On surfaces with prescribed shape operator

The problem of immersing a simply connected surface with a prescribed shape operator is discussed. I show that, aside from some special degenerate cases, such as when the shape operator can be realized by a surface with one family of principal curves being geodesic, the space of such realizations is a convex set in an affine space of dimension at most 3. The cases where this maximum dimension of realizability is achieved are analyzed and it is found that there are two such families of shape operators, one depending essentially on three arbitrary functions of one variable and another depending essentially on two arbitrary functions of one variable. The space of realizations is discussed in each case, along with some of their remarkable geometric properties. Several explicit examples are constructed.

Modelling fungal growth on surfaces

Fungal growth in time and space at the substrate surface was modelled for a simple system mimicking solid-state fermentation, using a polycarbonate Nucleopore membrane laid over a glucose solution. Biomass production depends on both tip density and the diffusion of glucose within the fungal hyphae. The model predicts early increases in both height and concentration, followed by a period in which the biomass profile moves with a constant wavefront. The rate of increase in height increases as tip diffusivity increases or as the Monod saturation constant for glucose decreases.

Explosion of smoothness from a point to everywhere for conjugacies between diffeomorphisms on surfaces

For diffeomorphisms on surfaces with basic sets, we show the following type of rigidity result: if a topological conjugacy between them is differentiable at a point in the basic set then the conjugacy has a smooth extension to the surface. These results generalize the similar ones of D. Sullivan, E. de Faria and ours for one-dimensional expanding dynamics.

Random graphs on surfaces

Counting labelled planar graphs, and typical properties of random labelled planar graphs, have received much attention recently. We start the process here of extending these investigations to graphs embeddable on any fixed surface S. In particular we show that the labelled graphs embeddable on S have the same growth constant as for planar graphs, and the same holds for unlabelled graphs. Also, if we pick a graph uniformly at random from the graphs embeddable on S which have vertex set {1, . . . , n}, then with probability tending to 1 as n → ∞, this random graph either is connected or consists of one giant component together with a few nodes in small planar components.

A computational and geometric approach to phase resetting curves and surfaces

"Vegeu el resum a l'inici del document del fitxer adjunt."

Supramolecular Organization of Metal Nanoparticles in Solution and of Phenyleneethynylenes on Surfaces

Most of the procedures reported for the synthesis of metal nanoparticles involve the use of strong reducing agents or elevated temperatures. This limits the possibility of developing metal nanoparticle based sensors for the in situ detection of analytes. One of the objectives of the present investigations is to (i) develop newer methodologies for the synthesis of metal nanoparticles in aqueous medium at ambient conditions and (ii) their use in the detection of metal cations by taking advantage of the unique coordination ability. Ideally, biocompatible molecules which possess both the reducing and stabilizing groups are desirable for such applications. Formation of stable supramolecular assembly, by bringing metal nanoparticles close to each other, results in plasmon coupling and this strategy can be effectively utilized for the development of metal nanoparticle based sensors.Another objective of the present study is to understand the supramolecular organization of molecules on surfaces. Various noncovalent interactions between the molecules and with surface play a decisive role in their organizations. An in-depth understanding of these interactions is essential for device fabrications. Recent photophysical studies have revealed that phenyleneethynylene based molecular systems are ideal for device application. The second objective of the thesis focuses on understanding the (i) organization of phenyleneethynylenes on highly oriented pyrolytic graphite (HOPG) surface with atomic level precision and (ii) weak intermolecular interactions which drive their organization.

Chiral molecules on surfaces

chiral molecules can modify surfaces in many ways. Long-range chiral structures can be induced by local chirality, which can act as templates stereo-directing other molecules. Such templates are either based on the arrangement of molecules alone or involve reconstruction of the substrate suface. Stereo-direction can also be achieved buy direct local interaction between chiral moleculesx. Even the adsorption of achiral molecules onto achiral surfaces can induce local chirality due to a reduction ofsymmetry in the presence of the surface. Intrinsically chiral metal and oxide surfaces can act as templates for enantioselective adsorption and surface reactions without any surface modification.

