Functional Carbazole Liquid‐Crystal Block Codendrimers with Optical and Electronic Properties

The synthesis and characterisation of a family of block codendrimers consisting of highly versatile mesogenic and carbazole‐containing 2,2‐bis(hydroxymethyl)propionic acid (bis‐MPA) dendrons are reported. The liquid‐crystal behaviour was investigated by means of differential scanning calorimetry, polarised‐light optical microscopy and X‐ray diffraction. Depending on the chemical structure of the constituent dendrons, the codendrimers show lamellar or columnar mesophases. On the basis of the experimental results, models both at the molecular level and in the mesophase are proposed. The physical properties of the block codendrimers derived from the presence of the carbazole moiety in their structure were investigated: photoluminescence in solution and in the mesophase, electrochemical behaviour and hole transport. Electrodeposition of carbazole dendrons afforded a globular supramolecular conformation in which the mesogenic molecular side plays a key role.     

Stochastic signal analysis: Numerical representation and applications to system theory

Alternative procedures for representing a stochastic signal as a denumerable series with uncorrelated terms are developed. The study includes considerations about parametric rescaling and its repercussions on the orthogonal expansion, as well as numerical techniques for approaching such an expansion. In addition, applications to the Gaussian characterization of stochastic signals, filtering and stochastic modelling are treated.     

X-ray diffraction study of some mesogenic copper, nickel and vanadyl complexes

We present a comparative study of various metallomesogenic complexes, using X-ray diffraction methods. For a given ligand linked to different metal atoms (Cu, Ni, VO), the nature of this central atom influences mainly the magnetic susceptibilities of the mesophases. With different ligands, which keep the close neighbourhood of the metal atom unchanged, the apparent length of the mesogenic unit is longer for short ligands than for longer ones. This unexpected behaviour is qualitatively well explained by taking into account the global shape of the different complexes.     

Existence globale pour l'équation de Smoluchowski continue non homogène et comportement asymptotique des solutions

We prove global existence of solutions to the continuous nonhomogeneous Smoluchowski equation for coagulation rates satisfying a more general structure condition than the Galkin–Tupchiev monotony hypothesis considered in (Ph. Laurençot, S. Mischler, Arch. Rational Mech. Anal. 162 (1) (2002) 45–99). The Smoluchowski coagulation rate fulfils this condition as well as some rates which vanish on the diagonal. Under the condition of positivity of the coagulation rate outside of the diagonal we prove that solutions tend to 0 in the large time asymptotic. These results depend on a new estimate from below for the dissipation rate of the L^p-norm, p>1. To cite this article: S. Mischler, M. Rodriguez Ricard, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

A note about the Gaussian property of the Brownian bridge

The Gaussian property of the Brownian bridge is characterized as an application of Ramachandran's theorem in terms of the independence of the random variables that appear in the Karhunen-Loéve expansion of the process. A reference about the construction of the Brownian bridge by means of functional transformations is also included.     

Cartesian currents,weak diffeomorphisms and existence theorems in nonlinear elasticity

Summary In this paper we introduce some new classes of functions, among these a class of weak diffeomorphisms. In these classes we prove by direct methods the existence of minimizers for several kinds of variational integrals. In particular, we prove the existence of one-to-one orientation-preserving maps that minimize suitable energies associated with hyperelastic materials. The minimizers are also proved to satisfy equilibrium equations. Finally radial deformations are discussed in connection with cavitation.     

Macroporous poly(methyl methacrylate) produced by phase separation during polymerisation in solution

Polymethyl methacrylate (PMMA) sponges were obtained by polymerization in a solution with monomer/ethanol ratios up to 20:80. The material obtained after the elimination of the solvent present a homogeneous distribution of dispersed pores up to a monomer/ethanol ratio lower than 40:60. For higher ethanol contents in the reacting mixture, the morphology of the sponge corresponds to a network of PMMA microparticles, leaving large empty spaces leading to highly porous structure. The monomer/ethanol ratio during polymerization has a large influence on the porosity, thermal, and mechanical properties of the material and, for large solvent contents, on the size of the polymer microparticles.