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]

Generalized duality between local vector theories in D=2+1

The existence of an interpolating master action does not guarantee the same spectrum for the interpolated dual theories. In the specific case of a generalized self-dual (GSD) model defined as the addition of the Maxwell term to the self-dual model in D = 2 + 1, previous master actions have furnished a dual gauge theory which is either nonlocal or contains a ghost mode. Here we show that by reducing the Maxwell term to first order by means of an auxiliary field we are able to define a master action which interpolates between the GSD model and a couple of non-interacting Maxwell-Chern-Simons theories of opposite helicities. The presence of an auxiliary field explains the doubling of fields in the dual gauge theory. A generalized duality transformation is defined and both models can be interpreted as self-dual models. Furthermore, it is shown how to obtain the gauge invariant correlators of the non-interacting MCS theories from the correlators of the self-dual field in the GSD model and vice-versa. The derivation of the non-interacting MCS theories from the GSD model, as presented here, works in the opposite direction of the soldering approach.

Local order around of germanium atoms in Ga10Ge25S65 glass by EXAFS

Irreversible photoexpansion effect has been observed in amorphous Ga10Ge2S65 glasses when its surface was exposed to light with energy greater than the band gap, 3.52 eV. A volume change of about 5% was reached in bulk samples by controlling illumination time and the laser power density. To understand the atomic scale processes of the photoexpansion effect, extended X-ray absorption fine structure (EXAFS) spectroscopy has been used as a local probe of the germanium environment in the glass samples before and after illumination. Modifications are observed in the average coordination shell around Ge atoms in the illuminated sample compared to the non-illuminated one. For the non-illuminated sample, the Ge coordination shell is described by a distorted tetrahedron of sulfur atoms at around 2.20 Angstrom. After illumination, the EXAFS signal can be explained by introducing an additional contribution to this average environment. Based on an analysis of the EXAFS data we proposed a two-shell model of 0.5 oxygen atoms at 2.01 Angstrom and 3.6 sulfur atoms at a 2.20 Angstrom. The existence of Ge-O bonds in the glass after illumination was confirmed by infrared measurements. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Relationship between Crystal Shape, Photoluminescence, and Local Structure in SrTiO3 Synthesized by Microwave-Assisted Hydrothermal Method

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Existence of solutions for the 3D-micropolar fluid system with initial data in Besov-Morrey spaces

In this paper, we show a local-in-time existence result for the 3D micropolar fluid system in the framework of Besov-Morrey spaces. The initial data class is larger than the previous ones and contains strongly singular functions and measures. © 2013 Springer Basel.

Local attractors, degeneracy and analyticity: Symmetry effects on the locally coupled Kuramoto model

In this work we study the local coupled Kuramoto model with periodic boundary conditions. Our main objective is to show how analytical solutions may be obtained from symmetry assumptions, and while we proceed on our endeavor we show apart from the existence of local attractors, some unexpected features resulting from the symmetry properties, such as intermittent and chaotic period phase slips, degeneracy of stable solutions and double bifurcation composition. As a result of our analysis, we show that stable fixed points in the synchronized region may be obtained with just a small amount of the existent solutions, and for a class of natural frequencies configuration we show analytical expressions for the critical synchronization coupling as a function of the number of oscillators, both exact and asymptotic. © 2013 Elsevier Ltd. All rights reserved.

Weak local Nash equilibrium

In this paper, we consider a concept of local Nash equilibrium for non-cooperative games - the so-called weak local Nash equilibrium. We prove its existence for a significantly more general class of sets of strategies than compact convex sets. The theorems on existence of the weak local equilibrium presented here are applications of Brouwer and Lefschetz fixed point theorems. © 2013 Juliusz Schauder Centre for Nonlinear Studies Nicolaus Copernicus University.

Local order of Pb1-xLaxZr0.40Ti 0.60O3 ferroelectric ceramic materials probed by X-ray absorption and Raman spectroscopies

This paper reports on the structural characterization of Pb 1-xLaxZr0.40Ti0.60O3 (PLZT) ferroelectric ceramic compositions prepared by the conventional solid state reaction method. X-ray absorption spectroscopy (XAS) and Raman spectroscopy were used to probe the local structure of PLZT samples that exhibits a normal and relaxor ferroelectric behavior. From the Zr K-edge and Pb LIII-edge EXAFS spectra, a considerable dissymmetry of Zr and Pb sites was observed in all samples, including those showing a long-range order cubic symmetry and a relaxor behavior. The Raman spectroscopy results confirmed the existence of a local disorder in all PLZT samples through the observation of Raman active vibrational modes. The variation in the intensity of the E(TO 3) mode in the PLZT relaxor samples indicates that the process of correlation between nanodomains stabilizes at temperatures lower than T m. © 2013 Elsevier B.V. All rights reserved.

Competitividade e território: uma análise do arranjo produtivo local potencial de cerâmica artística do município de Porto Ferreira - SP

Pós-graduação em Geografia - IGCE

Selective protection of the cerebellum against intracerebroventricular LPS is mediated by local melatonin synthesis

Although melatonin is mainly produced by the pineal gland, an increasing number of extra-pineal sites of melatonin synthesis have been described. We previously demonstrated the existence of bidirectional communication between the pineal gland and the immune system that drives a switch in melatonin production from the pineal gland to peripheral organs during the mounting of an innate immune response. In the present study, we show that acute neuroinflammation induced by lipopolysaccharide (LPS) injected directly into the lateral ventricles of adult rats reduces the nocturnal peak of melatonin in the plasma and induces its synthesis in the cerebellum, though not in the cortex or hippocampus. This increase in cerebellar melatonin content requires the activation of nuclear factor kappa B (NF-κB), which positively regulates the expression of the key enzyme for melatonin synthesis, arylalkylamine N-acetyltransferase (AA-NAT). Interestingly, LPS treatment led to neuronal death in the hippocampus and cortex, but not in the cerebellum. This privileged protection of cerebellar cells was abrogated when G-protein-coupled melatonin receptors were blocked by the melatonin antagonist luzindole, suggesting that the local production of melatonin protects cerebellar neurons from LPS toxicity. This is the first demonstration of a switch between pineal and extra-pineal melatonin production in the central nervous system following a neuroinflammatory response. These results have direct implications concerning the differential susceptibility of specific brain areas to neuronal death.

Local classification of singular hexagonal 3-webs with holomorphic Chern connection form and infinitesimal symmetries

Implicit ODE, cubic in derivative, generically has no infinitesimal symmetries even at regular points with distinct roots. Cartan showed that at regular points, ODEs with hexagonal 3-web of solutions have symmetry algebras of the maximal possible dimension 3. At singular points such a web can lose all its symmetries. In this paper we study hexagonal 3-webs having at least one infinitesimal symmetry at singular points. In particular, we establish sufficient conditions for the existence of non-trivial symmetries and show that under natural assumptions such a symmetry is semi-simple, i.e. is a scaling in some coordinates. Using the obtained results, we provide a complete classification of hexagonal singular 3-web germs in the complex plane, satisfying the following two conditions: 1) the Chern connection form is holomorphic at the singular point, 2) the web admits at least one infinitesimal symmetry at this point. As a by-product, a classification of hexagonal weighted homogeneous 3-webs is obtained.