The Spectrum of a Parametrized Partial Differential Operator Occurring in Hydrodynamics

A partial differential operator associated with natural oscillationsof an incompressible fluid in the neighbourhood of an ellipticalflow is considered. The differentiation is only taken with respectto the angular variable, and thus the operator becomes a familyof ordinary differential operators parametrized by the radialvariable. It is shown that the spectra of these ordinary differentialoperators completely determine the spectrum of the given operatorwhich turns out to have a kind of skeleton structure.     

Quasi-solitonic behavior of self-written waveguides created by photopolymerization

We investigated the condition of unique self-written channel and multichannel propagation inside bulk photopolymerizable materials. Light was introduced in the medium by a single-mode optical fiber. At a very low beam power of 5 muW , a unique uniform-channel waveguide without any broadening was obtained by polymerization. When the input power is increased to 100 muW , the guide becomes chaotic and multichannel. We connected two fibers separated by a 1-cm distance. The results open the door to studies of the optical and electro-optical properties of photopolymerized guides doped by nonlinear optical chromophores and to possible applications in integrated optical devices.     

Creating ground state molecules with optical feshbach resonances in tight traps

We propose to create ultracold ground state molecules in an atomic Bose-Einstein condensate by adiabatic crossing of an optical Feshbach resonance. We envision a scheme where the laser intensity and possibly also frequency are linearly ramped over the resonance. Our calculations for (87)Rb show that for sufficiently tight traps it is possible to avoid spontaneous emission while retaining adiabaticity, and conversion efficiencies of up to 50% can be expected.     

The titration of clay minerals II. Structure-based model and implications for clay reactivity

The potentiometric titration and CEC data presented in part I are modeled in this paper, part II. Two models are compared: the two pK, three complexation sites plus exchange sites nonelectrostatic model developed by Baeyens and Bradbury and a model based on the MUSIC approach developed by Hiemstra and Van Riemsdijk. Both morphological and structural information is used to develop this new model. Morphological information is taken from the literature, while structural information is taken from the literature and constrained by supporting FTIR experiments. The Baeyens and Bradbury model is found to reproduce the general tendency of the titration curve, whereas the model based on the Hiemstra and Van Riemsdijk MUSIC approach provides a better fit to the experimental data. The former uses only 3 edge reaction sites, whereas the latter uses at least 27 edge reaction sites. Five main reactive sites are sufficient to fit the MUSIC model curve, but the model allows us to derive the properties of 22 other reactive sites. Logically, the greater the number of sites, the better the fit. Nevertheless, fewer adjustable parameters are necessary for the Hiemstra and Van Riemsdijk MUSIC model than for the Baeyens and Bradbury model, thanks to structural and morphological constraints. The precision of the potentiometric titration curve is insufficient to verify that the properties of the 27 sites given by the MUSIC model are effective. Thus, we coupled some properties of clay minerals, such as dissolution, to the modeled acid-base properties of these sites to assess our model. We then questioned the ability of simplified models such as the Baeyens and Bradbury model to predict the interactions between clay minerals and solutions in natural environments. In addition, we derived the cation exchange selectivity coefficients for CaCl+ ionic pairs and H+ from our CEC data and gave an estimate for the CaOH+ selectivity coefficient.