Vanishing Viscosity Limits and Boundary Layers for Circularly Symmetric 2D Flows

We continue the work of Lopes Filho, Mazzucato and Nussenzveig Lopes [LMN], on the vanishing viscosity limit of circularly symmetric viscous flow in a disk with rotating boundary, shown there to converge to the inviscid limit in $L^2$-norm as long as the prescribed angular velocity $\alpha(t)$ of the boundary has bounded total variation. Here we establish convergence in stronger $L^2$ and $L^p$-Sobolev spaces, allow for more singular angular velocities $\alpha$, and address the issue of analyzing the behavior of the boundary layer. This includes an analysis of concentration of vorticity in the vanishing viscosity limit. We also consider such flows on an annulus, whose two boundary components rotate independently. [LMN] Lopes Filho, M. C., Mazzucato, A. L. and Nussenzveig Lopes, H. J., Vanishing viscosity limit for incompressible flow inside a rotating circle, preprint 2006

Eigenfunctions of the Laplacian and associated Ruelle operator

Let $\Gamma$ be a co-compact Fuchsian group of isometries on the Poincar\'e disk \DD and $\Delta$ the corresponding hyperbolic Laplace operator. Any smooth eigenfunction $f$ of $\Delta$, equivariant by $\Gamma$ with real eigenvalue $\lambda=-s(1-s)$, where $s={1/2}+ it$, admits an integral representation by a distribution \dd_{f,s} (the Helgason distribution) which is equivariant by $\Gamma$ and supported at infinity \partial\DD=\SS^1. The geodesic flow on the compact surface \DD/\Gamma is conjugate to a suspension over a natural extension of a piecewise analytic map T:\SS^1\to\SS^1, the so-called Bowen-Series transformation. Let $\ll_s$ be the complex Ruelle transfer operator associated to the jacobian $-s\ln |T'|$. M. Pollicott showed that \dd_{f,s} is an eigenfunction of the dual operator $\ll_s^*$ for the eigenvalue 1. Here we show the existence of a (nonzero) piecewise real analytic eigenfunction $\psi_{f,s}$ of $\ll_s$ for the eigenvalue 1, given by an integral formula \psi_{f,s} (\xi)=\int \frac{J(\xi,\eta)}{|\xi-\eta|^{2s}} \dd_{f,s} (d\eta), \noindent where $J(\xi,\eta)$ is a $\{0,1\}$-valued piecewise constant function whose definition depends upon the geometry of the Dirichlet fundamental domain representing the surface \DD/\Gamma

Determinação de perdas de solo, água e nutrientes em Latossolo Amarelo, textura argilosa do Nordeste paraense.

bitstream/item/34520/1/ORIENTAL-BP19.pd

Spectrally narrow exciton luminescence from monolayer MoS2 exfoliated onto epitaxially grown hexagonal BN

The strong light-matter interaction in transition Metal dichalcogenides (TMDs) monolayers (MLs) is governed by robust excitons. Important progress has been made to control the dielectric environment surrounding the MLs, especially through hexagonal boron nitride (hBN) encapsulation, which drastically reduces the inhomogeneous contribution to the exciton linewidth. Most studies use exfoliated hBN from high quality flakes grown under high pressure. In this work, we show that hBN grown by molecular beam epitaxy (MBE) over a large surface area substrate has a similarly positive impact on the optical emission from TMD MLs. We deposit MoS$_2$ and MoSe$_2$ MLs on ultrathin hBN films (few MLs thick) grown on Ni/MgO(111) by MBE. Then we cover them with exfoliated hBN to finally obtain an encapsulated sample : exfoliated hBN/TMD ML/MBE hBN. We observe an improved optical quality of our samples compared to TMD MLs exfoliated directly on SiO$_2$ substrates. Our results suggest that hBN grown by MBE could be used as a flat and charge free substrate for fabricating TMD-based heterostructures on a larger scale.Comment: 5 pages, 3 figure

COMPUTER ANALYSIS OF THE GMAW AND GMAW-CW WELDING THERMAL CYCLES

A novel process of welding GMAW-CW (Gas Metal Arc Welding-Cold Wire) had been developed with it resemblance to the GMAW (Gas Metal Arc Welding), the GMAW-CW has an additional wire fed into de weld pool, allowing better deposition rates, while maintaining weld characteristics. However, there is a more complex situation related to the HAZ (Heat Affected Zone) and weld geometry prediction than the GMAW conventional. The welding energy is a high metallurgical important parameter because together with the geometric characteristics of the gasket and the preheat level is decisive in thermal cycles imposed to the material, and therefore in the possible microstructural transformations and behavior of the joint. The behavior of representative curves of thermal cycling reflects important aspects regarding the conditions used in welding. Usually such factors as the type of process, use or non- pre or post- heating, heat input, multipass welding, are able to establish differences in the form of a heat cycle curve. In this work, it was applied the dual ellipsoidal model of heat input, adapted to the GMAW-CW and compared to the same model over the GMAW, using existing experimental data and predicting the HAZ dimensions in function of weld and welding parameters. The results found had less than 10% error from experimental data in a more refined version of the model, whereas the difficulties to predict cold wire addition influences were not trivial