Soliton dynamics of NLS with singular potentials

We investigate the validity of a soliton dynamics behavior in the semi-relativistic limit for the nonlinear Schr\"odinger equation in $\R^{N}, N\ge 3$, in presence of a singular external potential.Comment: 23 page

Soliton dynamics for the generalized Choquard equation

We investigate the soliton dynamics for a class of nonlinear Schr\"odinger equations with a non-local nonlinear term. In particular, we consider what we call {\em generalized Choquard equation} where the nonlinear term is $(|x|^{\theta-N} * |u|^p)|u|^{p-2}u$. This problem is particularly interesting because the ground state solutions are not known to be unique or non-degenerate.Comment: 16 page

Global-local mixing for the Boole map

In the context of 'infinite-volume mixing' we prove global-local mixing for the Boole map, a.k.a. Boole transformation, which is the prototype of a non-uniformly expanding map with two neutral fixed points. Global-local mixing amounts to the decorrelation of all pairs of global and local observables. In terms of the equilibrium properties of the system it means that the evolution of every absolutely continuous probability measure converges, in a certain precise sense, to an averaging functional over the entire space.Comment: 15 pages, 2 figures. Final version to be published in Chaos, Solitons & Fractal

Infinite mixing for one-dimensional maps with an indifferent fixed point

We study the properties of `infinite-volume mixing' for two classes of intermittent maps: expanding maps $[0,1] \longrightarrow [0,1]$ with an indifferent fixed point at 0 preserving an infinite, absolutely continuous measure, and expanding maps $\mathbb{R}^+ \longrightarrow \mathbb{R}^+$ with an indifferent fixed point at $+\infty$ preserving the Lebesgue measure. All maps have full branches. While certain properties are easily adjudicated, the so-called global-local mixing, namely the decorrelation of a global and a local observable, is harder to prove. We do this for two subclasses of systems. The first subclass includes, among others, the Farey map. The second class includes the standard Pomeau-Manneville map $x \mapsto x+x^2$ mod 1. Morevoer, we use global-local mixing to prove certain limit theorems for our intermittent maps.Comment: Final version to be published in Nonlinearity. 39 pages, 2 figure

Pomeau-Manneville maps are global-local mixing

We prove that a large class of expanding maps of the unit interval with a $C^2$-regular indifferent point in 0 and full increasing branches are global-local mixing. This class includes the standard Pomeau-Manneville maps $T(x) = x + x^{p+1}$ mod 1 ($p \ge 1$), the Liverani-Saussol-Vaienti maps (with index $p \ge 1$) and many generalizations thereof.Comment: 23 pages. Final version produced for Discrete and Continuous Dynamical Systems - Series A. Numbering of equations, references et alia conforms to the published articl

A radial basis function neural network based approach for the electrical characteristics estimation of a photovoltaic module

The design process of photovoltaic (PV) modules can be greatly enhanced by using advanced and accurate models in order to predict accurately their electrical output behavior. The main aim of this paper is to investigate the application of an advanced neural network based model of a module to improve the accuracy of the predicted output I--V and P--V curves and to keep in account the change of all the parameters at different operating conditions. Radial basis function neural networks (RBFNN) are here utilized to predict the output characteristic of a commercial PV module, by reading only the data of solar irradiation and temperature. A lot of available experimental data were used for the training of the RBFNN, and a backpropagation algorithm was employed. Simulation and experimental validation is reported

Internal-wave billiards in trapezoids and similar tables

We call internal-wave billiard the dynamical system of a point particle that moves freely inside a planar domain (the table) and is reflected by its boundary according to this rule: reflections are standard Fresnel reflections but with the pretense that the boundary at any collision point is either horizontal or vertical (relative to a predetermined direction representing gravity). These systems are point particle approximations for the motion of internal gravity waves in closed containers, hence the name. For a class of tables similar to rectangular trapezoids, but with the slanted leg replaced by a general curve with downward concavity, we prove that the dynamics has only three asymptotic regimes: (1) minimality (all trajectories are dense); (2) there exist a global attractor and a global repellor, which are periodic and might coincide; (3) there exists a beam of periodic trajectories, whose boundary (if any) comprises an attractor and a repellor for all the other trajectories. Furthermore, in the prominent case where the table is an actual trapezoid, we study the sets in parameter space relative to the three regimes. We prove in particular that the set for (1) is a positive-measure fractal; the set for (2) has positive measure (giving a rigorous proof of the existence of Arnol'd tongues for internal-wave billiards); the set for (3) has measure zero.Comment: 23 pages, 6 figure

La pratique professionnelle des psychologues pédiatriques en milieu hospitalier lors de la transition d'adolescents en milieu adulte

Cette étude porte sur la pratique clinique des psychologues pédiatriques lors de la transition de jeunes patients atteints d’une maladie chronique ou dégénérative au milieu adulte. Étant donné que leur rôle dans ce domaine a été peu étudie, cette étude vise à combler cette lacune. Nous avons mené des entretiens semi-structurés auprès de dix psychologues. L’analyse thématique des verbatims a été utilisée afin de dégager des thèmes communs aux participants. Un premier article explore la façon dont les psychologues pédiatriques définissent la transition et vise à identifier les facilitateurs et les obstacles dans leur travail, alors que le deuxième décrit les éléments qui caractérisent les différents rôles joués par les psychologues dans la transition et fait état des recommandations visant l’amélioration de la pratique dans ce domaine

Soliton dynamics of NLS with singular potentials

We investigate the validity of a soliton dynamics behavior in the semi-classical limit for the nonlinear Schroedinger equation in R^N,N≥3, in presence of a singular external potential