On kinks and other travelling-wave solutions of a modified sine-Gordon equation

We give an exhaustive, non-perturbative classification of exact travelling-wave solutions of a perturbed sine-Gordon equation (on the real line or on the circle) which is used to describe the Josephson effect in the theory of superconductors and other remarkable physical phenomena. The perturbation of the equation consists of a constant forcing term and a linear dissipative term. On the real line candidate orbitally stable solutions with bounded energy density are either the constant one, or of kink (i.e. soliton) type, or of array-of-kinks type, or of "half-array-of-kinks" type. While the first three have unperturbed analogs, the last type is essentially new. We also propose a convergent method of successive approximations of the (anti)kink solution based on a careful application of the fixed point theorem.Comment: Latex file, 25 pages, 4 figures. Final version to appear in "Meccanica

Hydrodynamic impacts of short laser pulses on plasmas

We determine conditions allowing to simplify the description of the impact of a short and arbitrarily intense laser pulse onto a cold plasma at rest. If both the initial plasma density and pulse profile have plane simmetry, then suitable matched upper bounds on the maximum and the relative variations of the initial density, as well as the intensity and duration of the pulse, ensure a strictly hydrodynamic evolution of the electron fluid (without wave-breaking or vacuum-heating) during its whole interaction with the pulse, while ions can be regarded as immobile. We use a recently developed fully relativistic plane model whereby the system of the (Lorentz-Maxwell and continuity) PDEs is reduced into a family of highly nonlinear but decoupled systems of non-autonomous Hamilton equations with one degree of freedom, with the light-like coordinate $\xi=ct\!-\!z$ instead of time $t$ as an independent variable, and new apriori estimates (eased by use of a Liapunov function) of the solutions in terms of the input data (initial density and pulse profile). If the laser spot radius $R$ is finite but not too small the same conclusions hold for the part of the plasma close to the axis $\vec{z}$ of cylindrical symmetry. These results may help in drastically simplifying the study of extreme acceleration mechanisms of electrons.Comment: 29 pages, 8 figures. To appear in the Journal "Mathematics

FEA testing the pre-flight Ariel primary mirror

Ariel (Atmospheric Remote-sensing Infrared Exoplanet Large-survey) is an ESA M class mission aimed at the study of exoplanets. The satellite will orbit in the lagrangian point L2 and will survey a sample of 1000 exoplanets simultaneously in visible and infrared wavelengths. The challenging scientific goal of Ariel implies unprecedented engineering efforts to satisfy the severe requirements coming from the science in terms of accuracy. The most important specification – an all-Aluminum telescope – requires very accurate design of the primary mirror (M1), a novel, off-set paraboloid honeycomb mirror with ribs, edge, and reflective surface. To validate such a mirror, some tests were carried out on a prototype – namely Pathfinder Telescope Mirror (PTM) – built specifically for this purpose. These tests, carried out at the Centre Spatial de Liège in Belgium – revealed an unexpected deformation of the reflecting surface exceeding a peek-to-valley of 1µm. Consequently, the test had to be re-run, to identify systematic errors and correct the setting for future tests on the final prototype M1. To avoid the very expensive procedure of developing a new prototype and testing it both at room and cryogenic temperatures, it was decided to carry out some numerical simulations. These analyses allowed first to recognize and understand the reasoning behind the faults occurred during the testing phase, and later to apply the obtained knowledge to a new M1 design to set a defined guideline for future testing campaigns

Test of protected silver coating on aluminum samples of ARIEL main telescope mirror substrate material

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"Delirium Day": A nationwide point prevalence study of delirium in older hospitalized patients using an easy standardized diagnostic tool

Background: To date, delirium prevalence in adult acute hospital populations has been estimated generally from pooled findings of single-center studies and/or among specific patient populations. Furthermore, the number of participants in these studies has not exceeded a few hundred. To overcome these limitations, we have determined, in a multicenter study, the prevalence of delirium over a single day among a large population of patients admitted to acute and rehabilitation hospital wards in Italy. Methods: This is a point prevalence study (called "Delirium Day") including 1867 older patients (aged 65 years or more) across 108 acute and 12 rehabilitation wards in Italian hospitals. Delirium was assessed on the same day in all patients using the 4AT, a validated and briefly administered tool which does not require training. We also collected data regarding motoric subtypes of delirium, functional and nutritional status, dementia, comorbidity, medications, feeding tubes, peripheral venous and urinary catheters, and physical restraints. Results: The mean sample age was 82.0 \ub1 7.5 years (58 % female). Overall, 429 patients (22.9 %) had delirium. Hypoactive was the commonest subtype (132/344 patients, 38.5 %), followed by mixed, hyperactive, and nonmotoric delirium. The prevalence was highest in Neurology (28.5 %) and Geriatrics (24.7 %), lowest in Rehabilitation (14.0 %), and intermediate in Orthopedic (20.6 %) and Internal Medicine wards (21.4 %). In a multivariable logistic regression, age (odds ratio [OR] 1.03, 95 % confidence interval [CI] 1.01-1.05), Activities of Daily Living dependence (OR 1.19, 95 % CI 1.12-1.27), dementia (OR 3.25, 95 % CI 2.41-4.38), malnutrition (OR 2.01, 95 % CI 1.29-3.14), and use of antipsychotics (OR 2.03, 95 % CI 1.45-2.82), feeding tubes (OR 2.51, 95 % CI 1.11-5.66), peripheral venous catheters (OR 1.41, 95 % CI 1.06-1.87), urinary catheters (OR 1.73, 95 % CI 1.30-2.29), and physical restraints (OR 1.84, 95 % CI 1.40-2.40) were associated with delirium. Admission to Neurology wards was also associated with delirium (OR 2.00, 95 % CI 1.29-3.14), while admission to other settings was not. Conclusions: Delirium occurred in more than one out of five patients in acute and rehabilitation hospital wards. Prevalence was highest in Neurology and lowest in Rehabilitation divisions. The "Delirium Day" project might become a useful method to assess delirium across hospital settings and a benchmarking platform for future surveys

GLOBAL SOLUTIONS AND L(1)-STABILITY TO A NONLINEAR EVOLUTION PROBLEM IN THE DIFFUSION OF THE PARTICLES OF A MIXTURE

The global existence and L(1)-asymptotic stability of the solutions to a nonlinear evolution problem, in the diffusion of the particles of a mixture, is proved