Saturation Effects and the Concurrency Hypothesis: Insights from an Analytic Model

Sexual partnerships that overlap in time (concurrent relationships) may play a significant role in the HIV epidemic, but the precise effect is unclear. We derive edge-based compartmental models of disease spread in idealized dynamic populations with and without concurrency to allow for an investigation of its effects. Our models assume that partnerships change in time and individuals enter and leave the at-risk population. Infected individuals transmit at a constant per-partnership rate to their susceptible partners. In our idealized populations we find regions of parameter space where the existence of concurrent partnerships leads to substantially faster growth and higher equilibrium levels, but also regions in which the existence of concurrent partnerships has very little impact on the growth or the equilibrium. Additionally we find mixed regimes in which concurrency significantly increases the early growth, but has little effect on the ultimate equilibrium level. Guided by model predictions, we discuss general conditions under which concurrent relationships would be expected to have large or small effects in real-world settings. Our observation that the impact of concurrency saturates suggests that concurrency-reducing interventions may be most effective in populations with low to moderate concurrency

Optical properties of carbon grains: Influence on dynamical models of AGB stars

For amorphous carbon several laboratory extinction data are available, which show quite a wide range of differences due to the structural complexity of this material. We have calculated self-consistent dynamic models of circumstellar dust-shells around carbon-rich asymptotic giant branch stars, based on a number of these data sets. The structure and the wind properties of the dynamical models are directly influenced by the different types of amorphous carbon. In our test models the mass loss is not severely dependent on the difference in the optical properties of the dust, but the influence on the degree of condensation and the final outflow velocity is considerable. Furthermore, the spectral energy distributions and colours resulting from the different data show a much wider spread than the variations within the models due to the variability of the star. Silicon carbide was also considered in the radiative transfer calculations to test its influence on the spectral energy distribution.Comment: 12 pages, 6 figures. To appear in A&

Reconsidering the origin of the 21 micron feature: Oxides in carbon-rich PPNe?

The origin of the so-called "21 micron" feature which is especially prominent in the spectra of some carbon-rich protoplanetary nebulae (PPNe}) is the matter of a lively debate. A large number of potential band carriers have been presented and discarded within the past decade. The present paper gives an overview of the problems related to the hitherto proposed feature identifications, including the recently suggested candidate carrier silicon carbide. We also discuss the case for spectroscopically promising oxides. SiC is shown to produce a strong resonance band at 20-21 micron if coated by a layer of silicon dioxide. At low temperatures, core-mantle particles composed of SiC and amorphous SiO$_2$ indeed have their strongest spectral signature at a position of 20.1 micron, which coincides with the position of the "21 micron" emission band. The optical constants of another candidate carrier that has been relatively neglected so far -- iron monoxide -- are proven to permit a fairly accurate reproduction of the "21 micron" feature profile as well, especially when low-temperature measurements of the infrared properties of FeO are taken into account. As candidate carrier of the "21 micron" emission band, FeO has the advantage of being stable against further oxidation and reduction only in a narrow range of chemical and physical conditions, coinciding with the fact that the feature, too, is detected in a small group of objects only. However, it is unclear how FeO should form or survive particularly in carbon-rich PPNe.Comment: 28 pages, 15 figures, accepted for publication in ApJ (December

Stellar abundances and presolar grains trace the nucleosynthetic origin of molybdenum and ruthenium

This work presents a large consistent study of molybdenum (Mo) and ruthenium (Ru) abundances in the Milky Way. These two elements are important nucleosynthetic diagnostics. In our sample of 71 Galactic metal-poor field stars, we detect Ru and/or Mo in 51 of these (59 including upper limits). The sample consists of high-resolution, high signal-to-noise spectra covering both dwarfs and giants from [Fe/H]=-0.63 down to -3.16. Thus we provide information on the behaviour of Mo I and Ru I at higher and lower metallicity than is currently known. We find a wide spread in the Mo and Ru abundances, which is typical of heavy elements. This indicates that several formation processes, in addition to high entropy winds, can be responsible for the formation of Mo and Ru. The formation processes are traced by comparing Mo and Ru to elements (Sr, Zr, Pd, Ag, Ba, and Eu) with known formation processes. We find contributions from different formation channels, namely p-, slow (s-), and rapid (r-) neutron-capture processes. Molybdenum is a highly convolved element that receives contributions from several processes, whereas Ru is mainly formed by the weak r-process as is silver. We also compare our absolute elemental stellar abundances to relative isotopic abundances of presolar grains extracted from meteorites. Their isotopic abundances can be directly linked to the formation process (e.g. r-only isotopes) providing a unique comparison between observationally derived abundances and the nuclear formation process. The comparison to abundances in presolar grains shows that the r-/s-process ratios from the presolar grains match the total elemental chemical composition derived from metal-poor halo stars with [Fe/H]~ -1.5 to -1.1 dex. This indicates that both grains and stars around and above [Fe/H]=-1.5 are equally (well) mixed and therefore do not support a heterogeneous presolar nebula... Abridged.Comment: 18 pages, 12 figures, accepted by A&

