Gap soliton formation by nonlinear supratransmission in Bragg media

A Bragg medium in the nonlinear Kerr regime, submitted to incident cw-radiation at a frequency in a band gap, switches from total reflection to transmission when the incident energy overcomes some threshold. We demonstrate that this is a result of nonlinear supratransmission, which allows to prove that i) the threshold incident amplitude is simply expressed in terms of the deviation from the Bragg resonance, ii) the process is not the result of a shift of the gap in the nonlinear dispersion relation, iii) the transmission does occur by means of gap soliton trains, as experimentally observed [D. Taverner et al., Opt Lett 23 (1998) 328], iv) the required energy tends to zero close to the band edge.Comment: 5 figures, submitted to EuroPhysics Letter

First Order Logic and Twin-Width in Tournaments

We characterise the classes of tournaments with tractable first-order model checking. For every hereditary class of tournaments T, first-order model checking either is fixed parameter tractable, or is AW[*]-hard. This dichotomy coincides with the fact that T has either bounded or unbounded twin-width, and that the growth of T is either at most exponential or at least factorial. From the model-theoretic point of view, we show that NIP classes of tournaments coincide with bounded twin-width. Twin-width is also characterised by three infinite families of obstructions: T has bounded twin-width if and only if it excludes at least one tournament from each family. This generalises results of Bonnet et al. on ordered graphs. The key for these results is a polynomial time algorithm which takes as input a tournament T and computes a linear order < on V(T) such that the twin-width of the birelation (T, <) is at most some function of the twin-width of T. Since approximating twin-width can be done in FPT time for an ordered structure (T, <), this provides a FPT approximation of twin-width for tournaments

Variational solution of the Gross-Neveu model at finite temperature in the large N limit

We use a nonperturbative variational method to investigate the phase transition of the Gross-Neveu model. It is shown that the variational procedure can be generalized to the finite temperature case. The large N result for the phase transition is correctly reproduced.Comment: 12 p., 1 fig, this is the version which will appear in the Phys Lett B, it differs from the previous one in what concerns the introduction and conclusions (re written), several references have been adde

Nonlinear supratransmission in multicomponent systems

A method is proposed to solve the challenging problem of determining the supratransmission threshold (onset of instability of harmonic boundary driving inside a band gap) in multicomponent nonintegrable nonlinear systems. It is successfully applied to the degenerate three-wave resonant interaction in a birefringent quadratic medium where the process generates spatial gap solitons. No analytic expression is known for this model showing the broad applicability of the method to nonlinear systems.Comment: 4 pages, 3 figure

Quantification du taux d'invalidité d'applications temps réel à contraintes strictes

International audienceThis work is about an operational conception toolkit for real time applications. Temporal validation is usually based on tools with binary validation results. In this paper, we show how to build some quality indicators able to quantify invalidity numerically. First, we present an automata-based model and then its geometrical adaptation, which permits to compute a measure of invalidit

Validation temporelle de systèmes de tâches temps-réel strictes à durée variables à l'aide de langages rationnels

16 pagesInternational audiencewe show that real-time systems composed of both periodic and sporadic interdependents tasks wich CPU time is not fixed can be validated from a methodology based on rational languages. This property leads to the cyclicity of the scheduling sequences for such systems

Validation Temporelle d'Applications Temps Réel Distribuées à Contraintes Strictes

National audienceThis paper deals with temporal validation of distributed hard real time systems. We consider here the target machine physical properties. Indeed, several temporal characteristics of some tasks depend on hardware properties, and then influence the model. We suppose that there is no task migration, and we did not study the tasks allocation problem. We valid this method to the protocol CA

Quantification du taux d'invalidité d'applications temps réel : une approche géométrique

International audienceCe travail s'intègre dans un projet de conception d'outils d'aide à la spécification d'applications temps-réel à contraintes strictes : il s'agir, lorsqu'une application est invalide, d'identifier les causes de l'invalidité. Nous nous basons sur un modèle géométrique pour les applications temps-réel. Une mesure est définie à partir de ce modèle sur la base d'une distance géométrique. Les systèmes que nous traitons utilisent des ressources critiques et fonctionnent sur des architectures multiprocesseurs. Les tâches sont périodiques, non réentrantes, à départ différés

Big Step Normalisation for Type Theory

Big step normalisation is a normalisation method for typed lambda-calculi which relies on a purely syntactic recursive evaluator. Termination of that evaluator is proven using a predicate called strong computability, similar to the techniques used to prove strong normalisation of ?-reduction for typed lambda-calculi. We generalise big step normalisation to a minimalist dependent type theory. Compared to previous presentations of big step normalisation for e.g. the simply-typed lambda-calculus, we use a quotiented syntax of type theory, which crucially reduces the syntactic complexity introduced by dependent types. Most of the proof has been formalised using Agda