Dynamics of the time to the most recent common ancestor in a large branching population

If we follow an asexually reproducing population through time, then the amount of time that has passed since the most recent common ancestor (MRCA) of all current individuals lived will change as time progresses. The resulting "MRCA age" process has been studied previously when the population has a constant large size and evolves via the diffusion limit of standard Wright--Fisher dynamics. For any population model, the sample paths of the MRCA age process are made up of periods of linear upward drift with slope +1 punctuated by downward jumps. We build other Markov processes that have such paths from Poisson point processes on $\mathbb{R}_{++}\times\mathbb{R}_{++}$ with intensity measures of the form $\lambda\otimes\mu$ where $\lambda$ is Lebesgue measure, and $\mu$ (the "family lifetime measure") is an arbitrary, absolutely continuous measure satisfying $\mu((0,\infty))=\infty$ and $\mu((x,\infty))0$. Special cases of this construction describe the time evolution of the MRCA age in $(1+\beta)$-stable continuous state branching processes conditioned on nonextinction--a particular case of which, $\beta=1$, is Feller's continuous state branching process conditioned on nonextinction. As well as the continuous time process, we also consider the discrete time Markov chain that records the value of the continuous process just before and after its successive jumps. We find transition probabilities for both the continuous and discrete time processes, determine when these processes are transient and recurrent and compute stationary distributions when they exist.Comment: Published in at http://dx.doi.org/10.1214/09-AAP616 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Dynamics of a surface-gradient-driven liquid film rising from a reservoir onto a substrate

On a tilted heated substrate, surface tension gradients can draw liquid up out of a reservoir. The resulting film thickness profile is controlled by the tilt of the substrate, the imposed temperature gradient, and the thickness of a postulated thin precursor layer. We study the evolution of this film in time, using a lubrication model. A number of distinct behaviours are possible as the substrate tilt angle and other parameters are varied. We use recent results for the multiple stationary profiles possible near the meniscus and examine how these can interact with the advancing front. We show that it is in fact possible to systematically determine the evolution of the entire film profile from the meniscus to the apparent contact line. This allows a categorisation of the range of behaviours for a transversely-uniform profile, in a two-dimensional parameter space. In addition to combinations of meniscus profiles involving capillary fronts and double shock structures, we describe a new combination of a Type I meniscus with a rarefaction fan, and either undercompressive or classical waves for the advancing front, that arises for certain ranges of large substrate tilt and of precursor thickness

Management systems for sheep.

Trial 89KA6 Location: Kojonup To measure the effects of set stocking and strip (ration) grazing on: i) Pasture production, composition and quantity ii) Sheep production (liveweight, condition score, wool growth rate, fibre diameter, strength and vegetable matter contamination)

From bell shapes to pyramids . continuum model for self-assembled quantum dot growth

A continuum model for the growth of self-assembled quantum dots that incorporates surface diffusion, an elastically deformable substrate, wetting interactions and anisotropic surface energy is presented. Using a small slope approximation a thin film equation for the surface profile that describes facetted growth is derived. A linear stability analysis shows that anisotropy acts to destabilize the surface. It lowers the critical height of flat films and there exists an anisotropy strength above which all thicknesses are unstable. A numerical algorithm based on spectral differentiation is presented and simulation are carried out. These clearly show faceting of the growing islands and a logarithmically slow coarsening behavior

From bell shapes to pyramids: A continuum model for self-assembled quantum dot growth

A continuum model for the growth of self-assembled quantum dots that incorporates surface diffusion, an elastically deformable substrate, wetting interactions and anisotropic surface energy is presented. Using a small slope approximation a thin film equation for the surface profile that describes facetted growth is derived. A linear stability analysis shows that anisotropy acts to destabilize the surface. It lowers the critical height of flat films and there exists an anisotropy strength above which all thicknesses are unstable. A numerical algorithm based on spectral differentiation is presented and simulation are carried out. These clearly show faceting of the growing islands and a logarithmically slow coarsening behavior

Intermediate-asymptotic structure of a dewetting rim with strong slip

When a thin viscous liquid film dewets, it typically forms a rim which spreads outwards, leaving behind a growing dry region. We consider the dewetting behaviour of a film, when there is strong slip at a liquid-substrate interface. The film can be modelled by two coupled partial differential equations (PDEs) describing the film thickness and velocity. Using asymptotic methods, we describe the structure of the rim as it evolves in time, and the rate of dewetting, in the limit of large slip lengths. An inner region emerges, closest to the dewetted region, where surface tension is important; in an outer region, three subregions develop. This asymptotic description is compared with numerical solutions of the full system of PDEs

A survey of diffuse interstellar bands in the Andromeda galaxy: optical spectroscopy of M31 OB stars

We present the largest sample to-date of intermediate-resolution blue-to-red optical spectra of B-type supergiants in M31 and undertake the first survey of diffuse interstellar bands (DIBs) in this galaxy. Spectral classifications, radial velocities and interstellar reddenings are presented for 34 stars in three regions of M31. Radial velocities and equivalent widths are given for the 5780 and 6283 DIBs towards 11 stars. Equivalent widths are also presented for the following DIBs detected in three sightlines in M31: 4428, 5705, 5780, 5797, 6203, 6269, 6283, 6379, 6613, 6660, and 6993. All of these M31 DIB carriers reside in clouds at radial velocities matching those of interstellar Na I and/or H I. The relationships between DIB equivalent widths and reddening (E(B-V)) are consistent with those observed in the local ISM of the Milky Way. Many of the observed sightlines show DIB strengths (per unit reddening) which lie at the upper end of the range of Galactic values. DIB strengths per unit reddening are found (with 68% confidence), to correlate with the interstellar UV radiation field strength. The strongest DIBs are observed where the interstellar UV flux is lowest. The mean Spitzer 8/24 micron emission ratio in our three fields is slightly lower than that measured in the Milky Way, but we identify no correlation between this ratio and the DIB strengths in M31. Interstellar oxygen abundances derived from the spectra of three M31 H II regions in one of the fields indicate that the average metallicity of the ISM in that region is 12 + log[O/H] = 8.54 +- 0.18, which is approximately equal to the value in the solar neighbourhood