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.

Given any wave speed c (independently of its sign!), we construct a traveling wave solution of the harmonic heat flow with values in the unit sphere and defined in an infinitely long cylinder. The wave connects two locally stable and axially symmetric steady states at + and - infinity, and has a singular point on the cylinder axis. In view of the bistable character of the potential, the result is surprising, and it is intimately related to the nonuniqueness of the harmonic map flow itself. The result is counter-intuitive if c has the "wrong sign", i.e. if the steady state with higher energy invades the cylinder. We show that for only one wave speed the traveling wave behaves locally, near its singular point, as a symmetric harmonic map.

Many real life problems can be represented by an ordered sequence of digital images. At a given pixel a specific time course is observed which is morphologically related to the time courses at neighbor pixels. Useful information can be usually extracted from a set of such observations if we are able to classify pixels in groups, according to some features of interest for the final user. Moreover parameters with a physical meaning can be extracted from the time courses. In a continuous setting we can formalize the problem by assuming to observe a noisy version of a positive real function defined on a bounded set T ×\Omega ‚ R×R2, parameterized by a vector of unknown functions defined on R2 with discontinuities along regular curves in \Omega which separate regions with different features. Suitable regularity conditions on the parameters are also assumed in order to take into account the physical constraints. The problem consists in estimating the parameter functions, segmenting \Omega in subsets with regular boundaries and assigning to each subset a label according to the values that the parameters assume on the subset. A global model is proposed which allows to address all of the above subproblems in the same framework. A variational approach is then adopted to compute the solution and an algorithm has been developed. Some numerical results obtained by using the proposed method to solve a dynamic Magnetic Resonance imaging problem are reported.

The Mixmaster dynamics is revisited in a new light as revealing a series of transitions in the complex scale invariant scalar invariant of the Weyl curvature tensor best represented by the speciality index S, which gives a 4-dimensional measure of the evolution of the spacetime independent of all the 3-dimensional gauge-dependent variables except the time used to parametrize it. Its graph versus time with typical spikes in its real and imaginary parts corresponding to curvature wall collisions serves as a sort of electrocardiogram of the Mixmaster universe, with each such spike pair arising from a single circuit or “pulse” around the origin in the complex plane. These pulses in the speciality index seem to invariantly characterize some of the so called spike solutions in inhomogeneous cosmology and should play an important role in the current investigations of inhomogeneous Mixmaster dynamics.

Implantation of drug eluting stents following percutaneous trans- luminal angioplasty has revealed a well established technique for treating occlusions caused by the atherosclerotic plaque. However, due to the risk of vascular re-occlusion, other alternative therapeutic strategies of drug delivery are currently being investigated. Polymeric endoluminal pave stenting is an emerging technology for preventing blood erosion and for optimizing drug release. The classical and novel methodologies are compared through a mathematical model able to predict the evolution of the drug concentration in a cross-section of the wall. Though limited to an idealized configuration, the present model is shown to catch most of the relevant aspects of the drug dynamics in a delivery system. Results of numerical simulations shows that a bi-layer gel paved stenting guarantees a uniform drug elution and a prolonged perfusion of the tissues, and remains a promising and effective technique in drug delivery.