Liquid crystals boojum-colloids

Colloidal particles dispersed in a liquid crystal lead to distortions of the director field. The distortions are responsible for long-range effective colloidal interactions whose asymptotic behaviour is well understood. The short distance behaviour of the interaction, however, is sensitive to the structure and dynamics of the topological defects nucleated near the colloidal particles in the strong anchoring regime. The full non-linear theory is required in order to determine the interaction at short separations. Spherical colloidal particles with sufficiently strong planar degenerate anchoring nucleate a pair of antipodal surface topological defects, known as boojums. We use the Landau-de Gennes formalism in order to resolve the mesoscopic structure of the boojum cores and to determine the pairwise colloidal interaction. We compare the results in three (3D) and two (2D) spatial dimensions. The corresponding free energy functionals are minimized numerically using finite elements with adaptive meshes. Boojums are always point-like in 2D, but acquire a rather complex structure in 3D which depends on the combination of the anchoring potential, the radius of the colloid, the temperature and the LC elastic anisotropy. We identify three types of defect cores in 3D which we call single, double and split core boojums, and investigate the associated structural transitions. In the presence of two colloidal particles there are substantial re-arrangements of the defects at short distances, both in 3D and 2D. These re-arrangements lead to qualitative changes in the force-distance profile when compared to the asymptotic quadrupole-quadrupole interaction. In line with the experimental results, the presence of the defects prevents coalescence of the colloidal particles in 2D, but not in 3D systems.Comment: 18 pages, 21 figure

Colloidal interactions in two dimensional nematics

The interaction between two disks immersed in a 2D nematic is investigated (i) analitically using the tensor order parameter formalism for the nematic configuration around isolated disks and (ii) numerically using finite element methods with adaptive meshing to minimize the corresponding Landau-de Gennes free energy. For strong homeotropic anchoring, each disk generates a pair of defects with one-half topological charge responsible for the 2D quadrupolar interaction between the disks at large distances. At short distance, the position of the defects may change, leading to unexpected complex interactions with the quadrupolar repulsive interactions becoming attractive. This short range attraction in all directions is still anisotropic. As the distance between the disks decreases their preferred relative orientation with respect to the far-field nematic director changes from oblique to perpendicular.Comment: 7 pages, 7 figure

Argon assisted chemical vapor deposition of CrO2_2: an efficient process leading to high quality epitaxial films

A comparative study of the structural, microstructural and magnetic properties of CrO$_2$ thin films grown onto (110) and (100) TiO$_2$ rutile single crystal substrates by chemical vapor deposition (CVD), using CrO$_3$ as chromium precursor and either oxygen or argon as carrier gas is presented. Our results show that growth under argon carrier gas leads to high quality CrO$_2$ epilayers with structural and magnetic properties similar to those obtained using the more standard oxygen carrier gas. Furthermore, we interpret the larger magnetic coercivity observed for the (110) oriented films in terms of their microstructure, in particular of the highest strain and edge roughness of the building structures of the CrO$_2$ epilayers, which are settled by the substrate crystallographic orientation.Comment: 27 pages, 2 tables, 8 figure

Sensitivity of freshwater periphytic diatoms to agricultural herbicides

The biomonitoring of pesticide pollution in streams and rivers using algae such as diatoms remains difficult. The responses of diatomcommunities to toxic stress in streamwater are disturbed by the variations of environmental parameters. In this study, periphytic algae collected in situwere exposed under controlled conditions to two major herbicides used in French agriculture (isoproturon and s-metolachlor). Three exposure regimes were tested: 5 and 30gL−1 for 6 days and 30gL−1 for 3 days followed by a recovery period of 3 days. The algal biomasses were assessed from pigment concentrations (chlorophyll a and c) and from live cell density. The highest concentration (30gL−1) of isoproturon inhibited the biomass increase statistically significantly. In periphyton exposed to 5 and 30gL−1 of s-metolachlor, chlorophyll c concentration and live cell densitywere also statistically significantly lower than in the control. Periphyton left to recover after reduced exposure duration (3 days) showed higher growth rates after treatment with s-metolachlor than with isoproturon. Taxonomic identifications showed that species like Melosira varians, Nitzschia dissipata and Cocconeis placentula were not affected by the herbicide exposure. Other species like Eolimna minima and Navicula reichardtiana were more sensitive. Studying diatoms according to their trophic mode showed that facultative heterotroph specieswere statistically significantly favoured by isoproturon exposure at the highest concentration. Results obtained with s-metolachlor exposure showed a disturbance of cell multiplication rather than that of photosynthesis. These results suggest that photosynthesis inhibitors like isoproturon favour species able to survive when the autotroph mode is inhibited

Ultimate strength and design of lipped channel columns experiencing local/distortional mode interaction - Part I: Experimental investigation

This paper reports the results of an experimental investigation aimed at assessing the post-buckling behaviour and ultimate strength of fixed-ended cold-formed steel lipped channel columns experiencing local/distortional mode interaction. A total of 26 columns were tested and the specimens were carefully selected to ensure various levels of local/distortional interaction effects (more or less close local and distortional critical stresses). The experimental results presented consist of the specimen geometries, material properties, initial imperfections, non-linear equilibrium paths and ultimate strength values. Since the collapse of most columns combines local and distortional deformations, these experimental results may be used to (i) assess the relevance of local/distortional interaction, (ii) calibrate and validate numerical simulations and (iii) provide experimental data aimed at developing a Direct Strength Method (DSM) approach to design cold-formed steel lipped channel columns against local/distortional interaction - such a DSM approach is addressed in Part II of this paper.published_or_final_versionThe 6th International Conference on Advances in Steel Structures in conjunction with IJSSD Symposium on Progress in Structural Stability and Dynamics & IStructE Asia-Pacific Forum (ICASS '09 / IJSSD / IStructE Asia-Pacific Forum), Hong Kong, China, 16-18 December 2009. In Proceedings of the 6th ICASS, 2009, v. 1, p. 460-46

Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian

We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem. We write an equivalent characterization as a thin obstacle problem. In this way we are able to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary