Small amplitude steady internal waves in stratified fluids

We study the weakly non linear solutions of theDubreil-Jacotin—Long elliptic equation in a strip, which describes two dimensional gravity internal waves propagating steadily in a stratified fluid. In the neighborhood of the first critical value of the Froude number, the center manifold theorem ensures that small solutions are parametrized by two coordinates which verify a system of nonlinear ordinary differential equations. We compute numerically the coefficients of the normal form of this reduced system for a three parameters family of stratifications and show that the quadratic coefficient (the most important) may become small. In that case, nonusual waves such as fronts can propagate. The last part of our work studies the case when a smooth stratification converges towards a piecewise constant profile having one discontinuity. We observe formally that the small waves which propagate at the interface of two homogeneous fluids are limits at leading order of waves travelling in the region where the smooth density varies rapidly.     

Solving superelliptic Diophantine equations by Baker's method

We describe a method for complete solution of the superelliptic Diophantine equation ay^p=f(x). The method is based on Baker's theory of linear forms in the logarithms. The characteristic feature of our approach (as compared with the classical method) is that we reduce the equation directly to the linear forms in logarithms, without intermediate use of Thue and linear unit equations. We show that the reduction method of Baker and Davenport [3] is applicable for superelliptic equations, and develop a very efficient method for enumerating the solutions below the reduced bound. The method requires computing the algebraic data in number fields of degree pn(n-1)/2 at most; in many cases this number can be reduced. Two examples with p=3 and n=4 are given.     

Asymptotic Bayesian structure learning using graph supports for Gaussian graphical models

The theory of Gaussian graphical models is a powerful tool for independence analysis between continuous variables. In this framework, various methods have been conceived to infer independence relations from data samples. However, most of them result in stepwise, deterministic, descent algorithms that are inadequate for solving this issue. More recent developments have focused on stochastic procedures, yet they all base their research on strong a priori knowledge and are unable to perform model selection among the set of all possible models. Moreover, convergence of the corresponding algorithms is slow, precluding applications on a large scale. In this paper, we propose a novel Bayesian strategy to deal with structure learning. Relating graphs to their supports, we convert the problem of model selection into that of parameter estimation. Use of non-informative priors and asymptotic results yield a posterior probability for independence graph supports in closed form. Gibbs sampling is then applied to approximate the full joint posterior density. We finally give three examples of structure learning, one from synthetic data, and the two others from real data.     

Rheological behavior of sewage sludge and strain-induced dewatering

In order to study the strain-induced water release in sewage sludge and its connection with rheological behavior, two types of rheological tests have been carried out. The rheology of sewage sludge samples stemming from a urban sewer was first characterized using a Couette cell system. In particular, the yielding behavior and the elastic modulus of the sludge has been considered under shear flow conditions. In these pure shear tests the reproducibility of the measurements was rather poor, limiting this study to low strains. Consequently, a second type of rheological tests, namely the squeeze test, which is more appropriate for these paste-like materials, has been considered. The rheological behavior along with the dewatering efficiency have been studied under the squeeze flow conditions. Surprisingly, it was found that, under certain conditions, the strain-induced water release mechanism became more effective when decreasing the squeeze speed. This was interpreted in terms of a competition between the paste flow and the water filtration through the porous media made up by the flocs.     

Mixtures of foam and paste: suspensions of bubbles in yield stress fluids

We study the rheological behavior of mixtures of foams and pastes, which can be described as suspensions of bubbles in yield stress fluids. Model systems are designed by mixing monodisperse aqueous foams and concentrated emulsions. The elastic modulus of the bubble suspensions is found to depend on the elastic capillary number $\textit{Ca}_{_G}$ , defined as the ratio of the paste elastic modulus to the bubble capillary pressure. For values of $\textit{Ca}_{_G}$ larger than $\simeq 0.5$ , the dimensionless elastic modulus of the aerated material decreases as the bubble volume fraction $\phi $ increases, suggesting that bubbles behave as soft elastic inclusions. Consistently, this decrease is all the sharper as $\textit{Ca}_{_G}$ is high, which accounts for the softening of the bubbles as compared to the paste. By contrast, we find that the yield stress of most studied materials is not modified by the presence of bubbles. This suggests that their plastic behavior is governed by the plastic capillary number $\textit{Ca}_{\tau_y}$ , defined as the ratio of the paste yield stress to the bubble capillary pressure. At low $\textit{Ca}_{\tau_y}$ values, bubbles behave as nondeformable inclusions, and we predict that the suspension dimensionless yield stress should remain close to unity, in agreement with our data up to $\textit{Ca}_{\tau_y}=0.2$ . When preparing systems with a larger target value of $\textit{Ca}_{\tau_y}$ , we observe bubble breakup during mixing, which means that they have been deformed by shear. It then seems that a critical value $\textit{Ca}_{\tau_y}\simeq 0.2$ is never exceeded in the final material. These observations might imply that, in bubble suspensions prepared by mixing a foam and a paste, the suspension yield stress is always close to that of the paste surrounding the bubbles. Finally, at the highest $\phi $ investigated, the yield stress is shown to increase abruptly with $\phi $ : this is interpreted as a “foamy yield stress fluid” regime, which takes place when the paste mesoscopic constitutive elements (here, the oil droplets) are strongly confined in the films between the bubbles.     

