. Here I show that in budding yeast Saccharomyces cerevisiae, Pct1, the yeast homolog of CCTα, is intranuclear and translocates to the nuclear membrane in response to changes in membrane properties and the need for membrane PC synthesis. By aligning imaging with lipidomic analysis and data-driven modelling, Pct1 membrane association is demonstrated to correlate with membrane stored curvature elastic stress estimates. Furthermore, this process occurs inside the nucleus, although nuclear localization signal mutants can compensate for the loss of endogenous Pct1. These data suggest an ancient mechanism by which CCTα senses lipid packing defects and regulates phospholipid homeostasis from the nucleus. Additionally, I identified the importance of mammalian CCTα in early adipogenesis and investigated the enzymatic function of PCYT1A mutants in fibroblasts from lipodystrophic patients. The allele Val142Met is evaluated to be the main cause of loss-of-function in the compound heterozygous mutations by using yeast survival assay. These results collectively provide preliminary evidence for the pathogenicity of PCYT1A mutations in adipose tissue. From yeast to humans, this study uncovers the critical role of Pct1/CCTα in maintaining the internal membrane environment.
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Shen, Xiang. "Experimental and numerical study of surface curvature effects on the performance of the aerofoils used in small wind turbines." Thesis, Queen Mary, University of London, 2017. http://qmro.qmul.ac.uk/xmlui/handle/123456789/24739.
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The effects of surface curvature and slope-of-curvature on the performance of aerofoils used in small wind turbines are studied experimentally and numerically. A symmetric aerofoil NACA0012 and an asymmetric aerofoil E387 are judiciously selected as an example of an aerofoil with a surface curvature discontinuity and an example of an aerofoil with slope-of-curvature discontinuities respectively. The prescribed surface curvature distribution blade design (CIRCLE) method is applied to both aerofoils to remove the curvature and slope-ofcurvature discontinuities. The newly designed aerofoils have continuous curvature and slope-of-curvature distributions and have nearly identical geometry compared to the original aerofoils, denoted as QM13F and A7. Low-speed wind tunnel experiments, together with two numerical methods, are conducted to aerofoil E387 and A7 to investigate the effects of slope-of-curvature. The slope-of-curvature discontinuities of E387 result in a larger LSB, which causes higher drag at low angles of attack, and result in premature LSB bursting process at higher angles of attack, causing earlier stall. The impact of the slope-ofcurvature distribution on aerodynamic performance is more profound at higher angles of attack and lower Reynolds number. The aerodynamic improvements are estimated over a 3 kW small HAWT, resulting in up to 10% increase in instantaneous power and 1.6% increase in annual energy production. In terms of the effects of surface curvature, the curvature discontinuity at the leading edge affects aerofoil lift and drag performance near the stalling angle in the steady flow, and it is estimated in a 5 kW small VAWT that the power coefficient can be increased by 9.7% by removing the curvature discontinuity. Acoustic experimental measurements were performed on aerofoil E387 and A7 in an anechoic wind tunnel to investigate effects of slope-of-curvature on aerofoil acoustic performance. The in-house CFD code Cgles was modified to perform large eddy simulation (LES) the 3D aerofoil sections to further investigate the experimental phenomenon. The tonal noise of E387 at different angles of attack is reduced by removing slope-of-curvature discontinuities. It is experimentally and numerically concluded that continuous curvature and slope-of-curvature distributions can result in better aerodynamic performance of the aerofoil used in small wind turbines, leading to lower aerofoil self-noise and higher energy output efficiency.
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Browe, Bryan Everett. "Wave Scattering from Structures that Display Areas of Small Radii of Curvature in the Presence of an Extended Planar Surface." Thesis, Virginia Tech, 1999. http://hdl.handle.net/10919/9746.
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In many applications, it is necessary to simulate wave scattering from surfaces that have small radii of curvature relative to the incident wavelength. Surface features smaller than an electromagnetic wavelength are known to create diffracted fields over a wide range of scattering angles. In this thesis, the significance of such effects at low grazing angles with the presence of an extended planar surface is considered. The magnetic field integral equation (MFIE) describing the currents on such surfaces is used to solve for the bistatic scattered fields. The integral equations are discretized using the moment method and solved using the Method of Ordered Multiple Interactions (MOMI) iterative procedure. This thesis will concentrate on normal incidence and low grazing angle (LGA) incidence, specifically an incident angle of 80 degrees. The surface used in the analysis is a one-dimensional, perfectly-conducting wedge-on-a-plane with a varying radius of curvature at the wedge tip and Gaussian tails that smoothly extend the wedge to the plane surface. This surface displays continuous first and second derivatives over the entire surface. The radius of curvature at the wedge tip is varied between 0.0125 wavelengths and 8 wavelengths. The form of the bistatic scattered fields will be investigated for three different wedge height to wedge width geometries. The surface scattering mechanisms and their respective location and form in the scattered field will be discussed. The dependence of the scattered field pattern on the radius of curvature at the wedge tip and the beam width of the incident field will be considered. The difficulties associated with using a numerical technique on extended surfaces where a significant source of diffracted energy is present will also be examined. This includes the issue of sampling a surface that contains areas of small radii of curvature and the issue of surface truncation when significant currents due to tip diffraction are produced well outside the illuminated area. Both TE (VV) and TM (HH) polarization will be considered.
