Geometria e topologia das superfícies através de recorte e colagem

Pós-graduação em Matemática Universitária - IGCE

Domains in complex surfaces with non-compact automorphism groups

Let X be an arbitrary complex surface and D a domain in X that has a non-compact group of holomorphic automorphisms. A characterization of those domains D that admit a smooth, weakly pseudoconvex, finite type boundary orbit accumulation point is obtained.

Flat connections, geometric invariants and energy of harmonic functions on compact Riemann surfaces

A geometric invariant is associated to the space of fiat connections on a G-bundle over a compact Riemann surface and is related to the energy of harmonic functions.

Nanostructured hydroxyapatite surfaces-mediated adsorption alters recognition of BMP receptor IA and bioactivity of bone morphogenetic protein-2

Highly efficient loading of bone morphogenetic protein-2 (BMP-2) onto carriers with desirable performance is still a major challenge in the field of bone regeneration. Till now, the nanoscaled surface-induced changes of the structure and bioactivity of BMP-2 remains poorly understood. Here, the effect of nanoscaled surface on the adsorption and bioactivity of BMP-2 was investigated with a series of hydroxyapatite surfaces (HAPs): HAP crystal-coated surface (HAP), HAP crystal-coated polished surface (HAP-Pol), and sintered HAP crystal-coated surface (HAP-Sin). The adsorption dynamics of recombinant human BMP-2 (rhBMP-2) and the accessibility of the binding epitopes of adsorbed rhBMP-2 for BMP receptors (BMPRs) were examined by a quartz crystal microbalance with dissipation. Moreover, the bioactivity of adsorbed rhBMP-2 and the BMP-induced Smad signaling were investigated with C2C12 model cells. A noticeably high mass-uptake of rhBMP-2 and enhanced recognition of BMPR-IA to adsorbed rhBMP-2 were found on the HAP-Pol surface. For the rhBMP-2-adsorbed HAPs, both ALP activity and Smad signaling increased in the order of HAP-Sin < HAP < HAP-Pol. Furthermore, hybrid molecular dynamics and steered molecular dynamics simulations validated that BMP-2 tightly anchored on the HAP-Pol surface with a relative loosened conformation, but the HAP-Sin surface induced a compact conformation of BMP-2. In conclusion, the nanostructured HAPs can modulate the way of adsorption of rhBMP-2, and thus the recognition of BMPR-IA and the bioactivity of rhBMP-2. These findings can provide insightful suggestions for the future design and fabrication of rhBMP-2-based scaffolds/implants.

Flat connections, geometric invariants and the symplectic nature of the fundamental group of surfaces

In this paper we associate a new geometric invariant to the space of fiat connections on a G (= SU(2))-bundle on a compact Riemann surface M and relate it tcr the symplectic structure on the space Hom(pi(1)(M), G)/G consisting of representations of the fundamental group pi(1)(M) Of M into G module the conjugate action of G on representations.

3-MANIFOLD GROUPS, KÄHLER GROUPS AND COMPLEX SURFACES

Let G be a Kahler group admitting a short exact sequence 1 -> N -> G -> Q -> 1 where N is finitely generated. (i) Then Q cannot be non-nilpotent solvable. (ii) Suppose in addition that Q satisfies one of the following: (a) Q admits a discrete faithful non-elementary action on H-n for some n >= 2. (b) Q admits a discrete faithful non-elementary minimal action on a simplicial tree with more than two ends. (c) Q admits a (strong-stable) cut R such that the intersection of all conjugates of R is trivial. Then G is virtually a surface group. It follows that if Q is infinite, not virtually cyclic, and is the fundamental group of some closed 3-manifold, then Q contains as a finite index subgroup either a finite index subgroup of the three-dimensional Heisenberg group or the fundamental group of the Cartesian product of a closed oriented surface of positive genus and the circle. As a corollary, we obtain a new proof of a theorem of Dimca and Suciu in Which 3-manifold groups are Kahler groups? J. Eur. Math. Soc. 11 (2009) 521-528] by taking N to be the trivial group. If instead, G is the fundamental group of a compact complex surface, and N is finitely presented, then we show that Q must contain the fundamental group of a Seifert-fibered 3-manifold as a finite index subgroup, and G contains as a finite index subgroup the fundamental group of an elliptic fibration. We also give an example showing that the relation of quasi-isometry does not preserve Kahler groups. This gives a negative answer to a question of Gromov which asks whether Kahler groups can be characterized by their asymptotic geometry.

Compact polarization dependent EBG surface with fractal boundary patches

Patches with variants of fractal Minkowski curves as boundaries are used here to design a polarization dependent electromagnetic bandgap surface. Reflection phases of the proposed structure depends upon the polarization state of the incident wave and frequency. The phase difference between the x-polarized and y-polarized components of the reflected wave can be as high as 200 degrees and this is achieved without excessive increase in unit cell dimensions and vias. The performance of the surface is analyzed numerically using CST microwave studio. The potential applications of the surface are in polarization conversion surfaces, polarimetric radar calibration, and RCS reduction.

