Smoothed Affine Wigner Transform

We study a generalization of Husimi function in the context of wavelets. This leads to a nonnegative density on phase-space for which we compute the evolution equation corresponding to a Schr\"Aodinger equation

Strong and weak semiclassical limits for some rough Hamiltonians

We present several results concerning the semiclassical limit of the time dependent Schr\"odinger equation with potentials whose regularity doesn't guarantee the uniqueness of the underlying classical flow. Different topologies for the limit are considered and the situation where two bicharateristics can be obtained out of the same initial point is emphasized

Numerical simulations of X-rays Free Electron Lasers (XFEL)

We study a nonlinear Schr\"odinger equation which arises as an effective single particle model in X-ray Free Electron Lasers (XFEL). This equation appears as a first-principles model for the beam-matter interactions that would take place in an XFEL molecular imaging experiment in \cite{frat1}. Since XFEL is more powerful by several orders of magnitude than more conventional lasers, the systematic investigation of many of the standard assumptions and approximations has attracted increased attention. In this model the electrons move under a rapidly oscillating electromagnetic field, and the convergence of the problem to an effective time-averaged one is examined. We use an operator splitting pseudo-spectral method to investigate numerically the behaviour of the model versus its time-averaged version in complex situations, namely the energy subcritical/mass supercritical case, and in the presence of a periodic lattice. We find the time averaged model to be an effective approximation, even close to blowup, for fast enough oscillations of the external field. This work extends previous analytical results for simpler cases \cite{xfel1}.Comment: 14 page

THERAPEUTIC MUD OCCURRENCES IN GREECE: MINERALOGICAL AND GEOCHEMICAL COMPOSITION OF THE SAGIADA MUD (THESPROTIA PREFECTURE)

Η παρούσα εργασία αποτελεί μία πρώτη προσπάθεια χαρακτηρισμού των ορυκτολογικών και γεωχημικών χαρακτηριστικών του πηλού της Σαγιάδας (Νομός Θεσπρωτίας), όπου εντοπίζεται μία από τις πιο αντιπροσωπευτικές εμφανίσεις ιαματικού πηλού στην Ελλάδα. Η μελέτη αυτή αποτελεί τμήμα ενός ευρύτερου ερευνητικού προγράμματος που υλοποιείται από το Ι.Γ.Μ.Ε. για το χαρακτηρισμό των ελληνικών ιαματικών πηλών. Όπως προέκυψε από τα αποτελέσματα της περιθλασιμετρίας ακτίνων–X (XRD), διαφορικής θερμικής ανάλυσης (DTA), οπτικής μικροσκοπίας και ηλεκτρονικής μικροσκοπίας σάρωσης (SEM), ο πηλός της Σαγιάδας συνίσταται από χαλαζία, αστρίους, αργιλικά ορυκτά, όπως ιλλίτης, καολινίτης, χλωρίτης και βερμικουλίτης, και ασβεστίτη, καθώς και από δευτερεύοντα ορυκτά, όπως αλίτης και σιδηροπυρίτης. Επίσης εντοπίστηκαν ίχνη από μοσχοβίτη και γύψο. Οι χημικές αναλύσεις πραγματοποιήθηκαν με τη χρήση φασματομετρίας ακτίνων–X (XRF) και φασματομετρίας μάζας επαγωγικά συζευγμένου πλάσματος (ICP-MS), για τον προσδιορισμό των συγκεντρώσεων των πηλών σε κύρια στοιχεία και ιχνοστοιχεία, αντίστοιχα. Σε σύγκριση με πηλοειδή από την Ισπανία και το εύρος τιμών των πλημμυρικών ιζημάτων από την Ευρώπη, ο φυσικός πηλός της Σαγιάδας παρουσιάζει ανάλογη σύσταση.The current study presents the preliminary results of the mineralogical and geochemical characterization of the Sagiada mud (Prefecture of Thesprotia), which is considered as one of the most representative therapeutic mud occurrences in Greece. This work is part of a bigger project, conducted by IGME (Athens, Greece), for the characterization of the Greek therapeutic mud deposits. The mineralogical composition was determined using X-Ray Diffraction (XRD), Differential Thermal Analysis (DTA), optical microscopy and Scanning Electron Microscopy (SEM). The main mineral phases of the Sagiada mud are quartz, feldspars, clay minerals such as illite, kaolinite, chlorite and vermiculite, and calcite accompanied by minor phases such as halite and pyrite. Traces of muscovite and gypsum were also identified. Geochemical analyses were performed using X-Ray Fluorescence (XRF) and Inductively Coupled Plasma-Mass Spectrometry (ICP-MS) for the determination of major and trace element content, respectively. Compared to Spanish peloids and European floodplain sediments, the Sagiada mud reveals an analogue chemical composition

Propagation of acoustic-gravity waves in inhomogeneous ocean environment based on modal expansions and HP-FEM

A coupled mode model is presented for the propagation of acoustic-gravity waves in layered ocean waveguides. The analysis extends previous work for acoustic waves in inhomogeneous environment. The coupled mode system is derived by means of a variational principle in conjunction with local mode series expansion, obtained by utilizing eigenfunction systems defined in the vertical section. These are obtained through the solution of vertical eigenvalue problems formulated along the waveguide. A crucial factor is the inclusion of additional modes accounting for the effects of spatialy varying boundaries and interfaces. This enhancement provides an implicit summation for the slowly convergent part of the localmode series, rendering the series rapidly convergent, increasing substantialy the efficiency of the method. Particular aspects of the method include high order Lagrange Finite Element Methods for the solution of local vertical eigenvalue problems in the case of multilayered waveguides, and Gauss-type quadrature for the computation of the coupled-mode system coefficients. The above aspects make the present method quite efficient for long range propagation in extended waveguides, such as the ones found in geophysical applications, e.g. ocean basins, as only few modes are needed for the accurate representation of the wave field