Convergence rate of inertial Forward–Backward algorithm beyond Nesterov’s rule

Mathematical Programming - In this paper we study the convergence of an Inertial Forward–Backward algorithm, with a particular choice of an over-relaxation term. In particular we show that...     

Femtosecond time-resolved interferences of resonantly excited excitons in bulk GaN

It is shown that excitonic transients of bulk GaN can be accurately measured by an interferometric correlation technique used in reflection geometry. This is demonstrated for resonantly excited excitons in high quality GaN epilayers. The interferograms exhibit a clear modulation of the signal due the quantum beats between A and B excitons. The period of these beats is in good agreement with the A–B exciton energy splitting measured by means of frequency-resolved reflectivity. The decrease of the overall signal is mainly connected to the crystal quality and strongly dependent on the inhomogeneous broadening which can be extracted from the correlation spectra. These results are in agreement with numerical calculations based on the Fourier transform determination of the time-resolved reflection coefficient in the framework of linear semi-classical theory carried out in order to obtain the autocorrelation response.     

Modeling Very Oscillating Signals. Application to Image Processing

This article is a companion paper of a previous work where we have developed the numerical analysis of a variational model first introduced by Rudin et al. and revisited by Meyer for removing the noise and capturing textures in an image. The basic idea in this model is to decompose an image f into two components (u + v) and then to search for (u,v) as a minimizer of an energy functional. The first component u belongs to BV and contains geometrical information, while the second one v is sought in a space G which contains signals with large oscillations, i.e. noise and textures. In Meyer carried out his study in the whole ² and his approach is rather built on harmonic analysis tools. We place ourselves in the case of a bounded set of ² which is the proper setting for image processing and our approach is based upon functional analysis arguments. We define in this context the space G, give some of its properties, and then study in this continuous setting the energy functional which allows us to recover the components u and v. We present some numerical experiments to show the relevance of the model for image decomposition and for image denoising.     

Hydrogen and nitrogen ambient effects on epitaxial growth of GaN by hydride vapour phase epitaxy

This study presents the influence of the composition of the carrier gas on the growth of GaN by HVPE. Since no hydrogen is introduced in the vapour phase, the deposition is expected to be controlled by Cl desorption in the form of GaCl₃, as has been proposed for GaAs. However, our published model predicts much lower growth rates than those observed. We can account for both the observed parasitic deposition and GaN growth rate if we assume that GaCl₃ is not at its equilibrium pressure in the deposition zone and where nucleation takes place on the walls as well as on the substrate. This yields a high rate of parasitic nucleation even though the nominal supersaturation is vanishing small. Very little growth takes place on the substrate where the equilibrium pressure of GaCl₃ is reached. We describe similar experiments performed with a H₂/N₂ mixture as the carrier gas. In this case, we expect GaN deposition to be controlled by desorption of Cl as HCl, which is known as the H₂ mechanism. It is speculated that the results show the existence of a new growth mechanism.