Legendre spectral method for the fractional Bratu problem

In this paper, the Legendre spectral collocation method (LSCM) is applied for the solution of the fractional Bratu's equation. It shows the high accuracy and low computational cost of the LSCM compared with some other numerical methods. The fractional Bratu differential equation is transformed into a nonlinear system of algebraic equations for the unknown Legendre coefficients and solved with some spectral collocation methods. Some illustrative examples are also given to show the validity and applicability of this method, and the obtained results are compared with the existing studies to highlight its high efficiency and neglectable error.     

On pressure broadening of the ammonia inversion spectrum by inert gases (He,Ar)

We have calculated the linewidths of the inversion spectrum of NH₃ perturbed by inert gases (He, Ar) using a convergent theory proposed by Cattani. We have employed the Herman and Tipping potential for the dispersion interaction. Our theoretical results and those obtained from the Anderson and Tsao and Curnutte second and third approximations are compared with experimental results.     

Plane Waves in Cubically Nonlinear Elastic Media

The theory of plane waves in nonlinear materials described by the Murnaghan potential is proposed. The theory takes into account both the classical quadratic nonlinearity and the cubic nonlinearity of the basic wave equations. Some new opportunities for the wave interaction analysis are commented on: in addition to the second harmonics, a longitudinal plane wave generates the third one, a transverse plane wave generates the third harmonics, and horizontally and vertically polarized transverse plane waves jointly generate new waves     

Generation of the Third Harmonics by Plane Waves in Murnaghan Materials

We demonstrate that it is expedient to use the complete expansion of the potential in terms of strain gradients for materials whose deformation is described by Murnaghan's potential. The cubic terms are retained in the constitutive equations, in addition to the classical quadratic terms. An analysis of the nonlinear system of wave equations reveals that the third harmonics can be generated. As an example, the nonlinear interaction of plane waves is analyzed for the following three cases of waves entering a medium: (i) a longitudinal wave, (ii) a vertically polarized transverse wave, and (iii) vertically and horizontally polarized transverse waves     

Measurements of water vapor isotope ratios with wavelength-scanned cavity ring-down spectroscopy technology: new insights and important caveats for deuterium excess measurements in tropical areas in comparison with isotope-ratio mass spectrometry

The new infrared laser spectroscopic techniques enable us to measure the isotopic composition (δ(18)O and δ(2)H) of atmospheric water vapor. With the objective of monitoring the isotopic composition of tropical water vapor (West Africa, South America), and to discuss deuterium excess variability (d=δ(2)H - 8δ(18)O) with an accuracy similar to measurements arising from isotope-ratio mass spectrometry (IRMS), we have conducted a number of tests and calibrations using a wavelength-scanned cavity ring-down spectroscopy (WS-CRDS) technique. We focus in this paper on four main aspects regarding (1) the tubing material, (2) the humidity calibration of the instrument, (3) the water vapor concentration effects on δ, and (4) the isotopic calibration of the instrument. First, we show that Synflex tubing strongly affects δ(2)H measurements and thus leads to unusable d values. Second, we show that the mixing ratio as measured by WS-CRDS has to be calibrated versus atmospheric mixing ratio measurements and we also suggest possible non-linear effects over the whole mixing ratio range (~2 to 20 g/kg). Third, we show that significant non-linear effects are induced by water vapor concentration variations on δ measurements, especially for mixing ratios lower than ~5 g/kg. This effect induces a 5 to 10‰ error in deuterium excess and is instrument-dependent. Finally, we show that an isotopic calibration (comparison between measured and true values of isotopic water standards) is needed to avoid errors on deuterium excess that can attain ~10‰.