Analysis and finite element simulations of a second‐order fluid model in a bounded domain

This article is concerned with the equations governing the steady motion of a viscoelastic incompressible second‐order fluid in a bounded domain. A new proof of existence and uniqueness of strong solutions is given. In addition, using appropriate finite element methods to approximate a coupled equivalent problem, sharp error estimates are obtained using a fixed point argument. The method is applied to the two‐dimensional lid‐driven cavity problem, at low Reynolds number and in a certain range of values of the viscoelastic parameters, to analyze the combined effects of inertia and viscoelasticity on the flow. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Near-infrared laser photoacoustic detection of methane: the impact of molecular relaxation

A photoacoustic sensor has been developed for trace-gas monitoring using a near-infrared semiconductor laser emitting in the 2ν₃ band of methane at 1.65 μm. The apparatus was designed for on-line process control in the manufacturing of the novel low-water-peak fibres developed for optical telecommunications. The importance of collisional relaxation processes in the generation of the photoacoustic signal is reported in the particular case of CH₄ detection in dry O₂ and O₂–N₂ mixtures. The negative influence of these effects results in a strongly reduced and phase-shifted photoacoustic signal, induced by a fast resonant coupling between the vibrational states of methane and oxygen, associated with the slow relaxation of the excited oxygen molecules. An unusual parabolic response of the sensor with respect to the methane concentration has been observed and is discussed. Finally, the beneficial effect of several species, including water vapour and helium, acting as a catalyst to hasten the relaxation of the CH₄–O₂ system, is demonstrated. PACS 42.62.Fi; 33.20.Ea; 34.50.Ez     

Selective spatial localization of the atom displacements in one-dimensional hybrid quasi-regular (Thue-Morse and Rudin-Shapiro)/periodic structures

We have studied the vibrational frequencies and atom displacements of one-dimensional systems formed by combinations of Thue-Morse and Rudin-Shapiro quasi-regular stackings with periodic ones. The materials are described by nearest-neighbor force constants and the corresponding atom masses. These systems exhibit differences in the frequency spectrum as compared to the original simple quasi-regular generations and periodic structures. The most important feature is the presence of separate confinement of the atom displacements in one of the parts forming the total composite structure for different frequency ranges, thus acting as a kind of phononic cavity.     

Towards an universal classification of scale invariant processes

We consider fields which take random values over several decades. Starting from physical examples, we postulate that scale is not an absolute quantity. We then establish the equivalence between two existing approaches based on scale symmetry arguments as general as possible. This yields a classification of log-infinitely divisible laws, possibly universal. The physical significance of the parameters entering in the classification is discussed. Received: 7 November 1997 / Received in final form: 26 March 1998 / Accepted: 30 March 1998     

Collisions for the quantum Coulomb Hamiltonian

We study the propagation of phase space singularities for the time dependent Schrödinger equation with potential having Coulomb-type singularities in space dimension equal tothree. We prove that the singularities (frequency set) of the solution are reflected by a Coulomb center exactly as in the classical problem, i.e. the frequency set follows theregularized trajectories of Classical Mechanics after a collision.     

Photoinitiated polymerization in bicontinuous microemulsions: Fluorescence monitoring

The photopolymerization of bicontinuous microemulsions was simultaneously monitored with differential scanning calorimetry and fluorescence. The kinetics and mechanism of the reaction were studied throughout the entire photopolymerization reaction. The role played by the surfactant in the kinetics and morphology was studied. The nature of the surfactant changed the autoacceleration process and final conversion. The behavior was explained as a result of the differences in the interfacial properties. Anionic cetyltrimethylammonium bromide (CTAB) gave rise to a more flexible interfacial film than anionic sodium dodecyl sulfate (SDS), resulting in competition between the intramolecular and intermolecular reactions in the former systems. As cyclization did not contribute to the increase in the degree of crosslinking, SDS photopolymerization gave solids with a more rigid microstructure. Fluorescence methodology was applied to monitor bicontinuous microemulsion polymerization and to reveal the microstructure and morphology development during photopolymerization. The microemulsion composition was designed to prepare nanoporous, crosslinked materials. Even though the nanostructure of the precursor microemulsions was not retained because of phase separation during polymerization, mesoporous solids were obtained. Their morphologies depended on the nature of the surfactant, and membranes with open cells were successfully prepared with CTAB, whereas more complex morphologies resulted with SDS. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5291–5303, 2006     

Lightly crosslinked,mesomorphic networks obtained through the reaction of dimeric,liquid‐crystalline epoxy–imine monomers and heptanedioic acid

We reacted various dimeric, liquid‐crystalline epoxy–imine monomers, differing in the length of the central aliphatic spacer or the dipolar moments, with heptanedioic acid. The resulting systems showed a liquid‐crystalline phase in some cases, depending on the dimer and on the reaction conditions. The systems were characterized with respect to their mesomorphic properties and then were submitted to dynamic mechanical thermal analysis in both fixed‐frequency and frequency‐sweep modes in the shear sandwich configuration. The arrangement in the liquid‐crystalline phase seemed to be mainly affected both by the polarization of the mesogen and by the reaction temperature, which favored the liquid‐crystalline arrangement when it was lying in the range of stability of the dimer mesophase. In agreement with other recent literature data, dynamic mechanical thermal analysis results suggested that the presence of the mesogen directly incorporated into the main chain increased the lifetimes of the elastic modes both in the isotropic phase and in the liquid‐crystalline phase with respect to side‐chain liquid‐crystalline elastomers and that the time–temperature superposition principle did not hold through the liquid‐crystalline‐to‐isotropic transition. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44:6270–6286, 2006