Broad distribution effects in sums of lognormal random variables

The lognormal distribution describing, e.g., exponentials of Gaussian random variables is one of the most common statistical distributions in physics. It can exhibit features of broad distributions that imply qualitative departure from the usual statistical scaling associated to narrow distributions. Approximate formulae are derived for the typical sums of lognormal random variables. The validity of these formulae is numerically checked and the physical consequences, e.g., for the current flowing through small tunnel junctions, are pointed out.Comment: 14 pages, 9 figures. Minor changes + Gini coefficient and 4 refs. adde

Twisted Jacobi manifolds, twisted Dirac-Jacobi structures and quasi-Jacobi bialgebroids

We study twisted Jacobi manifolds, a concept that we had introduced in a previous Note. Twisted Jacobi manifolds can be characterized using twisted Dirac-Jacobi, which are sub-bundles of Courant-Jacobi algebroids. We show that each twisted Jacobi manifold has an associated Lie algebroid with a 1-cocycle. We introduce the notion of quasi-Jacobi bialgebroid and we prove that each twisted Jacobi manifold has a quasi-Jacobi bialgebroid canonically associated. Moreover, the double of a quasi-Jacobi bialgebroid is a Courant-Jacobi algebroid. Several examples of twisted Jacobi manifolds and twisted Dirac-Jacobi structures are presented

Unimodality of steady state distributions of growing cell populations

We consider an equation for the evolution of growing and dividing cells, and show, using a result of Kato and McLeod, that the probability density function for the stationary size distribution is necessarily unimodal

A Second Shell in the Fornax dSph Galaxy

In the search for tidal structure in Galactic satellite systems, we have conducted a photometric survey over a 10 square degree area centred on the Fornax dSph galaxy. The survey was made in two colours, and the resulting colour-magnitude data were used as a mask to select candidate Fornax RGB stars, thereby increasing the contrast of Fornax stars to background sources in the outer regions. Previously, we reported the presence of a shell (age 2 Gyr) located towards the centre of Fornax. In this contribution we reveal a second shell, significantly larger than the first, located 1.3 degrees NW from the centre of Fornax, outside the nominal tidal radius. Moreover, the distribution of Fornax RGB stars reveals two lobes extending to the spatial limit of our survey, and aligned with the minor axis and with the two shells. These results support the hypothesis of a merger between Fornax and a gas-rich companion approximately 2 Gyr ago.Comment: Four pages,accepted for the Publications of the Astronomical Society of Australia. Contribution the annual ASA meeting, Brisbane 200