Spectral flow and iteration of closed semi-Riemannian geodesics

We introduce the notion of spectral flow along a periodic semi-Riemannian geodesic, as a suitable substitute of the Morse index in the Riemannian case. We study the growth of the spectral flow along a closed geodesic under iteration, determining its asymptotic behavior.

On a formula for the spectral flow and its applications

We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms of the spectral flow of the restriction to a finite codimensional closed subspace. We also discuss the case of restrictions to a continuous path of finite codimensional closed subspaces. As an application of the formula, we introduce the notion of spectral flow for a periodic semi-Riemannian geodesic, and we compute its value in terms of the Maslov index. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Iteration of closed geodesics in stationary Lorentzian manifolds

Following the lines of Bott in (Commun Pure Appl Math 9:171-206, 1956), we study the Morse index of the iterates of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic Jacobi field. Given one such closed geodesic gamma, we prove the existence of a locally constant integer valued map Lambda(gamma) on the unit circle with the property that the Morse index of the iterated gamma(N) is equal, up to a correction term epsilon(gamma) is an element of {0,1}, to the sum of the values of Lambda(gamma) at the N-th roots of unity. The discontinuities of Lambda(gamma) occur at a finite number of points of the unit circle, that are special eigenvalues of the linearized Poincare map of gamma. We discuss some applications of the theory.

On a product formula for the Conley-Zelmder index of symplectic paths and its applications

Using invariance by fixed-endpoints homotopies and a generalized notion of symplectic Cayley transform, we prove a product formula for the Conley-Zehnder index of continuous paths with arbitrary endpoints in the symplectic group. We discuss two applications of the formula, to the metaplectic group and to periodic solutions of Hamiltonian systems.

An algebraic theory for generalized Jordan chains and partial signatures in the Lagrangian Grassmannian

We discuss an algebraic theory for generalized Jordan chains and partial signatures, that are invariants associated to sequences of symmetric bilinear forms on a vector space. We introduce an intrinsic notion of partial signatures in the Lagrangian Grassmannian of a symplectic space that does not use local coordinates, and we give a formula for the Maslov index of arbitrary real analytic paths in terms of partial signatures.

Evaluation of flow regimes in a semi-cylindrical spouted bed through statistical, mutual information, spectral and Hurst`s analysis

Hydrodynamic studies were conducted in a semi-cylindrical spouted bed column of diameter 150 mm, height 1000 mm, conical base included angle of 60 degrees and inlet orifice diameter 25 mm. Pressure transducers at several axial positions were used to obtain pressure fluctuation time series with 1.2 and 2.4 mm glass beads at U/U-ms from 0.3 to 1.6, and static bed depths from 150 to 600 mm. The conditions covered several flow regimes (fixed bed, incipient spouting, stable spouting, pulsating spouting, slugging, bubble spouting and fluidization). Images of the system dynamics were also acquired through the transparent walls with a digital camera. The data were analyzed via statistical, mutual information theory, spectral and Hurst`s Rescaled Range methods to assess the potential of these methods to characterize the spouting quality. The results indicate that these methods have potential for monitoring spouted bed operation.

Cadmium telluride nanocrystals as luminescent sensitizers in flow analysis

A fully automated multipumping flow system (MPFS) using water-soluble CdTe quantum dots (QD) as sensitizers is proposed for the chemiluminometric determination of the anti-diabetic drugs gliclazide and glipizide in pharmaceutical formulations. The nanocrystals acted as enhancers of the weak CL emission produced upon oxidation of sulphite by Ce(IV) in acidic medium, thus improving sensitivity and expanding the dynamical analytical concentration range. By interacting with the QD, the two analytes prevented their sensitizing effect yielding a chemiluminescence quenching of the Ce(IV)-SO(3)(2-)CdTe QD system. The pulsed flow inherent to MPFS assured a fast and efficient mixing of all solutions inside the flow cell, circumventing the need for a reaction coil and facilitating the monitoring of the short-lived generated chemiluminescent species. QD crystal size, concentration and spectral region for measurement were investigated. (C) 2011 Elsevier B.V. All rights reserved.

