A particle system in interaction with a rapidly varying environment: Mean field limits and applications

We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of fixed capacity). The transition rate of a particle is determined by its state, by the empirical distribution of all the particles and by a rapidly varying environment. The transitions of the environment are determined by the empirical distribution of the particles. We prove the propagation of chaos on the path space of the particles and establish that the limiting trajectory of the empirical measure of the states of the particles satisfies a deterministic differential equation. This deterministic differential equation involves the time averages of the environment process. We apply our results to analyze the performance of communication networks where users access some resources using random distributed multi-access algorithms. For these networks, we show that the environment process corresponds to a process describing the number of clients in a certain loss network, which allows us provide simple and explicit expressions of the network performance.Comment: 31 pages, 2 figure

Elemental Composition of Atmospheric Particulate, Water and Soil Samples From Urban and Polluted Environments

Chapter I deals with the reasons for the increased public concern over pollution of the environment, including the deaths of 43 people in Japan in 1953, and the death of over 50,000 seabirds in the Irish Sea in 1969. Chapter II discusses methods which have been used in the analysis of metals in environmental samples with comments on their strengths and weaknesses. The two methods which were used in this work, Activation Analysis and Atomic Absorption Spectroscopy are discussed in more detail. Chapter III deals with atmospheric levels of some 24 elements. Reasons for a study of elemental levels are given. Sampling problems such as best filter paper, filter blank values, pressure drop across the filter, etc. are considered. The accuracy of the methods used was checked using standard air pollution filters. The results of one site sampling over a period of 13 months are given and compared to other world centres. Attempts were made to correlate the levels with weather parameters with only partial success. It was found that although the weather has an effect on levels; fog and calm conditions increasing levels while rain decreased levels, this is not linear. Seasonal variations were also studied with peak values for most elements in winter except for Se and Sb which tend to peak in spring and summer. Levels at 13 other city sites and 2 rural sites were also measured but no area was found to be consistently high in all elements. The rural sites did in general show lower levels than the city. Particle size distribution of elements was also studied using a 5 stage cascade impactor the principles of which are discussed. The results are discussed in terms of implications to human health with disturbing results for Cd, Pb and Ni, large proportions of which can penetrate deep into the lung. The results are also compared favourably with those of Liege (Belgium). A term often used in studying atmospheric levels of elements is the enrichment factor (see Section 3.5. 3.3) where atmospheric levels are compared to some standard. When compared to soil the elements show two trends. One class has ratios close to those in soil while the other is enriched by 100 - 10,000 times. It has been suggested that this is consistent with a fuel burning source and is fully discussed. Good agreement has been found with this theory in all sections of this work. The results of 1 site sampling agree well with those of Liege (Belgium) while the enrichment factors for the other city and rural sites are remarkably constant in the first class (close to soil ratios) with higher and more varied factors for the others. Again the factors of the first class vary little with particle size, the variations being found in the second class. Chapter IV deals with metal levels in Glasgow's water supply a constant source of worry due to a combination of soft water and lead pipes. A survey was carried out analysing for 7 elements. The results indicate that Pb levels are higher than W. H. O. limits while Cu could become a problem if W. H. O. desirable limits are applied. Other elements are not a problem ac this stage. Leaching was also studied by a controlled experiment using standard lengths of pipes in common use. Results indicate that altering the material of plumbing will only change the problem of metal levels and not necessarily remove them. Chapter V deals with some problems associated with the dumping of coal mine waste on land (bings). Bing samples were analysed for 8 metals and the results discussed in terms of plant growth. Only Cu had higher than normal values for normal soil ranges. The effect on surrounding land was also investigated in terms of drainage into streams and seepage and blow-off on to land. The results suggest that these might be occurring but further work is required to confirm the tentative findings of this work

Alien Registration- Mcdonald, Charles L. (Bangor, Penobscot County)

https://digitalmaine.com/alien_docs/11826/thumbnail.jp

Alien Registration- Mcdonald, Charles S. (Limestone, Aroostook County)

https://digitalmaine.com/alien_docs/35424/thumbnail.jp

A study of factors affecting s-methyl cysteine sulphoxide content of kale (Brassica oleracea)

Factors affecting S- methyl cysteine sulphoxide (SMCO) content in Maris Kestrel kale were studied in field and glasshouse trials. SMCO is responsible for kale anaemia in ruminants.Higher plant populations reduced whole plant and stem SMCO in six trials, especially at harvests after October. Increasing plant density from 10 to 80 plants /m2 reduced whole plant SMCO in November or December by approximately 25 %.Nitrogen (N) fertiliser increased SMCO and dry matter (DM) yields in six out of seven trials, with SMCO increases ranging from 8 to 68% depending on soil fertility.There was a high correlation between SMCO (Y) and N (x) levels in mature kale from different sites (r = 0.92, n =26) . Using the relationship Y = 7.53x - 3.20, plant N could be measured as an estimate of the SMCO level.On free draining soils low in available sulphate at sowing (<12 ppm) applied sulphur (S) increased SMCO in two out of six trials, although only at early autumn harvests. On a soil with impeded drainage (sulphate = 12.5 ppm), S tended to increase (P <0.10) SMCO at a December harvest.As the crop aged, SMCO increased especially in leaves. This was not caused by frosting, but may have been affected by floral initiation, as stems with small inflorescences had higher (P <0.05) SMCO levels than non -flowering stems.July sown kale had less SMCO than June sown kale in September, but tended to have more SMCO in November, especially at higher populations and particularly in stems.SMCO was not affected by varying growing temperature ( -6 to 15°C) , moisture availability, chopping or wilting for 96 hours.Chrysol (13.1 g /kg DM) tended to have a higher SMCO content than Canson, Maris Kestrel, Merlin, Vulcan or Bittern (mean = 9.2 g /kg DM) . The lower yielding cultivars, Chrysol and Canson, contained most of their SMCO in leaf tissue. SMCO varied in different plant components, with SMCO in petioles having the highest correlation with whole plant SMCO (r = 0.73, n =8 and 18) .Near infrared reflectance (NIR) analysis accurately predicted N and moisture contents in different kale tissue types, with correlation coefficients (r) >0.95 between NIR predicted and Kjeldahl N or oven - dried moisture values. SMCO was only predicted satisfactorily by NIR for plant breeding purposes in entire leaves and young leaves, which had average standard errors of 2.3 and 1.7 respectively and correlations between SMCO values predicted by NIR and the autoanalysis method of r = 0.87 to 0.91. In stems and whole plants, which had average standard errors of 2.9 and 3.9 respectively and correlations (r) ranging from 0.69 to 0.84, NIR could only be used to separate low and high SMCO samples