On the stability of travelling waves with vorticity obtained by minimisation

We modify the approach of Burton and Toland [Comm. Pure Appl. Math. (2011)] to show the existence of periodic surface water waves with vorticity in order that it becomes suited to a stability analysis. This is achieved by enlarging the function space to a class of stream functions that do not correspond necessarily to travelling profiles. In particular, for smooth profiles and smooth stream functions, the normal component of the velocity field at the free boundary is not required a priori to vanish in some Galilean coordinate system. Travelling periodic waves are obtained by a direct minimisation of a functional that corresponds to the total energy and that is therefore preserved by the time-dependent evolutionary problem (this minimisation appears in Burton and Toland after a first maximisation). In addition, we not only use the circulation along the upper boundary as a constraint, but also the total horizontal impulse (the velocity becoming a Lagrange multiplier). This allows us to preclude parallel flows by choosing appropriately the values of these two constraints and the sign of the vorticity. By stability, we mean conditional energetic stability of the set of minimizers as a whole, the perturbations being spatially periodic of given period.Comment: NoDEA Nonlinear Differential Equations and Applications, to appea

Energy fluctuation relations and repeated quantum measurements

In this paper, we discuss the statistical description in non-equilibrium regimes of energy fluctuations originated by the interaction between a quantum system and a measurement apparatus applying a sequence of repeated quantum measurements. To properly quantify the information about energy fluctuations, both the exchanged heat probability density function and the corresponding characteristic function are derived and interpreted. Then, we discuss the conditions allowing for the validity of the fluctuation theorem in Jarzynski form 〈e−βQ〉=1, thus showing that the fluctuation relation is robust against the presence of randomness in the time intervals between measurements. Moreover, also the late-time, asymptotic properties of the heat characteristic function are analyzed, in the thermodynamic limit of many intermediate quantum measurements. In such a limit, the quantum system tends to the maximally mixed state (thus corresponding to a thermal state with infinite temperature) unless the system's Hamiltonian and the intermediate measurement observable share a common invariant subspace. Then, in this context, we also discuss how energy fluctuation relations change when the system operates in the quantum Zeno regime. Finally, the theoretical results are illustrated for the special cases of two- and three-levels quantum systems, now ubiquitous for quantum applications and technologies

On the stability of travelling waves with vorticity obtained by minimization

We modify the approach of Burton and Toland Comm. Pure Appl. Math. LXIV. 975-1007 (2011) to show the existence of periodic surface water waves with vorticity in order that it becomes suited to a stability analysis. This is achieved by enlarging the function space to a class of stream functions that do not correspond necessarily to travelling profiles. In particular, for smooth profiles and smooth stream functions, the normal component of the velocity field at the free boundary is not required a priori to vanish in some Galilean coordinate system. Travelling periodic waves are obtained by a direct minimization of a functional that corresponds to the total energy and that is therefore preserved by the time-dependent evolutionary problem (this minimization appears in Comm. Pure Appl. Math. LXIV. 975-1007 2011 after a first maximization). In addition, we not only use the circulation along the upper boundary as a constraint, but also the total horizontal impulse (the velocity becoming a Lagrange multiplier). This allows us to preclude parallel flows by choosing appropriately the values of these two constraints and the sign of the vorticity. By stability, we mean conditional energetic stability of the set of minimizers as a whole, the perturbations being spatially periodic of given period. Our proofs depend on the assumption that the surface offers some resistance to stretching and bendin

A dimension-breaking phenomenon for water waves with weak surface tension

It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schr\"odinger equation. The present paper contains an existence theory for three-dimensional periodically modulated solitary-wave solutions which have a solitary-wave profile in the direction of propagation and are periodic in the transverse direction; they emanate from the line solitary waves in a dimension-breaking bifurcation. In addition, it is shown that the line solitary waves are linearly unstable to long-wavelength transverse perturbations. The key to these results is a formulation of the water wave problem as an evolutionary system in which the transverse horizontal variable plays the role of time, a careful study of the purely imaginary spectrum of the operator obtained by linearising the evolutionary system at a line solitary wave, and an application of an infinite-dimensional version of the classical Lyapunov centre theorem.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-015-0941-

