In recent years, research activities in Italy concerning applied and industrial mathematics have been conducted by many scientists with different experience, from university, research institutions and industry. They addressed a number of specic subjects. Besides classical topics - such as fluid dynamics, elasticity, continuous mechanics - new problems have been considered, with application to a variety of situations and phenomena such as, for example, traffic modelling, hemodynamics, biofilms; moreover, a number of research projects of interest for the industry have also been developed.

It is known that, if u is a real valued function on R^n of bounded variation, then its total variation decreases under polarization. In this paper we identify the difference between the total variation of u and that one of its polar u_{\pi}.

The general relativistic version is developed for Robertson’s discussion of the Poynting-Robertson effect that he based on special relativity and Newtonian gravity for point radiation sources like stars. The general relativistic model uses a test radiation field of photons in outward radial motion with zero angular momentum in the equatorial plane of the exterior Schwarzschild or Kerr spacetime.

A hybrid lattice Boltzmann method (LBM) for binary mixtures based on the free-energy approach is proposed. Nonideal terms of the pressure tensor are included as a body force in the LBM kinetic equations, used to simulate the continuity and Navier-Stokes equations. The convection-diffusion equation is studied by finite-difference methods. Differential operators are discretized in order to reduce the magnitude of spurious velocities. The algorithm has been shown to be stable and reproducing the correct equilibrium behavior in simple test configurations and to be Galilean invariant. Spurious velocities can be reduced by approximately an order of magnitude with respect to standard discretization procedure.

We present a systematic study of capillary filling for multi-phase flows by using mesoscopic lattice Boltzmann models describing a diffusive interface moving at a given contact angle with respect to the walls. We compare the numerical results at changing the density ratio between liquid and gas phases, delta rho/rho and the ratio, delta xi/H, between the typical size of the capillary, H, and the interface width, delta xi. It is shown that numerical results yield quantitative agreement with the Washburn law when both ratios are large, i.e. as the hydrodynamic limit of a infinitely thin interface is approached. We also show that in the initial stage of the filling process, transient behaviour induced by inertial effects and "vena contracta" mechanisms, may induce significant departure from the Washburn law. Both effects are under control in our lattice Boltzmann equation and in good agreement with the phenomenology of capillary filling.

The motion of an air-fluid interface through an irregularly coated capillary is studied by analyzing the Lucas-Washburn equation with inertia, viscosity and a random capillary force. Below a critical velocity, the front enters a strongly intermittent dynamic regime, as recently observed in experiments. Analytical estimates for the average asymptotic front trajectory and pinning length distribution are obtained, and a numerical procedure for predicting quantities of experimental interest is also illustrated.

MIPAS is a Fourier transform spectrometer, operating onboard of the ENVISAT satellite since July 2002. The online retrieval algorithm produces geolocated profiles of temperature and of volume mixing ratios of six key atmospheric constituents: H2O, O3, HNO3, CH4, N2O and NO2. In the validation phase, oscillations beyond the error bars were observed in several profiles, particularly in CH4 and N2O. To tackle this problem, a Tikhonov regularization scheme has been implemented in the retrieval algorithm. The applied regularization is however rather weak in order to preserve the vertical resolution of the profiles. In this paper we present a self-adapting and altitudedependent regularization approach that detects whether the analyzed observations contain information about small-scale profile features, and determines the strength of the regularization accordingly. The objective of the method is to smooth out artificial oscillations as much as possible, while preserving the fine detail features of the profile when related information is detected in the observations. The proposed method is checked for self consistency, its performance is tested on MIPAS observations and compared with that of some other regularization schemes available in the literature. In all the considered cases the proposed scheme achieves a good performance, thanks to its altitude dependence and to the constraints employed, which are specific of the inversion problem under consideration. The proposed method is generally applicable to iterative Gauss- Newton algorithms for the retrieval of vertical distribution profiles from atmospheric remote sounding measurements.

A Lattice Boltzmann Method for van der Waals fluids with variable temperature is described. Thermo-hydrodynamic equations are correctly reproduced at second order of a Chapman-Enskog expansion. The method is applied to study initial stages of phase separation of a fluid quenched by contact with colder walls. Thermal equilibration is favoured by pressure waves which propagate with the sound velocity.

In this paper we consider Volterra integralequations with two constant delays y(t)=1+\int_{t-\tau_2}^{t-\tau_1}(\lambda+\mu(t-s))y(s)ds,\;t\in[\tau_2,T], and we carry out the stability analysis of direct quadrature methods with respect to the linear convolutiontestequation View the MathML source We investigate the analytical behavior of the solution of the testequation and derive the qualitative and quantitative properties of the numerical solution. The numerical experiments show that the stability conditions obtained represent sufficient conditions for the stability of the numerical method applied to a more general equation.

In this paper we develop a direct quadrature method for solving Volterra-Fredholm integral equations on an unbounded spatial domain. These problems, when related to some important physical and biological phenomena, are characterized by kernels that present variable peaks along space. The method we propose is adaptive in the sense that the number of spatial nodes of the quadrature formula varies with the position of the peaks. The convergence of the method is studied and its performances are illustrated by means of a few significative examples. The parallel algorithm which implements the method and its performances are described

We consider the problem of testing for additivity in the standard multiple nonparametric regression model. We derive optimal (in the minimax sense) non- adaptive and adaptive hypothesis testing procedures for additivity against the composite nonparametric alternative that the response function involves interactions of second or higher orders separated away from zero in L 2([0, 1] d )-norm and also possesses some smoothness properties. In order to shed some light on the theoretical results obtained, we carry out a wide simulation study to examine the finite sample performance of the proposed hypothesis testing procedures and compare them with a series of other tests for additivity available in the literature.

The Lagrangian description of turbulence is characterized by a unique con- ceptual simplicity and by an immediate connection with the physics of dis- persion and mixing. In this article, we report some motivations behind the Lagrangian description of turbulence and focus on the statistical properties of particles when advected by fully developed turbulent flows. By means of a detailed comparison between experimental and numerical results, we review the physics of particle acceleration, Lagrangian velocity structure functions, and pairs and shapes evolution. Recent results for nonideal particles are dis- cussed, providing an outlook on future directions.

A truly functional Bayesian method for detecting temporally differentially expressed genes between two experimental conditions is presented. The method distinguishes between two biologically different set ups, one in which the two samples are interchangeable, and one in which the second sample is a modification of the first, i.e. the two samples are non-interchangeable. This distinction leads to two different Bayesian models, which allow more flexibility in modeling gene expression profiles. The method allows one to identify differentially expressed genes, to rank them and to estimate their expression profiles. The proposed procedure successfully deals with various technical difficulties which arise in microarray time-course experiments, such as small number of observations, non-uniform sampling intervals and presence of missing data or repeated measurements. The procedure allows one to account for various types of error, thus offering a good compromise between nonparametric and normality assumption based techniques. In addition, all evaluations are carried out using analytic expressions, hence the entire procedure requires very little computational effort. The performance of the procedure is studied using simulated and real data.