Nicolas Raymond

Plane waveguides with corners in the small angle limit

The plane waveguides with corners considered here are infinite V-shaped strips with constant thickness. They are parametrized by their sole opening angle. We study the eigenpairs of the Dirichlet Laplacian in such domains when this angle tends to 0. We provide multi-scale asymptotics for eigenpairs associated with the lowest eigenvalues. For this, we investigate the eigenpairs of a one-dimensional model which can be viewed as their Born-Oppenheimer approximation. We also investigate the Dirichlet Laplacian on triangles with sharp angles. The eigenvalue asymptotics involve powers of the cube root of the angle, while the eigenvector asymptotics include simultaneously two scales in the triangular part, and one scale in the straight part of the guides.

Right ventricular failure secondary to chronic overload in congenital heart disease: An experimental model for therapeutic innovation

OBJECTIVE Mortality and morbidity related to right ventricular failure remain a problem for the long-term outcome of congenital heart diseases. Therapeutic innovation requires establishing an animal model reproducing right ventricular dysfunction secondary to chronic pressure-volume overload. METHODS Right ventricular tract enlargement by transvalvular patch and pulmonary artery banding were created in 2-month-old piglets (n = 6) to mimic repaired tetralogy of Fallot. Age-matched piglets were used as controls (n = 5). Right ventricular function was evaluated at baseline and 3 and 4 months of follow-up by hemodynamic parameters and electrocardiography. Right ventricular tissue remodeling was characterized using cellular electrophysiologic and histologic analyses. RESULTS Four months after surgery, right ventricular peak pressure increased to 75% of systemic pressure and pulmonary regurgitation significantly progressed, end-systolic and end-diastolic volumes significantly increased, and efficient ejection fraction significantly decreased compared with controls. At 3 months, the slope of the end-systolic pressure-volume relationship was significantly elevated compared with baseline and controls; a significant rightward shift of the slope, returning to the baseline value, was observed at 4 months, whereas stroke work progressed at each step and was significantly higher than in controls. Four months after surgery, QRS duration was significantly prolonged as action potential duration. Significant fibrosis and myocyte hypertrophy without myolysis and inflammation were observed in the operated group at 4 months. CONCLUSION Various aspects of early right ventricular remodeling were analyzed in this model. This model reproduced evolving right ventricular alterations secondary to chronic volumetric and barometric overload, as observed in repaired tetralogy of Fallot with usual sequelae, and can be used for therapeutic innovation.

Spectral asymptotics of a broken δ-interaction

This paper is concerned with the spectral analysis of a Hamiltonian with a

Semiclassical analysis with vanishing magnetic fields

\delta

Magnetic Effects in Curved Quantum Waveguides

-interaction supported along a broken line with angle

When the 3D Magnetic Laplacian Meets a Curved Edge in the Semiclassical Limit

\theta

Tunneling for the Robin Laplacian in smooth planar domains

. The bound states with energy slightly below the threshold of the essential spectrum are estimated in the semiclassical regime

Breaking a magnetic zero locus: Asymptotic analysis

\theta\to 0

Semiclassical 3D Neumann Laplacian with variable magnetic field: a toy model

.

Spectral asymptotics of the Dirichlet Laplacian in a conical layer

We analyze the 2D magnetic Laplacian in the semiclassical limit in the case when the magnetic field vanishes along a smooth curve. In particular, we prove local and micro-local estimates for the eigenfunctions and a complete asymptotic expansion of the eigenpairs.