Two examples of non strictly convex large deviations

We present two examples of a large deviations principle where the rate function is not strictly convex. This is motivated by a model used in mathematical finance (the Heston model), and adds a new item to the zoology of non strictly convex large deviations. For one of these examples, we show that the rate function of the Cramer-type of large deviations coincides with that of the Freidlin-Wentzell when contraction principles are applied.Comment: 11 page

Internal stresses and breakup of rigid isostatic aggregates in homogeneous and isotropic turbulence

By characterising the hydrodynamic stresses generated by statistically homogeneous and isotropic turbulence in rigid aggregates, we estimate theoretically the rate of turbulent breakup of colloidal aggregates and the size distribution of the formed fragments. The adopted method combines Direct Numerical Simulation of the turbulent field with a Discrete Element Method based on Stokesian dynamics. In this way, not only the mechanics of the aggregate is modelled in detail, but the internal stresses are evaluated while the aggregate is moving in the turbulent flow. We examine doublets and cluster-cluster isostatic aggregates, where the failure of a single contact leads to the rupture of the aggregate and breakup occurs when the tensile force at a contact exceeds the cohesive strength of the bond. Due to the different role of the internal stresses, the functional relationship between breakup frequency and turbulence dissipation rate is very different in the two cases. In the limit of very small and very large values, the frequency of breakup scales exponentially with the turbulence dissipation rate for doublets, while it follows a power law for cluster-cluster aggregates. For the case of large isostatic aggregates it is confirmed that the proper scaling length for maximum stress and breakup is the radius of gyration. The cumulative fragment distribution function is nearly independent of the mean turbulence dissipation rate and can be approximated by the sum of a small erosive component and a term that is quadratic with respect to fragment size.Comment: 31 pages, 19 figure

The Bizarre Spectral Variability of Central Stars of Planetary Nebulae

A radial velocity (RV) survey to detect central stars in binary systems was carried out between 2002 and 2004. De Marco et al. (2004) reported that 10 out of 11 monitored stars exhibited strong RV variability, but periods were not detected. Since other mechanisms, such as wind variability, can cause apparent RV variations, we monitored 4 of the 10 RV-variable stars at echelle resolutions to determine the origin of the variability. Although RV changes are confirmed for all four stars, none of them can be ascribed to binarity at this time. However, only for IC4593 is wind variability able to explain most (though not all) spectral variability. For BD+332642, no wind and no pulsations appear to be the origin of the RV changes. Finally, M1-77 and M2-54, both known to be irregular photometric variables, exhibit dramatic RV and line shape variability of the hydrogen and HeI absorption lines, as well as large RV variability of weaker lines, which do not change in shape. There is no satisfactory explanation of this variability, though a combination of wind variability and pulsations is still the best guess at what makes these stars so variable. We suggest that luminous central stars are ill suited to detect spectroscopic binaries, because winds (and possibly pulsations) are pervasive and would mask even strong periodicities. It it likely that a sample of intrinsically faint central stars would more readily yield binary information.Comment: 7 pages, 3 figures. To appear in the proceedings of the conference "Asymmetric Planetary Nebulae IV