Curvature Estimates for Submanifolds in Warped Products

We give estimates of the intrinsic and the extrinsic curvature of manifolds that are isometrically immersed as cylindrically bounded submanifolds of warped products. We also address extensions of the results in the case of submanifolds of the total space of a Riemannian submersion.

Affine and curvature collineations in space-time

Graham Hall

Hillslope curvature, clay mineralogy, and phosphorus adsorption in an Alfisol cultivated with sugarcane

As curvaturas do relevo promovem pedoambientes específicos que condicionam os atributos químicos e mineralógicos do solo e podem auxiliar na definição de zonas específicas de manejo. O fósforo (P) é um dos principais elementos limitantes ao desenvolvimento e longevidade do canavial. O teor e a constituição mineralógica da fração argila assumem papel importante na disponibilidade do P, sendo que a gibbsita (Gb), quando presente em altas proporções no solo, pode ser a principal responsável pela sua adsorção e indisponibilidade. Investigaram-se as relações e a variabilidade espacial da adsorção de P e a ocorrência de caulinita (Ct) e gibbsita na fração argila de um Argissolo Vermelho-Amarelo eutrófico originado de rochas areníticas sob diferentes curvaturas do relevo em área sob cultivo de cana-de-açúcar. Duas malhas de 1 ha foram delimitadas numa área côncava e outra área convexa. Foram coletadas 121 amostras em cada área para realização das análises granulométricas, químicas e mineralógicas. A capacidade máxima de adsorção de P foi obtida em seis amostras escolhidas ao acaso em cada área. Os resultados foram submetidos às análises estatísticas descritiva e geoestatística. Os menores valores médios de P disponível encontraram-se na área convexa. Nesta área, a proporção de gibbsita, expressa pelos valores da razão [Gb/(Gb+Ct)] e os valores de capacidade máxima de adsorção de fósforo foram maiores do que na área côncava.

Análise de desempenho de um fogão solar com parabola fabricada em material compósito

It is presented a solar cooker made with a parabolic reflector composed by a composite material. For this purpose, it was utilized a cast concrete with a parabolic profile obtained by means of modeling. It will be demonstrated the manufacturing process and settings, as well as tests results, in order to determine the contact temperature and cooking time of some foods. This solar cooker presents the following main characteristics: the concentration method, low cost and easy manufacturing process. It was performed by employing recycled materials such as cement, plaster, crushed polystyrene and wheels. The captation area measures 1 square meter and its parabole was covered with a mirrors measuring 25 cm2. A temperature higher than 650°C was obtained. Furthermore, it has been demonstrated that the cooking viability for several type of foods such as beans, potatoes, rice, yams and pasta can be used in two meals for a family of four. In addition, the advantages of this cooker were analysed in comparison with others described in literature as well as those operating on gas. Especially in Northeast of Brazil, where there is a potential for solar energy, this prototype is an important tool, because it avoids not only desertification, but also pollutants from burning firewoods which cause ecological imbalance

Force system evaluation of symmetrical beta-titanium T-loop springs preactivated by curvature and concentrated bends

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

Biological shape analysis by digital curvature

This paper reports the novel application of digital curvature as a feature for morphological characterization and classification of landmark shapes. By inheriting several unique features of the continuous curvature, the digital curvature provides invariance to translations, rotations, local shape deformations, and is easily made tolerant to scaling. In addition, the bending energy, a global shape feature, can be directly estimated from the curvature values. The application of these features to analyse patterns of cranial morphological geographic differentiation in the rodent species Thrichomys apereoides has led to encouraging results, indicating a close correspondence between the geographical and morphological distributions. (C) 2003 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

Effects of varying curvature and width on the electronic states of GaAs quantum rings

Stationary states of an electron in thin GaAs elliptical quantum rings are calculated within the effective-mass approximation. The width of the ring varies smoothly along the centerline, which is an ellipse. The solutions of the Schrödinger equation with Dirichlet boundary conditions are approximated by a product of longitudinal and transversal wave functions. The ground-state probability density shows peaks: (i) where the curvature is larger in a constant-with ring, and (ii) in thicker parts of a circular ring. For rings of typical dimensions, it is shown that the effects of a varying width may be stronger than those of the varying curvature. Also, a width profile which compensates the main localization effects of the varying curvature is obtained.

SMALLEST UNIVERSE OF NEGATIVE CURVATURE

The smallest known three-dimensional closed manifold of curvature k = -1 was discovered a few years ago by Weeks. This kind of manifold is constructed from a hyperbolic polyhedron with faces pair-wise identified. Here it is used as the comoving spatial section of a Friedmann cosmological model, in the spirit of Ellis and Schreiber's idea of small universes. Its nontrivial global topology has the effect of producing multiple images of single cosmic sources, and this is the basis of an attempt to solve a famous controversy about the redshifts of quasars.

