Vanishing Viscous Limits for 3D Navier-Stokes Equations with A Navier-Slip Boundary Condition

In this paper, we investigate the vanishing viscosity limit for solutions to the Navier-Stokes equations with a Navier slip boundary condition on general compact and smooth domains in $\mathbf{R}^3$. We first obtain the higher order regularity estimates for the solutions to Prandtl's equation boundary layers. Furthermore, we prove that the strong solution to Navier-Stokes equations converges to the Eulerian one in $C([0,T];H^1(\Omega))$ and L^\infty((0,T)\times\o), where $T$ is independent of the viscosity, provided that initial velocity is regular enough. Furthermore, rates of convergence are obtained also.Comment: 45page

Uniform regularity for the Navier-Stokes equation with Navier boundary condition

We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier-Stokes equation with Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal Sobolev space and has only one normal derivative bounded in $L^\infty$. This allows to get the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument

Estabelecimento in vitro de ápices caulinares de Liquidambar styraciflua.

Resumo

Investigation of the evolution of radiation-induced lung damage using serial CT imaging and pulmonary function tests

Background and purpose: Radiation-induced lung damage (RILD) is a common consequence of lung cancer radiotherapy (RT) with unclear evolution over time. We quantify radiological RILD longitudinally and correlate it with dosimetry and respiratory morbidity. Materials and methods: CTs were available pre-RT and at 3, 6, 12 and 24-months post-RT for forty-five subjects enrolled in a phase 1/2 clinical trial of isotoxic, dose-escalated chemoradiotherapy for locally advanced non-small cell lung cancer. Fifteen CT-based measures of parenchymal, pleural and lung volume change, and anatomical distortions, were calculated. Respiratory morbidity was assessed with the Medical Research Council (MRC) dyspnoea score and spirometric pulmonary function tests (PFTs): FVC, FEV1, FEV1/FVC and DLCO. Results: FEV1, FEV1/FVC and MRC scores progressively declined post-RT; FVC decreased by 6-months before partially recovering. Radiologically, an early phase (3–6 months) of acute inflammation was characterised by reversible parenchymal change and non-progressive anatomical distortion. A phase of chronic scarring followed (6–24 months) with irreversible parenchymal change, progressive volume loss and anatomical distortion. Post-RT increase in contralateral lung volume was common. Normal lung volume shrinkage correlated longitudinally with mean lung dose (r = 0.30–0.40, p = 0.01–0.04). Radiological findings allowed separation of patients with predominant acute versus chronic RILD; subjects with predominantly chronic RILD had poorer pre-RT lung function. Conclusions: CT-based measures enable detailed quantification of the longitudinal evolution of RILD. The majority of patients developed progressive lung damage, even when the early phase was absent or mild. Pre-RT lung function and RT dosimetry may allow to identify subjects at increased risk of RILD

Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array

In this paper we investigate the asymptotic validity of boundary layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl's solution to Navier-Stokes solutions at different $Re$ numbers. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions between the boundary layer and the outer flow. These interactions can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective

Fragility of ferromagnetic double exchange interactions and pressure tuning of magnetism in 3d-5d double perovskite Sr2FeOsO6

FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOThe ability to tune exchange (magnetic) interactions between 3d transition metals in perovskite structures has proven to be a powerful route to discovery of novel properties. Here we demonstrate that the introduction of 3d-5d exchange pathways in double perovskites enables additional tunability, a result of the large spatial extent of 5d wave functions. Using x-ray probes of magnetism and structure at high pressure, we show that compression of Sr2FeOsO6 drives an unexpected continuous change in the sign of Fe-Os exchange interactions and a transition from antiferromagnetic to ferrimagnetic order. We analyze the relevant electron-electron interactions, shedding light into fundamental differences with the more thoroughly studied 3d-3d systems.The ability to tune exchange (magnetic) interactions between 3d transition metals in perovskite structures has proven to be a powerful route to discovery of novel properties. Here we demonstrate that the introduction of 3d-5d exchange pathways in double perovskites enables additional tunability, a result of the large spatial extent of 5d wave functions. Using x-ray probes of magnetism and structure at high pressure, we show that compression of Sr2FeOsO6 drives an unexpected continuous change in the sign of Fe-Os exchange interactions and a transition from antiferromagnetic to ferrimagnetic order. We analyze the relevant electron-electron interactions, shedding light into fundamental differences with the more thoroughly studied 3d-3d systems.912317FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO2013/14338-3Work at Argonne is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. L.S.I.V. is supported by FAPESP (SP-Brazil) under Contract No. 2013/14338-3. M.v.V. was supported by DOE-BES under Grant No. DE-FG02-03ER46097. This research was supported in part by the World Premier International Research Center of the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, the Japan Society for the Promotion of Science (JSPS) through a Grant-in-Aid for Scientific Research (25289233). We would like to thank Changyong Park and Curtis Kenney-Benson for their assistance at 16-BM-D beamline, Sergey N. Tkachev for assistance with gas loading, and Richard Rosenberg for help with soft x-ray measurements. We also thank GSECARS for use of the gas loading and laser drilling facilities