Cell adhesion and growth on surfaces modified by plasma and ion implantation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Occurrence of pathogenic environmental mycobacteria on surfaces in health institutions

The presence of environmental mycobacteria on surfaces in two public health institutions, namely a health center and a hospital in upstate São Paulo (Brazil), was identified by polymerase chain reaction-restriction enzyme analysis (PRA). The possible sources of contamination by these microorganisms were evaluated, contributing to epidemiology studies. Methods: From June 2005 to June 2006, a total of 632 samples were collected from exposed surfaces, such as washbasins, drinking fountains, and other accessible sites, and the mycobacteria present in the samples were isolated and cultured. Results: Sixty-five mycobacteria were isolated from the 632 samples; 47 of which were detected in samples from the health center and 18 in samples collected from the hospital. The isolates were identified by DNA restriction patterns obtained by PRA, and potentially pathogenic species were found to be prevalent among the identified mycobacteria. This study shows that the PRA technique can be employed as a fast and easy method for identification of nontuberculous mycobacteria in public areas. Conclusions: The isolation of environmental mycobacteria from the two health institutions demonstrates that these surfaces are reservoirs of potentially pathogenic mycobacteria and indicates the need for continuous maintenance and monitoring. These data will add to the study of the epidemiology of these microorganisms.

Einstein-like geometric structures on surfaces

An AH (affine hypersurface) structure is a pair comprising a projective equivalence class of torsion-free connections and a conformal structure satisfying a compatibility condition which is automatic in two dimensions. They generalize Weyl structures, and a pair of AH structures is induced on a co-oriented non-degenerate immersed hypersurface in flat affine space. The author has defined for AH structures Einstein equations, which specialize on the one hand to the usual Einstein Weyl equations and, on the other hand, to the equations for affine hyperspheres. Here these equations are solved for Riemannian signature AH structures on compact orientable surfaces, the deformation spaces of solutions are described, and some aspects of the geometry of these structures are related. Every such structure is either Einstein Weyl (in the sense defined for surfaces by Calderbank) or is determined by a pair comprising a conformal structure and a cubic holomorphic differential, and so by a convex flat real projective structure. In the latter case it can be identified with a solution of the Abelian vortex equations on an appropriate power of the canonical bundle. On the cone over a surface of genus at least two carrying an Einstein AH structure there are Monge-Amp`ere metrics of Lorentzian and Riemannian signature and a Riemannian Einstein K"ahler affine metric. A mean curvature zero spacelike immersed Lagrangian submanifold of a para-K"ahler four-manifold with constant para-holomorphic sectional curvature inherits an Einstein AH structure, and this is used to deduce some restrictions on such immersions.

Ricci flows on surfaces related to the Einstein weyl and Abelian vortex equations

There are described equations for a pair comprising a Riemannian metric and a Killing field on a surface that contain as special cases the Einstein Weyl equations (in the sense of D. Calderbank) and a real version of a special case of the Abelian vortex equations, and it is shown that the property that a metric solve these equations is preserved by the Ricci flow. The equations are solved explicitly, and among the metrics obtained are all steady gradient Ricci solitons (e.g. the cigar soliton) and the sausage metric; there are found other examples of eternal, ancient, and immortal Ricci flows, as well as some Ricci flows with conical singularities.

Ordered restriction endonuclease maps of yeast artificial chromosomes created by optical mapping on surfaces.

We have developed a surface mounting technology for the rapid construction of ordered restriction maps from individual DNA molecules. Optical restriction maps constructed from yeast artificial chromosome DNA molecules mounted on specially derivatized glass surfaces are accurate and reproducible, and the technology is amenable to automation. The mounting procedures described here should also be useful for fluorescence in situ hybridization studies. We believe these improvements to optical mapping will further stimulate the development of nonelectrophoretic approaches to genome analysis.

Growth of Carbon Nanotubes on Surfaces: The Effects of Catalyst and Substrate

We report a study of synthesising air-stable, nearly monodispersed bimetallic colloids of Co/Pd and Fe/Mo of varying compositions as active catalysts for the growth of carbon nanotubes. Using these catalysts we have investigated the effects of catalyst and substrate on the carbon nanostructures formed in a plasma-enhanced chemical vapour deposition (PECVD) process. We will show how it is possible to assess the influence of both the catalyst and the support on the controlled growth of carbon nanotube and nanofiber arrays. The importance of the composition of the catalytic nuclei will be put into perspective with other results from the literature. Furthermore, the influence of other synthetic parameters such as the nature of the nanoparticle catalysts will also be analysed and discussed in detail.