Exact Wave Solutions to 6D Gauged Chiral Supergravity

We describe a broad class of time-dependent exact wave solutions to 6D gauged chiral supergravity with two compact dimensions. These 6D solutions are nontrivial warped generalizations of 4D pp-waves and Kundt class solutions and describe how a broad class of previously-static compactifications from 6D to 4D (sourced by two 3-branes) respond to waves moving along one of the uncompactified directions. Because our methods are generally applicable to any higher dimensional supergravity they are likely to be of use for finding the supergravity limit of time-dependent solutions in string theory. The 6D solutions are interesting in their own right, describing 6D shock waves induced by high energy particles on the branes, and as descriptions of the near-brane limit of the transient wavefront arising from a local bubble-nucleation event on one of the branes, such as might occur if a tension-changing phase transition were to occur.Comment: 22 pages, 1 figure. Minor clarifications added. Accepted in JHE

A comparison of the responses of mature and young clonal tea to drought.

To assist commercial producers with optimising the use of irrigation water, the responses to drought of mature and young tea crops (22 and 5 years after field planting respectively) were compared using data from two adjacent long-term irrigation experiments in Southern Tanzania. Providing the maximum potential soil water deficit was below about 400-500 mm for mature, and 200-250 mm for young plants (clone 6/8), annual yields of dry tea from rainfed or partially irrigated crops were similar to those from the corresponding well-watered crops. At deficits greater than this, annual yields declined rapidly in young tea (up to 22 kg (ha mm)-1) but relatively slowly in mature tea (up to 6.5 kg (ha mm)- 1). This apparent insensitivity of the mature crop to drought was due principally to compensation that occurred during the rains for yield lost in the dry season. Differences in dry matter distribution and shoot to root ratios contributed to these contrasting responses. Thus, the total above ground dry mass of well-irrigated, mature plants was about twice that for young plants. Similarly, the total mass of structural roots (>1 mm diameter), to 3 m depth, was four times greater in the mature crop than in the young crop and, for fine roots (<1 mm diameter), eight times greater. The corresponding shoot to root ratios (dry mass) were about 1:1 and 2:1 respectively. In addition, each unit area of leaf in the canopy of a mature plant had six times more fine roots (by weight) available to extract and supply water than did a young plant. Despite the logistical benefits resulting from more even crop distribution during the year when crops are fully irrigated, producers currently prefer to save water and energy costs by allowing a substantial soil water deficit to develop prior to the start of the rains, up to 250 mm in mature tea, knowing that yield compensation will occur later

Scaling Solutions to 6D Gauged Chiral Supergravity

We construct explicitly time-dependent exact solutions to the field equations of 6D gauged chiral supergravity, compactified to 4D in the presence of up to two 3-branes situated within the extra dimensions. The solutions we find are scaling solutions, and are plausibly attractors which represent the late-time evolution of a broad class of initial conditions. By matching their near-brane boundary conditions to physical brane properties we argue that these solutions (together with the known maximally-symmetric solutions and a new class of non-Lorentz-invariant static solutions, which we also present here) describe the bulk geometry between a pair of 3-branes with non-trivial on-brane equations of state.Comment: Contribution to the New Journal of Physics focus issue on Dark Energy; 28 page

D-Brane Dynamics and NS5 Rings

We consider the classical motion of a probe D-brane moving in the background geometry of a ring of NS5 branes, assuming that the latter are non-dynamical. We analyse the solutions to the Dirac-Born-Infield (DBI) action governing the approximate dynamics of the system. In the near horizon (throat) approximation we find several exact solutions for the probe brane motion. These are compared to numerical solutions obtained in more general cases. One solution of particular interest is when the probe undergoes oscillatory motion through the centre of the ring (and perpendicular to it). By taking the ring radius sufficiently large, this solution should remain stable to any stringy corrections coming from open-strings stretching between the probe and the NS5-branes along the ring.Comment: 17 pages, Latex, 8 figures; References adde

An overview of tea research in Tanzania - with special reference to the Southern Highlands.

The history of tea development in Tanzania from the early part of this century to the present is summarised. Average yields of made tea from well managed estates in the Mufindi district have increased from around 600 kg ha-1 in the late 1950s to 3000 kg ha-1 at the present time: by comparison, yields from smallholder farms have remained much lower, averaging only 400-500 kg ha-1. There have been a large number of technical, economic and other changes over the last 30 to 40 years. The removal of shade trees, the use of herbicides, the application of NPK compound fertilisers, the introduction of irrigation (on some estates) and changes in harvesting policy have all contributed to the increases in yield. Financial and infrastructural problems have contributed to the low yields from many smallholders and others, and have limited the uptake of new technology. The contribution of research is reviewed, from the start of the Tea Research Institute of East Africa in Kenya in 1951, through to the development of the Marikitanda Tea Research Centre in Amani in 1967; the Ngwazi Tea Research Unit in Mufindi (1967 to 1970, and from 1986), and lastly the Kifyulilo Tea Research Station, also in Mufindi in 1986. The yield potential of well fertilized and irrigated clonal tea, grown at an altitude of 1800 m, is around 6000 kg ha-1. This potential is reduced by drought, lack of fertilizer, bush vacancies and inefficient harvesting practices. The corresponding potential yields at high (2200 m) and low (1200 m) altitude sites range from 3000-3500 kg ha-1 up to 9000-10000 kg ha-1 and are largely a function of temperature. The opportunities for increasing yields of existing tea, smallholder and estate, are enormous. Tea production in the Southern Highlands of Tanzania is about to expand rapidly. Good, appropriate research is needed to sustain this development over the long term, and suggestions on how best this is done in order to assist the large scale producers as well as the smallholders, are discussed

Duality, the Semi-Circle Law and Quantum Hall Bilayers

There is considerable experimental evidence for the existence in Quantum Hall systems of an approximate emergent discrete symmetry, $\Gamma_0(2) \subset SL(2,Z)$. The evidence consists of the robustness of the tests of a suite a predictions concerning the transitions between the phases of the system as magnetic fields and temperatures are varied, which follow from the existence of the symmetry alone. These include the universality of and quantum numbers of the fixed points which occur in these transitions; selection rules governing which phases may be related by transitions; and the semi-circular trajectories in the Ohmic-Hall conductivity plane which are followed during the transitions. We explore the implications of this symmetry for Quantum Hall systems involving {\it two} charge-carrying fluids, and so obtain predictions both for bilayer systems and for single-layer systems for which the Landau levels have a spin degeneracy. We obtain similarly striking predictions which include the novel new phases which are seen in these systems, as well as a prediction for semicircle trajectories which are traversed by specific combinations of the bilayer conductivities as magnetic fields are varied at low temperatures.Comment: 12 pages, 8 figures; discussion of magnetic field dependence modified and figures and references updated in v