How long does it take to compute the eigenvalues of a random symmetric matrix?

We present the results of an empirical study of the performance of the QR algorithm (with and without shifts) and the Toda algorithm on random symmetric matrices. The random matrices are chosen from six ensembles, four of which lie in the Wigner class. For all three algorithms, we observe a form of universality for the deflation time statistics for random matrices within the Wigner class. For these ensembles, the empirical distribution of a normalized deflation time is found to collapse onto a curve that depends only on the algorithm, but not on the matrix size or deflation tolerance provided the matrix size is large enough (see Figure 4, Figure 7 and Figure 10). For the QR algorithm with the Wilkinson shift, the observed universality is even stronger and includes certain non-Wigner ensembles. Our experiments also provide a quantitative statistical picture of the accelerated convergence with shifts.Comment: 20 Figures; Revision includes a treatment of the QR algorithm with shift

Analysis of ASTEC-Na capabilities for simulating a loss of flow CABRI experiment

Abstract This paper presents simulation results of the CABRI BI1 test using the code ASTEC-Na, currently under development, as well as a comparison of the results with available experimental data. The EU-JASMIN project (7th FP of EURATOM) centres on the development and validation of the new severe accident analysis code ASTEC-Na (Accident Source Term Evaluation Code) for sodium-cooled fast reactors whose owner and developer is IRSN. A series of experiments performed in the past (CABRI/SCARABEE experiments) and new experiments to be conducted in the new experimental sodium facility KASOLA have been chosen to validate the developed ASTEC-Na code. One of the in-pile experiments considered for the validation of ASTEC-Na thermal–hydraulic models is the CABRI BI1 test, a pure loss-of-flow transient using a low burnup MOX fuel pin. The experiment resulted in a channel voiding as a result of the flow coast-down leading to clad melting. Only some fuel melting took place. Results from the analysis of this test using SIMMER and SAS-SFR codes are also presented in this work to check their suitability for further code benchmarking purposes

Electrical effects on droplet behaviour

The effect of charge on water droplets modulates various aspects of their behaviour. These include the droplet stability, evaporation, and lifetime. Microphysical models have been developed such that a reasonably good understanding of these processes has been achieved. However, the specific effects of charge deserve further scrutiny as they are an intrinsic component of the factors controlling droplet characteristics. Describing the effects of these requires an understanding of the electrostatic pressure present in the droplet and its surface tension. One way to test these effects and assess droplet response to charge is to take an experimental approach to make observations directly. In this study, individual droplets are levitated in an acoustic wave to allow isolated measurements to be taken. The droplets are monitored using a CCD camera with a microscope objective lens. In some cases, with sufficient charge present, effects on droplet stability can be observed as Rayleigh explosions, where a sudden drop in mass is seen superimposed on the evaporation profile. These events also allow the charge on the droplet to be calculated, which is then compared with the droplet evaporation. Another factor that plays a part in droplet behaviour is droplet composition. Different substances have different surface tension, and this is explored by performing some experiments on sulphuric acid droplets. Theory predicts that the more highly charged a droplet is, the more resistant to evaporation it becomes. Experimental data collected during this study agrees with this, with more highly charged droplets observed to have slower evaporation rates. However, highly charged drops were also observed to periodically become unstable during evaporation and undergo Rayleigh explosions. Each instability of a highly charged drop removes mass, reducing the overall droplet lifetime regardless of the slower evaporation rate. The sulphuric acid droplets were observed to be much more resistant to evaporation and no Rayleigh instabilities were observed

The transformation of earth-system observations into information of socio-economic value in GEOSS

