Uma introdução à geometria esférica

Pós-graduação em Matemática em Rede Nacional - IBILCE

New constraints on H-0 and Omega(m) from SZE/X-ray data and baryon acoustic oscillations

The Hubble constant, H-0, sets the scale of the size and age of the Universe and its determination from independent methods is still worthwhile to be investigated. In this article, by using the Sunyaev-Zeldovich effect and X-ray surface brightness data from 38 galaxy clusters observed by Bonamente et al. (Astrophys J 647:25, 2006), we obtain a new estimate of H-0 in the context of a flat Lambda CDM model. There is a degeneracy on the mass density parameter (Omega(m)) which is broken by applying a joint analysis involving the baryon acoustic oscillations (BAO) as given by Sloan Digital Sky Survey. This happens because the BAO signature does not depend on H-0. Our basic finding is that a joint analysis involving these tests yield H-0 = 76.5(-3.33)(+3.35) km/s/mpc and Omega(m) = 0.27(-0.02)(+0.03). Since the hypothesis of spherical geometry assumed by Bonamente et al. is questionable, we have also compared the above results to a recent work where a sample of galaxy clusters described by an elliptical profile was used in analysis.

Rotational diffusion membrane and fluorescence anisotropy.

Structural properties of model membranes, such as lipid vesicles, may be investigated through the addition of fluorescent probes. After incorporation, the fluorescent molecules are excited with linearly polarized light and the fluorescence emission is depolarized due to translational as well as rotational diffusion during the lifetime of the excited state. The monitoring of emitted light is undertaken through the technique of time-resolved fluorescence: the intensity of the emitted light informs on fluorescence decay times, and the decay of the components of the emitted light yield rotational correlation times which inform on the fluidity of the medium. The fluorescent molecule DPH, of uniaxial symmetry, is rather hydrophobic and has collinear transition and emission moments. It has been used frequently as a probe for the monitoring of the fluidity of the lipid bilayer along the phase transition of the chains. The interpretation of experimental data requires models for localization of fluorescent molecules as well as for possible restrictions on their movement. In this study, we develop calculations for two models for uniaxial diffusion of fluorescent molecules, such as DPH, suggested in several articles in the literature. A zeroth order test model consists of a free randomly rotating dipole in a homogeneous solution, and serves as the basis for the study of the diffusion of models in anisotropic media. In the second model, we consider random rotations of emitting dipoles distributed within cones with their axes perpendicular to the vesicle spherical geometry. In the third model, the dipole rotates in the plane of the of bilayer spherical geometry, within a movement that might occur between the monolayers forming the bilayer. For each of the models analysed, two methods are used by us in order to analyse the rotational diffusion: (I) solution of the corresponding rotational diffusion equation for a single molecule, taking into account the boundary conditions imposed by the models, for the probability of the fluorescent molecule to be found with a given configuration at time t. Considering the distribution of molecules in the geometry proposed, we obtain the analytical expression for the fluorescence anisotropy, except for the cone geometry, for which the solution is obtained numerically; (II) numerical simulations of a restricted rotational random walk in the two geometries corresponding to the two models. The latter method may be very useful in the cases of low-symmetry geometries or of composed geometries.

Monte-Carlo simulation of hard spherocylinders under confinement

When a liquid crystal is confined to a cavity its director field becomes subject to competing forces: on the one hand, the surface of the cavity orients the director field (``surface anchoring''), on the other hand deformations of the director field cost elastic energy. Hence the equilibrium director field is determined by a compromise between surface anchoring and elasticity. One example of a confined liquid crystal that has attracted particular interest from physicists is the nematic droplet. In this thesis a system of hard rods is considered as the simplest model for nematic liquid crystals consisting of elongated molecules. First, systems of hard spherocylinders in a spherical geometry are investigated by means of canonical Monte Carlo simulations. In contrast to previous simulation work on this problem, a continuum model is used. In particular, the effects of ordering near hard curved walls are studied for the low-density regime. With increasing density, first a uniaxial surface film forms and then a biaxial surface film, which eventually fills the entire cavity. We study how the surface order, the adsorption and the shape of the director field depend on the curvature of the wall. We find that orientational ordering at a curved wall in a cavity is stronger than at a flat wall, while adsorption is weaker. For densities above the isotropic-nematic transition, we always find bipolar configurations. As a next step, an extension of the Asakura-Oosawa-Vrij model for colloid-polymer mixtures to anisotropic colloids is considered. By means of computer simulations we study how droplets of hard, rod-like particles optimize their shape and structure under the influence of the osmotic compression caused by the presence of spherical particles that act as depletion agents. At sufficiently high osmotic pressures the rods that make up the drops spontaneously align to turn them into uniaxial nematic liquid crystalline droplets. The nematic droplets or ``tactoids'' that so form are not spherical but elongated, resulting from the competition between the anisotropic surface tension and the elastic deformation of the director field. In agreement with recent theoretical predictions we find that sufficiently small tactoids have a uniform director field, whilst large ones are characterized by a bipolar director field. From the shape and director-field transformation of the droplets we estimate the surface anchoring strength.

