Runoff on rooted trees

We introduce an idealised model for overland flow generated by rain falling on a hill-slope. Our prime motivation is to show how the coalescence of runoff streams promotes the total generation of runoff. We show that, for our model, as the rate of rainfall increases in relation to the soil infiltration rate, there is a distinct phase-change. For low rainfall (the subcritical case) only the bottom of the hill-slope contributes to the total overland runoff, while for high rainfall (the supercritical case) the whole slope contributes and the total runoff increases dramatically. We identify the critical point at which the phase-change occurs, and show how it depends on the degree of coalescence. When there is no stream coalescence the critical point occurs when the rainfall rate equals the average infiltration rate, but when we allow coalescence the critical point occurs when the rainfall rate is less than the average infiltration rate, and increasing the amount of coalescence increases the total expected runoff

Physiological Aspects of Genetics

A considerable amount of evidence indicates that desoxyribonucleic acid is capable of duplicating itself, a property also possessed by genes. (By a self-duplicating material, we mean one which plays some essential role in its own production.) Watson & Crick (1) have proposed a new structure for desoxyribonucleic acid which not only takes into account the existing analytical and x-ray diffraction data but also seems capable of explaining the mechanism of duplication. Their model consists of two helical chains coiled around the same axis, the purine and pyrimidine bases on the inside, the phosphate groups on the outside. The chains are held together by hydrogen bonds between the bases, the adenine residues of either chain being bonded specifically to thymine in the other, and similarly guanine to cytosine. The sequence of bases along one chain is not restricted, but once fixed the sequence along the other chain is determined. This complementarity, which is the most novel feature of the structure, suggests that duplication takes place by separation of the two chains, followed by the synthesis of its complement alongside each chain. The model is supported by recent x-ray diffraction studies (2, 3)

Construction of weakly CUD sequences for MCMC sampling

In Markov chain Monte Carlo (MCMC) sampling considerable thought goes into constructing random transitions. But those transitions are almost always driven by a simulated IID sequence. Recently it has been shown that replacing an IID sequence by a weakly completely uniformly distributed (WCUD) sequence leads to consistent estimation in finite state spaces. Unfortunately, few WCUD sequences are known. This paper gives general methods for proving that a sequence is WCUD, shows that some specific sequences are WCUD, and shows that certain operations on WCUD sequences yield new WCUD sequences. A numerical example on a 42 dimensional continuous Gibbs sampler found that some WCUD inputs sequences produced variance reductions ranging from tens to hundreds for posterior means of the parameters, compared to IID inputs.Comment: Published in at http://dx.doi.org/10.1214/07-EJS162 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Migrant workers in the East Midlands labour market 2007

This report provides a profile of international migrants in the East Midlands and their role in the regional labour marke

Directly comparing coronal and solar wind elemental fractionation

As the solar wind propagates through the heliosphere, dynamical processes irreversibly erase the signatures of the near-Sun heating and acceleration processes. The elemental fractionation of the solar wind should not change during transit however, making it an ideal tracer of these processes. We aimed to verify directly if the solar wind elemental fractionation is reflective of the coronal source region fractionation, both within and across different solar wind source regions. A backmapping scheme was used to predict where solar wind measured by the Advanced Composition Explorer (ACE) originated in the corona. The coronal composition measured by the Hinode Extreme ultraviolet Imaging Spectrometer (EIS) at the source regions was then compared with the in-situ solar wind composition. On hourly timescales there was no apparent correlation between coronal and solar wind composition. In contrast, the distribution of fractionation values within individual source regions was similar in both the corona and solar wind, but distributions between different sources have significant overlap. The matching distributions directly verifies that elemental composition is conserved as the plasma travels from the corona to the solar wind, further validating it as a tracer of heating and acceleration processes. The overlap of fractionation values between sources means it is not possible to identify solar wind source regions solely by comparing solar wind and coronal composition measurements, but a comparison can be used to verify consistency with predicted spacecraft-corona connections.Comment: Accepted version; 8 pages, 7 figure

Light Trapping Textures Designed by Electromagnetic Optimization for Sub-Wavelength Thick Solar Cells

Light trapping in solar cells allows for increased current and voltage, as well as reduced materials cost. It is known that in geometrical optics, a maximum 4n^2 absorption enhancement factor can be achieved by randomly texturing the surface of the solar cell, where n is the material refractive index. This ray-optics absorption enhancement limit only holds when the thickness of the solar cell is much greater than the optical wavelength. In sub-wavelength thin films, the fundamental questions remain unanswered: (1) what is the sub-wavelength absorption enhancement limit and (2) what surface texture realizes this optimal absorption enhancement? We turn to computational electromagnetic optimization in order to design nanoscale textures for light trapping in sub-wavelength thin films. For high-index thin films, in the weakly absorbing limit, our optimized surface textures yield an angle- and frequency-averaged enhancement factor ~39. They perform roughly 30% better than randomly textured structures, but they fall short of the ray optics enhancement limit of 4n^2 ~ 50