Theoretical and experimental investigation of the second hyperpolarizabilities of methyl orange

We describe experimental and theoretical studies of the third-order nonlinear optical coefficients of methyl orange solutions under different pH conditions. A combination of semiempirical and ab initio methods was adopted to investigate the most stable geometrical structures possible for this molecule. The experimental data obtained using the Z-scan technique for the third-order nonlinear optical properties of this compound has allowed the determination of the nonlinear refractive index and nonlinear absorption coefficient under picosecond excitation in the visible (532 nm) spectral region. From those experimental results, the second hyperpolarizability of methyl orange was inferred both for acidic and alkaline solutions. Comparison of these values to the results predicted by semiempirical methods suggests that even at low pH, when the probability of cis-trans isomerization is increased, the trans conformation of the methyl orange molecule should dominate the nonlinear spectra of this compound. The theoretical results were used as an auxiliary tool to identify possible trends on the nonlinear properties changes as a function of the distinct molecular conformations adopted by the methyl orange molecule under different pH conditions.     

Mössbauer analysis of crystallization processes in iron-soda-lime-silicate glasses

⁵⁷Fe Mössbauer spectroscopy was used to observe the crystallization process in glasses with composition denoted by [0.50SiO₂, 0.45Na₂O, 0.05CaO]100-x(Fe₂O₃)_x with x equal to 4, 10 and 16 mol%. It is shown that Mössbauer spectroscopy is a very suitable technique for detecting and checking the very early stages of crystallite formation in amorphous materials. The crystallization process was observed and qualitatively analysed by means of classical volume nucleation theory.     

Influence of magnetic dipolar interaction on one- and two-magnon scattering of light in ferromagnets

It is shown that the presence of magnetic dipolar interaction in a ferromagnetic medium changes the polarization selection rules of light scattered by magnons. In addition it provides a new mechanism for two-magnon scattering.     

Finding isometry groups in theory and practice

An algorithm is given for determining the isometry group of an arbitrary spacetime (in four dimensions). Numerous examples are given and the partial implementation of this algorithm using the symbolic manipulation package CLASSI is discussed.     

Two-photon absorption in hexagonal-CdS

The “composite sample technique” has been used to investigate the two-photon absorption coefficient (β) of CdS at 3.91 eV. The absolute value of β and its optical anisotropy have been studied for samples with different carrier densities. The present results may provide a new interpretation of experiments on CdS and other semiconductors reported in the literature.     

Capillary Rise in Porous Media

Capillary rise experiments were performed in columns filled with glass beads and Berea sandstones, using visual methods to register the advance of the water front. For the glass bead filled columns, early time data are well fitted by the Washburn equation. However, in the experiments, the advancing front exceeded the predicted equilibrium height. For large times, an algebraic behavior of the velocity of the front is observed (T. Delker et al., Phys. Rev. Lett. 76, 2902 (1996)). A model for studying the capillary pressure evolution in a regular assembly of spheres is proposed and developed. It is based on a quasi-static advance of the meniscus with a piston-like motion and allows us to estimate the hydraulic equilibrium height, with values very close to those obtained by fitting early time data to a Washburn equation. The change of regime is explained as a transition in the mechanism of advance of the meniscus. On the other hand, only the Washburn regime was observed for the sandstones. The front velocity was fitted to an algebraical form with an exponent close to 0.5, a value expected from the asymptotic limit of the Washburn equation. Copyright 2001 Academic Press.     

Infinitesimal Lyapunov functions for singular flows

We present an extension of the notion of infinitesimal Lyapunov function to singular flows, and from this technique we deduce a characterization of partial/sectional hyperbolic sets. In absence of singularities, we can also characterize uniform hyperbolicity. These conditions can be expressed using the space derivative $DX$ of the vector field $X$ together with a field of infinitesimal Lyapunov functions only, and are reduced to checking that a certain symmetric operator is positive definite at the tangent space of every point of the trapping region.     

A method for determination of COD in a domestic wastewater treatment plant by using near-infrared reflectance spectrometry of seston

This paper proposes a method for determination of chemical oxygen demand (COD) in domestic wastewater. The proposed method is based on near-infrared reflectance (NIRR) measurements of seston collected from wastewater samples by filtration. The analysis does not require any special reagent, catalyst or solvent. Inherent baseline and noise features present in NIRR spectra are removed by a Savitzky-Golay derivative procedure followed by wavelet denoising. The resulting wavelet approximation coefficients are used for partial-least-squares modelling and subsequent prediction of COD values in new samples. The model is calibrated by using COD values obtained according to the American Public Health Association (APHA) reference method. The proposed method is applied to effluent samples from the anaerobic ponds of the Mangabeira municipal wastewater treatment plant in the city of João Pessoa (Paraíba, Brazil). By comparing the NIRR prediction results with the APHA reference values, a root-mean-square error of prediction (RMSEP) of 19 mg O₂ L⁻¹ and a correlation of 0.97 were obtained. Such results are deemed adequate in view of the joint estimate of the standard error of the reference method, which was calculated as 21 mg O₂ L⁻¹.     

Development of new Cd2+ and Pb2+ Lennard-Jones parameters for liquid simulations

We present new Lennard-Jones parameters for Cd2+ and Pb2+ ion-water interactions and describe a general methodology to obtain these parameters for any ion. Our strategy is based on the adjustment of ion parameters to reproduce simultaneously experimental absolute hydration free energy and structural properties, namely, g(r) and coordination numbers, obtained from X-ray liquid scattering and quantum mechanical/molecular mechanical (QM/MM) calculations. The validation of the obtained parameters is made by the calculation of dynamical properties and comparing them with experimental values and theoretical results from the literature. The transferability of parameters is checked by the calculation of thermodynamic, structural, and dynamical properties cited above with four different water models. The results obtained for Cd2+ and Pb2+ show an overall agreement with reference values. The absolute hydration free energy calculated with the TIP3P, SPC/E, SPC, and TIP4P water models presents, respectively, percent differences of 3.8, 3.0, 4.3, and 7.2% for lead(II) and 9.8, 8.4, 10.2, and 14.1% for cadmium(II) when compared with experimental values. Ion-water mean distance and coordination numbers for the first coordination shell are in good agreement with experimental and QM/MM results for both ions. Cd2+ shows a lesser diffusion coefficient compared to that of Pb2+ despite its smaller atomic radius, indicating a more persistent first coordination shell for the cadmium(II) ion, a result confirmed with calculations of the mean residence time of water molecules in the first coordination shell.