Floquet stability analysis of the flow around an oscillating cylinder

This investigative work is concerned with the flow around a circular cylinder submitted to forced transverse oscillations. The goal is to investigate how the transition to turbulence is initiated in the wake for cases with different Reynolds numbers (Re) and displacement amplitudes (A). For each Re the motion frequency is kept constant, close to the Strouhal number of the flow around a fixed cylinder at the same Re. Stability analysis of two-dimensional periodic flows around a forced-oscillating cylinder is carried out with respect to three-dimensional infinitesimal perturbations. The procedure consists of performing a Floquet type analysis of time-periodic base flows, computed using the spectral/hp element method. With the results of the Floquet calculations, considerations regarding the stability of the system are drawn, and the form of the instability at its onset is obtained. The critical Reynolds number is observed to change with the amplitude of oscillation. With respect to instabilities, unstable modes with the same symmetry as mode A of a fixed cylinder are observed; however, they present different wavelengths. Also, the instabilities observed for the oscillating cylinder are distinctively stronger in the braid shear layers. Other unstable modes similar to mode B are found. Quasi-periodic modes are observed in the 2S wake, and subharmonic mode occurrences are reported in P + S wakes. (C) 2009 Elsevier Ltd. All rights reserved.

Uso do teste ML-Flow como auxiliar na classificação e tratamento da hanseníase

FUNDAMENTOS: O tratamento da hanseníase é definido pela classificação de pacientes em paucibacilares (PB) e multibacilares (MB). A OMS (Organização Mundial de Saúde) classifica os doentes de acordo com o número de lesões, mas Ridley-Jopling (R&J) utiliza também exames complementares, porém é de difícil utilização fora dos serviços de referência. Em 2003 foi desenvolvido um teste denominado ML-Flow, uma alternativa à sorologia por ELISA para auxiliar na classificação de pacientes em PB e MB e auxiliar na decisão terapêutica. OBJETIVOS: Observar a concordância entre o teste de ML-Flow e baciloscopia de linfa, exame já consagrado para detecção de MB. Analisar a utilidade do teste de ML-Flow em campo. MATERIAL E MÉTODOS: Estudo retrospectivo avaliando prontuário de 55 pacientes virgens de tratamento, diagnosticados como PB ou MB por R&J. Submetidos à baciloscopia e ao teste de ML-Flow. RESULTADOS: Nos MB, a baciloscopia foi positiva em 80% dos casos, o ML-flow foi positivo em 82,5%. Entre os PB, o ML-Flow foi positivo em 37,5% e a baciloscopia do esfregaço foi negativa em 100% dos casos. A concordância entre os resultados da baciloscopia do esfregaço e ML-Flow foi de 87,5%, kappa=0,59, p<0,001. CONCLUSÃO: Nenhum teste laboratorial é 100% sensível e específico para a correta classificação de todas as formas de hanseníase. O ML-Flow é um teste rápido, de fácil manuseio em campo, menos invasivo que a baciloscopia podendo ser útil para auxiliar na decisão terapêutica em locais de difícil acesso a serviços de referência.

Forced convection to laminar flow of liquid egg yolk in circular and annular ducts

The steady-state heat transfer in laminar flow of liquid egg yolk - an important pseudoplastic fluid food - in circular and concentric annular ducts was experimentally investigated. The average convection heat transfer coefficients, determined by measuring temperatures before and after heating sections with constant temperatures at the tube wall, were used to obtain simple new empirical expressions to estimate the Nusselt numbers for fully established flows at the thermal entrance of the considered geometries. The comparisons with existing correlations for Newtonian and non-Newtonian fluids resulted in excellent agreement. The main contribution of this work is to supply practical and easily applicable correlations, which are, especially for the case of annulus, rather scarce and extensively required in the design of heat transfer operations dealing with similar shear-thinning products. In addition, the experimental results may support existing theoretical analyses.