Global distributions of Phaeocystis sp. abundance and biomass - Gridded data product (NetCDF) - Contribution to the MAREDAT World Ocean Atlas of Plankton Functional Types

The planktonic haptophyte Phaeocystis has been suggested to play a fundamental role in the global biogeochemical cycling of carbon and sulphur, but little is known about its global biomass distribution. We have collected global microscopy data of the genus Phaeocystis and converted abundance data to carbon biomass using species-specific carbon conversion factors. Microscopic counts of single-celled and colonial Phaeocystis were obtained both through the mining of online databases and by accepting direct submissions (both published and unpublished) from Phaeocystis specialists. We recorded abundance data from a total of 1595 depth-resolved stations sampled between 1955-2009. The quality-controlled dataset includes 5057 counts of individual Phaeocystis cells resolved to species level and information regarding life-stages from 3526 samples. 83% of stations were located in the Northern Hemisphere while 17% were located in the Southern Hemisphere. Most data were located in the latitude range of 50-70° N. While the seasonal distribution of Northern Hemisphere data was well-balanced, Southern Hemisphere data was biased towards summer months. Mean species- and form-specific cell diameters were determined from previously published studies. Cell diameters were used to calculate the cellular biovolume of Phaeocystis cells, assuming spherical geometry. Cell biomass was calculated using a carbon conversion factor for Prymnesiophytes (Menden-Deuer and Lessard, 2000). For colonies, the number of cells per colony was derived from the colony volume. Cell numbers were then converted to carbon concentrations. An estimation of colonial mucus carbon was included a posteriori, assuming a mean colony size for each species. Carbon content per cell ranged from 9 pg (single-celled Phaeocystis antarctica) to 29 pg (colonial Phaeocystis globosa). Non-zero Phaeocystis cell biomasses (without mucus carbon) range from 2.9 - 10?5 µg l-1 to 5.4 - 103 µg l-1, with a mean of 45.7 µg l-1 and a median of 3.0 µg l-1. Highest biomasses occur in the Southern Ocean below 70° S (up to 783.9 µg l-1), and in the North Atlantic around 50° N (up to 5.4 - 103 µg l-1).

Compression of matter by hypersphsericla shock waves

A novel compression scheme is proposed, in which hollow targets with specifically curved structures initially filled with uniform matter, are driven by converging shock waves. The self-similar dynamics is analyzed for converging and diverging shock waves. The shock-compressed densities and pressures are much higher than those achieved using spherical shocks due to the geometric accumulation. Dynamic behavior is demonstrated using two-dimensional hydrodynamic simulations. The linear stability analysis for the spherical geometry reveals a new dispersion relation with cut-off mode numbers as a function of the specific heat ratio, above which eigenmode perturbations are smeared out in the converging phase.

Student mathematical notebook of Ephraim Eliot, 1779

Handwritten mathematical notebook of Ephraim Eliot, kept in 1779 while he was a student at Harvard College. The volume contains rules, definitions, problems, drawings, and tables on arithmetic, geometry, trigonometry, surveying, calculating distances, and dialing. Some of the exercises are illustrated by unrefined hand-drawn diagrams, as well as a sketch of a mariner’s compass. The sections on navigation, mensuration of heights, and spherical geometry are titled but not completed. The ink of the later text, beginning with Trigonometry, is faded.

