6,307 research outputs found
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
with intensity measures of the form where is
Lebesgue measure, and (the "family lifetime measure") is an arbitrary,
absolutely continuous measure satisfying and
. Special cases of this construction
describe the time evolution of the MRCA age in -stable continuous
state branching processes conditioned on nonextinction--a particular case of
which, , 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)
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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
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