Genericity of the Morse-Smale Property for Damped Wave Equations

We prove that for damped hyperbolic equations the Morse-Smale property (hyperbolicity of equilibria and transversal intersection of stable and unstable manifolds) is generic. More precisely, we prove that in an appropriate functional space of nonlinear terms in the equation, the set of functions for which the latter has the Morse-Smale property is residual, i.e., it is a countable intersection of open dense sets. The result extends a similar result proved in [1] for reaction diffusion equations. However, because of the absence of knowledge about nodal sets of polutions new ideas were needed in the proof.     

Lagrangian skeletons,periodic geodesic flows and symplectic cuttings

In this paper, we investigate symplectic manifolds endowed with a Morse–Bott function with only two critical submanifolds, one of which is Lagrangian while the other one is symplectic.     

Corner spontaneous magnetization

Details are given of a new method allowing an exact calculation of the spontaneous magnetization in the corner as well as along the edge at an arbitrary distance of the corner for a rectangular planar Ising ferromagnet.     

Rotational temperature and density measurements in a hypersonic flow by dual-line CARS

Rotational temperature and nitrogen number density are measured in the shock wave/boundary layer interaction region in the vicinity of a two-dimensional compression corner disposed in a low pressure, 55 K, Mach 10 hypersonic air flow. Spatially-resolved data are recorded using a nonlinear optical technique named dual-line coherent anti-Stokes Raman scattering (DLCARS). Averaged temperature and density profiles are compared with those predicted by a Navier-Stokes solver. Good agreement is found.     

High-order harmonic generation with a strong laser field and an attosecond-pulse train: The Dirac-Delta comb and monochromatic limits

In recent publications, it has been shown that high-order harmonic generation can be manipulated by employing a time delayed attosecond-pulse train superposed to a strong, near-infrared laser field. It is an open question, however, which is the most adequate way to approximate the attosecond-pulse train in a semianalytic framework. Employing the strong-field approximation and saddle-point methods, we make a detailed assessment of the spectra obtained by modeling the attosecond-pulse train by either a monochromatic wave or a Dirac-Delta comb. These are the two extreme limits of a real train, which is composed by a finite set of harmonics. Specifically, in the monochromatic limit, we find the downhill and uphill sets of orbits reported in the literature, and analyze their influence on the high-harmonic spectra. We show that, in principle, the downhill trajectories lead to stronger harmonics, and pronounced enhancements in the low plateau region. These features are analyzed in terms of quantum interference effects between pairs of quantum orbits, and compared to those obtained in the Dirac-Delta limit.     

On almost-sure versions of classical limit theorems for dynamical systems

The purpose of this article is to support the idea that “whenever we can prove a limit theorem in the classical sense for a dynamical system, we can prove a suitable almost-sure version based on an empirical measure with log-average”. We follow three different approaches: martingale methods, spectral methods and induction arguments. Our results apply, among others, to Axiom A maps or flows, to systems inducing a Gibbs–Markov map, and to the stadium billiard.     

On the distribution of the number of customers in the symmetric M/G/1 queue

We consider an M/G/1 queue with symmetric service discipline. The class of symmetric service disciplines contains, in particular, the preemptive last-come-first-served discipline and the processor-sharing discipline. It has been conjectured in Kella et al. [1] that the marginal distribution of the queue length at any time is identical for all symmetric disciplines if the queue starts empty. In this paper we show that this conjecture is true if service requirements have an Erlang distribution. We also show by a counterexample, involving the hyperexponential distribution, that the conjecture is generally not true. AMS Subject Classifications Primary—60K25; Secondary—90B22     

A two-fraction model for the calculation of the resonance spectra of the complex permittivity of ice in the far infrared

A two-fraction model that makes it possible to calculate analytically the complex dielectric permittivity of ice in the far infrared and submillimeter wavelength ranges is proposed. The librational and vibrational fractions are considered. The first fraction, consisting of rigid dipoles executing anharmonic reorientations in defects of the structure, gives rise to the librational band of ice at 800 cm^?1. The second fraction consists of elastically vibrating oppositely charged H-bonded molecules. This fraction describes two bands of ice in the range 100–300 cm^?1, and the nonresonant background of dielectric losses in the submillimeter wavelength range. The dielectric permittivity spectra of ice calculated for the temperature of ?7°C are consistent with the experimental spectra. The spectra of ice at the temperature ?30°C are predicted.