Pierluigi Maponi

Carlo Boldrighini, Sandro Frigio, Pierluigi Maponi

We consider some complex-valued solutions of the Navier-Stokes equations in $R^{3}$ for which Li and Sinai proved a finite time blow-up. We show that there are two types of solutions, with different divergence rates, and report results of computer simulations, which give a detailed picture of the blow-up for both types. They reveal in particular important features not, as yet, predicted by the theory, such as a concentration of the energy and the enstrophy around a few singular points, while elsewhere the "fluid" remains quiet.

Carlo Boldrighini, Sandro Frigio, Pierluigi Maponi

We present a study by computer simulations of a class of complex-valued solutions of the three-dimensional Navier-Stokes equations in the whole space, which, according to Li and Sinai, present a blow-up (singularity) at a finite time. The computer results allow a detailed study of the blow-up mechanism, and show interesting features of the behavior of the solutions near the blow-up time, such as the concentration of energy and enstrophy in a small region around a few points of physical space, while outside this region the "fluid" remains "quiet".

Nadaniela Egidi, Josephin Giacomini, Paolo Leonesi et al.

Motion Magnification (MM) is a collection of relative recent techniques within the realm of Image Processing. The main motivation of introducing these techniques in to support the human visual system to capture relevant displacements of an object of interest; these motions can be in object color and in object location. In fact, the goal is to opportunely process a video sequence to obtain as output a new video in which motions are magnified and visible to the viewer. We propose a numerical technique using the Phase-Based Motion Magnification which analyses the video sequence in the Fourier Domain and rely on the Fourier Shifting Property. We describe the mathematical foundation of this method and the corresponding implementation in a numerical algorithm. We present preliminary experiments, focusing on some basic test made up using synthetic images.

Pierluigi Maponi, Riccardo Piergallini, Filippo Santarelli

We propose a new gradient-based method for the extraction of the orientation field associated to a fingerprint, and a regularisation procedure to improve the orientation field computed from noisy fingerprint images. The regularisation algorithm is based on three new integral operators, introduced and discussed in this paper. A pre-processing technique is also proposed to achieve better performances of the algorithm. The results of a numerical experiment are reported to give an evidence of the efficiency of the proposed algorithm.