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

Analysis of complex singularities in high-Reynolds-number Navier-Stokes solutions

Numerical solutions of the laminar Prandtl boundary-layer and Navier-Stokes equations are considered for the case of the two-dimensional uniform flow past an impulsively-started circular cylinder. 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 that 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

ENGINEERING AND ANALYTICAL METHODS FOR PRECISION MEDICINE

ThesisAim of this thesis is to exploit modern technologies and statistical methods to support precision medicine in both the gathering and analysis of data. Real-time measurements of clinical parameters and identification of molecular signatures are thought to be crucial to tailor medications on the individual needs and likeliness of response. This thesis explores both aspects. The first part of the thesis studies the issues related to the safe real-time collection of parameters in connection to ultrasound communications of intra-body sensor networks. A testbed has been developed and a complete characterisation of a high water concentration channel — comparable to human body — is provided. The second part focuses on the analysis of transcriptomic data to predict successful treatments in non-communicable diseases. To reach this aim we will present a novel pathway-based tool together with the results from two clinical trials

Complex singularity analysis for vortex layer flows

We study the evolution of a 2D vortex layer at high Reynolds number. Vortex layer flows are characterized by intense vorticity concentrated around a curve. In addition to their intrinsic interest, vortex layers are relevant configurations because they are regularizations of vortex sheets. In this paper, we consider vortex layers whose thickness is proportional to the square-root of the viscosity. We investigate the typical roll-up process, showing that crucial phases in the initial flow evolution are the formation of stagnation points and recirculation regions. Stretching and folding characterizes the following stage of the dynamics, and we relate these events to the growth of the palinstrophy. The formation of an inner vorticity core, with vorticity intensity growing to infinity for larger Reynolds number, is the final phase of the dynamics. We display the inner core's self-similar structure, with the scale factor depending on the Reynolds number. We reveal the presence of complex singularities in the solutions of Navier-Stokes equations; these singularities approach the real axis with increasing Reynolds number. The comparison between these singularities and the Birkhoff-Rott singularity seems to suggest that vortex layers, in the limit, behave differently from vortex sheets

Glacio RADAR system and results

Since 1997 the Istituto Nazionale di Geofisica e Vulcanologia (INGV) in Italy has been involved in the development of the airborne RES system named Glacio RADAR, which is continuously upgraded. Radio Echo Sounding (RES) techniques are widely used in glaciological measurements. They are based on the use of radar systems, to obtain information concerning ice thickness of ice sheets and ice shelves, internal layering of glaciers, detection of inhomogeneities, exploration of subglacial lakes and identification of physical nature of subglacial interface. The Glacio RADAR is mounted on an aircraft and flies at an altitude around 300m above the ice surface during the survey. The first prototype operates in bistatic mode with separate transmit and receive one wire folded dipole installed beneath the aircraft wings. It works at 60 MHz with an envelope pulse width variable between 0.3 s and 1 s. The receiving window is 64 s which implies a maximum penetration depth (range) in the ice of about 5.3 km. The horizontal sampling rate is 10 traces/s at a mean aircraft speed of about 70 m/s. This would produce roughly 143 traces per kilometre (horizontal resolution of 1 trace every 7 m). The Navigation and geographical information is based on a on board GPS receiver giving longitude, latitude, altitude and time for the acquired radar trace. This radar was used in several Italian Antarctic Expeditions (1997, 1999, 2001 and 2003) and highlights of data results from these expeditions are presented here

Rilevamento delle sorgenti doppler della ionosfera tramite radar-HF

Il presente lavoro contiene un insieme di concetti di base utili per comprendere la cosiddetta tecnica della “interferometria doppler”, usata, nell’ambito degli studi sulla ionosfera, per ricavare informazioni sulla conformazione e velocità degli strati riflettenti (operazione chiamata anche sky mapping). È utile ricordare, infatti, che il sondaggio ionosferico tradizionale consente solo la determinazione dell’altezza virtuale di ogni strato, pensato come un unico oggetto riflettente piano. Tale determinazione è giunta nel tempo ad avere una risoluzione molto spinta, dell’ordine di qualche chilometro, tuttavia una ionosonda tradizionale non possiede la capacità di individuare la struttura degli strati riflettenti

Cardiovascular autonomic function and MCI in Parkinson's disease

Introduction: dysautonomic dysfunction and cognitive impairment represent the most disabling non-motor features of Parkinson's Disease (PD). Recent evidences suggest the association between Orthostatic Hypotension (OH) and PD-Dementia. However, little is known on the interactions between cardiovascular dysautonomia and Mild Cognitive Impairment (MCI). We aimed to evaluate the association between cardiovascular dysautonomia and MCI in patients with PD. Methods: non-demented PD patients belonging to the PACOS cohort underwent a comprehensive instrumental neurovegetative assessment including the study of both parasympathetic and sympathetic function (30:15 ratio, Expiratory-Inspiratory ratio [E-I] and presence of Orthostatic Hypotension [OH]). Diagnosis of MCI was made according to the MDS criteria level II. Results: we enrolled 185 PD patients of whom 102 (55.1%) were men, mean age was 64.6 ± 9.7 years, mean disease duration of 5.6 ± 5.5 years with a mean UPDRS-ME score of 31.7 ± 10.9. MCI was diagnosed in 79 (42.7%) patients. OH was recorded in 52 (28.1%) patients, altered 30:15 ratio was recorded in 39 (24.1%) patients and an altered E-I ratio was found in 24 (19.1%) patients. Presence of MCI was associated with an altered 30:15 ratio (adjOR 2.83; 95%CI 1.25–6.40) but not with an altered E-I ratio, while OH was associated only with the amnestic MCI subgroup (OR 2.43; 95% CI 1.05–5.06). Conclusion: in our study sample, MCI was mainly associated with parasympathetic dysfunction in PD