On continuation of inviscid vortex patches

This investigation concerns solutions of the steady-state Euler equations in two dimensions featuring finite area regions with constant vorticity embedded in a potential flow. Using elementary methods of the functional analysis we derive precise conditions under which such solutions can be uniquely continued with respect to their parameters, valid also in the presence of the Kutta condition concerning a fixed separation point. Our approach is based on the Implicit Function Theorem and perturbation equations derived using shape-differentiation methods. These theoretical results are illustrated with careful numerical computations carried out using the Steklov–Poincaré method which show the existence of a global manifold of solutions connecting the point vortex and the Prandtl–Batchelor solution, each of which satisfies the Kutta condition.     

An FDTD approach to the simulation of quantum-well infrared photodetectors

A Finite Difference Time Domain approach is used to design and to optimize quantum-well based infrared photodetectors. Results showing the influence of some parameters on the performance of these devices are presented and discussed.     

Formation of cerium titanate,CeTi<Subscript>2</Subscript>O<Subscript>6</Subscript>, in sol–gel films studied by XRD and FAR infrared spectroscopy

The process of formation of cerium titanate films as a function of annealing temperature and composition has been studied by combining X-ray diffraction analysis and far infrared spectroscopy. The films have been prepared by a sol–gel synthesis using metal chlorides as precursors; the synthesis allows obtaining cerium titanate films upon annealing in air. A brannerite type, CeTi₂O₆, phase has been identified by X-ray diffraction and Rietveld analysis on thin films. CeTi₂O₆ is formed upon annealing at 700 °C and in a limited range of ceria-titania mixed compositions. The far infrared spectra are useful to observe the formation of crystalline phases at the beginning of the crystallization process at lower firing temperatures, when the XRD analysis is not enough sensitive.     

Assessment of Cardiorespiratory Interactions during Apneic Events in Sleep via Fuzzy Kernel Measures of Information Dynamics

Apnea and other breathing-related disorders have been linked to the development of hypertension or impairments of the cardiovascular, cognitive or metabolic systems. The combined assessment of multiple physiological signals acquired during sleep is of fundamental importance for providing additional insights about breathing disorder events and the associated impairments. In this work, we apply information-theoretic measures to describe the joint dynamics of cardiorespiratory physiological processes in a large group of patients reporting repeated episodes of hypopneas, apneas (central, obstructive, mixed) and respiratory effort related arousals (RERAs). We analyze the heart period as the target process and the airflow amplitude as the driver, computing the predictive information, the information storage, the information transfer, the internal information and the cross information, using a fuzzy kernel entropy estimator. The analyses were performed comparing the information measures among segments during, immediately before and after the respiratory event and with control segments. Results highlight a general tendency to decrease of predictive information and information storage of heart period, as well as of cross information and information transfer from respiration to heart period, during the breathing disordered events. The information-theoretic measures also vary according to the breathing disorder, and significant changes of information transfer can be detected during RERAs, suggesting that the latter could represent a risk factor for developing cardiovascular diseases. These findings reflect the impact of different sleep breathing disorders on respiratory sinus arrhythmia, suggesting overall higher complexity of the cardiac dynamics and weaker cardiorespiratory interactions which may have physiological and clinical relevance.     

From Kerr to Heisenberg

In this paper, we consider the space-time of a charged mass endowed with an angular momentum. The geometry is described by the exact Kerr–Newman solution of the Einstein equations. The peculiar symmetry, though exact, is usually described in terms of the gravito-magnetic field originated by the angular momentum of the source. A typical product of this geometry is represented by the generalized Sagnac effect. We write down the explicit form for the right/left asymmetry of the times of flight of two counter-rotating light beams along a circular trajectory. Letting the circle shrink to the origin the asymmetry stays finite. Furthermore it becomes independent both from the charge of the source (then its electromagnetic field) and from Newton’s constant: it is then associated only to the symmetry produced by the gravitomagnetic field. When introducing, for the source, the spin of a Fermion, the lowest limit of the Heisenberg uncertainty formula for energy and time appears.