Correzioni gravimetriche per la rete di livellazione geometrica italiana: stato dell’arte e l’esempio della Provincia di Trento

Riassunto Il sistema di riferimento altimetrico ufficiale italiano è definito attraverso una rete di livellazione geometrica materializzata e periodicamente rilevata dall’Istituto Geografico Militare (IGM). Le quote dinamiche, ortometriche e normali dei capisaldi di una rete di livellazione si ottengono dalla compensazione ai minimi quadrati dei dislivelli geometrici osservati, opportunamente corretti per gli effetti di gravità. Il Politecnico di Milano (POLIMI), nell’ambito di una convenzione con l’IGM, sta effettuando il calcolo delle correzioni (dinamiche, ortometriche e normali) da apportare alle nuove osservazioni di livellazione eseguite nel contempo dall’IGM sull’intero territorio nazionale per l’aggiornamento del sistema di altezze italiano. I valori di gravità necessari al calcolo delle correzioni sono ricavati dal database utilizzato per il nuovo Geoide Italiano. Il Servizio Catasto della Provincia Autonoma di Trento in accordo con IGM e POLIMI partecipa all’acquisizione delle osservazioni della sotto-rete trentina e al successivo calcolo delle relative correzioni. Lo stato dell’arte nella definizione del sistema di riferimento delle altezze, con richiami sul calcolo delle correzioni gravimetriche classiche e su una nuova formulazione sviluppata di recente nell’ambito della teoria di Molodensky costituiscono l’oggetto della presente comunicazione insieme ai risultati preliminari ottenuti sui dati del Trentino.Abstract The official italian height system is defined through a spirit leveling network periodically surveyed by the Istituto Geografico Militare (IGM). Dynamic, orthometric and normal heights of the network benchmarks are obtained form the least squares adjustment of the observed height differences, properly corrected for the gravity effects. In agreement with IGM, the Politecnico di Milano (POLIMI) is computing the corrections (dynamic, orthometric and normal) for the new spirit leveling observations, carried out in the meanwhile by the IGM to update the italian height datum. The gravity observations needed to evaluate the corrections are obtained from the same database used for the Italian Geoid. The Cadastral service of Provincia Autonoma di Trento in agreement with IGM and POLIMI is involved in the observation collection of the Trentino sub network as well as in the connected correction computation. The presentation is about the state of the art in the definition of the italian height datum and a short review on the gravity correction formulas as well as on a new formulation of the normal correction term in the framework of Molodensky’s theory. Preliminary results on the Trentino sub network will be presented as well

Influence of climatic variables on crown condition in pine forests of Northern Spain

Producción CientíficaThe aim of this study was to find relationships between crown condition and some climatic parameters to identify which are those having a main influence on crown condition, and how this influence is shown in the tree (crown transparency), and to contribute to the understanding of how these parameters will affect under future climate change scenarios

Cancer mortality in a cohort of asbestos textile workers

A cohort of 889 men and 1077 women employed for at least 1 month between 1946 and 1984 by a former Italian leading asbestos (mainly textile) company, characterised by extremely heavy exposures often for short durations, was followed up to 1996, for a total of 53 024 person-years of observation. Employment data were obtained from factory personnel records, while vital status and causes of death were ascertained through municipality registers and local health units. We observed 222 cancer deaths compared with 116.4 expected (standardized mortality ratio, SMR=191). The highest ratios were found for pleural (SMR=4105), peritoneal (SMR=1817) and lung (SMR=282) cancers. We observed direct relationships with duration of employment for lung and peritoneal cancer, and with time since first employment for lung cancer and mesothelioma. Pleural cancer risk was independent from duration (SMR=3428 for employment <1 year, 7659 for 1–4 years, 2979 for 5–9 years and 2130 for ⩾10 years). Corresponding SMRs for lung cancer were 139, 251, 233 and 531. Nonsignificantly increased ratios were found for ovarian (SMR=261), laryngeal (SMR=238) and oro-pharyngeal (SMR=226) cancers. This study confirms and further quantifies the central role of latency in pleural mesothelioma and of cumulative exposure in lung cancer