Solving the brachistochrone and other variational problems with soap films

We show a method to solve the problem of the brachistochrone as well as other variational problems with the help of the soap films that are formed between two suitable surfaces. We also show the interesting connection between some variational problems of dynamics, statics, optics, and elasticity.Comment: 16 pages, 11 figures. This article, except for a small correction, has been submitted to the American Journal of Physic

Ensemble based quantum metrology

The field of quantum metrology promises measurement devices that are fundamentally superior to conventional technologies. Specifically, when quantum entanglement is harnessed the precision achieved is supposed to scale more favourably with the resources employed, such as system size and the time required. Here we consider measurement of magnetic field strength using an ensemble of spins, and we identify a third essential resource: the initial system polarisation, i.e. the low entropy of the original state. We find that performance depends crucially on the form of decoherence present; for a plausible dephasing model, we describe a quantum strategy which can indeed beat the standard quantum limit

Quantum metrology with molecular ensembles

This work was supported by the EPSRC through QIP IRC (Grants No. GR/S82176/01 and No. GR/S15808/01), the National Research Foundation and Ministry of Education, Singapore, the DAAD, and the Royal Society.The field of quantum metrology promisesmeasurement devices that are fundamentally superior to conventional technologies. Specifically, when quantum entanglement is harnessed, the precision achieved is supposed to scale more favorably with the resources employed, such as system size and time required. Here, we consider measurement of magnetic-field strength using an ensemble of spin-active molecules. We identify a third essential resource: the change in ensemble polarization (entropy increase) during the metrology experiment. We find that performance depends crucially on the form of decoherence present; for a plausible dephasing model, we describe a quantum strategy, which can indeed beat the standard strategy.Publisher PDFPeer reviewe

Global Optical Control of a Quantum Spin Chain

Quantum processors which combine the long decoherence times of spin qubits together with fast optical manipulation of excitons have recently been the subject of several proposals. I show here that arbitrary single- and entangling two-qubit gates can be performed in a chain of perpetually coupled spin qubits solely by using laser pulses to excite higher lying states. It is also demonstrated that universal quantum computing is possible even if these pulses are applied {\it globally} to a chain; by employing a repeating pattern of four distinct qubit units the need for individual qubit addressing is removed. Some current experimental qubit systems would lend themselves to implementing this idea.Comment: 5 pages, 3 figure

Evaluation of Potential Sources of Allelochemicals in Lalang

Aqueous leachates from fragmented lalang (I. cylindrica (L) Raeuschel var. major) dead leaves in situ, caused delayed germination in biossays of all six species of pasture legumes tested, while radicle and shoot growth were inhibited in two of the test species. Phytotoxicity was dependent on the quantity of plant residues available in the proximity of germinating phytometer species. Leachates from rhizome and root fragments exhibited strong inhibitory activity even at the 5% (w/v) level while leaf leachates were inhibitory at the 10% level and higher. In pot experiments with soil containing living lalang tillers or incorporated with rhizome or root fragments, phytotoxicity development in the soil extracts was evident at four weeks of growth or decay. In soils with decaying roots or rhizomes there was a sub-sequent loss in activity over the eight week incubation period. Extracts of soils with living tillers showed loss of activity at six weeks of growth followed by a significant stimulatory response at eight weeks. The use of two controls (control-soil extract and distilled water control) enabled detection of inherent stimulatory activity in the control soiL Comparison with both controls to eliminate such influences showed only living tillers, and decaying rhizomes and roots as major potential sources of inhibitory substances. The common soil organism, Bacillus cereus (Frankland & Frankland), Alcaligenes faecalis Castellani & Chalmers) and a Trichoderma sp. were found to be associated with the decay of rhizomes resulting in an initial stimulatory growth reponse in the phytometer species followed by inhibition and subsequent loss in activity. The nature of these organisms suggest that the release ofPhytotoxins through decay of rhizomes as a common, natural phenomenon in most soils. The dead leaves accumulating as litter in mature lalang vegetation may serve as an additional source of water leachable allelochemicals if sufficient quantities were available in contact with the soil

