Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Actively shielded multi-layer gradient coil designs with improved cooling properties

In standard cylindrical gradient coils consisting of a single layer of wires, a limiting factor in achieving very large magnetic field gradients is the rapid increase in coil resistance with efficiency. This is a particular problem in small-bore scanners, such as those used for MR microscopy. By adopting a multi-layer design in which the coil wires are allowed to spread out into multiple layers wound at increasing radii, a more favourable scaling of resistance with efficiency is achieved, thus allowing the design of more powerful gradient coils with acceptable resistance values. Previously this approach has been applied to the design of unshielded, longitudinal, and transverse gradient coils. Here, the multi-layer approach has been extended to allow the design of actively shielded multi-layer gradient coils, and also to produce coils exhibiting enhanced cooling characteristics. An iterative approach to modelling the steady-state temperature distribution within the coil has also been developed. Results indicate that a good level of screening can be achieved in multi-layer coils, that small versions of such coils can yield higher efficiencies at fixed resistance than conventional two-layer (primary and screen) coils, and that performance improves as the number of layers of increases. Simulations show that by optimising multi-layer coils for cooling it is possible to achieve significantly higher gradient strengths at a fixed maximum operating temperature. A four-layer coil of 8 mm inner diameter has been constructed and used to test the steady-state temperature model. (C) 2003 Elsevier Inc. All rights reserved.

Multilayer transverse gradient coil design

In small, cylindrical gradient coils consisting of a single layer of wires, the limiting factor in achieving large magnetic field gradients is the rapid increase in coil resistance with efficiency. This behavior results from the decrease in the maximum usable wire diameter as the number of turns is increased. By adopting a multilayer design in which the coil wires are allowed to spread out into multiple layers wound at increasing radii, a more favorable scaling of resistance with efficiency is achieved, thus allowing the design of more powerful gradient coils with acceptable resistance values. By extending the theory used to design standard cylindrical gradient coils, mathematical expressions have been developed that allow the design of multilayer coils. These expressions have previously been applied to the design of a four-layer z-gradient coil. As a further development, the equations have now been modified to allow the design of multilayer transverse gradient coils. The variation in coil performance with the number of layers employed has been investigated for coils of a size suitable for use in NMR microscopy, and the effect of constructing the coil using wires or cuts in a continuous conducting surface has also been assessed. We find that at fixed resistance a small wire-wound two-layer coil offers an increase in efficiency of a factor of about 1.5 compared with a single-layer coil. In addition, a two-layer coil of 10-mm inner diameter has been designed and built. This coil had an efficiency of 0.41 Tm-1 A(-1), a resistance of 0.96 +/- 0.01 Omega, and an inductance of 22.3 +/- 0.2 muH. The coil produces a gradient that deviates from linearity by less than 5% over a central cylindrical region of interest of height and length 6.2 mm. (C) 2003 Wiley Periodicals, Inc.

Applied physiology and game analysis of rugby union

Increased professionalism in rugby has elicited rapid changes in the fitness profile of elite players. Recent research, focusing on the physiological and anthropometrical characteristics of rugby players, and the demands of competition are reviewed. The paucity of research on contemporary elite rugby players is highlighted, along with the need for standardised testing protocols. Recent data reinforce the pronounced differences in the anthropometric and physical characteristics of the forwards and backs. Forwards are typically heavier, taller, and have a greater proportion of body fat than backs. These characteristics are changing, with forwards developing greater total mass and higher muscularity. The forwards demonstrate superior absolute aerobic and anaerobic power, and Muscular strength. Results favour the backs when body mass is taken into account. The scaling of results to body mass can be problematic and future investigations should present results using power function ratios. Recommended tests for elite players include body mass and skinfolds, vertical jump, speed, and the multi-stage shuttle run. Repeat sprint testing is a possible avenue for more specific evaluation of players. During competition, high-intensity efforts are often followed by periods of incomplete recovery. The total work over the duration of a game is lower in the backs compared with the forwards; forwards spend greater time in physical contact with the opposition while the backs spend more time in free running, allowing them to cover greater distances. The intense efforts undertaken by rugby players place considerable stress on anaerobic energy sources, while the aerobic system provides energy during repeated efforts and for recovery. Training should focus on repeated brief high-intensity efforts with short rest intervals to condition players to the demands of the game. Training for the forwards should emphasise the higher work rates of the game, while extended rest periods can be provided to the backs. Players should not only be prepared for the demands of competition, but also the stress of travel and extreme environmental conditions. The greater professionalism of rugby union has increased scientific research in the sport; however, there is scope for significant refinement of investigations on the physiological demands of the game, and sports-specific testing procedures.