Effects of direction and curvature on variable error pattern of reaching movements

A number of studies have analyzed various indices of the final position variability in order to provide insight into different levels of neuromotor processing during reaching movements. Yet the possible effects of movement kinematics on variability have often been neglected. The present study was designed to test the effects of movement direction and curvature on the pattern of movement variable errors. Subjects performed series of reaching movements over the same distance and into the same target. However, due either to changes in starting position or to applied obstacles, the movements were performed in different directions or along the trajectories of different curvatures. The pattern of movement variable errors was assessed by means of the principal component analysis applied on the 2-D scatter of movement final positions. The orientation of these ellipses demonstrated changes associated with changes in both movement direction and curvature. However, neither movement direction nor movement curvature affected movement variable errors assessed by area of the ellipses. Therefore it was concluded that the end-point variability depends partly, but not exclusively, on movement kinematics.

Curvature versus V-bends in a group B titanium T-loop spring

Objective: To compare the system of forces acting on curvature and preactivated V-bends in titanium T-loop springs (TTLSs) made of 0.017- X 0.025-inch TMA (titanium molibdenium alloy) wire.Materials and Methods: Pictures of TTLSs preactivated by curvature and V-bends were inserted in the LOOP software program to design both TTLSs. Symmetry was assured using the program. Both TTLSs used the same amount (length) of wire and had the same angulation between their anterior and posterior extremities when passive. The loops were activated 7 mm, and forces and moments were registered after each 0.5 mm of deactivation. The brackets were at the same height, separated by 23 mm and angulated 0 degrees.Results: The preactivated curvature TTLS delivered horizontal forces ranging from 34 gF to 456 gF, while the TTLS preactivated by V-bends delivered forces ranging from 54 gF to 517 gF. The forces decreased more (30 gF vs 33 gF) with every 0.5 mm of activation on the preactivated V-bend TTLS than on the preactivated curvature TTLS. Vertical forces were low and clinically insignificant for both TTLSs. The moment to force (MF) ratios were systematically higher on the preactivated curvature than on the preactivated V-bend TTLS (from 5.8 mm to 38.8 mm vs 4.7 mm to 28.3 mm).Conclusions: Although both loops show symmetrical moments in their anterior and posterior extremities and can be used for group B anchorage, the curvature preactivated TTLS delivers lower horizontal forces and higher MF ratios than the acute preactivated V-bend TTLS.

Tau-functions and dressing transformations for zero-curvature affine integrable equations

The solutions of a large class of hierarchies of zero-curvature equations that includes Toda- and KdV-type hierarchies are investigated. All these hierarchies are constructed from affine (twisted or untwisted) Kac-Moody algebras g. Their common feature is that they have some special vacuum solutions corresponding to Lax operators lying in some Abelian (up to the central term) subalgebra of g; in some interesting cases such subalgebras are of the Heisenberg type. Using the dressing transformation method, the solutions in the orbit of those vacuum solutions are constructed in a uniform way. Then, the generalized tau-functions for those hierarchies are defined as an alternative set of variables corresponding to certain matrix elements evaluated in the integrable highest-weight representations of g. Such definition of tau-functions applies for any level of the representation, and it is independent of its realization (vertex operator or not). The particular important cases of generalized mKdV and KdV hierarchies as well as the Abelian and non-Abelian affine Toda theories are discussed in detail. © 1997 American Institute of Physics.

Birth of a closed universe of negative spatial curvature

We propose a modified form of the spontaneous birth of the universe by quantum tunneling. It proceeds through topology change and inflation, to eventually become a universe with closed spatial sections of negative spatial curvature and nontrivial global topology.

Braneworlds scenarios in a gravity model with higher order spatial three-curvature terms

In this work we study a Hořava-like 5-dimensional model in the context of braneworld theory. The equations of motion of such model are obtained and, within the realm of warped geometry, we show that the model is consistent if and only if λ takes its relativistic value 1. Furthermore, we show that the elimination of problematic terms involving the warp factor second order derivatives are eliminated by imposing detailed balance condition in the bulk. Afterwards, Israel's junction conditions are computed, allowing the attainment of an effective Lagrangian in the visible brane. In particular, we show that the resultant effective Lagrangian in the brane corresponds to a (3 + 1)-dimensional Hořava-like model with an emergent positive cosmological constant but without detailed balance condition. Now, restoration of detailed balance condition, at this time imposed over the brane, plays an interesting role by fitting accordingly the sign of the arbitrary constant β, insuring a positive brane tension and a real energy for the graviton within its dispersion relation. Also, the brane consistency equations are obtained and, as a result, the model admits positive brane tensions in the compactification scheme if, and only if, β is negative and the detailed balance condition is imposed. © 2013 Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica.