15,499 research outputs found

    Generalised Space-time and Gauge Transformations

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    We consider the generalised space-time introduced by the author in 2003 in the context of the non-linear realisation of the semi-direct product of E11 and its first fundamental representation. For all the fields we propose gauge transformations which are compatible with the underlying E11 structure. A crucial role is played by the generalised vielbein that the generalised space-time possess. We work out the explicit form of the gauge transformations, at low levels, in four, five and eleven dimensions.Comment: 33 page

    Generalised geometry, eleven dimensions and E11

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    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

    Maps for Africa

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    [Introduction] Opening address by Oakley West at exhibition: Maps: Knowledge and Power - A Teaching Exhibition at the Albany Museum, November 1992. Maps, like art, reflect man's perception of the world in which he lives. Often they are coloured both by the known and unknown, by fact and fancy, myth and mystery. Maps are not just merely bits of paper. They are, and have been, important instruments in conquest and empire building. They reflect not only the perceived glory of war and occupation, but survival under siege, the protection or defence of people, property and resources, and, believe it or not, the accidental inheritance of territory, like India. Maps reflect the build-up of nations bent on expansion, resulting in the dreadful years of trench warfare in 1914 - 1918. And who of us can honestly admit that we knew exactly where Kuwait was before that conflict began? Thus in many cases lands were often first claimed on paper before they were effectively occupied. It has been said that no place is truly discovered until it has been mapped and as much as guns and warships, they have played significant roles in manifesting the realities of conquest and empire building. Maps are storehouses of knowledge and information and often it is in that very knowledge that lies the power to conquer, control, defend, divide or develop, to govern or administer or even mislead or misinform. This exhibition attempts to trace almost 2 000 years of cartography. It starts with the great insights of Claudius Ptolomy and his Geographia, continues through the retrogressive perceptions of the Church fathers and their decrees that Jerusalem was the centre of the world, to the perception of a flat Earth and a rather whimsical look at modern "upside-down" cartography which has proved to be only 300 years late in its conception. One can explore the opening up of the dark continent of Africa with its myths and mysteries, the source of the Nile, Mountains of the Moon and the mythical kingdom of Monomatapa. One can "see" the gradual growth of knowledge as first the coasts and later the interior was discovered and made known by men like Diaz, Da Gama, Livingstone, Stanley and Andersson. The discoveries of these explorers were recorded in the great maps of cartographers like John Arrowsmith and Henry Hall, the former incidentally never ever having visited Africa. A quantum leap takes us to some of the newest techniques, the satellite image, which still reflects the historical heritage in the shapes and patterns formed, in what has become known as Settler Country, from as early as the 1800s. By these images one is still able to appreciate the ravages of drought, overgrazing and perhaps the mismanagement of natural resources. Maps show us a different Grahamstown, a Graham's Town lit by gaslamp light. They help us to "see" prison gangs building the Queen's Road to Fort Beaufort, or appreciate the scramble for river frontage farming land. We see the early conceptualization of a harbour scheme at the mouth of the Kowie River, dreamed of by those intent on opening up a gateway to the Eastern Frontier through its wide waters. (A scheme, incidentally, which finally found a different, but nonetheless effective, realisation in the Marina built in the 1990s). Dreams were dreamed of a wide-spread colonial administration, though not without its nostalgic overtones: King William's Town would be the principal town in the county of Middlesex and Komga that of the county Cambridge in British Kaffraria! One can trace in maps the expanding horizons of the colonial powers as they appropriated land in the name of civilisation. As the church and the courts moved in to replace tribal customs and laws, maps reflected the more tangible results of expansion - telegraph, road and rail networks, as well as the more abstract and intangible - the spread of violence. On the other hand, we can follow the development of a great city, the city of London, though almost 400 years, witnessing the growth of its urban sprawl, the depiction of the famous bridges over. the Thames and who could not but be thrilled by the panoramic sweep of London from the Houses of Parliament through St Pauls to the sailing ship harbour, cartography par excellence which evidences the birth of a rail system with engines looking distinctly more akin to Stevenson's rocket than the locomotives we are used to seeing. An exceptionally fine relief model of the Western and Southern Cape coastal area serves to highlight the unending struggle of cartographers to portray that troublesome third dimension, height, on flat pieces of paper. Such struggles are revealed both in maps of topographic landscape as well as the urban complex - some successful, some not so. Finally, the exhibition touches lightly on the wonders of satellite imagery and the coming of the computer to cartography, as in all things. An attempt is made to explain in simple terms the art, science and technology of the cartographer in the production of the multicoloured maps we are all so familiar with

