Lower bounds on blow up solutions of the three-dimensional Navier-Stokes equations in homogeneous Sobolev spaces

Suppose that u(t) is a solution of the three-dimensional Navier-Stokes equations, either on the whole space or with periodic boundary conditions, that has a singularity at time T. In this paper we show that the norm of u(T - t) in the homogeneous Sobolev space (H)over dot(s) must be bounded below by c(s)t(-(2s-1)/4) for 1/2 < s < 5/2 (s not equal 3/2), where c(s) is an absolute constant depending only on s; and by c(s)parallel to u(0)parallel to((5-2s)/5)(L2)t(-2s/5) for s > 5/2. (The result for 1/2 < s < 3/2 follows from well-known lower bounds on blowup in Lp spaces.) We show in particular that the local existence time in (H)over dot(s)(R-3) depends only on the (H)over dot(s)-norm for 1/2 < s < 5/2, s not equal 3/2. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4762841]

Finite time blow-up and breaking of solitary wind waves

The evolution of surface water waves in finite depth under wind forcing is reduced to an antidissipative Korteweg-de Vries-Burgers equation. We exhibit its solitary wave solution. Antidissipation accelerates and increases the amplitude of the solitary wave and leads to blow-up and breaking. Blow-up occurs in finite time for infinitely large asymptotic space so it is a nonlinear, dispersive, and antidissipative equivalent of the linear instability which occurs for infinite time. Due to antidissipation two given arbitrary and adjacent planes of constant phases of the solitary wave acquire different velocities and accelerations inducing breaking. Soliton breaking occurs in finite space in a time prior to the blow-up. We show that the theoretical growth in amplitude and the time of breaking are both testable in an existing experimental facility.

Sliding Vector Fields via Slow-Fast Systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Powder Diffraction of Components Subject to Corrosion in Fuse Cutouts with CeramicInsulation

Aiming identification of the components most affected by corrosion under saline environment conditions, we have carried out X-ray diffraction measurements in ceramic and bond materials, all in the powder form. The ceramic is analyzed before and after thermal annealing at 1000 degrees C, showing the same DRX peaks, although better defined after annealing. Identification suggests the presence of Al(6)Si(2)O(13) (Mullite) and SiO(2) (Quartz). Analysis of the junction (bond) material shows similar peaks, but a metallic preponderance is observed. Thermal annealing of the junction is done at much lower temperature, because it melts in the range 135 degrees C-170 degrees C, when a whitish smoke begins to show up along with strong sulfur odor.

Generic Bifurcations of Planar Filippov Systems via Geometric Singular Perturbations

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

Study of Singularities in Nonsmooth Dynamical Systems via Singular Perturbation

In this article we describe some qualitative and geometric aspects of nonsmooth dynamical systems theory around typical singularities. We also establish an interaction between nonsmooth systems and geometric singular perturbation theory. Such systems are represented by discontinuous vector fields on R(l), l >= 2, where their discontinuity set is a codimension one algebraic variety. By means of a regularization process proceeded by a blow-up technique we are able to bring about some results that bridge the space between discontinuous systems and singularly perturbed smooth systems. We also present an analysis of a subclass of discontinuous vector fields that present transient behavior in the 2-dimensional case, and we dedicate a section to providing sufficient conditions in order for our systems to have local asymptotic stability.

Um estudo de bifurcações de codimensão dois de campos de vetores

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

Um estudo global de campos de vetores planares

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

Assentamento Horto Florestal Guarany, no município de Pradópolis/SP: uma real conquista ou uma difícil realidade?

