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]

Pb-210 and composition data of near-surface sediments and interstitial waters evidencing anthropogenic inputs in Amazon River mouth, Macapa, Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Thermally activated dynamics in La2CuO4+delta: tilts of the CuO6 octahedra and interstitial O

An intense peak of the elastic energy loss versus temperature is found in La2CuO4 at 150 K (in the LTO phase), at a vibration frequency of similar to 280 Hz. From the dependence of the dissipation curve on frequency it is deduced that the relaxation rate has an activation enthalpy of 0.23 eV. The peak is ascribed to a thermally activated dynamics of the tilts of the CuO6 octahedra which form the La2CuO4 lattice, a fraction of which are supposed to be able to switch between energetically equivalent configurations. The peak is suppressed by interstitial O; this is explained by supposing that each interstitial atom can block several octahedra into a configuration that can accommodate the distortion due to its presence. Increasing the content of excess O, two new thermally activated processes develop, attributed to the hopping of interstitial O atoms which are isolated and which are paired or otherwise aggregated. The activation enthalpy for the diffusion of O at low values of 6 is 0.48 eV.

Stress induced ordering due to interstitial elements in Nb and Ta by frequency analysis

It is well known that the interstitial elements present in solid solution in metals interact with the matrix by a relaxation process known as stress induced ordering. Traditionally this relaxation process is observed in the internal friction measurements. It is a common practice that researchers present the results of the frequency together with internal friction without giving any analysis. In this work we apply an expression which relates the variation of frequency with temperature and analyse the experimental results cited in the literature of the relaxation process due to the stress induced ordering of oxygen and nitrogen present in niobium and tantalum.

Effect of interstitial impurities on internal friction measurements in niobium

Measurements of internal friction as a function of temperature were carried out in samples of mobium containing different amounts of interstitial solutes (oxygen and nitrogen) and one sample of mobium containing initially only nitrogen as interstitial solute. The experimental spectra of internal friction as a function of temperature were obtained with a torsion pendulum of the inverted Ke-type and resolved, using the method of successive subtraction, into a series of constituent Debye peaks corresponding to different interactions. For each relaxation process it was possible to obtain the height (Q(max)(-1)) and temperature (T-p) of the peak, the activation energy (E) and the relaxation time (t(o)). The height, shape and temperature of these peaks depend on the concentration of interstitial elements. The observed peaks were associated with matrix-interstitial (Nb-O, Nb-N) and interstitial-interstitial (O-N) interaction processes. (C) 2003 Elsevier B.V. All rights reserved.

On the hardy space H¹ on products of half-spaces

We show that the Hardy space H¹ anal (R2+ x R2+) can be identified with the class of functions f such that f and all its double and partial Hubert transforms Hk f belong to L¹ (R2). A basic tool used in the proof is the bisubharmonicity of |F|q, where F is a vector field that satisfies a generalized conjugate system of Cauchy-Riemann type.

Structure, mobility and clustering of interstitial O in La2CuO4+delta in the limit of small delta

Anelastic spectra (elastic energy absorption as a function of temperature) are reported which provide evidence that excess O in La2CuO4+delta starts forming two different types of defects already at very low concentrations, where no phase separation or changes in the type of O intercalation are believed to occur. The absorption peak with the lowest activation enthalpy, H/k(B) = 5600 K, is visible at lowest values of delta and is attributed to the hopping of single interstitial O2- ions. The second process, with a slightly slower dynamics, appears at higher values of delta and soon becomes preponderant over the former process. The latter process is proposed to be due to stable pairs of O atoms and is put in connection with the formation of partially covalent bonds between interstitial and apical oxygen; such bonds would reduce the doping efficiency of excess O at increasing delta. The geometry of the interstitial O defect is discussed. O 1998 Published by Elsevier B.V. B.V. All rights reserved.

Magnetic behavior of interstitial Fe impurities in divalent Ca, Sr, and Yb hosts

We have used a first-principles real-space approach to investigate the electronic structure and the magnetic behavior of interstitial Fe impurities in divalent Ca, Sr, and Yb hosts. The dependence of the local moment as a function of lattice relaxation around the impurity is obtained and contrasted with that of interstitial Fe in trivalent and tetravalent Zr, Y, Ti, and Sc hosts. The trends obtained for local moment formation at the impurity site an in agreement with experimental time-differential perturbed gamma-ray angular distribution technique observations.

Interstitial oxygen mobility in superconducting samples of Bi2Sr2CaCu2O8+y

Since high-temperature superconductors were discovered, several studies have been made on their physical properties, attempting to associate them to the origin of superconductivity. Obviously, the oxygen atoms interstitially dissolved in the matrix have an important role in superconductivity, since they move easily in the lattice. In addition, they contribute to hole creation in the CuO2 planes. Anelastic spectroscopy ( internal friction) measurements are sensitive tools for the study of defects in solids, in particular for oxygen mobility. In this paper, Bi2Sr2CaCu2O8+y samples with several different amounts of interstitial oxygen were analysed by means of anelastic spectroscopy measurements. The measurements were performed by using a torsion pendulum operating at a frequency of about 40 Hz. Complex relaxation structures were observed and attributed to the shift of the oxygen interstitial atoms in BiO chains.

