Representations of G+++ and the role of space-time

We consider the decomposition of the adjoint and fundamental representations of very extended Kac-Moody algebras G+++ with respect to their regular A type subalgebra which, in the corresponding non-linear realisation, is associated with gravity. We find that for many very extended algebras almost all the A type representations that occur in the decomposition of the fundamental representations also occur in the adjoint representation of G+++. In particular, for E8+++, this applies to all its fundamental representations. However, there are some important examples, such as An+++, where this is not true and indeed the adjoint representation contains no generator that can be identified with a space-time translation. We comment on the significance of these results for how space-time can occur in the non-linear realisation based on G+++. Finally we show that there is a correspondence between the A representations that occur in the fundamental representation associated with the very extended node and the adjoint representation of G+++ which is consistent with the interpretation of the former as charges associated with brane solutions.Comment: 45 pages, 9 figures, 9 tables, te

Solent Disturbance and Mitigation Project Phase II: Predicting the impact of human disturbance on overwintering birds in the Solent.

The Solent coastline provides feeding grounds for internationally protected populations of overwintering waders and wildfowl, and is also extensively used for recreation. In response to concerns over the impact of recreational pressure on birds within protected areas in the Solent, the Solent Forum initiated the Solent Disturbance and Mitigation Project to determine visitor access patterns around the coast and how their activities may influence the birds. The project has been divided into two phases. Phase I collated and reviewed information on housing, human activities and birds around the Solent, and reviewed the potential impact of disturbance on birds. Phase II has involved a programme of major new data collection to (i) estimate visitor rates to the coast from current and future housing, (ii) measure the activities and distances moved by people on the shore and intertidal habitats, and (iii) measure the distances and time for which different bird species respond to different activities. The current report represents the culmination of Phase II, in which the primary data are used to predict whether disturbance may be reducing the survival of birds. Predictions are derived for wader species by developing detailed computer models of birds and disturbance within Southampton Water and Chichester Harbour. These models create a virtual environment within the computer incorporating the intertidal invertebrate food supply of the birds, the exposure and covering of this food through the tidal cycle, disturbance from human activities, and the energy requirements and behaviour of the birds as they avoid humans and search for food. The invertebrate food supply of birds in the models was derived from previous intertidal surveys, and the exposure of intertidal habitat predicted from a tidal model of the Solent. The models incorporate the costs that birds incur when avoiding human activities (e.g. increased density in non-disturbed areas, reduced time for feeding and increased energy demands when flying away), but also their abilities to compensate for these costs (e.g. by feeding for longer or avoiding more disturbed areas). The predictions indicate how disturbance may be effecting the survival of waders throughout the Solent. The following waders were included in the models: Dunlin Calidris alpina, Ringed Plover Charadrius hiaticula, Redshank Tringa totanus, Grey Plover Pluvialis squatarola, Black-tailed Godwit Limosa limosa, Bar-tailed Godwit Limosa lapponica (Chichester Harbour model only), Oystercatcher Haematopus ostralegus and Curlew Numenius arquata. A simpler approach was used to assess how disturbance may be effecting Brent Geese in the Solent. As with any models, the predictions of the models used in this project depend on the data with which they are parameterised and the assumptions they make about the real system. The current and future visitor rates used in the models were themselves predicted using statistical analyses of household survey and on-site visitor data. The responses of birds to disturbance were parameterised using on-site observations of the responses of birds to disturbance. Furthermore, models are a simplification of real systems, and it is important to recognise this when interpreting their predictions. The report considers how the model parameters and assumptions may influence predictions. These include: (i) the way in which the disturbance data were measured and assumptions made about how birds and people are distributed in space and time; (ii) the way in which the behaviour of birds to disturbance differs between sites; (iii) the effect of extreme weather on the birds; (iv) how rare or localised activities are incorporated into the models; and (v) how consumption of food by species other than waders is included. The project predicted changes in visitor numbers to the Solent coast. Local authorities in the Solent region provided projections of future housing developments in the region. These were combined with data on visitor rates to different parts of the coast and the distance travelled to visit the coast, to predict coastal visitor rates with current and future housing. Using current housing levels, 52 million household visits per year to the Solent coast were predicted (i.e. the shore from Hurst Castle to Chichester Harbour, including the north shore of the Isle of Wight). Using the housing data provided by local authorities, visitor numbers were predicted to rise by around 8 million household visits, to a total of 60 million, an overall increase of 15%. Within Chichester Harbour, the food supply surveyed was not predicted to be able to support the majority of wading birds modelled. This implied that either the invertebrate survey underestimated the intertidal food supply, or that other food was available either terrestrially, or from neighbouring intertidal sites such as Langstone Harbour. Similar invertebrate