Pós-graduação em Serviço Social - FCHS

Avaliação microscópica da movimentação dentária induzida em dentes traumatizados: um estudo experimental em ratos

Pós-graduação em Odontologia - FOA

Tide-topography interaction along the eastern Brazilian shelf

In the Tropics, continental shelves governed by western boundary currents are considered to be among the least productive ocean margins in the world, unless eddy-induced shelf-edge upwelling becomes significant. The eastern Brazilian shelf in the Southwest Atlantic is one of these, and since the slight nutrient input from continental sources is extremely oligotrophic. It is characterized by complex bathymetry with the presence of shallow banks and seamounts. In this work, a full three-dimensional nonlinear primitive equation ocean model is used to demonstrate that the interaction of tidal currents and the bottom topography of the east Brazil continental shelf is capable of producing local upwelling of South Atlantic Central Water, bringing nutrients up from deep waters to the surface layer. Such upper layer enrichment is found to be of significance in increasing local primary productivity. (c) 2005 Elsevier Ltd. All rights reserved.

Abundance of sedentary consumers and sessile organisms along the wave exposure gradient of subtropical rocky shores of the south-west Atlantic

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

Dens invaginatus type III: report of a case and 10-year radiographic follow-up

Aim the purpose of this article is to report the 10-year follow-up of a right mandibular central incisor with 'dens invaginatus' that was root filled.Summary 'Dens invaginatus ' is a rare malformation of teeth, probably resulting from an infolding of the dental papilla during tooth development. It has alternatively been called 'dens in dente' and 'dilated composite odontome'. Radiographic examination may clearly demonstrate this feature, although no signs may be recognized clinically. If no entrance to the invagination can be detected and there are no signs of pulp pathosis, then no treatment is required other than fissure sealing of the invagination. In deep invaginations, it is likely that root-canal treatment may be required. Occasionally, when the tooth has an immature root, apexification is necessary. Root-canal treatment of a right mandibular central incisor with 'dens invaginatus ' is described along with 10-year follow-up.Key learning pointsBoth clinical and radiographic examinations are necessary to determine morphological features of teeth before root-canal treatment.Sensibility testing to determine the pulp condition is critical prior to treatment.

Consolidation and break-up of the South American platform in southeastern Brazil: Tectonothermal and denudation histories

The different tectonic stages that occurred at the end of the Proterozoic and during the Phanerozoic have an important bearing on the tectonothermal history of the South American Platform and its consolidation. Geochronological data (U/Pb monazite, Ar-40/Ar-39 whole rock) and apatite fission-track analysis, from Precambrian rocks of the southeastern Brazilian coastline, permit the modeling of a long-term thermal history of the crust and constrain variable denudation rates.Using these data, a temperature-time diagram reflects a period of accelerated exhumation during the end of the Brasiliano Orogeny, followed by long stability and reactivation of the platform during the Rifting Phase of the South Atlantic Ocean.U/Pb zircon and monazite (blocking temperature of ca. 650degreesC) data from a series of igneous bodies suggest that a tangential and transpressional tectonic regime occurred between 625 and 610 Ma. During the following escape tectonics, between 610 and 590 Ma the exhumation process indicates cooling rates of ca. 12degreesC/Ma. Ar-40/Ar-39 biotite ages between 540 and 510 Ma (ca. 300degreesC) and a corrected fission-track age on apatites (100degreesC) of 480 Ma indicate an exhumation event related to block tectonics with huge vertical displacement along shear zones.A long stabilization phase, with low exhumation, and cooling rate around 0.25degreesC/Ma was recorded from the Cambro/Ordovician to the Mesozoic. At 65 Ma an acceleration of the exhumation through denudation and reworking of the South American surface with cooling rate of 1.5degreesC/Ma is observed.The uplift of the Mantiqueira and Serra do Mar mountain ranges along the southeast Brazilian coastline works as a climatic barrier provoking lateral erosional processes causing long-term scarp retreat, combined with intense, but progressive denudation towards the continent. A denudation of 2.5 to 4 km was calculated for such processes. This lateral retreat of escarpments and flexural response can provide important insights regarding marginal isostatic uplift and the evolution of offshore sedimentary basins of southeast Brazil.

Obtenção e caracterização de mantas fibrosas de poli(fluoreto de vinilideno) (PVDF) com poli(o-metoxianilina) (POMA) pela técnica de "Solution Blow Spinning"

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)