Heavy Traffic Limit for a Tandem Queue with Identical Service Times

We consider a two-node tandem queueing network in which the upstream queue is M/G/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. We investigate the amount of work in the second queue at certain embedded arrival time points, namely when the upstream queue has just emptied. We focus on the case of infinite-variance service times and obtain a heavy traffic process limit for the embedded Markov chain

Thermal Modeling in Polymer Extrusion

In this paper we consider thermal effects of polymer flows through a cylindrical die. First, we derive a model for the oscillatory behavior of polymer flow in an extruder given a functional relation between the pressure and flow rate. A simple isothermal but temperature dependent model is constructed to find this relation. Unfortunately, the model is shown to be invalid in the physical regime of interest. We present several arguments to suggest that the isothermal assumption is reasonable but that a more detailed understanding of the small-scale molecular dynamics near the boundary may be required. Second, we show that a simplified model for thermoflow multiplicity in a cooled tube is inconsistent, when the stationary non-Newtonian flow is assumed to be incompressible without radial pressure gradients and without radial velocity. This inconsistency can be removed by allowing for weak compressibility effects in the down-steam area

Evaluation of white spot syndrome virus variable DNA loci as molecular markers of virus spread at intermediate spatiotemporal scales

Variable genomic loci have been employed in a number of molecular epidemiology studies of white spot syndrome virus (WSSV), but it is unknown which loci are suitable molecular markers for determining WSSV spread on different spatiotemporal scales. Although previous work suggests that multiple introductions of WSSV occurred in central Vietnam, it is largely uncertain how WSSV was introduced and subsequently spread. Here, we evaluate five variable WSSV DNA loci as markers of virus spread on an intermediate (i.e. regional) scale, and develop a detailed and statistically supported model for the spread of WSSV. The genotypes of 17 WSSV isolates from along the coast of Vietnam – nine of which were newly characterized in this study – were analysed to obtain sufficient samples on an intermediate scale and to allow statistical analysis. Only the ORF23/24 variable region is an appropriate marker on this scale, as geographically proximate isolates show similar deletion sizes. The ORF14/15 variable region and variable-number tandem repeat (VNTR) loci are not useful as markers on this scale. ORF14/15 may be suitable for studying larger spatiotemporal scales, whereas VNTR loci are probably suitable for smaller scales. For ORF23/24, there is a clear pattern in the spatial distribution of WSSV: the smallest genomic deletions are found in central Vietnam, and larger deletions are found in the south and the north. WSSV genomic deletions tend to increase over time with virus spread in cultured shrimp, and our data are therefore congruent with the hypothesis that WSSV was introduced in central Vietnam and then radiated ou

On the Interpretation of the Age Distribution of Star Clusters in the Small Magellanic Cloud

We re-analyze the age distribution (dN/dt) of star clusters in the Small Magellanic Cloud (SMC) using age determinations based on the Magellanic Cloud Photometric Survey. For ages younger than 3x10^9 yr the dN/dt distribution can be approximated by a power-law distribution, dN/dt propto t^-beta, with -beta=-0.70+/-0.05 or -beta=-0.84+/-0.04, depending on the model used to derive the ages. Predictions for a cluster population without dissolution limited by a V-band detection result in a power-law dN/dt distribution with an index of ~-0.7. This is because the limiting cluster mass increases with age, due to evolutionary fading of clusters, reducing the number of observed clusters at old ages. When a mass cut well above the limiting cluster mass is applied, the dN/dt distribution is flat up to 1 Gyr. We conclude that cluster dissolution is of small importance in shaping the dN/dt distribution and incompleteness causes dN/dt to decline. The reason that no (mass independent) infant mortality of star clusters in the first ~10-20 Myr is found is explained by a detection bias towards clusters without nebular emission, i.e. cluster that have survived the infant mortality phase. The reason we find no evidence for tidal (mass dependent) cluster dissolution in the first Gyr is explained by the weak tidal field of the SMC. Our results are in sharp contrast to the interpretation of Chandar et al. (2006), who interpret the declining dN/dt distribution as rapid cluster dissolution. This is due to their erroneous assumption that the sample is limited by cluster mass, rather than luminosity.Comment: 8 pages, 4 figures, accepted for publication in Ap

The Living Rainforest Sustainable Greenhouses

The Living Rainforest (www.livingrainforest.org) is an educational charity that uses rainforest ecology as a metaphor for communicating general sustainability issues to the public. Its greenhouses and office buildings are to be renovated using the most sustainable methods currently available. This will be realised through construction of a high insulating greenhouse covering with a k-value of less than 2 Wm-2K-1, passive seasonal storage of excess summer solar energy in the ground by a ground source heat exchanger and exploitation of this low grade solar energy for heating in winter by a heat pump. In winter the heat pump will produce cold water to cool the ground allowing a passive cooling function in summer via the GSHE. It will be demonstrated that a GSHE is an alternative for an open aquifer in regions with no aquifer availability. The heat pump will deliver the heating baseload, the peak load will be delivered by a biomass boiler, fired with locally-sourced low-cost wood chips. It is expected that the energy saving will be about 75%, resulting in a major cost reduction. The low k-value of the covering is linked to a light transmission of 75 %. This is high enough for the demands of the vegetation in The Living Rainforest. Because the inner greenhouse climate demands are comparable to that of ornamentals, the results will be applicable to commercial ornamental production. In future low k-value coverings will also be available with high light transmission, allowing wider application of the results. This paper focuses on the correlation between k-value, light transmission and energy demand in order to investigate the trade-off between light transmittance (a major energy gain) and heat loss. The effects of these design parameters on storage and harvesting capacity are also considered but appear to have a low sensitivity. The renovated greenhouse site at The Living Rainforest will show that new greenhouses and ecology can be linked to sustainability and this will be communicated and demonstrated to the public

Runaway Merging of Black Holes: Analytical Constraint on the Timescale

Following the discovery of a black hole (BH) with a mass of 10^3-10^6 M(sun) in a starburst galaxy M82, we study formation of such a BH via successive merging of stellar-mass BHs within a star cluster. The merging has a runaway characteristic. This is because massive BHs sink into the cluster core and have a high number density, and because the merging probability is higher for more massive BHs. We use the Smoluchowski equation to study analytically the evolution of the BH mass distribution. Under favorable conditions, which are expected for some star clusters in starburst galaxies, the timescale of the runaway merging is at most of order 10^7 yr. This is short enough to account for the presence of a BH heavier than 10^3 M(sun) in an ongoing starburst region.Comment: 10 pages, no figures, to appear in The Astrophysical Journal (Letters