surveys have been used to parameterise 17 other similar models, and in all cases birds were predicted to have survival rates close to, or higher than those expected. Due to uncertainties with the Chichester Harbour invertebrate data, it was decided not to use the Chichester Harbour model to predict the effect of disturbance on the birds. However, it is important to note what the effect of low food abundance would be on the effect of disturbance on the birds. The impact of disturbance on survival and body condition will depend on the birds’ ability to compensate for lost feeding time and extra energy expenditure. Birds will be better able to compensate when more food is available, and so lower food abundance in a site will make it more likely that disturbance decreases survival and body condition. Within Southampton Water, in the absence of disturbance, all wader species modelled were predicted to have 100% survival and maintain their body masses at the target value throughout the course of winter. Disturbance from current housing was predicted to reduce the survival of Dunlin, Ringed Plover, Oystercatcher and Curlew. Increased visitor numbers as a result of future housing was predicted to further reduce the survival of Dunlin and Ringed Plover. Disturbance was predicted to have a relatively minor effect on the mean body mass of waders surviving to the end of winter, largely because the individuals with very low mass starved before the end of winter. The Southampton Water model provided evidence that current and future disturbance rates may reduce wader survival in this site. Hypothetical simulations were run to explore how intertidal habitat area, energy demands of the birds and the frequency of different activities may influence the survival of waders within Southampton Water. The survival rates of Dunlin, Ringed Plover, Oystercatcher and Curlew were predicted to be decreased by any reduction in intertidal habitat area (e.g. due to sea level rise) or increases in energy demands (e.g. due to disturbance at roosts or cold weather). Wader survival was predicted to increase if intertidal activities were moved to the shore. This meant that the disturbance from these activities was restricted to the top of the shore rather than the whole intertidal area, and so the proportion of intertidal habitat disturbed was reduced. Reductions in the number of dogs that were off leads were also predicted to increase the survival of some wader species. Removing bait digging from simulations did not increase wader survival. However, this happened because bait-digging was assumed to be a relatively infrequent activity. This does not mean that bait-digging could not adversely affect the birds if it occurs at a higher frequency, and the simulations did not incorporate the depletion of the invertebrate prey of the birds caused by bait digging, which would be an additional effect on the birds in addition to disturbance. Brent Geese were considered in the light of the Solent Waders and Brent Goose Strategy. Important issues are the size of individual sites, their spacing and the ease with which birds can move between the sites. A high proportion of each site needs to be further away from visitor access routes than the distances over which birds are disturbed to ensure that disturbance to the birds is minimised. This could be achieved through a network of larger sites or by preventing visitor access through, or close to, smaller sites. Both intertidal and terrestrial food resources are important to the birds, intertidal food typically being of higher food value but dying back and / or becoming depleted during the autumn / early winter. Previous models of Brent Geese have predicted that the loss of terrestrial habitat typically has the highest effect on survival, and so such habitat is predicted to be particularly important for the birds. Maintaining a suitable network of saltmarsh sites will be increasingly important as the total area of saltmarsh declines with sea level rise. The findings of the present project are in general support with the recommendations of the Solent Waders and Brent Goose Strategy. Predicted current visitor rates varied widely throughout the Solent, but were relatively high within Southampton Water. The highest percentage increases in visitor rates were on the Isle of Wight (50-75%). Wader survival was predicted to be decreased in Southampton Water when daily visitor rates to coastal sections were greater than 30 per ha of intertidal habitat. The potential impact of visitors on wader survival throughout the Solent was calculated by comparing visitor densities throughout the Solent (expressed relative to maximum intertidal habitat area) to the visitor densities predicted to decrease bird survival within Southampton Water. The intertidal food supply within Chichester Harbour was insufficient to support the model birds and so any disturbance (by reducing feeding area or time, or increasing energy demands) would have decreased predicted survival in this site. There is also doubt as to the food supply within the other harbours and so some caution is appropriate when applying the results from Southampton Water to these sites. Coastal sections with daily visitor rates over 30 per ha are identified. The predictions of the Southampton Water model suggest that birds within these sections may have reduced survival due to disturbance from visitors. Whether or not such visitor rates will reduce survival will depend on the food abundance in the coastal sections themselves as well as that in neighbouring sections. The area of overlap between an activity / development and the distribution of birds is often used as a measure of the impact of the activity on the birds, with 1% overlap often taken as the threshold for impact (note however that this 1% overlap does not necessarily mean that an activity will have an adverse effect on the survival or body condition of birds). Therefore, the percentage of intertidal habitat disturbed within each coastal section was calculated as an index of the potential impact of disturbance on the birds. Assuming the maximum intertidal area and only including intertidal visitors, over 50% of the area of many coastal sections was predicted to be disturbed, with an average of 42%

