Rigid motions: action-angles, relative cohomology and polynomials with roots on the unit circle

Revisiting canonical integration of the classical solid near a uniform rotation, canonical action angle coordinates, hyperbolic and elliptic, are constructed in terms of various power series with coefficients which are polynomials in a variable $r^2$ depending on the inertia moments. Normal forms are derived via the analysis of a relative cohomology problem and shown to be obtainable without the use of ellitptic integrals (unlike the derivation of the action-angles). Results and conjectures also emerge about the properties of the above polynomials and the location of their roots. In particular a class of polynomials with all roots on the unit circle arises.Comment: 26 pages, 1 figur

Percolation model for nodal domains of chaotic wave functions

Nodal domains are regions where a function has definite sign. In recent paper [nlin.CD/0109029] it is conjectured that the distribution of nodal domains for quantum eigenfunctions of chaotic systems is universal. We propose a percolation-like model for description of these nodal domains which permits to calculate all interesting quantities analytically, agrees well with numerical simulations, and due to the relation to percolation theory opens the way of deeper understanding of the structure of chaotic wave functions.Comment: 4 pages, 6 figures, Late

Local entanglement generation in the adiabatic regime

We study entanglement generation in a pair of qubits interacting with an initially correlated system. Using time independent perturbation theory and the adiabatic theorem, we show conditions under which the qubits become entangled as the joint system evolves into the ground state of the interacting theory. We then apply these results to the case of qubits interacting with a scalar quantum field. We study three different variations of this setup; a quantum field subject to Dirichlet boundary conditions, a quantum field interacting with a classical potential and a quantum field that starts in a thermal state.Comment: 9 pages, 6 figures. v2: reference [14] adde

Gauss Sums and Quantum Mechanics

By adapting Feynman's sum over paths method to a quantum mechanical system whose phase space is a torus, a new proof of the Landsberg-Schaar identity for quadratic Gauss sums is given. In contrast to existing non-elementary proofs, which use infinite sums and a limiting process or contour integration, only finite sums are involved. The toroidal nature of the classical phase space leads to discrete position and momentum, and hence discrete time. The corresponding `path integrals' are finite sums whose normalisations are derived and which are shown to intertwine cyclicity and discreteness to give a finite version of Kelvin's method of images.Comment: 14 pages, LaTe

Hazard ranking method for populations exposed to arsenic in private water supplies: relation to bedrock geology

Approximately one million people in the UK are served by private water supplies (PWS) where main municipal water supply system connection is not practical or where PWS is the preferred option. Chronic exposure to contaminants in PWS may have adverse effects on health. South West England is an area with elevated arsenic concentrations in groundwater and over 9000 domestic dwellings here are supplied by PWS. There remains uncertainty as to the extent of the population exposed to arsenic (As), and the factors predicting such exposure. We describe a hazard assessment model based on simplified geology with the potential to predict exposure to As in PWS. Households with a recorded PWS in Cornwall were recruited to take part in a water sampling programme from 2011 to 2013. Bedrock geologies were aggregated and classified into nine Simplified Bedrock Geological Categories (SBGC), plus a cross-cutting “mineralized” area. PWS were sampled by random selection within SBGCs and some 508 households volunteered for the study. Transformations of the data were explored to estimate the distribution of As concentrations for PWS by SBGC. Using the distribution per SBGC, we predict the proportion of dwellings that would be affected by high concentrations and rank the geologies according to hazard. Within most SBGCs, As concentrations were found to have log-normal distributions. Across these areas, the proportion of dwellings predicted to have drinking water over the prescribed concentration value (PCV) for As ranged from 0% to 20%. From these results, a pilot predictive model was developed calculating the proportion of PWS above the PCV for As and hazard ranking supports local decision making and prioritization. With further development and testing, this can help local authorities predict the number of dwellings that might fail the PCV for As, based on bedrock geology. The model presented here for Cornwall could be applied in areas with similar geologies. Application of the method requires independent validation and further groundwater-derived PWS sampling on other geological formation