In-situ FT-IR spectroscopic studies of fuel cell electro-catalysis: From single-crystal to nanoparticle surfaces

The work presented in this article shows the power of the variable temperature, in-situ FT-IR spectroscopy system developed in Newcastle with respect to the investigation of fuel cell electro-catalysis. On the Ru(0001) electrode surface, CO co-adsorbs with the oxygen-containing adlayers to form mixed [CO+(2x2)-O(H)] domains. The electro-oxidation of the Ru(0001) surface leads to the formation of active (1x1)-O(H) domains, and the oxidation of adsorbed CO then takes place at the perimeter of these domains. At 20 degrees C, the adsorbed CO is present as rather compact islands. In contrast, at 60 degrees C, the COads is present as a relatively looser and weaker adlayer. Higher temperature was also found to facilitate the surface diffusion and oxidation of COads. No dissociation or electro-oxidation of methanol was observed at potentials below approximately 950mV; however, the Ru(0001) surface at high anodic potentials was observed to be very active. On both Pt and PtRu nanoparticle surfaces, only one linear bond CO adsorbate was formed from methanol adsorption, and the PtRu surface significantly promoted both methanol dissociative adsorption to CO and its further oxidation to CO2. Increasing temperature from 20 to 60 degrees C significantly facilitates the methanol turnover to CO2.

Artificial surfaces of intertwined square spirals:A CPW model

Intertwining planar spirals arranged in doubly periodic arrays enables a substantially subwavelength response of the unit cell smaller than 1/40 of wavelength with large fractional bandwidths. These properties are important for application at low frequencies, conformal curved surfaces, or with compact radiators. It is shown that interleaving counter-wound spiral arms extended into adjacent unit cells dramatically increase the array equivalent capacitance while reducing the inductance. A coplanar waveguide (CPW) model has been developed to analytically estimate the equivalent capacitance and inductance of intertwined spiral array elements in terms of their geometrical parameters. The proposed CPW model is shown to provide an accurate prediction of the fundamental resonance frequency and can be instrumental in the design of the arrays for a specified frequency response. © 2012 IEEE.

The use of a novel compact fluorosensor for in situ monitoring of the photocatalytic destruction of methylene blue dye effluents

The use of TiO 2 photocatalysis for the destruction of dyes such as methylene blue has been extensively reported. One of the challenges faced in both the laboratory and large scale water treatment plants is the fact that the samples have to be removed from the reactor vessel and the catalyst separated prior to analysis being undertaken. In this paper we report the development of a simple fluorimeter instrument and its use in monitoring the photocatalytic destruction of methylene blue dyes in the presence of catalyst suspensions. The results reported show that the instrument provides an effective method for in situ monitoring of the photocatalytic destruction of fluorescent dyes hence allowing more accurate measurement due to the minimisation of sample loss and cross contamination. Furthermore it also provides a method for real time monitoring of the dye pollutant destruction in large scale photocatalytic reactors.

Surfaces de Riemann compactes et formule de trace d'Eichler

Dans ce mémoire, nous étudierons quelques propriétés algébriques, géométriques et topologiques des surfaces de Riemann compactes. Deux grand sujets seront traités. Tout d'abord, en utilisant le fait que toute surface de Riemann compacte de genre g plus grand ou égal à 2 possède un nombre fini de points de Weierstrass, nous allons pouvoir conclure que ces surfaces possèdent un nombre fini d'automorphismes. Ensuite, nous allons étudier de plus près la formule de trace d'Eichler. Ce théorème nous permet de trouver le caractère d'un automorphisme agissant sur l'espace des q-différentielles holomorphes. Nous commencerons notre étude en utilisant la quartique de Klein. Nous effectuerons un exemple de calcul utilisant le théorème d'Eichler, ce qui nous permettra de nous familiariser avec l'énoncé du théorème. Finalement, nous allons démontrer la formule de trace d'Eichler, en prenant soin de traiter le cas où l'automorphisme agit sans point fixe séparément du cas où l'automorphisme possède des points fixes.