Superabsorption of light via quantum engineering

Almost 60 years ago Dicke introduced the term superradiance to describe a signature quantum effect: N atoms can collectively emit light at a rate proportional to N^2. Even for moderate N this represents a significant increase over the prediction of classical physics, and the effect has found applications ranging from probing exciton delocalisation in biological systems, to developing a new class of laser, and even in astrophysics. Structures that super-radiate must also have enhanced absorption, but the former always dominates in natural systems. Here we show that modern quantum control techniques can overcome this restriction. Our theory establishes that superabsorption can be achieved and sustained in certain simple nanostructures, by trapping the system in a highly excited state while extracting energy into a non-radiative channel. The effect offers the prospect of a new class of quantum nanotechnology, capable of absorbing light many times faster than is currently possible; potential applications of this effect include light harvesting and photon detection. An array of quantum dots or a porphyrin ring could provide an implementation to demonstrate this effect

Predicting tree distributions in an East African biodiversity hotspot : model selection, data bias and envelope uncertainty

The Eastern Arc Mountains (EAMs) of Tanzania and Kenya support some of the most ancient tropical rainforest on Earth. The forests are a global priority for biodiversity conservation and provide vital resources to the Tanzanian population. Here, we make a first attempt to predict the spatial distribution of 40 EAM tree species, using generalised additive models, plot data and environmental predictor maps at sub 1 km resolution. The results of three modelling experiments are presented, investigating predictions obtained by (1) two different procedures for the stepwise selection of predictors, (2) down-weighting absence data, and (3) incorporating an autocovariate term to describe fine-scale spatial aggregation. In response to recent concerns regarding the extrapolation of model predictions beyond the restricted environmental range of training data, we also demonstrate a novel graphical tool for quantifying envelope uncertainty in restricted range niche-based models (envelope uncertainty maps). We find that even for species with very few documented occurrences useful estimates of distribution can be achieved. Initiating selection with a null model is found to be useful for explanatory purposes, while beginning with a full predictor set can over-fit the data. We show that a simple multimodel average of these two best-model predictions yields a superior compromise between generality and precision (parsimony). Down-weighting absences shifts the balance of errors in favour of higher sensitivity, reducing the number of serious mistakes (i.e., falsely predicted absences); however, response functions are more complex, exacerbating uncertainty in larger models. Spatial autocovariates help describe fine-scale patterns of occurrence and significantly improve explained deviance, though if important environmental constraints are omitted then model stability and explanatory power can be compromised. We conclude that the best modelling practice is contingent both on the intentions of the analyst (explanation or prediction) and on the quality of distribution data; generalised additive models have potential to provide valuable information for conservation in the EAMs, but methods must be carefully considered, particularly if occurrence data are scarce. Full results and details of all species models are supplied in an online Appendix. (C) 2008 Elsevier B.V. All rights reserved

High-frequency monitoring of nitrogen and phosphorus response in three rural catchments to the end of the 2011–2012 drought in England

This paper uses high-frequency bankside measurements from three catchments selected as part of the UK government-funded Demonstration Test Catchments (DTC) project. We compare the hydrological and hydrochemical patterns during the water year 2011–2012 from the Wylye tributary of the River Avon with mixed land use, the Blackwater tributary of the River Wensum with arable land use and the Newby Beck tributary of the River Eden with grassland land use. The beginning of the hydrological year was unusually dry and all three catchments were in states of drought. A sudden change to a wet summer occurred in April 2012 when a heavy rainfall event affected all three catchments. The year-long time series and the individual storm responses captured by in situ nutrient measurements of nitrate and phosphorus (total phosphorus and total reactive phosphorus) concentrations at each site reveal different pollutant sources and pathways operating in each catchment. Large storm-induced nutrient transfers of nitrogen and or phosphorus to each stream were recorded at all three sites during the late April rainfall event. Hysteresis loops suggested transport-limited delivery of nitrate in the Blackwater and of total phosphorus in the Wylye and Newby Beck, which was thought to be exacerbated by the dry antecedent conditions prior to the storm. The high rate of nutrient transport in each system highlights the scale of the challenges faced by environmental managers when designing mitigation measures to reduce the flux of nutrients to rivers from diffuse agricultural sources. It also highlights the scale of the challenge in adapting to future extreme weather events under a changing climate