Monopole wall

We construct, numerically, a solution of the SU(2) Bogomolny equations corresponding to a sheet of BPS monopoles. It represents a domain wall between a vacuum region and a region of constant energy density, and it is the smoothed-out version of the planar sheet of Dirac monopoles obtained by linear superposition

Estimating numbers of properties susceptible to groundwater flooding in England

In the wake of widespread groundwater flooding that affected properties and infrastructure in southern England during 2014, a review has been undertaken of the number of properties in England that might be vulnerable during episodes of high groundwater levels, and an estimate made of how many properties might be affected in susceptible areas. Groundwater flooding can happen in many geological environments, but is a particular problem on Chalk and Limestone aquifers, where around 920,000 properties are in areas where groundwater emergence could occur. This represents fewer properties than previously estimated for these areas. However, a further 3,800,000 properties are in areas underlain by other aquifer types that could be affected by groundwater flooding or shallow water tables. The actual impact of groundwater flooding on properties is often mitigated by building design or natural/artificial drainage systems which act to lower water tables and move emergent water to rivers. As a result only a small percentage of properties identified above are likely to be impacted by groundwater flooding. Although there is limited observational data, we believe that up to 138,000 properties might be impacted in chalk and limestone areas and up to 151,600 in other areas. This means the revised estimate of the number of properties in areas at risk of groundwater flooding is between 122,000 and 290,000. Groundwater may play a role in the flooding of a further 980,000 properties in areas that are also at risk from river and/or coastal flooding. In addition, groundwater flooding is a significant issue for subsurface infrastructure. Note that this latter issue has not been assessed in this report

Geometry of Periodic Monopoles

Bogomol’nyi-Prasad-Sommerfield monopoles on R 2 ×S 1 correspond, via the generalized Nahm transform, to certain solutions of the Hitchin equations on the cylinder R×S 1 . The moduli space M of two monopoles with their center of mass fixed is a four-dimensional manifold with a natural hyperkähler metric, and its geodesics correspond to slow-motion monopole scattering. The purpose of this paper is to study the geometry of M in terms of the Nahm-Hitchin data, i.e., in terms of structures on R×S 1 . In particular, we identify the moduli, derive the asymptotic metric on M , and discuss several geodesic surfaces and geodesics on M . The latter include novel examples of monopole dynamics

How to find discrete contact symmetries

This paper describes a new algorithm for determining all discrete contact symmetries of any differential equation whose Lie contact symmetries are known. The method is constructive and is easy to use. It is based upon the observation that the adjoint action of any contact symmetry is an automorphism of the Lie algebra of generators of Lie contact symmetries. Consequently, all contact symmetries satisfy various compatibility conditions. These conditions enable the discrete symmetries to be found systematically, with little effort

Anti-self-dual conformal structures with null Killing vectors from projective structures

Using twistor methods, we explicitly construct all local forms of four--dimensional real analytic neutral signature anti--self--dual conformal structures $(M,[g])$ with a null conformal Killing vector. We show that $M$ is foliated by anti-self-dual null surfaces, and the two-dimensional leaf space inherits a natural projective structure. The twistor space of this projective structure is the quotient of the twistor space of $(M,[g])$ by the group action induced by the conformal Killing vector. We obtain a local classification which branches according to whether or not the conformal Killing vector is hyper-surface orthogonal in $(M, [g])$. We give examples of conformal classes which contain Ricci--flat metrics on compact complex surfaces and discuss other conformal classes with no Ricci--flat metrics.Comment: 43 pages, 4 figures. Theorem 2 has been improved: ASD metrics are given in terms of general projective structures without needing to choose special representatives of the projective connection. More examples (primary Kodaira surface, neutral Fefferman structure) have been included. Algebraic type of the Weyl tensor has been clarified. Final version, to appear in Commun Math Phy

A note on the appearance of self-dual Yang-Mills fields in integrable hierarchies

A family of mappings from the solution spaces of certain generalized Drinfeld-Sokolov hierarchies to the self-dual Yang-Mills system on R^{2,2} is described. This provides an extension of the well-known relationship between self-dual connections and integrable hierarchies of AKNS and Drinfeld-Sokolov type

