Gravitational instantons, extra dimensions and form fields

A broad class of higher dimensional instanton solutions are found for a theory which contains gravity, a scalar field and antisymmetric tensor fields of arbitrary rank. The metric used, a warp product of an arbitrary number of any compact Einstein manifolds, includes many of great interest in particle physics and cosmology. For example 4D FRW universes with additional dimensions compactified on a Calabi-Yau three fold, a torus, a compact hyperbolic manifold or a sphere are all included. It is shown that the solution of this form which dominates the Hartle Hawking path integral is always a higher dimensional generalisation of a Hawking Turok instanton when the potential of the scalar field is such that these instantons can exist. On continuation to Lorentzian signature such instantons give rise to a spacetime in which all of the spatial dimensions are of equal size and where the spatial topology is that of a sphere. The extra dimensions are thus not hidden. In the case where the potential for the scalar field is generated solely by a dilatonic coupling to the form fields we find no integrable instantons at all. In particular we find no integrable solutions of the type under consideration for the supergravity theories which are the low energy effective field theories of superstrings.Comment: 11 pages, 4 figure

A two-dimensional model of the quasi biennial oscillation of ozone

The largest amplitudes of the observed Quasi Biennial Oscillation (QBO) in column ozone are found in high latitudes and this must be taken into account in any explanation of the increased depletion of ozone in the southern polar spring during the 1980's. A QBO in zonal wind, temperature and column ozone has been successfully modelled in a two-dimensional dynamical/chemical model by the introduction of a parameterization scheme to model the transfer of momentum to the zonal flow associated with the damping of vertically propagating Kelvin and Rossby-Gravity waves. The largest anomalies in column ozone of approximately 20 DU are present at high latitudes. The equatorial ozone QBO is out of phase with the mid- and high-latitude ozone QBO, in good agreement with observations

VIPER : a 25-MHz, 100-MIPS peak VLIW micro-processor

This paper describes the design and implementation of a very long instruction word (VLIW) microprocessor. The VIPER (VLIW integer processor) contains four pipelined functional units, and can achieve 100 MIPS peak performance at 25 MHz. The procesor is capable of performing multiway branch operations, two load/store operations and up to four ALU operations in each clock cycle, with full register file access to each functional unit. VIPER is the first VLIW microprocessor known that can achieve this level of performance. Designed in twelve months, the processor is integrated with an instruction cache controller and a data cache, requiring 450,000 transistors and a die size of 12.9 by 9.1 mm in a 1.2 µm technology

Gravitational instantons and internal dimensions

We Study instanton solutions in general relativity with a scalar field. The metric ansatz we use is composed of a particular warp product of general Einstein metrics, such as those found in a number of cosmological settings, including string cosmology, supergravity compactifications and general Kaluza Klein reductions. Using the Hartle-Hawking prescription the instantons we obtain determine whether metrics involving extra compact dimensions of this type are favoured as initial conditions for the universe. Specifically, we find that these product metric instantons, viewed as constrained instantons, do have a local minima in the action. These minima are then compared with the higher dimensional version of the Hawking-Turok instantons, and we argue that the latter always have lower action than those associated with these product metrics.Comment: 10 pages, 5 figure

Porting Spotlight Range Migration Algorithm Processor from Matlab to Virtex 6

This paper describes the implementation and optimization of a Synthetic Aperture Radar process Spotlight Range Migration Algorithm processor on FPGA Virtex 6 DSP kit that fits on the chip. The mean/max error compared to a software implementation is -54/-28.74dB for 55 elements and 882 samples

FMCW rail-mounted SAR: Porting spotlight SAR imaging from MATLAB to FPGA

In this work, a low-cost laptop-based radar platform derived from the MIT open courseware has been implemented. It can perform ranging, Doppler measurement and SAR imaging using MATLAB as the processor. In this work, porting the signal processing algorithms onto a FPGA platform will be addressed as well as differences between results obtained using MATLAB and those obtained using the FPGA platform. The target FPGA platforms were a Virtex6 DSP kit and Spartan3A starter kit, the latter was also low-cost to further reduce the cost for students to access radar technology

Human sperm accumulation near surfaces: a simulation study

A hybrid boundary integral/slender body algorithm for modelling flagellar cell motility is presented. The algorithm uses the boundary element method to represent the ‘wedge-shaped’ head of the human sperm cell and a slender body theory representation of the flagellum. The head morphology is specified carefully due to its significant effect on the force and torque balance and hence movement of the free-swimming cell. The technique is used to investigate the mechanisms for the accumulation of human spermatozoa near surfaces. Sperm swimming in an infinite fluid, and near a plane boundary, with prescribed planar and three-dimensional flagellar waveforms are simulated. Both planar and ‘elliptical helicoid’ beating cells are predicted to accumulate at distances of approximately 8.5–22 μm from surfaces, for flagellar beating with angular wavenumber of 3π to 4π. Planar beating cells with wavenumber of approximately 2.4π or greater are predicted to accumulate at a finite distance, while cells with wavenumber of approximately 2π or less are predicted to escape from the surface, likely due to the breakdown of the stable swimming configuration. In the stable swimming trajectory the cell has a small angle of inclination away from the surface, no greater than approximately 0.5°. The trapping effect need not depend on specialized non-planar components of the flagellar beat but rather is a consequence of force and torque balance and the physical effect of the image systems in a no-slip plane boundary. The effect is relatively weak, so that a cell initially one body length from the surface and inclined at an angle of 4°–6° towards the surface will not be trapped but will rather be deflected from the surface. Cells performing rolling motility, where the flagellum sweeps out a ‘conical envelope’, are predicted to align with the surface provided that they approach with sufficiently steep angle. However simulation of cells swimming against a surface in such a configuration is not possible in the present framework. Simulated human sperm cells performing a planar beat with inclination between the beat plane and the plane-of-flattening of the head were not predicted to glide along surfaces, as has been observed in mouse sperm. Instead, cells initially with the head approximately 1.5–3 μm from the surface were predicted to turn away and escape. The simulation model was also used to examine rolling motility due to elliptical helicoid flagellar beating. The head was found to rotate by approximately 240° over one beat cycle and due to the time-varying torques associated with the flagellar beat was found to exhibit ‘looping’ as has been observed in cells swimming against coverslips