    Little Groups of Preon Branes

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    Little groups for preon branes (i.e. configurations of branes with maximal (n-1)/n fraction of survived supersymmetry) for dimensions d=2,3,...,11 are calculated for all massless, and partially for massive orbits. For massless orbits little groups are semidirect product of d-2 translational group Td−2T_{d-2} on a subgroup of (SO(d-2) ×\times R-invariance) group. E.g. at d=9 the subgroup is exceptional G2G_2 group. It is also argued, that 11d Majorana spinor invariants, which distinguish orbits, are actually invariant under d=2+10 Lorentz group. Possible applications of these results include construction of field theories in generalized space-times with brane charges coordinates, different problems of group's representations decompositions, spin-statistics issues.Comment: LaTeX, 11 page

    Saprolegnia diclina IIIA and S. parasitica employ different infection strategies when colonizing eggs of Atlantic salmon, Salmo salar L.

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    Acknowledgements The work has been funded by the European Commission through the EU Marie Curie ITN project SAPRO (238550) (MMS, AW). We would also like to acknowledge support from the BBSRC and the University of Aberdeen (PvW) and Landcatch and AquaGen for providing salmon eggs. Elin Rolen's assistance with sequencing of the strains is highly appreciated.Peer reviewedPublisher PD

    A Study of Runoff from Small Drainage Areas and the Openings in Attendant Drainage Structures

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    In 1926, John T. Lynch read to the Kentucky Academy of Sciences a paper entitled, The Relation Between Drainage Area and Waterway Required for Culverts and Small Bridges in Kentucky. The paper was based on a study of many small drainage structures then existing in the highway system, and a general evaluation of the performance of the structures in relation to rainfall and runoff from contributing watersheds. As a result of this report, and in accordance with the suggestions contained in it, the Department of Highways adopted a system of runoff coefficients applicable to different sections of the state and usable in the empirical Talbot formula for computing the quantity of flow from a drainage area. This information was contained in the booklet of instructions for bridge and culvert surveys which has been in effect for almost 25 years

    E11, generalised space-time and equations of motion in four dimensions

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    We construct the non-linear realisation of the semi-direct product of E11 and its first fundamental representation at low levels in four dimensions. We include the fields for gravity, the scalars and the gauge fields as well as the duals of these fields. The generalised space-time, upon which the fields depend, consists of the usual coordinates of four dimensional space-time and Lorentz scalar coordinates which belong to the 56-dimensional representation of E7. We demand that the equations of motion are first order in derivatives of the generalised space-time and then show that they are essentially uniquely determined by the properties of the E11 Kac-Moody algebra and its first fundamental representation. The two lowest equations correctly describe the equations of motion of the scalars and the gauge fields once one takes the fields to depend only on the usual four dimensional space-time

    Spectral fluctuations and 1/f noise in the order-chaos transition regime

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    Level fluctuations in quantum system have been used to characterize quantum chaos using random matrix models. Recently time series methods were used to relate level fluctuations to the classical dynamics in the regular and chaotic limit. In this we show that the spectrum of the system undergoing order to chaos transition displays a characteristic f−γf^{-\gamma} noise and γ\gamma is correlated with the classical chaos in the system. We demonstrate this using a smooth potential and a time-dependent system modeled by Gaussian and circular ensembles respectively of random matrix theory. We show the effect of short periodic orbits on these fluctuation measures.Comment: 4 pages, 5 figures. Modified version. To appear in Phys. Rev. Let

    The local symmetries of M-theory and their formulation in generalised geometry

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    In the doubled field theory approach to string theory, the T-duality group is promoted to a manifest symmetry at the expense of replacing ordinary Riemannian geometry with generalised geometry on a doubled space. The local symmetries are then given by a generalised Lie derivative and its associated algebra. This paper constructs an analogous structure for M-theory. A crucial by-product of this is the derivation of the physical section condition for M-theory formulated in an extended space.Comment: 20 pages, v2: Author Name corrected, v3: typos correcte
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