Normalizations of Eisenstein integrals for reductive symmetric spaces

We construct minimal Eisenstein integrals for a reductive symmetric space G/H as matrix coefficients of the minimal principal series of G. The Eisenstein integrals thus obtained include those from the \sigma-minimal principal series. In addition, we obtain related Eisenstein integrals, but with different normalizations. Specialized to the case of the group, this wider class includes Harish-Chandra's minimal Eisenstein integrals.Comment: 66 pages. Minor revisions. To be published in Journal of Functional Analysi

KK-invariant cusp forms for reductive symmetric spaces of split rank one

Let $G/H$ be a reductive symmetric space of split rank $1$ and let $K$ be a maximal compact subgroup of $G$. In a previous article the first two authors introduced a notion of cusp forms for $G/H$. We show that the space of cusp forms coincides with the closure of the $K$-finite generalized matrix coefficients of discrete series representations if and only if there exist no $K$-spherical discrete series representations. Moreover, we prove that every $K$-spherical discrete series representation occurs with multiplicity $1$ in the Plancherel decomposition of $G/H$.Comment: 12 page

Emulsification in binary liquids containing colloidal particles: a structure-factor analysis

We present a quantitative confocal-microscopy study of the transient and final microstructure of particle-stabilised emulsions formed via demixing in a binary liquid. To this end, we have developed an image-analysis method that relies on structure factors obtained from discrete Fourier transforms of individual frames in confocal image sequences. Radially averaging the squared modulus of these Fourier transforms before peak fitting allows extraction of dominant length scales over the entire temperature range of the quench. Our procedure even yields information just after droplet nucleation, when the (fluorescence) contrast between the two separating phases is scarcely discernable in the images. We find that our emulsions are stabilised on experimental time scales by interfacial particles and that they are likely to have bimodal droplet-size distributions. We attribute the latter to coalescence together with creaming being the main coarsening mechanism during the late stages of emulsification and we support this claim with (direct) confocal-microscopy observations. In addition, our results imply that the observed droplets emerge from particle-promoted nucleation, possibly followed by a free-growth regime. Finally, we argue that creaming strongly affects droplet growth during the early stages of emulsification. Future investigations could clarify the link between quench conditions and resulting microstructure, paving the way for tailor-made particle-stabilised emulsions from binary liquids.Comment: http://iopscience.iop.org/0953-8984/22/45/455102

Gas phase polymerization of ethylene with a silica-supported metallocene catalyst: influence of temperature on deactivation

Ethylene was polymerized at 5 bar in a stirred powder bed reactor with silica supported rac-Me2Si[Ind]2ZrCl2/methylaluminoxane (MAO) at temperatures between 40°C and 80°C using NaCl as support bed and triethylaluminium (TEA) as a scavenger for impurities. For this fixed recipe and a given charge of catalyst. the average catalyst activity is reproducible within 10% for low temperatures. The polymerization rate and the rate of deactivation increase with increasing temperature. The deactivation could be modeled using a first order dependence with respect to the polymerization rate

Maternal and perinatal complications in triplet compared with twin pregnancy

Objective: To compare maternal and perinatal complications in triplet and twin pregnancies. Study design: Case-controlled study in the setting of a University Hospital. Each pregnancy of a consecutive series of 40 triplet pregnancies of 20 weeks or more was matched for parity and maternal age with two sets of twins delivered in the same year. Primary end points of the analysis were maternal complications and perinatal outcome. Results: Of the triplets 82% and of the twins 36% were a result of assisted reproduction. Pre-term labor occurred significantly more often in triplet than in twin gestation. Triplets had a significantly lower median birth-weight (1478 vs. 2030 g) and gestational age at delivery (32 vs. 35.5 weeks). The mean neonatal hospital stay was significantly longer in triplets, mainly related to the lower birth-weight, but there was no significant difference between triplets and twins in the incidence of major neonatal complications. Conclusion: This data of the anticipated perinatal outcome in triplet and twin pregnancies may be used to counsel women with a triplet pregnancy considering selective reduction to twins. All methods of assisted reproduction should aim at prevention of multifetal gestation

Experimental evidence of solitary wave interaction in Hertzian chains

We study experimentally the interaction between two solitary waves that approach one to another in a linear chain of spheres interacting via the Hertz potential. When these counter propagating waves collide, they cross each other and a phase shift respect to the noninteracting waves is introduced, as a result of the nonlinear interaction potential. This observation is well reproduced by our numerical simulations and it is shown to be independent of viscoelastic dissipation at the beads contact. In addition, when the collision of equal amplitude and synchronized counter propagating waves takes place, we observe that two secondary solitary waves emerge from the interacting region. The amplitude of secondary solitary waves is proportional to the amplitude of incident waves. However, secondary solitary waves are stronger when the collision occurs at the middle contact in chains with even number of beads. Although numerical simulations correctly predict the existence of these waves, experiments show that their respective amplitude are significantly larger than predicted. We attribute this discrepancy to the rolling friction at the beads contacts during solitary wave propagation