Discrete coherent states and probability distributions in finite-dimensional spaces

Operator bases are discussed in connection with the construction of phase space representatives of operators in finite-dimensional spaces, and their properties are presented. It is also shown how these operator bases allow for the construction of a finite harmonic oscillator-like coherent state. Creation and annihilation operators for the Fock finite-dimensional space are discussed and their expressions in terms of the operator bases are explicitly written. The relevant finite-dimensional probability distributions are obtained and their limiting behavior for an infinite-dimensional space are calculated which agree with the well known results. (C) 1996 Academic Press, Inc.

Influence of interstitial elements on internal friction measurements in Nb and Nb-Zr alloys

Internal friction and frequency measurements as a function of temperature have been carried out in Nb and Nb-Zr policrystalline samples, using a torsion pendulum in the temperature range between 300K and 700K the heating rate was 1K/min and the pressure was kept better than 5x10(-3) mbar. Metals with bce lattice containing solute atoms dissolved interstitially often show anelastic behaviour due to a process know as stress-induced ordering responsible for the appearance of Snoek peaks. In the Nb sample it has been identified two constituent peaks corresponding to the interstitial-matrix interactions (Nb-O and Nb-N), but for the Nb-Zr samples with interstitial solute concentrations very close to those measured for the unalloyed Nb, it was not observed any mechanical relaxation peaks due to the presence of oxygen and nitrogen in solid solution.

Dynamics in discrete phase spaces and time interval operators

The von Neumann-Liouville time evolution equation is represented in a discrete quantum phase space. The mapped Liouville operator and the corresponding Wigner function are explicitly written for the problem of a magnetic moment interacting with a magnetic field and the precessing solution is found. The propagator is also discussed and a time interval operator, associated to a unitary operator which shifts the energy levels in the Zeeman spectrum, is introduced. This operator is associated to the particular dynamical process and is not the continuous parameter describing the time evolution. The pair of unitary operators which shifts the time and energy is shown to obey the Weyl-Schwinger algebra. (C) 1999 Elsevier B.V. B.V. All rights reserved.

CLOSED SPACES IN COSMOLOGY

This paper deals with two aspects of relativistic cosmologies with closed spatial sections. These spacetimes are based on the theory of general relativity, and admit a foliation into space sections S(t), which are spacelike hypersurfaces satisfying the postulate of the closure of space: each S(t) is a three-dimensional closed Riemannian manifold. The topics discussed are: (i) a comparison, previously obtained, between Thurston geometries and Bianchi-Kantowski-Sachs metrics for such three-manifolds is here clarified and developed; and (ii) the implications of global inhomogeneity for locally homogeneous three-spaces of constant curvature are analyzed from an observational viewpoint.

Stress-induced ordering due heavy interstitial atoms in Nb-0.3 wt.% Ti alloys

The mechanical properties of metals with bee structure, such as niobium and their alloys, are changed of a significant way by the introduction of heavy interstitial elements. These interstitial elements (oxygen, for example) present in the metallic matrix occupy octahedral sites and constitute an elastic dipole of tetragonal symmetry and might produce anelastic relaxation. Polycrystalline samples of Nb-0.3 wt.% Ti (Nb-Ti) alloy with oxygen in solid solution were analysed. The anelastic spectroscopy measurements had been made in a torsion pendulum, with frequencies in the Hz range, in a temperature range between 300 and 700 K. The results showed thermally activated relaxation structures were identified four relaxation process attributed to stress-induced ordering of single oxygen, nitrogen and carbon atoms around niobium and stress-induced ordering of single oxygen atoms around titanium atoms. (c) 2005 Elsevier B.V. All rights reserved.

Phase II clinical study of an association for the treatment of interstitial cystitis (Cystex (R))

Painful bladder syndrome associated with interstitial cystitis (PBS/IC) is a clinical condition characterized pelvic pain, urinary urgency, and urinary frequency. In this study, 22 patients were assigned to make two visits over a three weeks period. The patients were randomly, double-blinded assigned in two groups. The first group received Cystex (R) capsules. The second group received placebo capsules. Two capsules were taken three times a day away from meals. The change from baseline in the O'Leary-Sant IC symptom and problem index was the primary outcome parameter. Changes in functional bladder capacity and intensity of pain and urgency have been chosen as secondary outcome parameters. Mood as well as physical and sexual activity were rated by 10 questions on a scale 0 to 6. The ratings were analyzed and the average for each patient in both groups Cystex (R) and placebo was determined as the quality of life index. For the primary outcome there was a statistically significant difference between the groups. Mean symptom score-sum decreased from 28.4 to 20.5 in the Cystex (R) group compared with 29.5 to 26.8 in the placebo group (p<0.05). For the secondary end points, pain and urgency intensity improved statistically significantly in the Cystex (R) group compared with the placebo group (p<0.05). The frequency and functional bladder capacity improved to greater degree in the Cystex (R) group. The differences were statistically significant for comparison of frequency (p<0.05) and not for functional bladder capacity (p>0.05). In our study, Cystex (R) enhanced quality of life over the placebo showing a statistically significant. This trial have shown that the efficacy and safety of therapy with Cystex (R) in the treatment of interstitial cystitis and is an alternative for patients suffering from this pathology. Therefore, it can be concluded that the composition of Cystex (R), increased the quality of life in treated patients.