Local non-negative initial data scalar characterization of the Kerr solution

For any vacuum initial data set, we define a local, non-negative scalar quantity which vanishes at every point of the data hypersurface if and only if the data are Kerr initial data. Our scalar quantity only depends on the quantities used to construct the vacuum initial data set which are the Riemannian metric defined on the initial data hypersurface and a symmetric tensor which plays the role of the second fundamental form of the embedded initial data hypersurface. The dependency is algorithmic in the sense that given the initial data one can compute the scalar quantity by algebraic and differential manipulations, being thus suitable for an implementation in a numerical code. The scalar could also be useful in studies of the non-linear stability of the Kerr solution because it serves to measure the deviation of a vacuum initial data set from the Kerr initial data in a local and algorithmic way.

Equivalente teleparalelo de algumas soluções da relatividade geral

Pós-graduação em Física - IFT

Kerr-Newman solution as a Dirac particle

For m(2) < a(2) + q(2), with m, a, and q respectively the source mass, angular momentum per unit mass, and electric charge, the Kerr-Newman (KN) solution of Einstein's equation reduces to a naked singularity of circular shape, enclosing a disk across which the metric components fail to be smooth. By considering the Hawking and Ellis extended interpretation of the KN spacetime, it is shown that, similarly to the electron-positron system, this solution presents four inequivalent classical states. Making use of Wheeler's idea of charge without charge, the topological structure of the extended KN spatial section is found to be highly non-trivial, leading thus to the existence of gravitational states with half-integral angular momentum. This property is corroborated by the fact that, under a rotation of the space coordinates, those inequivalent states transform into themselves only after a 4π rotation. As a consequence, it becomes possible to naturally represent them in a Lorentz spinor basis. The state vector representing the whole KN solution is then constructed, and its evolution is shown to be governed by the Dirac equation. The KN solution can thus be consistently interpreted as a model for the electron-positron system, in which the concepts of mass, charge and spin become connected with the spacetime geometry. Some phenomenological consequences of the model are explored.

Self-defocusing effects in an ethanol solution of chlorophyll

The thermally induced optical nonlinearity in a chlorophyll ethanol solution is examined. A theory is presented which shows good agreement with experiment. The theory models an optically thick but physically thin medium whose only heat transport mechanism is conduction. An average nz was found for the medium which corresponds well with previous results but the thermal medium is shown to be fundamentally different from a Kerr medium.

Stabilization of a (3+1)-dimensional soliton in a Kerr medium by a rapidly oscillating dispersion coefficient

Using the numerical solution of the nonlinear Schrodinger equation and a variational method it is shown that (3 + 1)-dimensional spatiotemporal optical solitons can be stabilized by a rapidly oscillating dispersion coefficient in a Kerr medium with cubic nonlinearity. This has immediate consequence in generating dispersion-managed robust optical soliton in communication as well as possible stabilized Bose-Einstein condensates in periodic optical-lattice potential via an effective-mass formulation. We also critically compare the present stabilization with that obtained by a rapid sinusoidal oscillation of the Kerr nonlinearity parameter.

Stabilization of a light bullet in a layered Kerr medium with sign-changing nonlinearity

Using the numerical solution of the nonlinear Schrodinger equation and a variational method, it is shown that (3+1)-dimensional spatiotemporal optical solitons, known as light bullets, can be stabilized in a layered Kerr medium with sign-changing nonlinearity along the propagation direction.

Soliton propagation in a medium with Kerr nonlinearity and resonant impurities: A variational approach

The soliton propagation in a medium with Kerr nonlinearity and resonant impurities was studied by a variational approach. The existence of a solitary wave was shown within the framework of a combined nonintegrable system composed of one nonlinear Schrödinger and a pair of Bloch equations. The analytical solution which was obtained, was tested through numerical simulations confirming its solitary wave nature.

Dipole moments and Kerr effect of poly(n-vinylcarbazole) and its complexes with trinitrofluorenone

N-vinylcarbazole was polymerised using the free radical catalyst (azo-bisisobutyronitrile) and cationic catalysts (boron-trifluoride etherate and aluminium chloride). The polymers produced were characterised by molecular weight measurements and powder x-ray diffraction. The tacticity of the polymer samples was determined using proton and carbon-13 nuclear magnetic resonance spectroscopy. Measurements of their static dielectric permittivity and electro-optical birefringence (Kerr effect) in solution in 1,4-dioxane were carried out over a range of temperatures. The magnitudes of the dipole moments and Kerr constants were found to vary with changes in the tacticity of poly(N-vinylcarbazole). The results of these measurements support the view that the stereostructure of poly(N-vinylcarbazole) is sensitive to the mechanism of polymerisation. These results, together with proton and carbon-13 N.M.R. data, are discussed in terms of the possible conformations of the polymer chains and the relative orientation of the bulky carbazole side groups. The dielectric and molecular Kerr effect studies have also been carried out on complexes formed between 2,4,7-trinitro-9-fluorenone (TNF) and different stereoregular forms of poly(N-vinylcarbazole) in solution in 1,4-dioxane. The differences in the molar Kerr constants between pure (uncomplexed) and complexed poly(N-vinylcarbazole) samples were attributed to changes in optical anisotropy and dipole moments. A molecular modelling computer program Desktop Molecular Modeller was used to examine the 3/1 helical isotactic and 2/1 helical syndiotactic forms of poly(N-vinylcarbazole). These models were used to calculate the pitch distances of helices and the results were interpreted in terms of van der Waal's radii on TNF. This study indicated that the pitch distance in 3/1 isotactic helices was large enough to accommodate the bulky TNF molecules to form sandwich type charge transfer complexes whereas the pitch distance in syndiotactic poly(N-vinylcarbazole) was smaller and would not allow a similar type of complex formation.

