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Bernhard Riemann, the ear, and an atom of consciousness
(2021)SAM Research ReportWhy did Bernhard Riemann (1826–1866), arguably the most original mathematician of his generation, spend the last year of life investigating the mechanism of hearing? Fighting tuberculosis and the hostility of eminent scientists such as Hermann Helmholtz, he appeared to forsake mathematics to prosecute a case close to his heart. Only sketchy pages from his last paper remain, but here we assemble some significant clues and triangulate from ...Report -
Homogenization of sound-absorbing and high-contrast acoustic metamaterials in subcritical regimes
(2021)SAM Research ReportReport -
Modal decompositions and point scatterer approximations near the Minnaert resonance frequencies
(2021)SAM Research ReportAs a continuation of the previous works [13, 4, 15], this paper provides several contributions to the mathematical analysis of subwavelength resonances in a high-contrast medium containing N acoustic obstacles. Our approach is based on an exact decomposition formula which reduces the solution of the sound scattering problem to that of a N dimensional linear system, and characterizes resonant frequencies as the solutions to a N-dimensional ...Report -
On the validity of the tight-binding method for describing systems of subwavelength resonators
(2021)SAM Research ReportThe goal of this paper is to relate the capacitance matrix formalism to the tight-binding approximation. By doing so, we open the way to the use of mathematical techniques and tools from condensed matter theory in the mathematical and numerical analysis of metamaterials, in particular for the understanding of their topological properties. We firstly study how the capacitance matrix formalism, both when the material parameters are static ...Report -
Dynamic Spike Super-resolution and Applications to Ultrafast Ultrasound Imaging
(2018)SAM Research ReportWe consider the dynamical super-resolution problem consisting in the recovery of positions and velocities of moving particles from low-frequency static measurements taken over multiple time steps. The standard approach to this issue is a two-step process: first, at each time step some static reconstruction method is applied to locate the positions of the particles with super-resolution and, second, some tracking technique is applied to ...Report -
Close-to-touching acoustic subwavelength resonators: eigenfrequency separation and gradient blow-up
(2020)SAM Research ReportIn this paper, we study the behaviour of the coupled subwavelength resonant modes when two high-contrast acoustic resonators are brought close together. We consider the case of spherical resonators and use bispherical coordinates to derive explicit representations for the capacitance coefficients which, we show, capture the system's resonant behaviour at leading order. We prove that the pair of resonators has two subwavelength resonant ...Report -
Honeycomb-lattice Minnaert bubbles
(2018)SAM Research ReportThe aim of this paper is to rigorously show the existence of a Dirac dispersion cone in a bubbly honeycomb phononic crystal comprised of bubbles of arbitrary shape. The main result is an asymptotic formula for the quasi-periodic Minnaert resonance frequencies close to the symmetry points K in the Brilloun zone. This shows the linear dispersion relation of a Dirac cone. Our findings in this paper are illustrated in the case of circular ...Report -
The equivalent media generated by bubbles of high contrasts: Volumetric metamaterials and metasurfaces
(2018)SAM Research ReportThe aim of this paper is to derive equivalent fields when a cluster of bubbles is appropriately distributed (but not necessarily periodically) in a bounded domain.Report -
Linearized Reconstruction for Diffuse Optical Spectroscopic Imaging
(2018)SAM Research ReportIn this paper, we present a novel reconstruction method for diffuse optical spectroscopic imaging with a commonly used tissue model of optical absorption and scattering. It is based on linearization and group sparsity, which allows recovering the diffusion coefficient and absorption coefficient simultaneously, provided that their spectral profiles are incoherent and a sufficient number of wavelengths are judiciously taken for the measurements. ...Report -
Mathematical framework for multi-frequency identification of thin insulating and small conductive inhomogeneities
(2015)SAM Research ReportWe are aiming to identify the thin insulating inhomogeneities and small conductive inhomogeneities inside an electrically conducting medium by using multi-frequency electrical impedance tomography (mfEIT). The thin insulating inhomogeneities are considered in the form of tubular neighborhood of a curve and small conductive inhomogeneities are regarded as circular disks. Taking advantage of the frequency dependent behavior of insulating ...Report