REFIR is a Fourier Transform Spectrometer designed to measure the upwelling IR Earth's emission from space in the spectral range 100 to 1000 cm -1 with an unapodized spectral resolution of about 0.5 cm -1. One of the main scientific objectives of REFIR is to monitor the far IR planetary emission and the principal drivers of this emission, with particular attention being paid to the poorly understood mid and upper troposphere. The expected retrieval performance for temperature and water vapor profiles, from a subset of REFIR measurements, is evaluated and presented in this paper. ©2003 Copyright SPIE - The International Society for Optical Engineering.

Inversion of the radiative transfer equation to retrieve the vertical profile of temperature from high resolution radiance spectra is an important problem in remote sensing of atmosphere. Because of its non linearity and ill conditioning, regularization techniques have been resorted in order to reduce the error of the retrieval. In this paper Generalized Singular Value Decomposition (GSVD) and Truncated Generalized Singular Value Decomposition (TGSVD) have been used to solve the linear model; the optimal regularization parameter for the proper amount of smoothing have been chosen by the L-curve criterion. A significant test problem has been worked out with reference to the Infrared Atmospheric Sounding Interferometer (IASI). The effectiveness of the methods to reduce variance and bias in the output profile has been addressed. We show that GSVD plus L-curve criterion or TGSVD plus L-curve are really effective in reducing error, variance and bias of the retrieved profile.

CHIARA (Convolution of High-resolution Interferograms for Advanced Retrieval in the Atmosphere) is an integrated tool intended for the simulation and inversion of spectra. In this paper application of CHIARA to IMG spectra is presented and discussed.

The spinodal decomposition of binary mixtures in uniform shear flow is studied in the context of the time-dependent Ginzburg-Landau equation, approximated at one-loop order. We show that the structure factor obeys a generalized dynamical scaling with different growth exponents alpha(x) = 5/4 and alpha(y) = 1/4 in the flow and in the shear directions, respectively. The excess viscosity Delta eta after reaching a maximum relaxes to zero as gamma(-2)t(-3/2), gamma being the shear rate. Delta eta and other observables exhibit log-time periodic oscillations which can be interpreted as due to a growth mechanism where stretching and breakup of domains cyclically occur.

We show how a lattice-Boltzmann approach can be extended to ternary fluid mixtures with the aim of modeling the diverse behavior of oil-water-surfactant systems. We model the mixture using a Ginzburg-Landau free energy with two scalar order parameters which allows us to define a lattice-Boltzmann scheme in the spirit of the Cahn-Hilliard approach to nonequilibrium dynamics. Results are presented for the spontaneous emulsification of an oil-water droplet and for spinodal decomposition in the presence of a surfactant.

We consider a class of integral equations of Volterra type with constant coefficients containing a logarithmic difference kernel. This class coincides for a=0 with the Symm's equation. We can transform the general integral equation into an equivalent singular equation of Cauchy type which allows us to give an explicit formula for the solution g. The numerical method proposed in this paper consists in substituting the Lagrange polynomial interpolating the known function f in the expression of the solution g. Then, with the aid of the invariance properties of the orthogonal polynomials for the Cauchy integral equations, we obtain an easy expression for the approximate solution. Moreover, we show that the previous numerical method is a collocation method where the coefficient of the polynomial approximating the solution can be easily computed. We give weighted norm estimates for the error of this method. The paper concludes with some numerical examples.

We consider a class of integral equations of Volterra type with constant coefficients containing a logarithmic difference kernel. This class coincides for a=0 with the Symm's euqtion. We can transform the general integral equation into an equivalent singular equation of Cauchy type which allows us to give the explicit formula for the solution. The numerical method proposed in this paper consists in substituting this in the experrsion of the solution g. Then, with the aid of the inveriance properties of the orthogonal polynomials for the Cauchy integral equation, we obtain an approximate solution of the function g. We give weighted norm estimates for the error of this method. The paper concludes with some numerical examples.

We propose a time-advancing scheme for the discretization of the unsteady incompressible Navier-Stokes equations. At any time step, we are able to decouple velocity and pressure by solving some suitable elliptic problems. In particular, the problem related with the determination of the pressure does not require boundary conditions. The divergence free condition is imposed as a penalty term, according to an appropriate restatement of the original equations. Some experiments are carried out by approximating the space variables with the spectral Legendre collocation method. Due to the special treatment of the pressure, no spurious modes are generated.

A generalization of mesoscopic Lattice-Boltzmann models aimed at describing flows with solid/liquid phase transitions is presented. It exhibits lower computational costs with respect to the numerical schemes resulting from differential models, Moreover it is suitable to describe chaotic motions in the mushy zone.

The authors introduce a new Lagrange and Hermite interpolation process and study the behaviour in some functional spaces.

Collocation and quadrature methods for singular integro-differential equations of Prandtl's type are studied in weighted Sobolev spaces. A fast algorithm basing on the quadrature method is proposed. Convergence results and error estimates are given.