The Group on Earth Observations System of Systems, GEOSS, is a co-ordinated initiative by many nations to address the needs for earth-system information expressed by the 2002 World Summit on Sustainable Development. We discuss the role of earth-system modelling and data assimilation in transforming earth-system observations into the predictive and status-assessment products required by GEOSS, across many areas of socio-economic interest. First we review recent gains in the predictive skill of operational global earth-system models, on time-scales of days to several seasons. We then discuss recent work to develop from the global predictions a diverse set of end-user applications which can meet GEOSS requirements for information of socio-economic benefit; examples include forecasts of coastal storm surges, floods in large river basins, seasonal crop yield forecasts and seasonal lead-time alerts for malaria epidemics. We note ongoing efforts to extend operational earth-system modelling and assimilation capabilities to atmospheric composition, in support of improved services for air-quality forecasts and for treaty assessment. We next sketch likely GEOSS observational requirements in the coming decades. In concluding, we reflect on the cost of earth observations relative to the modest cost of transforming the observations into information of socio-economic value

Evidence for proton acceleration up to TeV energies based on VERITAS and Fermi-LAT observations of the Cas A SNR

We present a study of $\gamma$-ray emission from the core-collapse supernova remnant Cas~A in the energy range from 0.1GeV to 10TeV. We used 65 hours of VERITAS data to cover 200 GeV - 10 TeV, and 10.8 years of \textit{Fermi}-LAT data to cover 0.1-500 GeV. The spectral analysis of \textit{Fermi}-LAT data shows a significant spectral curvature around $1.3 \pm 0.4_{stat}$ GeV that is consistent with the expected spectrum from pion decay. Above this energy, the joint spectrum from \textit{Fermi}-LAT and VERITAS deviates significantly from a simple power-law, and is best described by a power-law with spectral index of $2.17\pm 0.02_{stat}$ with a cut-off energy of $2.3 \pm 0.5_{stat}$ TeV. These results, along with radio, X-ray and $\gamma$-ray data, are interpreted in the context of leptonic and hadronic models. Assuming a one-zone model, we exclude a purely leptonic scenario and conclude that proton acceleration up to at least 6 TeV is required to explain the observed $\gamma$-ray spectrum. From modeling of the entire multi-wavelength spectrum, a minimum magnetic field inside the remnant of $B_{\mathrm{min}}\approx150\,\mathrm{\mu G}$ is deduced.Comment: 33 pages, 9 Figures, 6 Table

Mapping the effects of ozone pollution and mixing on floral odour plumes and their impact on plant-pollinator interactions

The critical ecological process of animal-mediated pollination is commonly facilitated by odour cues. These odours consist of volatile organic compounds (VOCs), often with short chemical lifetimes, which form the strong concentration gradients necessary for pollinating insects to locate a flower. Atmospheric oxidants, including ozone pollution, may react with and chemically alter these VOCs, impairing the ability of pollinators to locate a flower, and therefore the pollen and nectar on which they feed. However, there is limited mechanistic empirical evidence to explain these processes within an odour plume at temporal and spatial scales relevant to insect navigation and olfaction. We investigated the impact of ozone pollution and turbulent mixing on the fate of four model floral VOCs within odour plumes using a series of controlled experiments in a large wind tunnel. Average rates of chemical degradation of α-terpinene, β-caryophyllene and 6-methyl-5-hepten-2-one were slightly faster than predicted by literature rate constants, but mostly within uncertainty bounds. Mixing reduced reaction rates by 8–10% in the first 2 m following release. Reaction rates also varied across the plumes, being fastest at plume edges where VOCs and ozone mixed most efficiently and slowest at plume centres. Honeybees were trained to learn a four VOC blend equivalent to the plume released at the wind tunnel source. When subsequently presented with an odour blend representative of that observed 6 m from the source at the centre of the plume, 52% of honeybees recognised the odour, decreasing to 38% at 12 m. When presented with the more degraded blend from the plume edge, recognition decreased to 32% and 10% at 6 and 12 m respectively. Our findings highlight a mechanism by which anthropogenic pollutants can disrupt the VOC cues used in plant-pollinator interactions, which likely impacts on other critical odour-mediated behaviours such as mate attraction