Hong-Ou-Mandel-like two-droplet correlations

We present a numerical study of two-droplet pair correlations for in-phase droplets walking on a vibrating bath. Two such walkers are launched towards a common origin. As they approach, their carrier waves may overlap and the droplets have a non-zero probability of forming a two-droplet bound state. The likelihood of such pairing is quantified by measuring the probability of finding the droplets in a bound state at late times. Three generic types of two-droplet correlations are observed: promenading, orbiting and chasing pair of walkers. For certain parameters, the droplets may become correlated for certain initial path differences and remain uncorrelated for others, while in other cases the droplets may never produce droplet pairs. These observations pave the way for further studies of strongly correlated many-droplet behaviors in the hydrodynamical quantum analogs of bouncing and walking droplets.Comment: 8 pages, 5 figure

From flux to dust mass: Does the grain-temperature distribution matter for estimates of cold dust masses in supernova remnants?

The amount of dust estimated from infrared to sub-millimetre (submm) observations strongly depends on assumptions of different grain sizes, compositions and optical properties. Here we use a simple model of thermal emission from cold silicate/carbon dust at a range of dust grain temperatures and fit the spectral energy distribution (SED) of the Crab Nebula as a test. This can lower the derived dust mass for the Crab by ~50% and 30-40% for astronomical silicates and amorphous carbon grains compared to recently published values (0.25M_sun -> 0.12M_sun and 0.12M_sun -> 0.072M_sun, respectively), but the implied dust mass can also increase by as much as almost a factor of six (0.25M_sun -> 1.14M_sun and 0.12M_sun -> 0.71M_sun) depending on assumptions regarding the sizes/temperatures of the coldest grains. The latter values are clearly unrealistic due to the expected metal budget, though. Furthermore, we show by a simple numerical experiment that if a cold-dust component does have a grain-temperature distribution, it is almost unavoidable that a two-temperature fit will yield an incorrect dust mass estimate. But we conclude that grain temperatures is not a greater uncertainty than the often poorly constrained emissivities (i.e., material properties) of cosmic dust, although there is clearly a need for improved dust emission models. The greatest complication associated with deriving dust masses still arises in the uncertainty in the dust composition.Comment: 13 pages, 7 figures, to appear in MNRA

On the (in)variance of the dust-to-metals ratio in galaxies

Recent works have demonstrated a surprisingly small variation of the dust-to-metals ratio in different environments and a correlation between dust extinction and the density of stars. Naively, one would interpret these findings as strong evidence of cosmic dust being produced mainly by stars. But other observational evidence suggest there is a significant variation of the dust-to-metals ratio with metallicity. As we demonstrate in this paper, a simple star-dust scenario is problematic also in the sense that it requires that destruction of dust in the interstellar medium (e.g., due to passage of supernova shocks) must be highly inefficient. We suggest a model where stellar dust production is indeed efficient, but where interstellar dust growth is equally important and acts as a replenishment mechanism which can counteract the effects of dust destruction. This model appears to resolve the seemingly contradictive observations, given that the ratio of the effective (stellar) dust and metal yields is not universal and thus may change from one environment to another, depending on metallicity.Comment: 10 pages, 4 figures. Accepted for publication in MNRA

A Dynamically Diluted Alignment Model Reveals the Impact of Cell Turnover on the Plasticity of Tissue Polarity Patterns

The polarisation of cells and tissues is fundamental for tissue morphogenesis during biological development and regeneration. A deeper understanding of biological polarity pattern formation can be gained from the consideration of pattern reorganisation in response to an opposing instructive cue, which we here consider by example of experimentally inducible body axis inversions in planarian flatworms. Our dynamically diluted alignment model represents three processes: entrainment of cell polarity by a global signal, local cell-cell coupling aligning polarity among neighbours and cell turnover inserting initially unpolarised cells. We show that a persistent global orienting signal determines the final mean polarity orientation in this stochastic model. Combining numerical and analytical approaches, we find that neighbour coupling retards polarity pattern reorganisation, whereas cell turnover accelerates it. We derive a formula for an effective neighbour coupling strength integrating both effects and find that the time of polarity reorganisation depends linearly on this effective parameter and no abrupt transitions are observed. This allows to determine neighbour coupling strengths from experimental observations. Our model is related to a dynamic $8$-Potts model with annealed site-dilution and makes testable predictions regarding the polarisation of dynamic systems, such as the planarian epithelium.Comment: Preprint as prior to first submission to Journal of the Royal Society Interface. 25 pages, 6 figures, plus supplement (18 pages, contains 1 table and 7 figures). A supplementary movie is available from https://dx.doi.org/10.6084/m9.figshare.c388781