This thesis also analyzes the scattered fields for a perfect electric conducting (PEC) ridge and well in the presence of an extended planar surface for an incident angle of 70 degrees. The dual-surface magnetic field integral equation (DMFIE) formulation for a one-dimensional extended surface will be used to solve for the unknown currents on the surface of the scatterer. The DMFIE formulation leads to a second kind integral equation that can be solved via the MOMI series with the proper choice of the parameters appearing in the DMFIE formulation. The bistatic scattered fields for several ridge and well geometries are examined for both TE and TM polarization.Master of Science
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Bezerra, Geziel Damasceno. "Uma caracterização das superfícies de delaunay." Universidade Federal do Amazonas, 2012. http://tede.ufam.edu.br/handle/tede/3674.
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Admits that in a complete surface, connected and oriented immersed in R3 with non-zero constant mean curvature, there is a geodesic triangle whose interior angles satisfy a relationship involving the integral mean curvature and the angle formed by unit vector parallel to a coordinate axis of either R3 and the unit vector normal to the surface, and in such cases shows that the immersion is a surface of revolution, ie, a surface Delaunay. Then give a characterization of the sphere is changing some hypotheses on the previous result.
Admite-se que, numa superfície completa, conexa e orientada imersa no espaço euclidiano tri-dimensional com curvatura média constante não nula, existe um triângulo geodésico cujos ângulos internos satisfazem uma relação integral envolvendo a curvatura média e o ângulo formado pelo vetor unitário paralelo a um eixo coordenado qualquer do espaço ambiente e o vetor unitário normal a superfície, e sob tais hipóteses mostra-se que a imersão é uma superfície de revolução, ou seja, uma superfície de Delaunay. Em seguida darse uma caracterização da esfera alterando-se algumas hipóteses no resultado anterior.
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Huang, Conglin. "3D RECONSTRUCTION USING MULTI-VIEW IMAGING SYSTEM." UKnowledge, 2009. http://uknowledge.uky.edu/gradschool_theses/600.
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This thesis presents a new system that reconstructs the 3D representation of dental casts. To maintain the integrity of the 3D representation, a standard model is built to cover the blind spots that the camera cannot reach. The standard model is obtained by scanning a real human mouth model with a laser scanner. Then the model is simplified by an algorithm which is based on iterative contraction of vertex pairs. The simplified standard model uses a local parametrization method to obtain the curvature information. The system uses a digital camera and a square tube mirror in front of the camera to capture multi-view images. The mirror is made of stainless steel in order to avoid double reflections. The reflected areas of the image are considered as images taken by the virtual cameras. Only one camera calibration is needed since the virtual cameras have the same intrinsic parameters as the real camera. Depth is computed by a simple and accurate geometry based method once the corresponding points are identified. Correspondences are selected using a feature point based stereo matching process, including fast normalized cross-correlation and simulated annealing.
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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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Beverly, Lesa Lynn. "The Creation of Algorithms Designed for Analyzing Periodic Surfaces of Crystals and Mineralogically Important Sites in Molecular Models of Crystals: Understanding the Electron Density Function Through Visual Examinations of the Curvature and Shape of the Equi-Value Laplacian Surfaces." Diss., Virginia Tech, 2000. http://hdl.handle.net/10919/28376.
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The goals of the research presented in this dissertation were to create algorithms that produce images of complex phenomena, to study the efficacy of the algorithms, and to apply these algorithms to important mineralogical problems. The algorithms that were created include the Sphere Projection method, the Chicken Wire method, and methods for calculating the curvature at any point on a surface. The Sphere Projection method is best applied to roughly spherical surfaces. A theorem about the "fit" to a sphere determines the accuracy of the model in this special case and gives some insight into the limitations of this method. The Chicken Wire method was developed to model those surfaces for which the Sphere Projection method was ineffective. The effectiveness of the Chicken Wire method was also determined.
The algorithms were used to produce images of equi-value surfaces of the Laplacian of the electron density function in selected molecules. The water molecule, H2O, was studied to demonstrate that these new methods are capable of reproducing known features. The disiloxane molecule, H6Si2O7, was studied because it serves as a model for bonding in quartz and other important silicates. Lastly, the molecule NaLi2Si2OF9 was examined as a molecular model for low albite. A new discovery suggests that these algorithms will be an important tool in mineralogy.Ph. D.
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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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Li, Huibin. "Towards three-dimensional face recognition in the real." Phd thesis, Ecole Centrale de Lyon, 2013. http://tel.archives-ouvertes.fr/tel-00998798.
