Complex singularities and PDEs

In this paper we give a review on the computational methods used to characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the singularity tracking method based on the analysis of the Fourier spectrum. We then introduce other methods generally used to detect the hidden singularities. In particular we show some applications of the Pad\'e approximation, of the Kida method, and of Borel-Polya method. We apply these techniques to the study of the singularity formation of some nonlinear dispersive and dissipative one dimensional PDE of the 2D Prandtl equation, of the 2D KP equation, and to Navier-Stokes equation for high Reynolds number incompressible flows in the case of interaction with rigid boundaries

Cyclic Fluctuations, Climatic Changes and Role of Noise in Planktonic Foraminifera in the Mediterranean Sea

The study of Planktonic Foraminifera abundances permits to obtain climatic curves on the basis of percentage ratio between tropical and temperate/polar forms. Climatic changes were controlled by several phenomena as: (i) Milankovitch's cycles, produced by variations of astronomical parameters such as precession, obliquity and eccentricity; (ii) continental geodynamic evolution and orogenic belt; (iii) variations of atmospheric and oceanic currents; (iv) volcanic eruptions; (v) meteor impacts. But while astronomical parameters have a quasi-regular periodicity, the other phenomena can be considered as "noise signal" in natural systems. The interplay between cyclical astronomical variations, the "noise signal" and the intrinsic nonlinearity of the ecologic system produces strong glacial or interglacial period according to the stochastic resonance phenomenon.Comment: 6 pages, 4 figure

An unusual case of intramural Meckel's diverticulum as a lead point for ileoileal intussusception - Laparoscopically assisted management

Intussusception is a frequent cause of intestinal obstruction in children. Ileoileal intussusception is rare and it is secondary to pathological or congenital lead points. We report an unusual case of an intramural Meckel's diverticulum as a lead point for ileoileal intussusception presenting with acute lower intestinal bleeding. Laparoscopically assisted resection of the involved ileum was successfully accomplished

Similarity of nuclear structure in 132Sn and 208Pb regions: proton-neutron multiplets

Starting from the striking similarity of proton-neutron multiplets in 134Sb and 210Bi, we perform a shell-model study of nuclei with two additional protons or neutrons to find out to what extent this analogy persists. We employ effective interactions derived from the CD-Bonn nucleon-nucleon potential renormalized by use of the V-low-k approach. The calculated results for 136Sb, 212Bi, 136I, and 212At are in very good agreement with the available experimental data. The similarity between 132Sn and 208Pb regions is discussed in connection with the effective interaction, emphasizing the role of core polarization effects.Comment: 4 pages, 3 figures, 2 table

Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array

In this paper we investigate the asymptotic validity of boundary layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl's solution to Navier-Stokes solutions at different $Re$ numbers. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions between the boundary layer and the outer flow. These interactions can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective

Looking for common fingerprints in Leonardo’s pupils through nondestructive pigment characterization

Non-invasive, portable analytical techniques are becoming increasingly widespread for the study and conservation in the field of cultural heritage, proving that a good data handling, supported by a deep knowledge of the techniques themselves, and the right synergy can give surprisingly substantial results when using portable but reliable instrumentation. In this work, pigment characterization was carried out on 21 Leonardesque paintings applying in situ X-ray fluorescence (XRF) and fiber optic reflection spectroscopy (FORS) analyses. In-depth data evaluation allowed to get information on the color palette and the painting technique of the different artists and workshops . Particular attention was paid to green pigments (for which a deeper study of possible pigments and alterations was performed with FORS analyses), flesh tones (for which a comparison with available data from cross-sections was made), and ground preparation

Spreading of information on a network: a quantum view

This paper concerns with the modeling of the spreading of information through a complex, multi-layered network, where the information is transferred from an initial transmitter to a final receiver. The mathematical model is deduced within the framework of operatorial methods, according to the formal mathematical apparatus typical of quantum mechanics. Two different approaches are considered: one based on the ($H,\rho$)-induced dynamics, and one on the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. For each method, numerical results are presented.Comment: 31 pages, 35 image

Spreading of Information on a Network: A Quantum View

This paper concerns the modeling of the spread of information through a complex, multilayered network, where the information is transferred from an initial transmitter to a final receiver. The mathematical model is deduced within the framework of operatorial methods, according to the formal mathematical apparatus typical of quantum mechanics. Two different approaches are considered: one based on the (H, \rho)-induced dynamics and one on the Gorini–Kossakowski–Sudarshan– Lindblad (GKSL) equation. For each method, numerical results are presented

Hydrophilic interaction chromatography – mass spectrometry for metabolomics and proteomics:state-of-the-art and current trends

Among all the –omics approaches, proteomics and metabolomics have received increased attention over the last decade. Both approaches have reached a certain level of maturity, showing their relevance in numerous clinical applications, including biomarkers discovery, improved diagnosis, staging, and prognosis of diseases, as well as a better knowledge on various (patho-)physiological processes. Analytically, reversed-phase liquid chromatography – mass spectrometry (RPLC-MS) is considered the golden standard in proteomics and metabolomics, due to its ease of use and reproducilibity. However, RPLC-MS alone is not sufficient to resolve the complexity of the proteome, while very polar metabolites are typically poorly retained. In this context, hydrophilic interaction chromatography (HILIC) represents an attractive complementary approach, due to its orthogonal separation mechanism. This review presents an overview of the literature reporting the application of HILIC-MS in metabolomics and proteomics. For metabolomics the focus is on the analysis of bioactive lipids, amino acids, organic acids, and nucleotides/nucleosides, whereas for proteomics the analysis of complex samples and protein post-translational modifications therein using bottom-up, middle up/down proteomics and intact protein analysis is discussed. The review handles the technological aspects related to the use of HILIC-MS in both proteomics and metabolomics, paying attention to stationary phases, mobile phase conditions, injection volume and column temperature. Recent trends and developments in the application of HILIC-MS in proteomics and metabolomics are also presented and discussed, highlighting the advantages the technique can provide in addition or complementary to RPLC-MS, as well as the current limitations and possible solutions

Route to chaos in the weakly stratified Kolmogorov flow

We consider a two-dimensional fluid exposed to Kolmogorov’s forcing cos(ny) and heated from above. The stabilizing effects of temperature are taken into account using the Boussinesq approximation. The fluid with no temperature stratification has been widely studied and, although relying on strong simplifications, it is considered an important tool for the theoretical and experimental study of transition to turbulence. In this paper, we are interested in the set of transitions leading the temperature stratified fluid from the laminar solution [U∝cos(ny),0, T ∝ y] to more complex states until the onset of chaotic states. We will consider Reynolds numbers 0 < Re ≤ 30, while the Richardson numbers shall be kept in the regime of weak stratifications (Ri ≤ 5 × 10 −3 ). We shall first review the non-stratified Kolmogorov flow and find a new period-tripling bifurcation as the precursor of chaotic states. Introducing the stabilizing temperature gradient, we shall observe that higher Re are required to trigger instabilities. More importantly, we shall see new states and phenomena: the newly discovered period-tripling bifurcation is supercritical or subcritical according to Ri; more period-tripling and doubling bifurcations may depart from this new state; strong enough stratifications trigger new regions of chaotic solutions and, on the drifting solution branch, non-chaotic bursting solutions