Regulatory practice and transport modelling for nitrate pollution in groundwater

This report forms the first deliverable of a project jointly funded by BGS and the Environment Agency to consider the potential for incorporating the outputs from the BGS unsaturated zone travel time work in assessing the risks to water from nitrate. This is to help to inform the nitrate vulnerable zones (NVZs) designation process. In England, the Environment Agency advises Defra on identifying areas for designation as NVZs. Over time, the designation process has developed and become more complex since the first round of designations in 1996. The designation process for groundwater initially used only public supply monitoring data and the associated source catchment area. In December 2000, the European Court of Justice held that the UK had failed to designate sufficient NVZs for the protection of all waters, not just for drinking water sources. This resulted in the development of revised methodologies for the designation of NVZs which separately address surface waters, groundwater and waters at risk of eutrophication. This was implemented in 2002. Further reviews have been carried out in 2008 and 2012 and as a result, modifications and improvements to methods have been made at each designation round. For groundwater the Environment Agency developed a numerical risk assessment procedure that uses a range of risk factors including both nitrate concentration data and nitrate-loading data to assess the risk of nitrate pollution. The loading data is based on farm census returns made to Defra and combined using the NEAP-N methodology developed by ADAS (Lord and Anthony, 2000). The overall risk assessment considers both current observed concentrations and predicted future concentrations as well as current loadings. However, this approach has a number of disadvantages including a lack of a specific term for the time of travel to the water table and emergence of pollutant both into groundwater and to groundwater discharge points that support surface water features. Instead, these issues are considered at the conceptual level in workshops with local EA hydrogeologists. A key question for Defra and the Agency is how long it will take for nitrate concentrations to peak and then stabilise at an acceptable, lower level, in response to existing and future land management control measures. This is most important for soils, for aquifers, for lakes and for groundwater-fed wetland systems that respond less quickly to changes in loading. Groundwater and lake catchment numerical models can provide first-order estimates of likely response times, but can be difficult and costly to set-up for many different situations and are difficult to apply consistently at the national scale. A previous review of nitrate vulnerable zones suggests a range of further needs: • to understand the recent developments in nitrate pollution simulation and particularly the potential to understand/characterise past nitrate loading from changing land management practices and correlate these with observed nitrate concentrations over time; • to evaluate the retention of nitrate in catchments, particularly in the unsaturated zone of soils and aquifers; • to simulate the recent and future anticipated decreases in nitrate loading by sectors within the UK; • to understand the likely time taken for nitrate concentrations to peak and then stabilise at an acceptable, lower level, in response to existing and future control measures. Without evidence of how long it may take systems to recover it is difficult to evaluate the effectiveness of existing measures or decide whether additional measures are necessary. The aim of this project is to investigate the use of new models to inform decision-making on nitrate pollution in groundwater and the potential for incorporating unsaturated zone processes in future NVZ designations. The work described here forms the first task of this project and aims to review NVZ methodology and recent designation experience. As part of this we will: • collate information from the Agency on the recent application of the methodology; • provide case study examples of designation in different time-lag settings and/or where these are not corroborated by water quality

A case study based assessment of potential cumulative impacts on groundwater from shale gas production in Northern England

The UK shale gas industry might see significant growth in the near future, with many energy companies already having gained approval and others in the stages of seeking approval for exploration. Exploratory boreholes have been in place in the Vale of Pickering, North Yorkshire, and the Fylde Basin, Lancashire, since 2013 and 2010 respectively. Since then, several other sites around the UK have been earmarked for future exploration. The current absence of producing shale gas wells within the UK means it is too early to assess any actual impact of these operations at the local, regional and national scale. However, international analogues may provide some indications based on areas elsewhere in the world where a shale gas industry is more developed (e.g. the Marcellus Shale, USA) albeit with obvious limitations due to differences in geology and setting. While regulation and compliance of shale gas operations varies between countries, the process and method of extraction and the environmental risks are comparable. The general requirements for water, drilling mud/fluids, hydraulic fracturing fluids (“frac fluids”) and the design of wells and well pads can all be extracted from an already mature international experience. However, the requirements in the UK will be modified by the regulatory requirements and restrictions that exist. There are ongoing discussions within the UK to determine whether shale gas is beneficial, economically viable and environmentally safe. In this report, the impact on land use, groundwater quality and water resources of one well in a selection of approved Petroleum Exploration and Development Licence (PEDL) areas will be considered, followed by an estimation of the cumulative impacts that may result from multiple extraction sites within these areas. The exercise will depend on ranges of input parameters informed by international analogues applied in a UK geo-environmental setting. To recognise the variability in parameters and uncertainty in UK industry development, a range of impact scenarios - low, moderate and high – have been considered

Quantisation of twistor theory by cocycle twist

We present the main ingredients of twistor theory leading up to and including the Penrose-Ward transform in a coordinate algebra form which we can then `quantise' by means of a functorial cocycle twist. The quantum algebras for the conformal group, twistor space CP^3, compactified Minkowski space CMh and the twistor correspondence space are obtained along with their canonical quantum differential calculi, both in a local form and in a global *-algebra formulation which even in the classical commutative case provides a useful alternative to the formulation in terms of projective varieties. We outline how the Penrose-Ward transform then quantises. As an example, we show that the pull-back of the tautological bundle on CMh pulls back to the basic instanton on S^4\subset CMh and that this observation quantises to obtain the Connes-Landi instanton on \theta-deformed S^4 as the pull-back of the tautological bundle on our \theta-deformed CMh. We likewise quantise the fibration CP^3--> S^4 and use it to construct the bundle on \theta-deformed CP^3 that maps over under the transform to the \theta-deformed instanton.Comment: 68 pages 0 figures. Significant revision now has detailed formulae for classical and quantum CP^

Summary report on the geology of the proposed HS2 Route (3) in the Chesham and Amersham Constituency

This brief open-file report summarises the information available from the British Geological Survey (BGS), a component body of the Natural Environment Research Council (NERC), on the geology, hydrogeology and potential geological hazards of the proposed HS2 Route 3 within the Chesham and Amersham Constituency, and surrounding areas. The report summarises the geology and hydrogeology of the district and highlights geological and hydrogeological considerations that may need further investigation along the route. Further review and analysis of existing data and possible field investigation would be required to confirm details of the local geology. The report was requested by Mrs Cheryl Gillan MP following a meeting with Dr Martin Smith, Head of Geology & Landscapes programme, on Monday 16th May 2011 at the offices of the Secretary of State for Wales in Whitehall