Multi‐stage high order semi‐Lagrangian schemes for incompressible flows in Cartesian geometries

Efficient transport algorithms are essential to the numerical resolution of incompressible fluid‐flow problems. Semi‐Lagrangian methods are widely used in grid based methods to achieve this aim. The accuracy of the interpolation strategy then determines the properties of the scheme. We introduce a simple multi‐stage procedure, which can easily be used to increase the order of accuracy of a code based on multilinear interpolations. This approach is an extension of a corrective algorithm introduced by Dupont & Liu (2003, 2007). This multi‐stage procedure can be easily implemented in existing parallel codes using a domain decomposition strategy, as the communication pattern is identical to that of the multilinear scheme. We show how a combination of a forward and backward error correction can provide a third‐order accurate scheme, thus significantly reducing diffusive effects while retaining a non‐dispersive leading error term. Copyright © 2016 John Wiley & Sons, Ltd.     

Computing the conditioning of the components of a linear least‐squares solution

In this paper, we address the accuracy of the results for the overdetermined full rank linear least‐squares problem. We recall theoretical results obtained in (SIAM J. Matrix Anal. Appl. 2007; 29 (2):413–433) on conditioning of the least‐squares solution and the components of the solution when the matrix perturbations are measured in Frobenius or spectral norms. Then we define computable estimates for these condition numbers and we interpret them in terms of statistical quantities when the regression matrix and the right‐hand side are perturbed. In particular, we show that in the classical linear statistical model, the ratio of the variance of one component of the solution by the variance of the right‐hand side is exactly the condition number of this solution component when only perturbations on the right‐hand side are considered. We explain how to compute the variance–covariance matrix and the least‐squares conditioning using the libraries LAPACK (LAPACK Users' Guide (3rd edn). SIAM: Philadelphia, 1999) and ScaLAPACK (ScaLAPACK Users' Guide. SIAM: Philadelphia, 1997) and we give the corresponding computational cost. Finally we present a small historical numerical example that was used by Laplace (Théorie Analytique des Probabilités. Mme Ve Courcier, 1820; 497–530) for computing the mass of Jupiter and a physical application if the area of space geodesy. Copyright © 2008 John Wiley & Sons, Ltd.     

Environmentally benign nanomixing by sonication in high-pressure carbon dioxide

Due to the increased use of nanocomposites, mixing at nanoscale has become important. Current mixing techniques can be classified into: (a) dry mixing (mechanical mixing), (b) wet mixing, and (c) simultaneous production of mixed nanoparticles (when possible). Dry mixing is in general not effective in achieving desired mixing at nanoscale, whereas wet mixing suffers from different disadvantages like nanomaterial of interest should be insoluble, has to wet the liquid, and involves additional steps of filtration and drying. This paper examines the use of pressurized carbon dioxide having high density and low viscosity to replace the liquids (e.g., n-hexane, toluene). Ultrasound is applied to the suspension of nanopowders in gaseous and supercritical carbon dioxide where high impact collisions during sonication help mixing and the final mixture is obtained by simple depressurization. The method is tested for binary mixture of alumina/silica, silica/titania, MWNT (multiwalled carbon nanotubes)/silica, and MWNT/titania. The effects of sonication intensity and pressure on the degree of mixing are studied. Comparative study is also done with liquid n-hexane as a mixing media. Quantitative characterization (e.g., mean composition standard deviation, intensity of segregation) of mixing of alumina/silica and silica/titania is done with energy-dispersive X-ray spectroscopy, and that of MWNT/silica and MWNT/titania is done using field-emission scanning electron microscopy and day-light illumination spectrophotometry. Results show that mixing in carbon dioxide at higher ultrasound amplitudes is as good as in liquid n-hexane, and the final mixed product does not contain any residual media as in the case of liquid n-hexane.     

A minimal amount of acrylonitrile turns the nitroxide‐mediated polymerization of methyl methacrylate into an almost ideal controlled/living system

Nitroxide‐mediated controlled/living free‐radical polymerization of methyl methacrylate initiated by the SG1‐based alkoxyamine BlocBuilder was successfully performed in bulk at 80–99 °C with the help of a very small amount of acrylonitrile (AN, 2.2–8.8 mol %) as a comonomer. Well‐defined PMMA‐rich P(MMA‐co‐AN) copolymers were prepared with the number‐average molar mass, M_n, in the 6.1–32 kg mol^?1 range and polydispersity indexes as low as 1.24. Incorporation of AN in the copolymers was demonstrated by ¹H and ¹³C NMR spectroscopy, and its effect on the chain thermal properties was evaluated by DSC and TGA analyses. Investigation of chain‐end functionalization by an alkoxyamine group was performed by means of ³¹P NMR spectroscopy and chain extensions from a P(MMA‐co‐AN)‐SG1 macroinitiator. It demonstrated the very high proportion of SG1‐terminated polymer chains, which opened the door to block copolymer synthesis with a high quality of control. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 34–47, 2010     

Photo-irradiation effects on the surface morphology of poly(p-phenylene vinylene) films

In this work, we have studied the surface morphology of photo-irradiated poly(p-phenylene vinylene) (PPV) thin films by using atomic force microscopy (AFM). We have analyzed the first-order statistical parameters, the height distribution and the distance between selected peaks. The second-order statistical analysis was introduced calculating the auto-covariance function to determine the correlation length between heights. We have observed that the photo-irradiation process produces a surface topology more homogeneous and isotropic such as a normal surface. In addition, the polymer surface irradiation can be used as a new methodology to obtain materials optically modified.