Lensing effects in Q-switched unstable laser cavities with side-pumped Nd:YAG and ruby crystal rods

We present a comprehensive numerical model that accounts for non-uniform pumping and a related thermal and electronic lensing effects in Q-switched unstable laser cavities. We study the influence of these effects on the output beam profile in Nd:YAG and ruby laser systems with side-pumped crystal rods. We also constructed both lasers to experimentally validate the numerical results and found very good agreement. The results show that both types of lensing effects are particularly detrimental in ruby, while they are insignificant in Nd:YAG.     

Characteristic times of relaxation peaks of magnetic fluids

The use of the Fokker–Planck equation in theoretical studies of relaxation processes in single-domain particle systems is a well-established technique. However this method has a particular disadvantage in that it can give analytical results solely in some limiting cases. An alternative method, which avoids this difficulty, is that of the use of the integral relaxation time, τ_int, which is presented in this work.     

In-situ XAS study on the Cu and Ce local structural changes in a CuO-CeO2/Al2O3 catalyst under propane reduction and re-oxidation

The redox behaviour of a CuO-CeO₂/Al₂O₃ catalyst is studied under propane reduction and re-oxidation. The evolution of the local Cu and Ce structure is studied with in-situ transmission X-ray absorption spectroscopy (XAS) at the Cu K and Ce L₃ absorption edges.CuO and CeO₂ structures are present in the catalyst as such. No structural effect on the local Cu structure is observed upon heating in He up to 873 K or after pre-oxidation at 423 K.Exposure to propane at reaction temperature (600-763 K) fully reduces the Cu²⁺ cations towards metallic Cu⁰. Quick EXAFS spectra taken during reduction show a small amount of intermediate Cu¹⁺ species. Parallel to the CuO reduction, CeO₂ is also reduced in the same temperature range. About 25% of the Ce⁴⁺ reduces rapidly to Ce³⁺ in the 610-640 K temperature interval, while beyond 640 K a further slower reduction of Ce⁴⁺ to Ce³⁺ occurs. At 763 K, Ce reduction is still incomplete with 32% of Ce³⁺.Re-oxidation of Cu and Ce is fast and brings back the original oxides.The propane reduction of the CuO-CeO₂/Al₂O₃ catalyst involves both CuO and CeO₂ reduction at similar temperatures, which is ascribed to an interaction between the two compounds.     

Interaction soliton–sable dans un canal en eau peu profonde

Interaction between solitons and a sandy bed in shallow water is investigated. In our experiments, solitons are generated on the background of a harmonic wave, in a wave flume used in resonant mode. It is found that the sand ripples formed by the solitons propagation induce a significant decrease of solitons amplitude and of the phase shift between the soliton and the harmonic wave. However, the amplitude of the harmonic wave is approximately constant. The possible physical processes of such behaviour for the soliton amplitude and for the harmonic wave amplitude are discussed. To cite this article: F. Marin et al., C. R. Mecanique 333 (2005).     

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.     

The effect of molecular weight distribution on the elongational properties of linear polymers

The elongational properties of a series of six polypropylene and two polystyrene samples have been studied at constant rate of strain. A Wagner-type constitutive equation has been used to fit the experimental data, and the shape of the damping function has been correlated with the polydispersity index of the samples. As the memory function or relaxation function of linear viscoelasticity may be derived from the molecular-weight distribution using either molecular or phenomenological models, it is therefore possible to calculate the stress growth function of a linear polymer in elongation from its molecular-weight distribution.     

Strongly indecomposable finite groups

Motivated by examples in infinite group theory, we classify the finite groups whose subgroups can never be decomposed as direct products.