Variation of Raman spectrum after optical excitation in amorphous As2Se3 at 1.6°K

Several experiments, involving electronic states have shown that amorphous As₂Se₃ is modified at low temperature by the action of not very strongly absorbed light (α～10²cm^?1). This paper presents Raman scattering results before and after illumination. The shape of the Raman spectrum is changed by illumination: its high energy side has grown near 260 cm^?1. This light induced modification of the vibrational states is discussed within the framework of a previous qualitative model involving changes in local atomic configuration.     

Luminescence lineshape of free excitons and electron-hole drops in Si

We study experimentally and theoretically the lineshape of the TO-LO and TA phonon assisted luminescence of free excitons and electron-hole drops in Si. We show that, in the case of the TA replica, the appropriate electron-phonon matrix element should be taken k-dependent, contrary to previous investigations.     

Time of flight of excitonic polaritons in CdSe

Time of flight of polaritons is studied in the forbidden, mixed and allowed modes of propagation. With only one adjustable parameter, we obtain a very good agreement between all the experimental data and the usual oscillator model. In the calculation, the excited states of the A exciton and the n = 1 state of the B exciton are taken into account. The longitudinal-transverse splitting energy ?ω_LT is found to be equal to 1.3 meV. We show that very close to resonances, it is not possible to describe the temporal evolution of the pulse by the group velocity of the wave packet. We give an example which shows we have to use the Fourier transform method.     

Tuning organogels and mesophases with phenanthroline ligands and their copper complexes by inter- to intramolecular hydrogen bonds

A novel family of highly functionalized molecules consisting of a central 4-methyl-3,5-diacylaminobenzene platform linked in close proximity to the methyl group by two lateral aromatic rings each equipped with two long alkoxy chains has been rationally designed. The presence of amide tethers and a chelating phenanthroline fragment connected via an ester dipole formed a new class of gelating reagents and mesomorphic materials. A few of these compounds have the tendency to form macromolecule-like aggregates through noncovalent interactions in hydrocarbon solvents and were found to exhibit thermotropic cubic mesophases. In light of the X-ray molecular structure of the methoxy ligand, an infinite network maintained by intermolecular hydrogen bonds as well as by pi-pi stacking of the phenyl subunits was evidenced. FT-IR studies confirm that the common driving force for aggregation in the organogels and microsegregation in the mesophase is the occurrence of a tight intermolecular H-bonded network that does not persist in diluted solution. This situation is switched when the ligands are interlocked by a copper(I) cation. A strong intramolecular H-bond confirmed by X-ray diffraction of a single crystal for the methoxy case provides very stable complexes but inhibits the gelation of the solvents. Heating the complexes bearing long paraffin chains (n = 12 and 16) in the dried state leads to a self-organization into a columnar liquid-crystalline phase in which the columns are arranged along a 2D oblique symmetry as deduced from powder XRD experiments. In this case, the complexes with the appended counteranions self-assemble in a specific way to form columns. A striking observation is that the intramolecular hydrogen bond persists in the mesophase as it does in solution without any evidence of an extended network. As far as we are aware, these ligands and complexes are rare examples in which organogelation and thermotropic mesomorphic behavior could be observed in parallel with molecules bearing a chelating platform. Due to the synthetic availability of the 4-methyl-3,5-diacylaminobenzene core and the simplicity by which the chelating platforms can be graphed, this methodology represents a practical alternative to the production of functionalized organogelators and mesomorphic materials.     

Large structural modification with conserved conformation: analysis of delta(3)-fused aryl prolines in model beta-turns

For the first time, the influence of a fused Delta3-arylproline on peptide conformation has been studied by the synthesis and comparison of the conformations of peptides containing proline and pyrrolo-proline, 3 (PyPro). Pyrrolo-proline was demonstrated to be a conservative replacement for Pro in model beta-turns, 4 and 5, as shown by their similar DMSO titration curves, cis/trans-isomer populations, and NOESY spectral data. Pyrrolo-proline may thus be used for studying the structure activity relationships of Pro-containing peptides with minimal modification of secondary structures.