On a free boundary problem for the Reynolds equation derived from the Stokes system with Tresca boundary conditions

The asymptotic behaviour of a Stokes flow with Tresca free boundary friction conditions when one dimension of the fluid domain tends to zero is studied. A specific Reynolds equation associated with variational inequalities is obtained and uniqueness is proved.     

Kinetics of the bromate–bromide reaction at high bromide concentrations

At bromide concentrations higher than 0.1 M, a second term must be added to the classical rate law of the bromate–bromide reaction that becomes ?d[BrO₃^?]/dt = [BrO₃^?][H⁺]²(k₁[Br^?] + k₂[Br^?]²). In perchloric solutions at 25°C, k₁ = 2.18 dm³ mol^?3 s^?1 and k₂ = 0.65 dm⁴ mol^?4 s^?1 at 1 M ionic strength and k₁ = 2.60 dm³ mol³ s^?1and k₂ = 1.05 dm⁴ mol^?4 s^?1 at 2 M ionic strength. A mechanism explaining this rate law, with Br₂O₂ as key intermediate species, is proposed. Errors that may occur when using the Guggenheim method are discussed. © 2006 Wiley Periodicals, Inc. Int J Chem Kinet 39: 17–21, 2007     

Acetylene weak bands at 2.5 μm from intracavity Cr:ZnSe laser absorption observed with time-resolved Fourier transform spectroscopy

The spectral dynamics of a mid-infrared multimode Cr(2+):ZnSe laser located in a vacuum sealed chamber containing acetylene at low pressure is analyzed by a stepping-mode high-resolution time-resolved Fourier transform interferometer. Doppler-limited absorption spectra of C(2)H(2) in natural isotopic abundance are recorded around 4000 cm(-1) with kilometric absorption path lengths and sensitivities better than 3 10(-8) cm(-1). Two cold bands are newly identified and assigned to the ν(1)+ν(4) (1) and ν(3)+ν(5) (1) transitions of (12)C(13)CH(2). The ν(1)+ν(5) (1) band of (12)C(2)HD and fourteen (12)C(2)H(2) bands are observed, among which for the first time ν(2)+2ν(4) (2)+ν(5) (-1).     

The LPCTrap experiment: measurement of the β–ν angular correlation in 6He using a transparent Paul trap

We report on the status of the LPCTrap experiment, devoted to measure the β–ν angular correlation in the pure Gamow–Teller decay of ⁶He. This measurement is motivated by the search for the presence of tensor type contributions to the weak interaction. The ⁶He ions are confined in a novel transparent Paul trap. The β particles and the recoil ions are detected in coincidence to deduce the angular correlation parameter. The commissioning run performed in 2005 has given the proof of principle of this experiment. Up to 10⁵ coincidences were recorded during a second run in 2006.     

A geometric theory forL 2-stability of the inverse problem in a one-dimensional elliptic equation from anH 1-observation

This study provides a stability theory for the nonlinear least-squares formulation of estimating the diffusion coefficient in a two-point boundary-value problem from an error-corrupted observation of the state variable. It is based on analysing the projection of the observation on the nonconvex attainable set.This research was started while G. Chavent visited the Technical University of Graz. Support through the Steiermaerkische Landesregierung is gratefully acknowledged.     

Complex polymer architectures through dimethoxymethyl 1,1‐diphenylethylene derivatives

The reactions of polystyryllithium and potassium on dimethoxymethyl 1,1‐diphenylethylene derivatives were studied in different solvents. In a polar medium, A₃ and A₆ star types were formed according to the stoichiometry, whereas in a nonpolar medium, hyperbranched structures were synthesized. Extensions of an already proposed mechanism in polar and nonpolar media were examined. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3329–3335, 2003     

Grafting of silica during the processing of silica‐filled SBR: Comparison between length and content of the silane

The treatment of nanoscopic silica grafted in the blend during the processing of silica‐filled styrene butadiene rubber was performed with silane, introduced at different concentrations, or at a constant concentration with a given length of alkyl chain. From swelling measurements in water and in solvent, the maximum silane content that can be grafted has been calculated as a function of the length of the silane alkyl chains as well as their efficiency to cover the silica surface. The found values are close to the values found in the literature for grafting in solution. Moreover, a direct correspondence between the length of the silane alkyl chains and their concentration has been deduced. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 143–152, 2006     

Assessment of filtered gas–solid momentum transfer models via a linear wave propagation speed test

The propagation speeds of linear waves in gas–solid suspensions depend strongly on the solids volume fraction and the wave frequency. The latter is due to gas–solid momentum transfer and allows a simple test on filtered gas–solid momentum transfer models. Such models may predict linear wave propagation speeds different from those obtained with the non-filtered model at wave frequencies higher than the filter frequency, but not at wave frequencies lower than the filter frequency.     

On random walks arising in queueing systems: ergodicity and transience via quadratic forms as lyapounov functions — Part I

A simple and quite general approach is proposed to derive criteria for transience and ergodicity of a certain class of irreducibleN-dimensional Markov chains in ₊ ^N assuming a boundedness condition on the second moment of the jumps. The method consists in constructing convenient smooth supermartingales outside some compact set. The Lyapounov functions introduced belong to the set of quadratic forms in ₊ ^N and do not always have a definite sign. Existence and construction of these forms is shown to be basically equivalent to finding vectors satisfying a system of linear inequalities.Part I is restricted toN=2, in which case a complete characterization is obtained for the type of random walks analyzed by Malyshev and Mensikov, thus relaxing their condition of boundedness of the jumps. The motivation for this work is partly from a large class of queueing systems that give rise to random walks in ₊ ^N