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Due to the natural, non-intrusive, easily collectible, widespread applicability, machine-based face recognition has received significant attention from the biometrics community over the past three decades. Compared with traditional appearance-based (2D) face recognition, shape-based (3D) face recognition is more stable to illumination variations, small head pose changes, and varying facial cosmetics. However, 3D face scans captured in unconstrained conditions may lead to various difficulties, such as non-rigid deformations caused by varying expressions, data missing due to self occlusions and external occlusions, as well as low-quality data as a result of some imperfections in the scanning technology. In order to deal with those difficulties and to be useful in real-world applications, in this thesis, we propose two 3D face recognition approaches: one is focusing on handling various expression changes, while the other one can recognize people in the presence of large facial expressions, occlusions and large pose various. In addition, we provide a provable and practical surface meshing algorithm for data-quality improvement. To deal with expression issue, we assume that different local facial region (e.g. nose, eyes) has different intra-expression/inter-expression shape variability, and thus has different importance. Based on this assumption, we design a learning strategy to find out the quantification importance of local facial regions in terms of their discriminating power. For facial description, we propose a novel shape descriptor by encoding the micro-structure of multi-channel facial normal information in multiple scales, namely, Multi-Scale and Multi-Component Local Normal Patterns (MSMC-LNP). It can comprehensively describe the local shape changes of 3D facial surfaces by a set of LNP histograms including both global and local cues. For face matching, Weighted Sparse Representation-based Classifier (W-SRC) is formulated based on the learned quantification importance and the LNP histograms. The proposed approach is evaluated on four databases: the FRGC v2.0, Bosphorus, BU-3DFE and 3D-TEC, including face scans in the presence of diverse expressions and action units, or several prototypical expressions with different intensities, or facial expression variations combine with strong facial similarities (i.e. identical twins). Extensive experimental results show that the proposed 3D face recognition approach with the use of discriminative facial descriptors can be able to deal with expression variations and perform quite accurately over all databases, and thereby has a good generalization ability. To deal with expression and data missing issues in an uniform framework, we propose a mesh-based registration free 3D face recognition approach based on a novel local facial shape descriptor and a multi-task sparse representation-based face matching process. [...]
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Chen, Xiaodong. "Fluid-Structure Interaction Modeling of Epithelial Cell Deformation during Microbubble Flows in Compliant Airways." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1332208862.
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Dicko, Mahamar. "Méthodes numériques pour la résolution d'EDP sur des surfaces. Application dans l'embryogenèse." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAM024/document.
Full textAbstract:
Nous développons une nouvelle approche éléments finis pour des équations aux dérivées partielles elliptiques de type élasticité linéaire ou Stokes sur une surface fermée de R3. La surface considérée est décrite par le zéro d'une fonction de niveau assez régulière. Le problème se ramène à la minimisation d'une fonctionnelle énergie pour le champ de vitesse sous contraintes. Les contraintes sont de deux types : (i) la vitesse est tangentielle à la surface, (ii) la surface est inextensible. Cette deuxième contrainte équivaut à l'incompressibilité surfacique du champ de vitesse. Nous abordons ce problème de deux façons : la pénalisation et l'introduction de deux multiplicateurs de Lagrange. Cette dernière méthode a l'avantage de traiter le cas de la limite incompressible d'un écoulement en surface dont nous présentons pour la première fois l'analyse théorique et numérique. Nous montrons des estimations d'erreurs sur la solution discrète et les tests numériques confirment l'optimalité des ces estimations. Pour cela, nous proposons plusieurs approches pour le calcul numérique de la normale et la courbure de la surface. L'implémentation utilise la librairie libre d'éléments finis Rheolef. Nous présentons aussi des résultats de simulations numériques pour une application en biologie : la morphogenèse de l'embryon de la drosophile, durant laquelle des déformations tangentielles d'une monocouche de cellules avec une faible variation d'aire. Ce phénomène est connu sous le nom de l'extension de la bande germinaleWe develop a novel finite element approach for linear elasticity or Stokes-type PDEs set on a closed surface of $mathbb{R}^3$. The surface we consider is described as the zero of a sufficiently smooth level-set function. The problem can be written as the minimisation of an energy function over a constrained velocity field. Constraints areof two different types: (i) the velocity field is tangential to the surface, (ii) the surface is inextensible. This second constraint is equivalent to surface incompressibility of the velocity field. We address thisproblem in two different ways: a penalty method and a mixed method involving two Lagrange multipliers. This latter method allows us to solve the limiting case of incompressible surface flow, for which we present a novel theoretical and numerical analysis. Error estimates for the discrete solution are given andnumerical tests shows the optimality of the estimates. For this purpose, several approaches for the numerical computation of the normal and curvature of the surface are proposed. The implementation relies on the Rheolef open-source finite element library. We present numerical simulations for a biological application: the morphogenesis of Drosophila embryos, duringwhich tangential flows of a cell monolayer take place with a low surface-area variation. This phenomenon is known as germ-band extension
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Ugail, Hassan, N. Jamil, and R. Satinoianu. "Method of numerical simulation of stable structures of fluid membranes and vesicles." WSEAS, 2006. http://hdl.handle.net/10454/2751.
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Guo, Li. "Shape blending using discrete curvature-variation functional /." View abstract or full-text, 2005. http://library.ust.hk/cgi/db/thesis.pl?IEEM%202005%20GUO.
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