Stabilization and Control for the Nonlinear Schrödinger Equation on a Compact Surface

In this paper, we study the stabilization property and the exact controllability for the nonlinear Schrödinger equation on a two dimensional compact Riemannian manifold, without boundary. We use a pseudo-differential dissipation. The proofs are based on a result of propagation of singularities and on recent dispersion estimates (Strichartz type inequalities) due to N. Burq, P. Gérard and N. Tzvetkov.     

Biocomposites based on Alfa fibers and starch‐based biopolymer

Biocomposite materials based on Alfa cellulose fibers (esparto grass plant) as reinforcing element and starch‐based biopolymer matrix were prepared and characterized in terms of mechanical performance, thermal properties, and water absorbance behavior. The fibers and the matrix were first mixed in the melted state under mechanical shearing using a plastograph and the obtained composites were molded by injection process. The tensile mechanical analysis showed a linear increase of the composite flexural and tensile modulus upon increasing the fiber content, together with a sharp decrease of the elongation at break. The fibers′ incorporation into the biopolymer matrix brings about an enhancement in the mechanical strength and the impact strength of the composite. Dynamic mechanical thermal analysis (DMTA) investigation showed two relaxations occurring at about ?30 and 35°C. The addition of Alfa fibers enhanced the storage modulus E′ before and after T_α, which is consistent with the reinforcing effect of Alfa cellulose fibers. Copyright © 2008 John Wiley & Sons, Ltd.     

Stabilization and control for the subcritical semilinear wave equation

In this paper, we analyze the exponential decay property of solutions of the semilinear wave equation in with a damping term which is effective on the exterior of a ball. Under suitable and natural assumptions on the nonlinearity we prove that the exponential decay holds locally uniformly for finite energy solutions provided the nonlinearity is subcritical at infinity. Subcriticality means, roughly speaking, that the nonlinearity grows at infinity at most as a power p<5. The method of proof combines classical energy estimates for the linear wave equation allowing to estimate the total energy of solutions in terms of the energy localized in the exterior of a ball, Strichartz's estimates and results by P. Gérard on microlocal defect measures and linearizable sequences. We also give an application to the stabilization and controllability of the semilinear wave equation in a bounded domain under the same growth condition on the nonlinearity but provided the nonlinearity has been cut-off away from the boundary.     

Observability estimates for the wave equation with rough coefficients

The goal of this note is to prove observability estimates for the wave equation with a density which is only continuous in the domain, and satisfies some multiplier-type condition only in the sense of distributions. Our main argument is that one can construct suitable approximations of such density by a sequence of smooth densities whose corresponding wave equations are uniformly observable. The end of the argument then consists in a rather standard passage to the limit.     

Evaluation and modeling of synergy to pheromone and plant kairomone in American palm weevil

Background  

Many behavioral responses to odors are synergistic, particularly in insects. In beetles, synergy often involves a pheromone and a plant odor, and pest management relies on them for the use of combined lures. To investigate olfactory synergy mechanisms, we need to distinguish synergistic effects from additive ones, when all components of the mixture are active.     

Bi(OTf)3-catalyzed cycloisomerization of aryl-allenes

Intramolecular hydroarylation of allenes was achieved under very mild conditions using bismuth(III) triflate as the catalyst. Efficient functionalization of activated and nonactivated aromatic nuclei led to C-C bond formation through a formal Ar-H activation. A tandem bis-hydroarylation of the allene moiety was also developed giving access to various interesting polycyclic structures.