Dielectric relaxation of polysiloxanes and kerr effect of p-phenylene vinylene oligomers

The dielectric relaxation behaviour of a series of cyclic and linear poly(dimethylsiloxanes) with overline nn in the range 28 to 99 has been studied, as a function of temperature (142.0K-157.5K) and frequency (12-105Hz). Activation energies for the -relaxation process, Davidson-Cole empirical distribution factors, , and mean-square dipole moments per repeat unit, < 2> , have been calculated. Differences in values of H_act reflected restricted dipolar rotation for the cyclic structures, compared to the linear structures, over the range of molecular weights studied. The dielectric relaxation behaviour of a series of linear oligomers of methyl phenyl siloxane, with n in the range 4 to 10, a series of linear fractions of poly(methyl phenyl siloxane), with overline n_n in the range 31 to 1370, and a cyclic oligomer of mehyl phenyl siloxane, with n = 10, has been studied as a function of temperature (155.5K-264.0K) and frequency (12-105Hz). Activation energies for the -relaxation process, Davidson-Cole and Cole-Cole empirical distribution factors, and , respectively, and mean-square dipole moments per repeat unit have been calculated. The reduced flexibility of short methyl phenyl siloxane chains, compared to dimethyl siloxane chains, was apparent from a comparison of dipole moment ratios. The dilectric relaxation behaviour of poly(methyl hydrogen siloxane) and poly(n-hexyl methyl siloxane) has been studied as a function of temperature and frequency. A polysiloxane liquid crystal has been synthesised and its dielectric relaxation behaviour has been studied, as a function of temperature and frequency, in the liquid crystalline phase and below T_g. Poly(p-phenylene vinylene) and related oligomers have been synthesised and characterised by a variety of experimental techniques. The Kerr effect of two oligomeric fractions, in solution in PPG 2025, has been measured. The electrical conductivities of the undoped and I_2-doped polymer and oligomers have been measured.

Comparison Of The Solution Of Histidine-tryptophan-alfacetoglutarate With Histidine-tryptophan-glutamate As Cardioplegic Agents In Isolated Rat Hearts: An Immunohistochemical Study.

Cardiac arrest during heart surgery is a common procedure and allows the surgeon to perform surgical procedures in an environment free of blood and movement. Using a model of isolated rat heart, the authors compare a new cardioplegic solution containing histidine-tryptophan-glutamate (group 2) with the histidine-tryptophan-alphacetoglutarate (group 1) routinely used by some cardiac surgeons. To assess caspase, IL-8 and KI-67 in isolated rat hearts using immunohistochemistry. 20 Wistar male rats were anesthetized and heparinized. The chest was opened, cardioctomy was performed and 40 ml/kg of the appropriate cardioplegic solution was infused. The hearts were kept for 2 hours at 4ºC in the same solution, and thereafter, placed in the Langendorff apparatus for 30 minutes with Ringer-Locke solution. Immunohistochemistry analysis of caspase, IL-8, and KI-67 were performed. The concentration of caspase was lower in group 2 and Ki-67 was higher in group 2, both P<0.05. There was no statistical difference between the values of IL-8 between the groups. Histidine-tryptophan-glutamate solution was better than histidine-tryptophan-alphacetoglutarate solution because it reduced caspase (apoptosis), increased KI-67 (cell proliferation), and showed no difference in IL-8 levels compared to group 1. This suggests that the histidine-tryptophan-glutamate solution was more efficient than the histidine-tryptophan-alphacetoglutarate for the preservation of hearts of rat cardiomyocytes.

Remediation Of 17-α-ethinylestradiol Aqueous Solution By Photocatalysis And Electrochemically-assisted Photocatalysis Using Tio2 And Tio2/wo3 Electrodes Irradiated By A Solar Simulator.

