Analysis of segregated boundary-domain integral equations for mixed variable-coefficient BVPs in exterior domains

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2011 Birkhäuser Boston.Some direct segregated systems of boundary–domain integral equations (LBDIEs) associated with the mixed boundary value problems for scalar PDEs with variable coefficients in exterior domains are formulated and analyzed in the paper. The LBDIE equivalence to the original boundary value problems and the invertibility of the corresponding boundary–domain integral operators are proved in weighted Sobolev spaces suitable for exterior domains. This extends the results obtained by the authors for interior domains in non-weighted Sobolev spaces.The work was supported by the grant EP/H020497/1 ”Mathematical analysis of localised boundary-domain integral equations for BVPs with variable coefficients” of the EPSRC, UK

Understanding bottom-up continuous hydrothermal synthesis of nanoparticles using empirical measurement and computational simulation

Continuous hydrothermal synthesis was highlighted in a recent review as an enabling technology for the production of nanoparticles. In recent years, it has been shown to be a suitable reaction medium for the synthesis of a wide range of nanomaterials. Many single and complex nanomaterials such as metals, metal oxides, doped oxides, carbonates, sulfides, hydroxides, phosphates, and metal organic frameworks can be formed using continuous hydrothermal synthesis techniques. This work presents a methodology to characterize continuous hydrothermal flow systems both experimentally and numerically, and to determine the scalability of a counter current supercritical water reactor for the large scale production (>1,000 T·year–1) of nanomaterials. Experiments were performed using a purpose-built continuous flow rig, featuring an injection loop on a metal salt feed line, which allowed the injection of a chromophoric tracer. At the system outlet, the tracer was detected using UV/Vis absorption, which could be used to measure the residence time distribution within the reactor volume. Computational fluid dynamics (CFD) calculations were also conducted using a modeled geometry to represent the experimental apparatus. The performance of the CFD model was tested against experimental data, verifying that the CFD model accurately predicted the nucleation and growth of the nanomaterials inside the reactor

Optical and nanostructural insights of oblique angle deposited layers applied for photonic coatings

Oblique angle deposition (OAD) is a nanostructuration method widely used to tune the optical properties of thin films. The introduction of porosity controlled by the deposition angle is used to develop the architecture of each layer and stack that enable modifying and optimizing the optical properties of the constituent layers for optimal design. However, optical properties of these nanostructured layers may differ greatly from those of dense layers due to the presence of anisotropy, refractive index gradient and scattering. This work focuses on OAD layers based on a reference photonic material such as SiO2 and it aims at taking into account all these effects in the description of the optical response. For that, the nanostructure has been analyzed with a complete SEM study and key parameters like the porosity gradient profile and aspect ratio of the nanocolumns were extracted. The samples were then characterized by generalized ellipsometry to evaluate the influence of morphological anisotropy and porosity gradient on the optical response of the films. Based on this microstructural study, an original optical model is presented to fit the features of new optical properties. A reliable correspondence is observed between the optical model parameters and the microstructure characteristics like the column angle and the porosity gradient. This demonstrates that such complex microstructural parameters can be easily accessed solely from optical measurements. All the work has enabled us to develop a two-layer anti-reflective coating that already demonstrate high level of transmission

Inverted finite elements for div-curl systems in the whole space

We use inverted finite element method (IFEM) for computing three-dimensional vector potentials and for solving div-curl systems in the whole space . IFEM is substantially different from the existing approaches since it is a non truncature method which preserves the unboundness of the domain. After developping the method, we analyze its convergence in term of weighted norms. We then give some three-dimensional numerical results which demonstrate the efficiency and the accuracy of the method and confirm its convergence