Random Surfaces that Suppress Single Scattering

We present a method for generating numerically a one-dimensional random surface, defined by the equation x_3 = \zx, that suppresses single-scattering processes in the scattering of light from it within a specified range of scattering angles. Rigorous numerical calculations of the scattering of light from surfaces generated by this approach show that the single-scattering contribution to the mean scattered intensity is indeed suppressed within that range of angles.Comment: 3 pagers (Latex), 3 figure

Zero differential resistance in two-dimensional electron systems at large filling factors

We report on a state characterized by a zero differential resistance observed in very high Landau levels of a high-mobility two-dimensional electron system. Emerging from a minimum of Hall field-induced resistance oscillations at low temperatures, this state exists over a continuous range of magnetic fields extending well below the onset of the Shubnikov-de Haas effect. The minimum current required to support this state is largely independent on the magnetic field, while the maximum current increases with the magnetic field tracing the onset of inter-Landau level scattering

Generalised geometry, eleven dimensions and E11

We construct the non-linear realisation of E11 and its first fundamental representation in eleven dimensions at low levels. The fields depend on the usual coordinates of space-time as well as two form and five form coordinates. We derive the terms in the dynamics that contain the three form and six form fields and show that when we restricted their field dependence to be only on the usual space-time we recover the correct self-duality relation. Should this result generalise to the gravity fields then the non-linear realisation is an extension of the maximal supergravity theory, as previously conjectured. We also comment on the connections between the different approaches to generalised geometry.Comment: 17 pages, Trivial typos corrected in version one and a substantial note added which gives the equation of motion relating the gravity field to its dua

Duality Symmetries and G^{+++} Theories

We show that the non-linear realisations of all the very extended algebras G^{+++}, except the B and C series which we do not consider, contain fields corresponding to all possible duality symmetries of the on-shell degrees of freedom of these theories. This result also holds for G_2^{+++} and we argue that the non-linear realisation of this algebra accounts precisely for the form fields present in the corresponding supersymmetric theory. We also find a simple necessary condition for the roots to belong to a G^{+++} algebra.Comment: 35 pages. v2: 2 appendices added, other minor corrections. v3: tables corrected, other minor changes, one appendix added, refs. added. Version published in Class. Quant. Gra