Croissance et ensemble nodal de fonctions propres du laplacien sur des surfaces

Dans cette thèse, nous étudions les fonctions propres de l'opérateur de Laplace-Beltrami - ou simplement laplacien - sur une surface fermée, c'est-à-dire une variété riemannienne lisse, compacte et sans bord de dimension 2. Ces fonctions propres satisfont l'équation $\Delta_g \phi_\lambda + \lambda \phi_\lambda = 0$ et les valeurs propres forment une suite infinie. L'ensemble nodal d'une fonction propre du laplacien est celui de ses zéros et est d'intérêt depuis les expériences de plaques vibrantes de Chladni qui remontent au début du 19ème siècle et, plus récemment, dans le contexte de la mécanique quantique. La taille de cet ensemble nodal a été largement étudiée ces dernières années, notamment par Donnelly et Fefferman, Colding et Minicozzi, Hezari et Sogge, Mangoubi ainsi que Sogge et Zelditch. L'étude de la croissance de fonctions propres n'est pas en reste, avec entre autres les récents travaux de Donnelly et Fefferman, Sogge, Toth et Zelditch, pour ne nommer que ceux-là. Notre thèse s'inscrit dans la foulée du travail de Nazarov, Polterovich et Sodin et relie les propriétés de croissance des fonctions propres avec la taille de leur ensemble nodal dans l'asymptotique $\lambda \nearrow \infty$. Pour ce faire, nous considérons d'abord les exposants de croissance, qui mesurent la croissance locale de fonctions propres et qui sont obtenus à partir de la norme uniforme de celles-ci. Nous construisons ensuite la croissance locale moyenne d'une fonction propre en calculant la moyenne sur toute la surface de ces exposants de croissance, définis sur de petits disques de rayon comparable à la longueur d'onde. Nous montrons alors que la taille de l'ensemble nodal est contrôlée par le produit de cette croissance locale moyenne et de la fréquence $\sqrt{\lambda}$. Ce résultat permet une reformulation centrée sur les fonctions propres de la célèbre conjecture de Yau, qui prévoit que la mesure de l'ensemble nodal croît au rythme de la fréquence. Notre travail renforce également l'intuition répandue selon laquelle une fonction propre se comporte comme un polynôme de degré $\sqrt{\lambda}$. Nous généralisons ensuite nos résultats pour des exposants de croissance construits à partir de normes $L^q$. Nous sommes également amenés à étudier les fonctions appartenant au noyau d'opérateurs de Schrödinger avec petit potentiel dans le plan. Pour de telles fonctions, nous obtenons deux résultats qui relient croissance et taille de l'ensemble nodal.

Compact Representations for Fast Nonrigid Registration of Medical Images

We develop efficient techniques for the non-rigid registration of medical images by using representations that adapt to the anatomy found in such images. Images of anatomical structures typically have uniform intensity interiors and smooth boundaries. We create methods to represent such regions compactly using tetrahedra. Unlike voxel-based representations, tetrahedra can accurately describe the expected smooth surfaces of medical objects. Furthermore, the interior of such objects can be represented using a small number of tetrahedra. Rather than describing a medical object using tens of thousands of voxels, our representations generally contain only a few thousand elements. Tetrahedra facilitate the creation of efficient non-rigid registration algorithms based on finite element methods (FEM). We create a fast, FEM-based method to non-rigidly register segmented anatomical structures from two subjects. Using our compact tetrahedral representations, this method generally requires less than one minute of processing time on a desktop PC. We also create a novel method for the non-rigid registration of gray scale images. To facilitate a fast method, we create a tetrahedral representation of a displacement field that automatically adapts to both the anatomy in an image and to the displacement field. The resulting algorithm has a computational cost that is dominated by the number of nodes in the mesh (about 10,000), rather than the number of voxels in an image (nearly 10,000,000). For many non-rigid registration problems, we can find a transformation from one image to another in five minutes. This speed is important as it allows use of the algorithm during surgery. We apply our algorithms to find correlations between the shape of anatomical structures and the presence of schizophrenia. We show that a study based on our representations outperforms studies based on other representations. We also use the results of our non-rigid registration algorithm as the basis of a segmentation algorithm. That algorithm also outperforms other methods in our tests, producing smoother segmentations and more accurately reproducing manual segmentations.

On the parameterization of turbulent surface fluxes over heterogeneous sea ice surfaces

Turbulent surface fluxes of momentum and sensible and latent heat as well as surface temperature, air temperature, air humidity, and wind speed were measured by the German Falcon research aircraft over the marginal ice zone (MIZ) of the northern Baltic Sea and the Fram Strait. Applying the bulk formulas and the stability functions to the measurements, the roughness lengths for momentum z0, sensible heat zT, and latent heat zq were calculated. As mean values over a wide range of sea ice conditions, we obtain z0 = 5 � 10�4 m, zT = 1 � 10�8 m, and zq = 1 � 10�7 m. These correspond to the following mean values (± standard deviations) of neutral transfer coefficients reduced to 10 m height, CDN10 = (1.9 ± 0.8) � 10�3, CHN10 = (0.9 ± 0.3) � 10�3, and CEN10 = (1.0 ± 0.2) � 10�3. An average ratio of z0/zT � 104 was observed over the range of 10�6 m < z0 < 10�2 m and differs from previously published results over compact sea ice (10�1 < z0/zT < 103). Other observational results over heterogeneous sea ice do not exist. However, our z0/zT ratio approximately agrees with observations over heterogeneous land surfaces. Flux parameterizations based on commonly used roughness lengths ratios (z0 = zT = zq) overestimate the surface heat fluxes compared to our measurements by more than 100%.