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 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

The world economy [June 2006]

Growth in the world economy remains robust with both China and India experiencing fast growth. The US continues to have strong growth despite a slight weakening in the last quarter of 2005. Consumption and investment are much more important in Japan now, driving growth forward. Exports are also contributing significantly to Japanese growth. The Euro Area grew below trend in 2005 but is forecast to have stronger performance in both 2006 and 2007. However, the main impetus to growth is external to the OECD. World growth is forecast to be 4.8 per cent per annum for the four years ending in 2007 compared to average growth of 3.4 per cent per annum for 1975 to 2003. Oil prices are expected to be close to $60 but the decreased dependency on oil of the advanced economies has meant that it has had little impact on inflation

The world economy [February 2005]

As stated in the previous quarter we still believe growth in the world economy is relatively strong (despite the weak data in the summer and a slight slowing in China). There signs of strong growth in the US, China and Japan although the Euro Area remains relatively weak. The world economy is expected to grow at a considerable pace (close to 4 per cent) in 2004 but growth is forecast to be slightly less in 2005. The Euro Area is expected to grow more strongly in 2005 as it is currently lagging the other regions of the world. World trade is forecast to grow rapidly in both 2004 and 2005 (just below 10 per cent for both years). Chinese trade flows and the importance of trade in Asia are the most significant contributions to this growth. Emerging markets are also expected to have strong trade growth in 2005. Sadly, while the human costs of the Tsunami were both tragic and huge the economic impact on the world economy will be relatively minor

Forecasts of the Scottish economy [July 2007]

Despite a slowing in the US, growth in the world economy remains relatively strong with the Euro Area performance strengthening. China continues to be a major driver of world growth and trade is forecast to drive growth up. Asian markets in particular are forecast to have robust growth. Japan continues to recover steadily and survey evidence for the world economy points to a further strengthening of growth in 2007Q2

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

Forecasts of the Scottish economy [November 2008]

For four years through to mid 2007 the ‘global economy boomed’ (International Monetary Fund, October 2008), with world growth averaging some 5% per annum, the strongest sustained rate for some three decades. Growth in developing and emerging economies was pronounced with China, India and Brazil reporting amongst the strongest annual growth rates. At the same time inflation remained modest and an image of macroeconomic stability prevailed in both political and financial circles. In the UK policies of targeting inflation levels have been evident since 1997 and a policy of low and stable inflation was evident in the US where Alan Greenspan led the US Federal Reserve