Partial melting in an upwelling mantle column

Decompression melting of hot upwelling rock in the mantle creates a region of partial melt comprising a porous solid matrix through which magma rises buoyantly. Magma transport and the compensating matrix deformation are commonly described by two-phase compaction models, but melt production is less often incorporated. Melting is driven by the necessity to maintain thermodynamic equilibrium between mineral grains in the partial melt; the position and amount of partial melting that occur are thus thermodynamically determined. We present a consistent model for the ascent of a one-dimensional column of rock and provide solutions that reveal where and how much partial melting occurs, the positions of the boundaries of the partial melt being determined by conserving energy across them. Thermodynamic equilibrium of the boundary between partial melt and the solid lithosphere requires a boundary condition on the effective pressure (solid pressure minus melt pressure), which suggests that large effective stresses, and hence fracture, are likely to occur near the base of the lithosphere. Matrix compaction, melt separation and temperature in the partially molten region are all dependent on the effective pressure, a fact that can lead to interesting oscillatory boundary-layer structures. © 2008 The Royal Society

Economics of organic farming (extension to OF0125)(0F0190)

This project OF0190 was an extension to OF0125 to cover completing the comparison data for 1997/98 and to extend the data collection by one further year (1998/99). The final reports for the two projects are therefore being submitted jointly. The OF0125 report covers the period 1995/96-1997/98, for which a detailed report was submitted to MAFF in July 1999, and a revised detailed report including a complete set of comparisons with conventional farms was submitted to MAFF, after revisions, in July 2000. That report has now been published at www.organic.aber.ac.uk/library/organic farm incomes.pdf. A detailed report for 1998/99 has been submitted to MAFF in March 2001, and will be published at the same internet site once accepted. The report presents results from research work carried out for the Ministry of Agriculture, Fisheries and Food (MAFF) on the financial performance of organic farms in 1998/99. The aim of the research was to assess the financial performance of organic farms differentiated by farm type, in order to inform MAFF policy-making with respect to organic farming, and to provide a basis for assessments by farmers, advisers and other interested parties of the farm-level implications of conversion to and continued organic farming. To provide an idea of the trends over time, where possible data for continuous samples of farms are presented for 1997/98 and 1998/99. The specific objectives were to extend the previous project (OF0125, covering 1995/96 to 1997/98) to collect and collate data on the financial performance of organic farms, differentiated by farm type . This was achieved through the collation of financial data collected under three different MAFF-funded research projects supplemented by data collected on other farm types. The samples of organic farms are small because of the limited number of organic holdings over 8 ESU (European Size Units) with identifiable holding numbers in 1996, when the previous study was started. As the sample is small there is limitation on how the results may be extrapolated to the wider population of organic farms, especially as the structure and objectives of those converting to organic production in the late 1990s may be different from those that converted in the 1970s and 1980s. Detailed financial input, output, income, liabilities and assets and some physical performance measures are presented for 1998/99. Where an identical sample of five farms is available, data are presented for 1997/98 and 1998/99 for the sample. The organic farm samples are so small that outliers (especially larger farms) have a large influence on the average. If the samples were larger, general trends would be more apparent and less influenced by individual farms; despite this, some explanation has been attempted of trends and changes in inputs, outputs and incomes. However, great care must be taken in extrapolating results. Of those farm types for which a continuous identical sample of five farms was available, Net Farm Incomes (NFI) increased for cropping (£281/ha) and dairy farms (£487/ha) in 1998/99 compared with 1997/98; in both cases outputs as well as inputs increased between years. Mixed farms showed an average reduction in outputs and increase in inputs, lowering the average NFI to £15/ha in 1998/99. The five lowland cattle and sheep farms improved a negative NFI of £161/ha in 1997/98 to a positive £7/ha in 1998/99 through an increase in livestock outputs with a similar level of inputs to that of 1997/98. Due to the high level of farmer and spouse labour on horticultural holdings, the average Management and Investment Income (MII) of the sample was negative, but the average NFI was £1,836/ha. On four holdings, 1998/99 average outputs were 92%, and inputs were 97% of the previous year, resulting in an average NFI in 1998/99 for that group of 75% of the 1997/98 result. The group of LFA farms, consisting of four cattle and sheep and one mixed farm, achieved an average NFI of £72/ha in 1998/99

Temperature surges in current-limiting circuit devices.

This paper studies the problem of heat transfer in a thermistor, which is used as a switching device in electronic circuits. The temperature field is coupled to the current flow by ohmic heating in the device, and the problem is rendered highly nonlinear by a very rapid variation of electrical conductivity with temperature. Approximate methods based on high activation energy asymptotics are developed to describe the transient heat flow, which occurs when the circuit is switched on. In particular, it is found that a transient 'surge' phenomenon (akin to thermal runaway, but self-saturating) occurs, and we conjecture that this phenomenon may be associated with cracking of thermistors, which sometimes occurs during operation

Nascent polypeptide chains exit the ribosome in the same relative position in both eucaryotes and procaryotes.