TiO2 and TiO2/WO3 electrodes, irradiated by a solar simulator in configurations for heterogeneous photocatalysis (HP) and electrochemically-assisted HP (EHP), were used to remediate aqueous solutions containing 10 mg L(-1) (34 μmol L(-1)) of 17-α-ethinylestradiol (EE2), active component of most oral contraceptives. The photocatalysts consisted of 4.5 μm thick porous films of TiO2 and TiO2/WO3 (molar ratio W/Ti of 12%) deposited on transparent electrodes from aqueous suspensions of TiO2 particles and WO3 precursors, followed by thermal treatment at 450 (°)C. First, an energy diagram was organized with photoelectrochemical and UV-Vis absorption spectroscopy data and revealed that EE2 could be directly oxidized by the photogenerated holes at the semiconductor surfaces, considering the relative HOMO level for EE2 and the semiconductor valence band edges. Also, for the irradiated hybrid photocatalyst, electrons in TiO2 should be transferred to WO3 conduction band, while holes move toward TiO2 valence band, improving charge separation. The remediated EE2 solutions were analyzed by fluorescence, HPLC and total organic carbon measurements. As expected from the energy diagram, both photocatalysts promoted the EE2 oxidation in HP configuration; after 4 h, the EE2 concentration decayed to 6.2 mg L(-1) (35% of EE2 removal) with irradiated TiO2 while TiO2/WO3 electrode resulted in 45% EE2 removal. A higher performance was achieved in EHP systems, when a Pt wire was introduced as a counter-electrode and the photoelectrodes were biased at +0.7 V; then, the EE2 removal corresponded to 48 and 54% for the TiO2 and TiO2/WO3, respectively. The hybrid TiO2/WO3, when compared to TiO2 electrode, exhibited enhanced sunlight harvesting and improved separation of photogenerated charge carriers, resulting in higher performance for removing this contaminant of emerging concern from aqueous solution.

Human Mitochondrial Hsp70 (mortalin): Shedding Light On Atpase Activity, Interaction With Adenosine Nucleotides, Solution Structure And Domain Organization.

The human mitochondrial Hsp70, also called mortalin, is of considerable importance for mitochondria biogenesis and the correct functioning of the cell machinery. In the mitochondrial matrix, mortalin acts in the importing and folding process of nucleus-encoded proteins. The in vivo deregulation of mortalin expression and/or function has been correlated with age-related diseases and certain cancers due to its interaction with the p53 protein. In spite of its critical biological roles, structural and functional studies on mortalin are limited by its insoluble recombinant production. This study provides the first report of the production of folded and soluble recombinant mortalin when co-expressed with the human Hsp70-escort protein 1, but it is still likely prone to self-association. The monomeric fraction of mortalin presented a slightly elongated shape and basal ATPase activity that is higher than that of its cytoplasmic counterpart Hsp70-1A, suggesting that it was obtained in the functional state. Through small angle X-ray scattering, we assessed the low-resolution structural model of monomeric mortalin that is characterized by an elongated shape. This model adequately accommodated high resolution structures of Hsp70 domains indicating its quality. We also observed that mortalin interacts with adenosine nucleotides with high affinity. Thermally induced unfolding experiments indicated that mortalin is formed by at least two domains and that the transition is sensitive to the presence of adenosine nucleotides and that this process is dependent on the presence of Mg2+ ions. Interestingly, the thermal-induced unfolding assays of mortalin suggested the presence of an aggregation/association event, which was not observed for human Hsp70-1A, and this finding may explain its natural tendency for in vivo aggregation. Our study may contribute to the structural understanding of mortalin as well as to contribute for its recombinant production for antitumor compound screenings.

Shelf-life of a 2.5% sodium hypochlorite solution as determined by arrhenius equation

Accelerated stability tests are indicated to assess, within a short time, the degree of chemical degradation that may affect an active substance, either alone or in a formula, under normal storage conditions. This method is based on increased stress conditions to accelerate the rate of chemical degradation. Based on the equation of the straight line obtained as a function of the reaction order (at 50 and 70 ºC) and using Arrhenius equation, the speed of the reaction was calculated for the temperature of 20 ºC (normal storage conditions). This model of accelerated stability test makes it possible to predict the chemical stability of any active substance at any given moment, as long as the method to quantify the chemical substance is available. As an example of the applicability of Arrhenius equation in accelerated stability tests, a 2.5% sodium hypochlorite solution was analyzed due to its chemical instability. Iodometric titration was used to quantify free residual chlorine in the solutions. Based on data obtained keeping this solution at 50 and 70 ºC, using Arrhenius equation and considering 2.0% of free residual chlorine as the minimum acceptable threshold, the shelf-life was equal to 166 days at 20 ºC. This model, however, makes it possible to calculate shelf-life at any other given temperature.

An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

We have considered a Bose gas in an anisotropic potential. Applying the the Gross-Pitaevskii Equation (GPE) for a confined dilute atomic gas, we have used the methods of optimized perturbation theory and self-similar root approximants, to obtain an analytical formula for the critical number of particles as a function of the anisotropy parameter for the potential. The spectrum of the GPE is also discussed.

Enhanced response of the fricke solution doped with hematoporphyrin under X-rays irradiation

The vials filled with Fricke solutions were doped with increasing concentrations of Photogem®, used in photodynamic therapy. These vials were then irradiated with low-energy X-rays with doses ranging from 5 to 20 Gy. The conventional Fricke solution was also irradiated with the same doses. The concentration of ferric ions for the Fricke and doped-Fricke irradiated solutions were measured in a spectrophotometer at 220 to 340 nm. The results showed that there was an enhancement in the response of the doped-Fricke solution, which was proportional to the concentration of the photosensitizer. The use of such procedure for studying the radiosensitizing property of photosensitizers based on the production of free radicals is also discussed.