David Gontier
École Normale Supérieure
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Publication
Featured researches published by David Gontier.
Applied and Computational Harmonic Analysis | 2014
David Gontier; Martin Vetterli
Sampling information using timing is an approach that has received renewed attention in sampling theory. The question is how to map amplitude information into the timing domain. One such encoder, called time encoding machine, was introduced by Lazar and Toth (2004 [23]) for the special case of band-limited functions. In this paper, we extend their result to a general framework including shift-invariant subspaces. We prove that time encoding machines may be considered as non-uniform sampling devices, where time locations are unknown a priori. Using this fact, we show that perfect representation and reconstruction of a signal with a time encoding machine is possible whenever this device satisfies some density property. We prove that this method is robust under timing quantization, and therefore can lead to the design of simple and energy efficient sampling devices
Siam Journal on Applied Mathematics | 2017
Habib Ammari; Brian Fitzpatrick; David Gontier; Hyundae Lee; Hai Zhang
The aim of this paper is to provide a mathematical and numerical framework for the analysis and design of bubble meta-screens. An acoustic meta-screen is a thin sheet with patterned subwavelength structures, which nevertheless has a macroscopic effect on acoustic wave propagation. In this paper, periodic subwavelength bubbles mounted on a reflective surface (with Dirichlet boundary condition) are considered. It is shown that the structure behaves as an equivalent surface with Neumann boundary condition at the Minnaert resonant frequency which corresponds to a wavelength much greater than the size of the bubbles. An analytical formula for this resonance is derived. Numerical simulations confirm its accuracy and show how it depends on the ratio between the periodicity of the lattice, the size of the bubble, and the distance from the reflective surface. The results of this paper formally explain the superabsorption behavior observed in [V. Leroy et al., Phys. Rev. B, 19 (2015), 02031].
international conference on robotics and automation | 2012
Péter L. Várkonyi; David Gontier; Joel W. Burdick
We investigate the local motion of a planar rigid body with unilateral constraints in the neighborhood of a two-contact frictional equilibrium configuration on a slope. A new sufficient condition of Lyapunov stability is developed in the presence of arbitrary external forces. Additionally, we construct an example, which is stable against perturbations by infinitesimal forces, but does not possess Lyapunov stability against infinitesimal displacements or impulses. The great difference between previous stability criteria and ours leads to further questions about the nature of the exact stability condition.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science | 2017
Habib Ammari; Brian Fitzpatrick; David Gontier; Hyundae Lee; Hai Zhang
The purpose of this paper is to investigate acoustic wave scattering by a large number of bubbles in a liquid at frequencies near the Minnaert resonance frequency. This bubbly media has been exploited in practice to obtain super-focusing of acoustic waves. Using layer potential techniques, we derive the scattering function for a single spherical bubble excited by an incident wave in the low frequency regime. We then propose a point scatterer approximation for N bubbles, and describe several numerical simulations based on this approximation, that demonstrate the possibility of achieving super-focusing using bubbly media.
Physical Review Letters | 2013
David Gontier
The N-representability problem for noncollinear spin-polarized densities was left open in the pioneering work of von Barth and Hedin [J. Phys. C 5, 1629 (1972)] setting up the Kohn-Sham density-functional theory for magnetic compounds. In this Letter, we demonstrate that, contrarily to the nonpolarized case, the sets of pure and mixed state N-representable densities are different in general. We provide a simple characterization of the latter by means of easily checkable necessary and sufficient conditions on the components ρ(αβ)(r) of the spin-polarized density.
Nonlinearity | 2015
David Gontier
The purpose of this article is to extend the work by Anantharaman and Cances (2009 Ann. Inst. Henri Poincare (C) 26 2425–55) and prove the existence of minimizers for the spin-polarized Kohn–Sham model in the presence of a magnetic field within the local spin density approximation. We show that for any magnetic field that vanishes at infinity, the existence of minimizers is ensured for neutral or positively charged systems. The proof relies on classical concentration-compactness techniques.
Reviews in Mathematical Physics | 2016
Eric Cancès; David Gontier; Gabriel Stoltz
This paper analyses the GW method for finite electronic systems. In a first step, we provide a mathematical framework for the usual one-body operators that appear naturally in many-body perturbation theory. We then discuss the GW equations which construct an approximation of the one-body Greens function, and give a rigorous mathematical formulation of these equations. Finally, we study the well-posedness of the GW0 equations, proving the existence of a unique solution to these equations in a perturbative regime.
Applied Mathematics Research Express | 2016
David Gontier; Salma Lahbabi
In this article, we study the speed of convergence of the supercell reduced Hartree-Fock~(rHF) model towards the whole space rHF model in the case where the crystal contains a local defect. We prove that, when the defect is charged, the defect energy in a supercell model converges to the full rHF defect energy with speed
international conference on intelligent engineering systems | 2011
Péter L. Várkonyi; David Gontier; Joel W. Burdick
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Annales de l'Institut Henri Poincaré C, Analyse non linéaire | 2018
Habib Ammari; Brian Fitzpatrick; David Gontier; Hyundae Lee; Hai Zhang
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