Magnetic WKB Constructions

This paper is devoted to the semiclassical magnetic Laplacian. Until now WKB expansions for the eigenfunctions were only established in presence of a non-zero electric potential. Here we tackle the pure magnetic case. Thanks to Feynman-Hellmann type formulas and coherent states decomposition, we develop here a magnetic Born-Oppenheimer theory. Exploiting the multiple scales of the problem, we are led to solve an effective eikonal equation in pure magnetic cases and to obtain WKB expansions. We also investigate explicit examples for which we can improve our general theorem: global WKB expansions, quasi-optimal estimates of Agmon and upper bound of the tunelling effect (in symmetric cases). We also apply our strategy to get more accurate descriptions of the eigenvalues and eigenfunctions in a wide range of situations analyzed in the last two decades

Ground Energy of the Magnetic Laplacian in Polyhedral Bodies

The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields and Neumann realization in polyhedral domains is characterized by a hierarchy of model problems. We investigate properties of the model problems (continuity, semi-continuity, existence of generalized eigenfunctions). We prove estimates for the remainders of our asymptotic formula. Lower bounds are obtained with the help of a classical IMS partition based on adequate coverings of the polyhedral domain, whereas upper bounds are established by a novel construction of quasimodes, qualified as sitting or sliding according to spectral properties of local model problems.Comment: 59 page

Holomorphic extension of the de Gennes function

This note is devoted to prove that the de Gennes function has a holomorphic extension on a strip containing the real axis

Grippes aviaires en Afrique. Cibler la vigilance

En 2006, la détection du virus de l'influenza (grippe) aviaire H5N1 en Afrique suscite une grande inquiétude : le virus pourrait se propager à l'ensemble du continent, puis être réintroduit en Europe par les oiseaux migrateurs. Des programmes de surveillance épidémiologique et de renforcement des dispositifs nationaux sont mis en place, appuyés par des organismes internationaux. En parallèle, des programmes de recherche sont lancés pour décrire et comprendre les processus de transmission de ce virus en Afrique, et évaluer les risques. Parmi eux, le projet Gripavi vise à caractériser la circulation des virus d'influenza aviaire et de la maladie de Newcastle à la fois dans l'avifaune sauvage et la volaille domestique. Il montre que le continent africain n'est pas exempt de risques et que la vigilance doit rester de mise. En précisant les modes de persistance du virus en Afrique et en identifiant des situations à risque, il met au jour des pistes pour cibler les stratégies de surveillance et de contrôle, et en améliorer ainsi l'efficacité

Magnetic Neumann Laplacian on a sharp cone

22 pagesThis paper is devoted to the spectral analysis of the Laplacian with constant magnetic field on a cone of aperture $\alpha$ and Neumann boundary condition. We analyze the influence of the orientation of the magnetic field. In particular, for any orientation of the magnetic field, we prove the existence of discrete spectrum below the essential spectrum in the limit $\alpha\to 0$ and establish a full asymptotic expansion for the $n$-th eigenvalue and the $n$-th eigenfunction

Breaking a magnetic zero locus: model operators and numerical approach

23 pagesThis paper is devoted to the spectral analysis of a Schrödinger operator in presence of a vanishing magnetic field. The influence of the smoothness of the magnetic zeros locus is studied. In particular, it is proved that breaking the magnetic zero locus induces discrete spectrum below the essential spectrum. Numerical simulations illustrate the theoretical results

Laryngo-tracheo-oesophageal clefts

A laryngo-tracheo-esophageal cleft (LC) is a congenital malformation characterized by an abnormal, posterior, sagittal communication between the larynx and the pharynx, possibly extending downward between the trachea and the esophagus. The estimated annual incidence of LC is 1/10,000 to 1/20,000 live births, accounting for 0.2% to 1.5% of congenital malformations of the larynx. These incidence rates may however be underestimated due to difficulty in diagnosing minor forms and a high mortality rate in severe forms. A slightly higher incidence has been reported in boys than in girls. No specific geographic distribution has been found. Depending on the severity of the malformation, patients may present with stridor, hoarse cry, swallowing difficulties, aspirations, cough, dyspnea and cyanosis through to early respiratory distress. Five types of laryngo-tracheo-esophageal cleft have been described based on the downward extension of the cleft, which typically correlates with the severity of symptoms: Type 0 laryngo-tracheo-esophageal cleft to Type 4 laryngo-tracheo-esophageal cleft. LC is often associated with other congenital abnormalities/anomalies (16% to 68%), mainly involving the gastro-intestinal tract, which include laryngomalacia, tracheo-bronchial dyskinesia, tracheo-bronchomalacia (mostly in types 3 and 4), and gastro-esophageal reflux disease (GERD). The syndromes most frequently associated with an LC are Opitz/BBB syndrome, Pallister Hall syndrome, VACTERL/VATER association, and CHARGE syndrome. Laryngeal clefts result from failure of fusion of the posterior cricoid lamina and abnormal development of the tracheo-esophageal septum. The causes of the embryological developmental anomalies leading to LC are not known but are thought to be multifactorial. LC appears to be mostly sporadic although some familial cases with suspected autosomal dominant transmission have been reported. The age of diagnosis depends mainly on the severity of the clinical symptoms and therefore on the extent of the LC. Diagnosis is made either based on clinical manifestations or on investigations, such as endoscopy, X-ray, CT scan, performed for other conditions. Differential diagnoses include tracheo-bronchial fistula, gastro-esophageal reflux disease and neurological swallowing disorders, as well as laryngomalacia and laryngeal palsy. Prenatal diagnosis of LC has never been reported, although associated anomalies may be detected on fetal ultrasonography. Once the cleft is diagnosed, it is essential to determine its length to orient the management and treatment approach. Management involves maintenance of satisfactory ventilation, prevention of secondary pulmonary complications as a result of repeated aspirations, and adequate feeding. Endotracheal intubation may be required for respiratory distress in severe cases. Treatment requires endoscopic or external surgery to close the cleft. Surgery should be performed as early as possible to avoid complications related to aspiration and gastric reflux, except in type 0 and type 1 cases in which conservative measures must first be attempted. The prognosis is variable depending on the severity of the LC and associated malformations. Early diagnosis and appropriate treatment and management help to reduce mortality and morbidity