An Eulerian Immersed Boundary Method for flow simulations over stationary and moving rigid bodies

The fluid flow over bodies with complex geometry has been the subject of research of many scientists and widely explored experimentally and numerically. The present study proposes an Eulerian Immersed Boundary Method for flows simulations over stationary or moving rigid bodies. The proposed method allows the use of Cartesians Meshes. Here, two-dimensional simulations of fluid flow over stationary and oscillating circular cylinders were used for verification and validation. Four different cases were explored: the flow over a stationary cylinder, the flow over a cylinder oscillating in the flow direction, the flow over a cylinder oscillating in the normal flow direction, and a cylinder with angular oscillation. The time integration was carried out by a classical 4th order Runge-Kutta scheme, with a time step of the same order of distance between two consecutive points in x direction. High-order compact finite difference schemes were used to calculate spatial derivatives. The drag and lift coefficients, the lock-in phenomenon and vorticity contour plots were used for the verification and validation of the proposed method. The extension of the current method allowing the study of a body with different geometry and three-dimensional simulations is straightforward. The results obtained show a good agreement with both numerical and experimental results, encouraging the use of the proposed method.

VUV spectral line emission measurements in the TCABR tokamak

The study of tokamak plasma light emissions in the vacuum ultraviolet (VUV) region is an important subject since many impurity spectral emissions are present in this region. These spectral emissions can be used to determine the plasma ion temperature and density from different species and spatial positions inside plasma according to their temperatures. We have analyzed VUV spectra from 500 Å to 3200 Å wavelength in the TCABR tokamak plasma including higher diffraction order emissions. There have been identified 37 first diffraction order emissions, resulting in 28 second diffraction order, 24 third diffraction order, and 7 fourth diffraction order lines. The emissions are from impurity species such as OII, OIII, OIV, OV, OVI, OVII, CII, CIII, CIV, NIII, NIV, and NV. All the spectra beyond 1900 Å are from higher diffraction order emissions, and possess much better spectral resolution. Each strong and isolated spectral line, as well as its higher diffraction order emissions suitable for plasma diagnostic is identified and discussed. Finally, an example of ion temperature determination using different diffraction order is presented.

Electrochemical degradation of the dye reactive orange 16 using electrochemical flow-cell

Electrochemical removals of color and organic load from solutions containing the dye reactive orange 16 (RO16) were performed in an electrochemical flow-cell, using a platinum working electrode. The influence of the process variables flow-rate, such as NaCl concentration, applied potential and solution pH, were studied. The best color removal achieved was 93% (λ = 493 nm) after 60 min at 2.2 V vs. RHE electrolysis, using 1.00 g L-1 NaCl as supporting electrolyte. The rises in the concentration of NaCl and applied potential increased the color removal rate. The best total organic carbon removal (57%) was obtained at 1.8 V, without the separating membrane, indicating that the ideal conditions for the color removal are not necessarily the same as those to remove the total organic carbon. The degradation efficiency decreased with the solution pH decrease.

Evaluation of a simple hyphenated system for flow injection solid-phase pre-concentration and capillary electrophoresis

In this work, the development and evaluation of a hyphenated flow injection-capillary electrophoresis system with on-line pre-concentration is described. Preliminary tests were performed to investigate the influence of flow rates over the analytical signals. Results revealed losses in terms of sensitivity of the FIA-CE system when compared to the conventional CE system. To overcome signal decrease and to make the system more efficient, a lower flow rate was set and an anionic resin column was added to the flow manifold in order to pre-concentrate the analyte. The pre-concentration FIA-CE system presented a sensitivity improvement of about 660% and there was only a small increase of 8% in total peak dispersion. These results have confirmed the great potential of the proposed system for many analytical tasks especially for low concentration samples.

Determination of paracetamol at a graphite-polyurethane composite electrode as an amperometric flow detector

A bare graphite-polyurethane composite was evaluated as an amperometric flow injection detector in the determination of paracetamol (APAP) in pharmaceutical formulations. A linear analytical curve was observed in the 5.00 x 10-5 to 5.00 x 10-3 mol L-1 range with a minimum detectable net concentration of 18.9 µmol L-1 and 180 determinations h-1, after optimization of parameters such as the detection potential, sample loop volume, and carrier solution flow rate. Interference of ascorbic acid was observed, however, it was possible overcome the interference, reaching results that agreed with HPLC within 95% confidence level. These results showed that the graphite-polyurethane composite can be used as an amperometric detector for flow analysis in the determination of APAP.