LIDAR mapping of ozone-episode dynamics in Paris and intercomparison with spot analyzers Supplementary material available at http://link.springer.de/journals/apb

Continuous mapping of an ozone episode in Paris in June 1999 has been performed using a differential absorption lidar system. The 2D ozone concentration vertical maps recorded over 33 h at the Champ de Mars are compiled in a video clip that gives access to local photochemical dynamics with unprecedented precision. The lidar data are compared over the whole period with point monitors located at 0-, 50-, and 300-m altitudes on the Eiffel Tower. Very good agreement is found when spatial resolution, acquisition time, and required concentration accuracy are optimized. Sensitivity to these parameters for successful intercomparison in urban areas is discussed. Received: 11 February 2002 / Published online: 14 March 2002     

An algebraic multigrid solver for Navier-Stokes problems

An efficient numerical method is presented for solving the equations of motion for viscous fluids. The equations are discretized on the basis of unstructured finite element meshes and then solved by direct iteration. Advective fluxes are temporarily fixed at each iteration to provide a linearized set of coupled equations which are then also solved by iteration using a fully implicit algebraic multigrid (AMG) scheme. A rapid convergence to machine accuracy is achieved that is almost mesh-independent. The scaling of computing time with mesh size is therefore close to the optimum.     

On complementability of certain generalized hypercenters in Artinian modules

We prove that, in an Artinian module, the upper FC-hypercenter over an infinite FC-hypercentral locally solvable group has a direct complement. Thus, we obtain a generalization of one of Zaitsev’s theorems and one of Duan’s theorems.     

UV curing of a novel resin derived from poly(ethylene terephthalate)

The synthesis and characterization of photopolymerizable unsaturated polyester resins based on PET waste are described. The resins came from a depolymerization process based on the glycolysis of PET by diethylene glycol (DEG). Different molecular weights of glycolysates were synthesized. Then, the latter was functionalized by a methyl hemiester of maleic acid to obtain unsatured α,ω‐bismaleate PET oligomers. In the presence of an electron donor monomer, such as triethylene glycol divinyl ether, these electron acceptor oligomers were copolymerized by way of charge‐transfer complexes under UV irradiation. The reaction was monitored in situ by real‐time IR spectroscopy to study the kinetics of photopolymerization. This one was studied in relation with the physical and chemical characteristics of oligoesters and the composition of mixtures containing divinyl ethers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1324–1335, 2007     

Fast switching anisotropic networks obtained by in situ photopolymerization of liquid crystal molecules

Lightly cross-linked anisotropic networks with uniaxial and π/2 twisted orientations were produced by photopolymerization of monotropic mixtures containing liquid crystal mono and diacrylates. In this way the polymer backbone was immobilized and became decoupled from the motion of the mesogenic side groups. The networks showed very good reversibility and even after becoming isotropic, upon cooling, the initial orientation was recovered. In the same way, in the presence of electric fields the mesogenic groups could be reoriented in the direction of the electric field, reverting back to the initial orientation on removal of the field at a rate comparable with those observed in the monomeric state. Combining viscoelastic measurements with the dielectric behaviour of the monomeric liquid crystal and the anisotropic network, a comparison between the internal and bulk rotational viscosities was also made.     

ON SOME INTERPRETATIONS OF CLASSICAL LOGIC

In distinction from the well-known double-negation embeddings of the classical logic we consider some variants of single-negation embeddings and describe some classes of superintuitionistic first-order predicate logics in which the classical first-order calculus is interpretable in such a way. Also we find the minimal extensions of Heyting's logic in which the classical predicate logic can be embedded by means of these translations.     

Application of the variation principle for the problem of buckling of a nonlinearly elastic ring nonuniform along its thickness

There has been considerable recent attention given to the stressed and buckled states of items with complicated configuration made of different nonlinearly elastic materials joined by complete adhesion. However, effective analytical solutions for such problems have been hindered by mathematical difficulties. Approximate methods have thus been developed for such problems. A variational combined principle has been formulated in this communication. A nonlinear geometrical approach has been used for formulating a mixed-type functional with physical relationships given by Euler equations, nonlinear equilibrium equations, and nonlinear boundary conditions for a piecewise-nonuniform nonlinearly elastic body composed of finite elements (particles). As an example, buckling along the nonuniform thickness of nonlinearly elastic rings was analyzed hypothetically assuming plane cross-sections. Options for two-, three-, four-, five-, and six-layered rings in a periodical structure have been reviewed. The critical buckling forces for an even number of layers have been found to be equal to each other. The ratios of the critical forces, elasticity moduli, and proportionality levels were determined for all five variants by the Runge-Kutta method.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 2, pp. 262–268, March–April, 1995.