On the initiation of surface waves by turbulent shear flow

An analytical model is developed for the initial stage of surface wave generation at an air-water interface by a turbulent shear flow in either the air or in the water. The model treats the problem of wave growth departing from a flat interface and is relevant for small waves whose forcing is dominated by turbulent pressure fluctuations. The wave growth is predicted using the linearised and inviscid equations of motion, essentially following Phillips [Phillips, O.M., 1957. On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417-445], but the pressure fluctuations that generate the waves are treated as unsteady and related to the turbulent velocity field using the rapid-distortion treatment of Durbin [Durbin, P.A., 1978. Rapid distortion theory of turbulent flows. PhD thesis, University of Cambridge]. This model, which assumes a constant mean shear rate F, can be viewed as the simplest representation of an oceanic or atmospheric boundary layer. For turbulent flows in the air and in the water producing pressure fluctuations of similar magnitude, the waves generated by turbulence in the water are found to be considerably steeper than those generated by turbulence in the air. For resonant waves, this is shown to be due to the shorter decorrelation time of turbulent pressure in the air (estimated as proportional to 1/Gamma), because of the higher shear rate existing in the air flow, and due to the smaller length scale of the turbulence in the water. Non-resonant waves generated by turbulence in the water, although being somewhat gentler, are still steeper than resonant waves generated by turbulence in the air. Hence, it is suggested that turbulence in the water may have a more important role than previously thought in the initiation of the surface waves that are subsequently amplified by feedback instability mechanisms.

Integrating control systems defined on the frame bundles of the space forms

This paper considers left-invariant control systems defined on the orthonormal frame bundles of simply connected manifolds of constant sectional curvature, namely the space forms Euclidean space E-3, the sphere S-3 and Hyperboloid H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1, 3). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to left-invariant control systems defined on Lie groups. In this paper a method for integrating these systems is given where the controls are time-independent. In the Euclidean case the elements of the Lie algebra se(3) are often referred to as twists. For constant twist motions, the corresponding curves g(t) is an element of SE(3) are known as screw motions, given in closed form by using the well known Rodrigues' formula. However, this formula is only applicable to the Euclidean case. This paper gives a method for computing the non-Euclidean screw motions in closed form. This involves decoupling the system into two lower dimensional systems using the double cover properties of Lie groups, then the lower dimensional systems are solved explicitly in closed form.

Threshold autoregressive and Markov switching models: an application to commercial real estate

Although financial theory rests heavily upon the assumption that asset returns are normally distributed, value indices of commercial real estate display significant departures from normality. In this paper, we apply and compare the properties of two recently proposed regime switching models for value indices of commercial real estate in the US and the UK, both of which relax the assumption that observations are drawn from a single distribution with constant mean and variance. Statistical tests of the models' specification indicate that the Markov switching model is better able to capture the non-stationary features of the data than the threshold autoregressive model, although both represent superior descriptions of the data than the models that allow for only one state. Our results have several implications for theoretical models and empirical research in finance.

PCJ River Basins' Water Availability Caused by Water Diversion Scenarios to Supply Metropolitan Areas of So Paulo

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Influência das Alterações Hemodinâmicas Maternas sobre o Desenvolvimento Fetal

Objetivo: avaliar as alterações hemodinâmicas e estruturais cardíacas maternas nos três trimestres da gestação e relacioná-las com a classificação do recém-nascido, de acordo com o peso/idade gestacional. Métodos: foi realizada avaliação ecocardiográfica em 22 gestantes, sem patologias, para estudo do débito cardíaco, pressão arterial média, diâmetro do átrio esquerdo e resistência periférica, em três períodos da gestação: antes da 12ª , na 26ª e na 36ª semanas de gestação. Dezessete gestantes deram à luz recém-nascidos com peso adequado, quatro, recém-nascidos pequenos, e uma gestante, recém-nascido grande para a idade gestacional. Resultados: nas mães que deram à luz recém-nascidos pequenos para a idade gestacional, o débito cardíaco e o diâmetro do átrio esquerdo mantiveram-se inalterados, com tendência de elevação da pressão arterial média e aumento de 28% da resistência periférica, durante a gestação. As mães que deram à luz recém-nascidos adequados para idade gestacional tiveram aumento médio do débito cardíaco de 19% entre o primeiro e segundo trimestres e de 8% entre o segundo e terceiro trimestres da gestação. O diâmetro do átrio esquerdo elevou-se próximo de 9% durante a gestação, com manutenção da pressão arterial média e tendência de queda da resistência periférica. Conclusões: os resultados obtidos nesse trabalho suportam a associação entre adaptação hemodinâmica e peso do RN

Some integrals occurring in a topology change problem

In a paper presented a few years ago, de Lorenci et al. showed, in the context of canonical quantum cosmology, a model which allowed space topology changes. The purpose of this present work is to go a step further in that model, by performing some calculations only estimated there for several compact manifolds of constant negative curvature, such as the Weeks and Thurston spaces and the icosahedral hyperbolic space (Best space). ©2000 The American Physical Society.

