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    The Parker Magnetostatic Theorem

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    We demonstrate the Parker Magnetostatic Theorem in terms of a small neighborhood in solution space containing continuous force-free magnetic fields in small deviations from the uniform field. These fields are embedded in a perfectly conducting fluid bounded by a pair of rigid plates where each field is anchored, taking the plates perpendicular to the uniform field. Those force-free fields obtainable from the uniform field by continuous magnetic footpoint displacements at the plates have field topologies that are shown to be a restricted subset of the field topologies similarly created without imposing the force-free equilibirum condition. The theorem then follows from the deduction that a continuous nonequilibrum field with a topology not in that subset must find a force-free state containing tangential discontinuities.Comment: 13 pages, no figur

    Packing Characteristics of Different Shaped Proppants for use with Hydrofracing - A Numerical Investigation using 3D FEMDEM

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    Forecasts of the Scottish economy [March 2006]

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    There has undoubtedly been a slight slowing in the world economy but it is more marked in the US than elsewhere. Japanese performance was better than expected however and has offset the deterioration in the US. While the Euro Area remains relatively weak there are clear signs of a strengthening of activity and a modest recovery is taking place. The US is forecast to grow by 2.9 per cent this year, Japanese growth is forecast to be 2.3 per cent and the Euro Area forecast is 1.9 per cent. Inflationary pressures have been building as oil prices have surged but there are few signs of this passing through to wage bargains and over the next year as monetary policy is further tightened; inflationary pressures are expected to abate

    The world economy [June 2003]

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    The world economy has weakened slightly further again this quarter. This is primarily due to weaker economic data at the end of 2002 and for the first quarter of 2003. The expectation is for activity to strengthen in the latter half of 2003 and for GDP growth to intensify in 2005 relative to 2004. The factors that have stabilised the world economy are the relative pick-up in global equity markets, the re-alignment of currencies (this may lead to an improvement in imbalances in the world economy) and oil price stability, although the fall in oil prices is smaller than was expected. Clearly the situation in Iraq has resolved according to the US plan and this has reduced uncertainty significantly. Despite this the West still has to be vigilant to any terrorist threat. The economic consequences of the war however are relatively minor

    Forecasts of the Scottish economy [December 2003]

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    The outlook for the world economy remains promising with the US driving growth. There is also strong growth in the Far East particularly in China. An area of concern is the Euro Area, which remains depressed compared to other major economies. This is largely due to the situation in Germany. Forward indicators for the Euro Zone are improving suggesting that recovery will take place in 2004 but that trend growth will not be achieved until 2005. The UK economy continues to perform well. GDP data for the UK has been revised up (mainly due to the construction sector) and growth is forecast to be 2.0 per cent in 2003 and 2.6 per cent in 2004. There are some inflationary pressures in the economy. The Bank of England is concerned over household debt and a strong housing market. These were significant factors in their decision to raise the Bank of England interest rate in November to 3.75 per cent. The UK labour market remains buoyant with employment growth and low unemployment. We are forecasting that the UK will return to trend growth by 2004 and certainly by 2005. The latest Scottish GDP data were encouraging overall. Manufacturing is still experiencing problems but the service sector continues to grow at just below 3 per cent on an annual basis up to the second quarter of 2003. Within services transport and communication, financial services and real estate and business services are the strongest growing sectors. We are forecasting that Scottish GDP growth will be 1.3 per cent in 2003 and 2.1 per cent in 2004. In 2005 we forecast growth of 2.3 per cent

    Forecasts of the Scottish economy [June 2006]

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    While the world economy slowed slightly in 2005 it is now clear that strong growth remains in the US, Japan, China, India and several other non-OECD countries. While the Euro Area has been a slow performer there are now signs of a broad based recovery even in Germany. We suggest that there is still a problem translating increased activity into higher incomes and therefore Germany could be losing out on some consumption gains

    The UK economy [April 2007]

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    The global economy remains relatively strong given the pick-up in growth in 2006 after the slower growth seen in 2005. Higher oil prices pushed inflation up slightly across the globe but in the second half of 2006 oil prices fell significantly especially in September. The US in particular slowed slightly in 2006 from previous expectations whereas the Euro Area outperformed expectations. In the UK growth was relatively strong but 2007 may see a slight slowing of growth across the globe as households and businesses feel the impact of higher prices and interest rates. Economic performance in China and India continued at a blistering pace. The outlook for the world economy remains good and all developed economies are forecast to grow at a reasonable pace

    The world economy [October 2006]

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    Growth in the world economy is still relatively strong, although US growth has slowed slightly. Inflationary pressures are clearly more visible than previously and the general trend for global monetary policy is for a tighter stance. Prices continue to be driven by energy prices, although there are few signs of this feeding through into wage bargains. Japan and China once again have performed strongly in the East while the Euro Area has shown significant improvements. There is still some concern over the pace of private consumption growth in Germany. The outlook for the world economy is still optimistic over the next two years

    The UK economy [October 2005]

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    The US, Japan, China and the UK were growing at above trend levels in 2004. This year growth has slowed slightly due to increasing oil prices but growth is still relatively strong in the US, China, and the UK and in other non- Japan Asian economies. Some emerging economies are also growing relatively strongly. While the oil price has risen there does not appear to be sustained global inflation simply because the dependency on oil is less than it was; oil revenues are recycled more quickly now; monetary policy is more appropriate and there is no spiral effects because of increased wage demands on the back of oil price increases. Consequently inflation is more subdued
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