We study the drift of slow variables in a slow-fast Hamiltonian system with several fast and slow degrees of freedom. For any periodic trajectory of the fast subsystem with the frozen slow variables we define an action. For a family of periodic orbits, the action is a scalar function of the slow variables and can be considered as a Hamiltonian function which generates some slow dynamics. These dynamics depend on the family of periodic orbits. Assuming the fast system with the frozen slow variables has a pair of hyperbolic periodic orbits connected by two transversal heteroclinic trajectories, we prove that for any path composed of a finite sequence of slow trajectories generated by action Hamiltonians, there is a trajectory of the full system whose slow component shadows the path.Comment: 18 pages, 1 figur

BackgroundThe World Health Organization recommends that national malaria programmes universally distribute long-lasting insecticide-treated bed nets (LLINs). LLINs provide effective insecticide protection for at least three years while conventional nets must be retreated every 6-12 months. LLINs may also promise longer physical durability (lifespan), but at a higher unit price. No prospective data currently available is sufficient to calculate the comparative cost effectiveness of different net types. We thus constructed a model to explore the cost effectiveness of LLINs, asking how a longer lifespan affects the relative cost effectiveness of nets, and if, when and why LLINs might be preferred to conventional insecticide-treated nets. An innovation of our model is that we also considered the replenishment need i.e. loss of nets over time.MethodsWe modelled the choice of net over a 10-year period to facilitate the comparison of nets with different lifespan (and/or price) and replenishment need over time. Our base case represents a large-scale programme which achieves high coverage and usage throughout the population by distributing either LLINs or conventional nets through existing health services, and retreats a large proportion of conventional nets regularly at low cost. We identified the determinants of bed net programme cost effectiveness and parameter values for usage rate, delivery and retreatment cost from the literature. One-way sensitivity analysis was conducted to explicitly compare the differential effect of changing parameters such as price, lifespan, usage and replenishment need.ResultsIf conventional and long-lasting bed nets have the same physical lifespan (3 years), LLINs are more cost effective unless they are priced at more than USD 1.5 above the price of conventional nets. Because a longer lifespan brings delivery cost savings, each one year increase in lifespan can be accompanied by a USD 1 or more increase in price without the cheaper net (of the same type) becoming more cost effective. Distributing replenishment nets each year in addition to the replacement of all nets every 3-4 years increases the number of under-5 deaths averted by 5-14% at a cost of USD 17-25 per additional person protected per annum or USD 1080-1610 per additional under-5 death averted.ConclusionsOur results support the World Health Organization recommendation to distribute only LLINs, while giving guidance on the price thresholds above which this recommendation will no longer hold. Programme planners should be willing to pay a premium for nets which have a longer physical lifespan, and if planners are willing to pay USD 1600 per under-5 death averted, investing in replenishment is cost effective.

A model intercomparison of the atmospheric dispersion of cesium-137 ( 137 Cs) emitted after the Fukushima Daiichi Nuclear Power Plant accident in Japan was conducted to understand the behavior of atmospheric 137 Cs in greater detail. The same meteorological data with a fine spatiotemporal resolution and an emission inventory were applied to all models to exclude the differences among the models originating from differences in meteorological and emission data. The meteorological data were used for initial, boundary, and nudging data or offline meteorological field. Furthermore, a horizontal grid with the same resolution as that of the meteorological data was adopted for all models. This setup enabled us to focus on model variability originating from the processes included in each model, for example, physical processes. The multimodel ensemble captured 40% of the atmospheric 137 Cs events observed by measurements, and the figure of merit in space for the total deposition of 137 Cs exceeded 80. The lower score of the atmospheric 137 Cs than that of the deposition originated from the difference in timing between observed and simulated atmospheric 137 Cs. Our analyses indicated that meteorological data were most critical for reproducing the atmospheric 137 Cs events. The results further revealed that differences in 137 Cs concentrations among the models originated from deposition and diffusion processes when the meteorological field was simulated reasonably well. The models with small deposition fluxes produced higher scores for atmospheric 137 Cs, and those with strong diffusion succeeded in capturing the high 137 Cs concentrations observed; however, they also tended to overestimate the concentrations.

On September 9 2014 several incidences of foul smell (rotten eggs) were reported on the coast of Norway (in particular in the vicinity of Molde) and then on September 10 in the interior parts of county Västerbotten, Sweden. One of the theories that were put forward was that the foul smell was due to degassing of the Bardarbunga volcano on Iceland. Using satellite images (GOME-1,-2) of the sulphur dioxide, 2 , contents in the atmosphere surrounding Iceland to estimate flux of 2 from the volcano and an atmospheric transport model, PELLO, we vindicate this theory: we argue that the cause for the foul smell was hydrogen sulphide originating from Bardarbunga.The model concentrations are also compared to 2 concentration measurements from Muonio, Finland.