Search
Results
-
Subwavelength resonances in 1D high-contrast acoustic media
(2022)SAM Research ReportWe propose a mathematical theory of acoustic wave scattering in one-dimensional finite high-contrast media. The system considered is constituted of a finite alternance of high-contrast segments of arbitrary lengths and interdistances, called the ``resonators'', and a background medium. We prove the existence of subwavelength resonances, which are the counterparts of the well-known Minnaert resonances in 3D systems. Our main contribution ...Report -
Transmission properties of space-time modulated metamaterials
(2022)SAM Research ReportWe prove the possibility of achieving exponentially growing wave propagation in space-time modulated media and give an asymptotic analysis of the quasifrequencies in terms of the amplitude of the time modulation at the degenerate points of the folded band structure. Our analysis provides the first proof of existence of k-gaps in the band structures of space-time modulated systems of subwavelength resonators.Report -
Topological phenomena in honeycomb Floquet metamaterials
(2022)SAM Research ReportBeing driven by the goal of finding edge modes and of explaining the occurrence of edge modes in the case of time-modulated metamaterials in the high-contrast and subwavelength regime, we analyse the topological properties of Floquet normal forms of periodically parameterized time-periodic linear ordinary differential equations. In fact, our main goal being the question whether an analogous principle as the bulk-boundary correspondence ...Report -
Topological classification of Floquet metamaterials based on Floquet theory
(2022)SAM Research ReportBeing driven by the goal of finding edge modes and of explaining the occurrence of edge modes in the case of time-modulated metamaterials in the high-contrast and subwavelength regime, we analyse the topological properties of Floquet-Lyapunov decompositions of periodically parameterized time-periodic ordinary differential equations. In fact, our main goal being the question whether an analogous principle as the bulk-boundary correspondence ...Report -
Mathematical foundation of sparsity-based multi-illumination super-resolution
(2022)SAM Research ReportIt is well-known that the resolution of traditional optical imaging system is limited by the so-called Rayleigh resolution or diffraction limit, which is of several hundreds of nanometers. By employing fluorescence techniques, modern microscopic methods can resolve point scatterers separated by a distance much lower than the Rayleigh resolution limit. Localization-based fluorescence subwavelength imaging techniques such as PALM and STORM ...Report -
Dynamic super-resolution in particle tracking problems
(2022)SAM Research ReportParticle tracking in a live cell environment is concerned with reconstructing the trajectories, locations, or velocities of the targeting particles, which holds the promise of revealing important new biological insights. The standard approach of particle tracking consists of two steps: first reconstructing statically the source locations in each time step, and second applying tracking techniques to obtain the trajectories and velocities. ...Report -
Nearly optimal resolution estimate for the two-dimensional super-resolution and a new algorithm for direction of arrival estimation with uniform rectangular array
(2022)SAM Research ReportIn this paper, we develop a new technique to obtain nearly optimal estimates of the computational resolution limits for two-dimensional super-resolution problems. Our main contributions are fivefold: (i) Our work improves the resolution estimates for number detection and location recovery in two-dimensional super-resolution problems to nearly optimal; (ii) As a consequence, we derive a stability result for a sparsity-promoting algorithm ...Report -
Unidirectional edge modes in time-modulated metamaterials
(2022)SAM Research ReportWe prove the possibility of achieving unidirectional edge modes in time-modulated supercell structures. Such finite structures consist of two trimers repeated periodically. Because of their symmetry, they admit degenerate edge eigenspaces. When the trimers are time-modulated with two opposite orientations, the degenerate eigenspace splits into two one-dimensional eigenspaces described by an analytical formula, each corresponds to a mode ...Report -
Anderson localization in the subwavelength regime
(2022)SAM Research ReportRandom media are ubiquitous in both natural and artificial structures and there are many important problems related to understanding their wave-scattering properties. In particular, the phenomenon of wave localization in random media, known as Anderson localization in certain settings, has proved difficult to understand, particularly in physically derived models and systems with long-range interactions. In this article, we show that the ...Report -
Subwavelength resonant acoustic scattering in fast time-modulated media
(2022)SAM Research ReportThis article provides a rigorous mathematical analysis of acoustic wave scattering induced by a high-contrast subwavelength resonator whose material density is periodically modulated in time, and with a modulation frequency that is much larger than the one of the incident wave. We find that in general, the effect of the fast modulation is averaged over time and that the system behaves as an unmodulated resonator with an apparent effective ...Report