2-dimensional localization of acoustic waves in random perturbation of periodic media

In this work we study internal band edges localization of acoustic waves in 2-dimensional space obtained by random perturbation of some periodic media. Our results rely on the study of Lifshitz tails for the integrated density of states for random acoustic operators of the form . Localization is then deduced by the standard multiscale argument.     

On a resolvent approach for perturbed semigroups and application to $$L^1$$-neutron transport theory

We give new sufficient and practical conditions in terms of the generators ensuring the stability of the critical or the essential type of a perturbed \(C_0\)-semigroup in general Banach spaces. We apply our theoretical results in order to investigate the control and in particular the time asymptotic behavior of solutions to a broad class of transport equations in \(L^1\)-spaces and higher dimension. Our results improve, complete and enrich several earlier works.     

Dunkl-Schrödinger semigroups and applications

We obtain dispersive estimates for the linear Dunkl–Schrödinger equations with and without quadratic potential. As a consequence, we prove the local well-posedness for semilinear Dunkl–Schrödinger equations with polynomial nonlinearity in certain magnetic field. Furthermore, we study many applications: as the uncertainty principles for the Dunkl transform via the Dunkl–Schrödinger semigroups, the embedding theorems for the Sobolev spaces associated with the generalized Hermite semigroup. Finally, almost every where convergence of the solutions of the Dunkl–Schrödinger equation is also considered.     

Mechanism of nanocapsules formation by the emulsion-diffusion process

A detailed investigation into the mechanisms of nanocapsule formation by means of the two stages "emulsion-diffusion" process is reported. Such widely used process is still poorly understood. An emulsion of oil, polymer and ethyl acetate is fabricated as a first step; dilution with pure water allows ethyl acetate to diffuse out from the droplets, leaving a suspension of nanocapsules at the end. It has been shown that the size of nanocapsules was related to the chemical composition of the organic phase and the size of primary emulsion through a simple geometrical relationship. As a consequence, most of the properties of the nanocapsules were decided at the emulsification step. The influence of several formulation and processing parameters of the primary emulsion was studied accordingly. The thin polymer membrane of nanocapsules was observed by means of cryo-fracture electron microscopy. Finally two experiments were designed for a mechanistic investigation of the diffusion step. A step-by-step diffusion of the organic solvent takes place by successive partition equilibria of ethyl acetate between the droplets and aqueous phase. A time-resolved experiment shows the fast diffusion (less than 20 ms) related to the small droplet size of the emulsion.     

Paley–Wiener Theorems of Generalized Fourier Transform Associated with a Cherednik Type Operator on the Real Line

We consider a singular differential-difference operator \(\Lambda \) on the real line which generalizes the Cherednik operator associated with the reflection group \(\mathbb {Z}_2\) on \(\mathbb {R}\). We establish the Paley–Wiener theorems for the generalized Fourier transform on \(\mathbb {R}\) tied to \(\Lambda \).     

Numerical and experimental studies of molten pool formation during an interaction of a pulse laser (Nd:YAG) with a magnesium alloy

A pulse laser (Nd:YAG) interaction with an AZ91 magnesium alloy has been experimentally and numerically studied. A two-dimensional (2D) axisymmetric model of a molten pool created by a laser heat source has been developed. The elaborated model solves the coupled equations of a laminar fluid flow and heat transfer to demonstrate the flow behavior in the pool. This model takes into account the coupled effects of buoyancy and Marangoni forces, the thermophysic variation properties with temperature, and the radiation and convection heat losses. Concerning numerical results, the molten temperature distribution, velocity field and molten shape were discussed. It was noted that the Marangoni flow significantly alters the characteristics of the thawing and solidifying processes, and makes the molten pool wider and shallower. On the other hand, the experimental results showed that the material thermal properties have significant effects on the transport phenomena which takes place in the molten pool, and consequently on the formation as well as the shape of the pool. Finally, a comparison between the numerical and experimental results exhibited a good agreement.     

Tandem diazonium salt electroreduction and click chemistry as a novel, efficient route for grafting macromolecules to gold surface

Bis-alkynylated oligoethyleneglycol (OEG) and a monopropargyl-functionalized perfluorinated ethylene glycol (FEG) were clicked to azide-functionalized gold surface (Au–N₃) at room temperature via the well known 1,3 cycloaddition click chemical reaction. The Au–N₃ substrate was obtained by nucleophilic attack of NaN₃ on gold substrates modified by the electrochemical reduction of the , ⁺N₂–C₆H₄–CH₂Br diazonium salt. This electrochemical process yields aryl layer-modified gold of the type Au–C₆H₄–CH₂Br (hereafter Au–Br). The untreated and modified gold plates were examined by XPS, PMIRRAS and contact angle measurements. XPS brought evidence for electrografting aryl layers by the detection of Br3d; azide functionalization by the increase of the N/Br atomic ratio; and click reaction of OEG with Au–N₃ by the increase of O/N ratio. In addition, the perfluorinated plate (Au-FEG) exhibited F1s and characteristic C1s peaks from -(CF₂)₇- chain and terminal CF₃. Infra red spectroscopy (PMIRRAS) evidenced (i) grafting N₃ to Au–Br; (ii) characteristic stretching bands, from ethylene glycol units, C–O–C (1100–1300 cm⁻¹); CF₂ (1000–1100 cm⁻¹) and CF₃ (1100–1350 cm⁻¹) from FEG grafts; and (iii) suppression of alkynyl bands from OEG and FEG after surface click chemistry. More importantly, PMIRRAS results support an important bridging of the bispropargyl oligoethylene glycol at the gold surface. Water drop contact angles were found to be 48.7° and 83.0° for Au-OEG and Au-FEG, respectively, therefore highlighting the control over the hydrophilic/hydrophobic character of the clicked substrate.This work shows that clicking macromolecules to grafted, diazonium salt-derived aryl layers is a novel, simple and valuable approach for designing robust, functional surface organic coatings.