EJVES vol 34, issue 2 (August 2007) - Spanish Translated Abstracts

Chronic exposure to arsenic (As) through the consumption of contaminated groundwaters is a major threat to public health in South and Southeast Asia. The source of As-affected groundwaters is important to the fundamental understanding of the controls on As mobilization and subsequent transport throughout shallow aquifers. Using the stable isotopes of hydrogen and oxygen, the source of groundwater and the interactions between various water bodies were investigated in Cambodia’s Kandal Province, an area which is heavily affected by As and typical of many circum-Himalayan shallow aquifers. Two-point mixing models based on δD and δ18O allowed the relative extent of evaporation of groundwater sources to be estimated and allowed various water bodies to be broadly distinguished within the aquifer system. Model limitations are discussed, including the spatial and temporal variation in end member compositions. The conservative tracer Cl/Br is used to further discriminate between groundwater bodies. The stable isotopic signatures of groundwaters containing high As and/or high dissolved organic carbon plot both near the local meteoric water line and near more evaporative lines. The varying degrees of evaporation of high As groundwater sources are indicative of differing recharge contributions (and thus indirectly inferred associated organic matter contributions). The presence of high As groundwaters with recharge derived from both local precipitation and relatively evaporated surface water sources, such as ponds or flooded wetlands, are consistent with (but do not provide direct evidence for) models of a potential dual role of surface-derived and sedimentary organic matter in As mobilization

Microbially mediated reduction of FeIII and AsV in Cambodian sediments amended with 13C-labelled hexadecane and kerogen

Microbial activity is generally accepted to play a critical role, with the aid of suitable organic carbon substrates, in the mobilisation of arsenic from sediments into shallow reducing groundwaters. The nature of the organic matter in natural aquifers driving the reduction of AsV to AsIII is of particular importance but is poorly understood. In this study, sediments from an arsenic rich aquifer in Cambodia were amended with two 13C-labelled organic substrates. 13C-hexadecane was used as a model for potentially bioavailable long chain n-alkanes and a 13C-kerogen analogue as a proxy for non-extractable organic matter. During anaerobic incubation for 8 weeks, significant FeIII reduction and AsIII mobilisation were observed in the biotic microcosms only, suggesting that these processes were microbially driven. Microcosms amended with 13C-hexadecane exhibited a similar extent of FeIII reduction to the non-amended microcosms, but marginally higher AsIII release. Moreover, gas chromatography–mass spectrometry analysis showed that 65 % of the added 13C-hexadecane was degraded during the 8-week incubation. The degradation of 13C-hexadecane was microbially driven, as confirmed by DNA stable isotope probing (DNA-SIP). Amendment with 13C-kerogen did not enhance FeIII reduction or AsIII mobilisation, and microbial degradation of kerogen could not be confirmed conclusively by DNA-SIP fractionation or 13C incorporation in the phospholipid fatty acids. These data are, therefore, consistent with the utilisation of long chain n-alkanes (but not kerogen) as electron donors for anaerobic processes, potentially including FeIII and AsV reduction in the subsurface

Random walks on graphs: ideas, techniques and results

Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and new ideas have been introduced, which can be fruitfully extended to different areas and disciplines. Here we aim at giving a brief but comprehensive perspective of these progresses, with a particular emphasis on physical aspects.Comment: LateX file, 34 pages, 13 jpeg figures, Topical Revie

The impact of Stieltjes' work on continued fractions and orthogonal polynomials

Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis on the theory of orthogonal polynomials

Biomarker-indicated extent of oxidation of plant-derived organic carbon (OC) in relation to geomorphology in an arsenic contaminated Holocene aquifer, Cambodia

The poisoning of rural populations in South and Southeast Asia due to high groundwater arsenic concentrations is one of the world’s largest ongoing natural disasters. It is important to consider environmental processes related to the release of geogenic arsenic, including geomorphological and organic geochemical processes. Arsenic is released from sediments when iron-oxide minerals, onto which arsenic is adsorbed or incorporated, react with organic carbon (OC) and the OC is oxidised. In this study we build a new geomorphological framework for Kandal Province, a highly studied arsenic affected region of Cambodia, and tie this into wider regional environmental change throughout the Holocene. Analyses shows that the concentration of OC in the sediments is strongly inversely correlated to grainsize. Furthermore, the type of OC is also related to grain size with the clay containing mostly (immature) plant derived OC and sand containing mostly thermally mature derived OC. Finally, analyses indicate that within the plant derived OC relative oxidation is strongly grouped by stratigraphy with the older bound OC more oxidised than younger OC