Ménard, Corentin Robert, Sebastien Lesselier, Dominique

The quality of ultrasound images of welds is highly penalized by the dendritic structure of the material that forms during cooling. The image of a flaw is all the more degraded as a reliable description of such a medium is most of the time not possible, due to the poor knowledge on the weld at time of inspection. In a previous work, we demonstrated...

Duchêne, Vincent

This memoir proposes an introduction to the asymptotic mathematical modeling of surface and interfacial gravity water waves. It aims at providing a unified approach to the derivation and rigorous justification of many standard and less-standard models.

Mouzard, Antoine

We define the Anderson Hamiltonian H on a two-dimensional manifold using high order paracontrolled calculus. It is a self-adjoint operator with pure point spectrum. We get lower and upper bounds on its eigenvalues which imply an almost sure Weyl-type law for H.

Morin, Léo Mouzard, Antoine

We define the random magnetic Laplacien with spatial white noise as magnetic field on the two-dimensional torus using paracontrolled calculus. It yields a random self-adjoint operator with pure point spectrum and domain a random subspace of nonsmooth functions in L 2. We give sharp bounds on the eigenvalues which imply an almost sure Weyl-type law....

Eynard, Bertrand Garcia-Failde, Elba Marchal, Olivier Orantin, Nicolas

We prove that the topological recursion formalism can be used to quantize any generic classical spectral curve with smooth ramification points and simply ramified away from poles. For this purpose, we build both the associated quantum curve, i.e. the differential operator quantizing the algebraic equation defining the classical spectral curve consi...

Carles, Rémi Ferriere, Guillaume

We analyze dynamical properties of the logarithmic Schrödinger equation under a quadratic potential. The sign of the nonlinearity is such that it is known that in the absence of external potential, every solution is dispersive, with a universal asymptotic profile. The introduction of a harmonic potential generates solitary waves, corresponding to g...

Morin, Léo

We consider the semiclassical magnetic Laplacian L_h on a Riemannian manifold, with a constant-rank and non-vanishing magnetic field B. Under the localization assumption that B admits a unique and non-degenerate well, we construct three successive Birkhoff normal forms to describe the spectrum of L_h in the semiclassical limit h → 0. We deduce an e...

Csirik, Mihaly Andras Laestadius, Andre

We propose a comprehensive mathematical framework for Coupled-Cluster-type methods. These aim at accurately solving the many-body Schrödinger equation. The present work has two main aspects. First, we rigorously describe the discretization scheme involved in Coupled-Cluster methods using graph-based concepts. This allows us to discuss different met...

Zakharov, Alexey Crosby, Matthew Fountas, Zafeirios

In model-based learning, an agent's model is commonly defined over transitions between consecutive states of an environment even though planning often requires reasoning over multi-step timescales, with intermediate states either unnecessary, or worse, accumulating prediction error. In contrast, intelligent behaviour in biological organisms is char...

Rollon de Pinedo, Alvaro Couplet, Mathieu Marie, Nathalie Marrel, Amandine MERLE, Elsa Sueur, Roman

This paper deals with the problem of finding outliers, i.e. data that differ distinctly from other elements of the considered dataset, when they belong to functional infinite-dimensional vector spaces. Functional data are widely present in the industry and may originate from physical measurements or numerical simulations. The automatic identificati...