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

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 [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 UK economy [April 2007]

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]

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 world economy [July 2005]

One of the most important developments at the end of 2004 was the depreciation of the effective exchange rate of the dollar by 4.5 per cent on the previous quarter and the rise of the Euro effective exchange rate by 7.2 per cent. The world economy is still adjusting to this and growth has slowed slightly in the main economies

The UK economy [October 2005]

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

The UK economy [June 2006]

The world economy continues to grow at a relatively strong rate with the US, Japan and some non-OECD countries being the principal areas driving growth. China and India in particular have experienced very fast growth and are forecast to continue at a similar pace over the next two years