The Parker Magnetostatic Theorem

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

Imperial Users onl

Forecasts of the Scottish economy [June 2006]

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

Forecasts of the Scottish economy [March 2006]

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

Forecasts of the Scottish economy [December 2003]

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

The world economy [June 2003]

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

The world economy [March 2006]

It would be tempting to say that all is rosy in the world economy with relatively strong growth and stable inflation. However inflation is rising across the globe but the impact of the rise in oil prices on wage inflation is weaker than expected. The effect is slightly more pronounced however in the US where unemployment is relatively low compared to Europe which has higher unemployment. This suggests that monetary policy will be more likely to be tightened in the US than elsewhere. It is probable that deflation in Japan will end this year and China and Asia are set to perform strongly despite rising oil prices. These economies have experienced strong export growth but increasingly the balance is shifting as domestic demand is driving these economies forward

The world economy [October 2003]

The most recent economic data suggests that the recovery is strengthening in the US and the Asian economies (excluding Japan) but is weaker in the Euro Area and Japan. Global domestic demand remains relatively weak but is expected to pick up in the second half of this year. There are mixed signals from consumer confidence measures with some remaining weak while others are showing signs of improvement. The labour markets also demonstrate mixed performance. The unemployment rate fell in the US but so did the employment rate. Oil prices have remained flat but there is little evidence to suggest that the world economy is experiencing any significant inflationary pressures. There are clear signs however from central banks that interest rates will have to rise shortly. While the hostilities in Iraq were brought to a rapid conclusion there is now more concern over "guerrilla warfare" from disaffected Iraqis and opposition groups. This is not only potentially destabilising for the Middle East but adds to the uncertainty in the world economy

The UK economy [October 2006]

Across the globe world economic growth remains relatively strong despite a slight slowing in the US. Inflationary pressures are more clearly seen as a threat to prices as energy costs continue to grow. The general trend is for a tightening of monetary policy to combat inflation. The performance of the US, Japanese and Chinese economies have all stimulated world demand and trade. The Euro Area is forecast to pick up significantly as activity strengthens there. The only real concern there is the growth of German consumption. Emerging markets and other Far East economies also continue to perform well

The world economy [December 2003]

The world economy is now picking up with strong growth in the US and the Far East economies. Europe remains relatively weak and since the last quarter has worsened slightly. It is not expected to improve until next year with a return to trend growth forecast for 2005. The forecasts for world growth and trade have both improved since the last quarter. The outlook for the world economy remains good. The downside risks are the uncertainty over terrorist attacks in the west, the size of the US deficit, and the continued weakness in Europe