Collective resonant modes of a meta-surface

A periodic layer of resonant scatterers is considered in the dipolar approximation. An asymptotic expression for the field diffracted is given in terms of an impedance operator. It is shown that surface Bloch modes appear as a collective effect due to the resonances of the scatterers.Comment: 9 pages, 7 figures, extended paper from SPIE Optics+Photonics, Nanostructured Thin Films VI;submitted to Journal of Nanophotonic

A mesoscopic description of radiative heat transfer at the nanoscale

We present a formulation of the nanoscale radiative heat transfer (RHT) using concepts of mesoscopic physics. We introduce the analog of the Sharvin conductance using the quantum of thermal conductance. The formalism provides a convenient framework to analyse the physics of RHT at the nanoscale. Finally, we propose a RHT experiment in the regime of quantized conductance

Geometric control condition for the wave equation with a time-dependent observation domain

We characterize the observability property (and, by duality, the controllability and the stabilization) of the wave equation on a Riemannian manifold $\Omega,$ with or without boundary, where the observation (or control) domain is time-varying. We provide a condition ensuring observability, in terms of propagating bicharacteristics. This condition extends the well-known geometric control condition established for fixed observation domains. As one of the consequences, we prove that it is always possible to find a time-dependent observation domain of arbitrarily small measure for which the observability property holds. From a practical point of view, this means that it is possible to reconstruct the solutions of the wave equation with only few sensors (in the Lebesgue measure sense), at the price of moving the sensors in the domain in an adequate way.We provide several illustrating examples, in which the observationdomain is the rigid displacement in $\Omega$ of a fixed domain, withspeed $v,$ showing that the observability property depends both on $v$and on the wave speed. Despite the apparent simplicity of some of ourexamples, the observability property can depend on nontrivial arithmeticconsiderations

Improving Optimization Bounds using Machine Learning: Decision Diagrams meet Deep Reinforcement Learning

Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower bounds that can be significantly better than classical bounding mechanisms, such as linear relaxations. It is well known that the quality of the bounds achieved through this flexible bounding method is highly reliant on the ordering of variables chosen for building the diagram, and finding an ordering that optimizes standard metrics is an NP-hard problem. In this paper, we propose an innovative and generic approach based on deep reinforcement learning for obtaining an ordering for tightening the bounds obtained with relaxed and restricted DDs. We apply the approach to both the Maximum Independent Set Problem and the Maximum Cut Problem. Experimental results on synthetic instances show that the deep reinforcement learning approach, by achieving tighter objective function bounds, generally outperforms ordering methods commonly used in the literature when the distribution of instances is known. To the best knowledge of the authors, this is the first paper to apply machine learning to directly improve relaxation bounds obtained by general-purpose bounding mechanisms for combinatorial optimization problems.Comment: Accepted and presented at AAAI'1

Paralic confinement: models and simulations

International audienceThis paper deals with the concept of confinement of paralic ecosystems. It is based on a recent paper that presents a modelling procedure in order to compute the confinement field of a lagoon. Here, we improve the existing model in order to account for tide oscillations in any kind of geometry such as a non-rectangular lagoons with a non-flat bottom. The new model, that relies on PDEs rather than ODEs, is then implemented thanks to the finite element method. Numerical results confirm the feasibility of confinement studies thanks to the introduced model.Cet article traite de la modélisation du confinement dans des écosystèmes paraliques. Il se base sur un travail récent dans lequel on trouve un modélisation qui permette de simuler le confinement dans des géométries simples. Ici, on améliore le modèle existant afin de permettre la prise en compte de la marée dans un lagon dont la géométrie est quelconque, avec un fond non nécessairement plat. Notre nouveau modèle, qui repose sur des équations aux dérivées partielles, est alors implémenté numériquement grâce à la méthode des éléments finis. Les résultats numériques confirment la faisabilité d'une étude du confinement grâce au modèle proposé

Rigorous Asymptotic Study of the Screened Electrostatic Potential in a Thin Dielectric Slab

The screened Coulomb potential plays a crucial role in the binding energies of excitons in a thin dielectric slab. The asymptotic behavior of this potential is studied when the thickness of the slab is very small as compared to the exciton Bohr radius. A regularized expression is given and the exact effective 2D potential is derived. These expressions may be useful for the computation of the exciton binding energy in 2D or quasi‐2D materials