We located the polypeptide nascent chain as it leaves cytoplasmic ribosomes from the plant Lemna gibba by immune electron microscopy using antibodies against the small subunit of the enzyme ribulose-1,5-bisphosphate carboxylase. Similar studies with Escherichia coli ribosomes, using antibodies directed against the enzyme beta-galactosidase, show that the polypeptide nascent chain emerges in the same relative position in plants and bacteria. The eucaryotic ribosomal exit site is on the large subunit, approximately 75 A from the interface between subunits and nearly 160 A from the central protuberance, the presumed site for peptidyl transfer. This is the first functional site on both the eucaryotic and procaryotic ribosomes to be determined

Transient energy excitation in shortcuts to adiabaticity for the time dependent harmonic oscillator

There is recently a surge of interest to cut down the time it takes to change the state of a quantum system adiabatically. We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes designed to reproduce the initial populations at some predetermined final frequency and time, providing lower bounds and examples. Implications for the limits imposed to the process times and for the principle of unattainability of the absolute zero, in a single expansion or in quantum refrigerator cycles, are drawn.Comment: 7 pages, 6 figure

The Equilibrium Distribution of Gas Molecules Adsorbed on an Active Surface

We evaluate the exact equilibrium distribution of gas molecules adsorbed on an active surface with an infinite number of attachment sites. Our result is a Poisson distribution having mean $X = {\mu P P_s \over P_e}$, with $\mu$ the mean gas density, $P_s$ the sticking probability, $P_e$ the evaporation probability in a time interval $\tau$, and $P$ Smoluchowski's exit probability in time interval $\tau$ for the surface in question. We then solve for the case of a finite number of attachment sites using the mean field approximation, recovering in this case the Langmuir isotherm.Comment: 14 pages done in late

Strong Shift Equivalence of C∗C^*-correspondences

We define a notion of strong shift equivalence for $C^*$-correspondences and show that strong shift equivalent $C^*$-correspondences have strongly Morita equivalent Cuntz-Pimsner algebras. Our analysis extends the fact that strong shift equivalent square matrices with non-negative integer entries give stably isomorphic Cuntz-Krieger algebras.Comment: 26 pages. Final version to appear in Israel Journal of Mathematic

Simplified methods of assessing the impact of grid frequency dynamics upon generating plants

The frequency of the national electricity grid is affected by fluctuations in supply and demand, and so continually "judders" in an essentially unpredictable fashion around 50 Hz. At present such perturbations do not seemingly affect Nuclear Electric as most of their plant is run at more or less constant load, but they would like to be able to offer the national grid a mode of operation in which they "followed" the grid frequency: i.e., as the frequency rose above or fell below 50 Hz, the plant's output would be adjusted so as to tend to restore the frequency to 50 Hz. The aim is to maintain grid frequency within 0.2 Hz of its notional value. Such a mode of operation, however, would cause a certain amount of damage to plant components owing to the consequent continual changes in temperature and pressure within them. Nuclear Electric currently have complex computational models of how plants will behave under these conditions, which allows them to compute plant data (e.g., reactor temperatures) from given grid frequency data. One approach to damage assessment would require several years'-worth of real grid data to be fed into this model and the corresponding damage computed (via "cycle distributions" created by their damage experts). The results of this analysis would demonstrate one of three possibilities: the damage may be acceptable under all reasonable operating conditions; or it may be acceptable except in the case of an exceptional abrupt change in grid frequency (caused by power transmission line failure, or another power station suddenly going off-line, for instance), in which case some kind of backup supply (e.g., gas boilers) would be required; or it may simply be unacceptable. However, their current model runs in approximately real time, making it inappropriate for such a large amount of data: our problem was to suggest alternative approaches. Specifically, we were asked the following questions: - Can component damage be reliably estimated directly from cycle distributions of grid frequency? i.e., are there maps from frequency cycle distributions to plant parameter cycle distributions? - Can a simple model of plant dynamics be used to assess the potential for such maps? - What methods can be used to select representative samples of grid frequency behaviour? - What weightings should be applied to the selections? - Is it possible to construct a "cycle transform" (Fourier transform) which will capture the essential features of grid frequency and which can then be inverted to generate simulated frequency transients? We did not consider this last question, other than to say "probably not". We were supplied with data of the actual grid frequency measurements for the evening of 29/7/95, and the corresponding plant responses (obtained using Nuclear Electric's current computational model). A simplified nonlinear mathematical model of the plant was also provided. Two main approaches were considered: statistical prediction and analytical modelling via a reduction of the simplified plant model

Variability Flagging in the Wide-field Infrared Survey Explorer Preliminary Data Release

The Wide-field Infrared Survey Explorer Preliminary Data Release Source Catalog contains over 257 million objects. We describe the method used to flag variable source candidates in the Catalog. Using a method based on the chi-square of single-exposure flux measurements, we generated a variability flag for each object, and have identified almost 460,000 candidate sources that exhibit significant flux variability with greater than ~7σ confidence. We discuss the flagging method in detail and describe its benefits and limitations. We also present results from the flagging method, including example light curves of several types of variable sources including Algol-type eclipsing binaries, RR Lyr, W UMa, and a blazar candidate