Infiltração de água em um podzólico vermelho-escuro sob dois métodos de preparo, usando chuva simulada com duas intensidades

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

Fluxo do grupo de renormalização dos modelos-'alfa' e as álgebras de Lie contínuas

Pós-graduação em Física - IFT

On bifurcation of solutions of the Yamabe problem in product manifolds

We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non-homothetic solutions of the Yamabe problem. Using local rigidity and some compactness results for solutions of the Yamabe problem, we also exhibit new examples of conformal classes (with positive Yamabe constant) for which uniqueness holds. (C) 2011 Elsevier Masson SAS. All rights reserved.

Riemannian Submersions with Discrete Spectrum

We prove some estimates on the spectrum of the Laplacian of the total space of a Riemannian submersion in terms of the spectrum of the Laplacian of the base and the geometry of the fibers. When the fibers of the submersions are compact and minimal, we prove that the spectrum of the Laplacian of the total space is discrete if and only if the spectrum of the Laplacian of the base is discrete. When the fibers are not minimal, we prove a discreteness criterion for the total space in terms of the relative growth of the mean curvature of the fibers and the mean curvature of the geodesic spheres in the base. We discuss in particular the case of warped products.

Collective Almost Synchronisation in Complex Networks

This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.

A NOTE ON THE UNIQUENESS OF SOLUTIONS FOR THE YAMABE PROBLEM

Using recent results on the compactness of the space of solutions of the Yamabe problem, we show that in conformal classes of metrics near the class of a nondegenerate solution which is unique (up to scaling) the Yamabe problem has a unique solution as well. This provides examples of a local extension, in the space of conformal classes, of a well-known uniqueness criterion due to Obata.

Equivariant inverse spectral theory and toric orbifolds

Let O-2n be a symplectic toric orbifold with a fixed T-n-action and with a tonic Kahler metric g. In [10] we explored whether, when O is a manifold, the equivariant spectrum of the Laplace Delta(g) operator on C-infinity(O) determines O up to symplectomorphism. In the setting of tonic orbifolds we shmilicantly improve upon our previous results and show that a generic tone orbifold is determined by its equivariant spectrum, up to two possibilities. This involves developing the asymptotic expansion of the heat trace on an orbifold in the presence of an isometry. We also show that the equivariant spectrum determines whether the toric Kahler metric has constant scalar curvature. (C) 2012 Elsevier Inc. All rights reserved.

Stable isotopes and calcium carbonate at DSDP Holes 85-574 and 85-574A

Detailed stable isotopic and calcium carbonate records (with a sampling resolution of 3000 yr.) from the middle Miocene section of hydraulic piston corer (HPC) Hole 574A provide a sequence that records the major shift in the oxygen isotopic composition of the world's oceans that occurred at about 14 Ma. The data suggest that this transition was rapid and spans about 30,000 yr. of sediment deposition. In intervals before and after the shift, the mean d18O values are characterized by a constant mean with a high degree of variability. The degree of variability in both the d18O and d13C records is comparable to that observed for the Pliocene and earliest Pleistocene and does not show a significant change before or after the major shift in the d18O record. Whereas the oxygen isotopic record is characterized by relatively stable mean values before and after the middle Miocene event, the d13C record shows a number of significant offsets in the mean value separated by intervals of high-frequency variations. Time and frequency domain analysis of all records from Hole 574A indicate that the frequency components shown to be related to orbital changes in the Pleistocene record are also present in the middle Miocene. The high variability observed in the Site 574 isotopic records places important constraints on models describing the role of formation of the Antarctic ice sheet during the middle Miocene climatic transitions. Thus, HPC Hole 574A provides a valuable sequence for detailed study of climatic variability during an important time in the Earth's history, although we cannot provide a definitive explanation of the major oxygen isotopic event of the middle Miocene.