Student mathematical notebook of William Emerson Faulkner, 1795

Leather hardcover notebook with unruled pages containing the handwritten mathematical exercises of William Emerson Faulkner, begun in 1795 while he was an undergraduate at Harvard College. The volume contains rules, definitions, problems, drawings, and tables on geometry, trigonometry, surveying, calculating distances, sailing, and dialing. Some of the exercises are illustrated by unrefined hand-drawn diagrams, including some of buildings and trees.

Influência da interação dipolar nas fases magnéticas de nanopartículas esféricas com estrutura núcleo@camada

Bi-magnetic core@shell nanoparticle has attracted attention several researchers because great applicability that they offer. The possibility of combining different functionalities of magnetic materials make them a key piece in many areas as in data processing permanent magnets and biomagnetics sistems. These nanoparticles are controlled by intrinsic properties of the core and shell materials as well as the interactions between them, besides size and geometry effects. Thus, it was developed in this thesis a theoretical study about dipolar interaction contribution between materials different magnetic properties in bi-magnetic core@shell nanoparticles conventional spherical geometry. The materials were analyzed CoFe2O4, MnFe2O4 e CoFe2 in various combinations and sizes. The results show that the impact of the core dipole field in the shell cause reverse magnetization early its, before of the core, in nanoparticle of CoFe2O4(22nm)@CoFe2(2nm), thereby causing a decrease coercivity field of 65% in comparection with simple nanoparticle of CoFe2O4 (HC=13.6 KOe) of same diameter. The large core anisotropy in conventional nanoparticle makes it the a stable dipolar field source in the shell, that varies length scale of the order of the core radius. Furthermore, the impact of dipolar field is greatly enhanced by the geometrical constraints and by magnetics properties of both core@shell materials. In systems with core coated with a thin shell of thickness less than the exchange length, the interaction interface can hold reversal the shell occurring an uniform magnetization reversal, however this effect only is relevant on systems where the dipole field effects is weak compared with the exchange interaction.

Influência da interação dipolar nas fases magnéticas de nanopartículas esféricas com estrutura núcleo@camada

Bi-magnetic core@shell nanoparticle has attracted attention several researchers because great applicability that they offer. The possibility of combining different functionalities of magnetic materials make them a key piece in many areas as in data processing permanent magnets and biomagnetics sistems. These nanoparticles are controlled by intrinsic properties of the core and shell materials as well as the interactions between them, besides size and geometry effects. Thus, it was developed in this thesis a theoretical study about dipolar interaction contribution between materials different magnetic properties in bi-magnetic core@shell nanoparticles conventional spherical geometry. The materials were analyzed CoFe2O4, MnFe2O4 e CoFe2 in various combinations and sizes. The results show that the impact of the core dipole field in the shell cause reverse magnetization early its, before of the core, in nanoparticle of CoFe2O4(22nm)@CoFe2(2nm), thereby causing a decrease coercivity field of 65% in comparection with simple nanoparticle of CoFe2O4 (HC=13.6 KOe) of same diameter. The large core anisotropy in conventional nanoparticle makes it the a stable dipolar field source in the shell, that varies length scale of the order of the core radius. Furthermore, the impact of dipolar field is greatly enhanced by the geometrical constraints and by magnetics properties of both core@shell materials. In systems with core coated with a thin shell of thickness less than the exchange length, the interaction interface can hold reversal the shell occurring an uniform magnetization reversal, however this effect only is relevant on systems where the dipole field effects is weak compared with the exchange interaction.

Elements of geometry : containing the first six books of Euclid, with a supplement on the quadrature of the circle, and the geometry of solids : to which are added, elements of plane and spherical trigonometry /

Mode of access: Internet.

Elements of geometry : containing the first six books of Euclid, with a supplement on the quadrature of the circle, and the geometry of solids: to which are added elements of plane and spherical trigonometry /

Mode of access: Internet.

Elements of descriptive geometry : with their application to spherical trigonometry, spherical projections, and warped surfaces /

Mode of access: Internet.

Elements of descriptive geometry : with their application to spherical trigonometry, spherical projections, and warped surfaces /

Mode of access: Internet.

Elements of geometry; : containing the first six books of Euclid, with a supplement on the quadrature of the circle and the geometry of solids; to which are added, Elements of plane and spherical trigonometry. /

"Errata"--P. [xvi]