Fast, scalable master equation solution algorithms. IV. Lanczos iteration with diffusion approximation preconditioned iterative inversion

In this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equation solution methods while maintaining the speed of a partial spectral decomposition. The method is tested using a master equation modeling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long-lived isomerizing intermediates. (C) 2003 American Institute of Physics.

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.

Selecting methods to solve multi-well master equations

There are several competing methods commonly used to solve energy grained master equations describing gas-phase reactive systems. When it comes to selecting an appropriate method for any particular problem, there is little guidance in the literature. In this paper we directly compare several variants of spectral and numerical integration methods from the point of view of computer time required to calculate the solution and the range of temperature and pressure conditions under which the methods are successful. The test case used in the comparison is an important reaction in combustion chemistry and incorporates reversible and irreversible bimolecular reaction steps as well as isomerizations between multiple unimolecular species. While the numerical integration of the ODE with a stiff ODE integrator is not the fastest method overall, it is the fastest method applicable to all conditions.

Impaired postural compensation for respiration in people with recurrent low back pain

This study evaluated the degree to which the disturbance to posture from respiration is compensated for in healthy normals and whether this is different in people with recurrent low back pain (LBP), and to compare the changes when respiratory demand is increased. Angular displacement of the lumbar spine and hips, and motion of the centre of pressure (COP), were recorded with high resolution and respiratory phase was recorded from ribcage motion. With subjects standing in a relaxed posture, recordings were made during quiet breathing, while breathing with increased dead-space to induce hypercapnoea, and while subjects voluntarily increased their respiration to match ribcage expansion that was induced in the hypercapnoea condition. The relationship between respiration and the movement parameters was measured from the coherence between breathing and COP and angular motion at the frequency of respiration, and from averages triggered from the respiratory data. Small angular changes in the lumbopelvic and hip angles were evident at the frequency of respiration in both groups. However, in quiet standing, the LBP subjects had a greater displacement of their COP that was associated with respiration than the control subjects. The LBP group had a trend for less hip motion. There were no changes in the movement parameters when respiratory demand increased involuntarily via hypercapnoea, but when respiration increased voluntarily, the amplitude of motion and the displacement of the COP increased in both groups. The present data suggest that the postural compensation to respiration counteracts at least part of the disturbance to posture caused by respiration and that this compensation may be less effective in people with LBP.

Effect of lifter design on drying performance in rotary dryers

Lifter use in dryers improves mass transfer by increasing the amount of surface area available for transfer and also by increasing the velocity of gas over the particle surface. An even cross-sectional distribution of particles in a dryer improves the efficiency of operation by ensuring that evaporation from falling particles is taking place for the maximum fraction of the rotation period of the drier. Studies on lifter design to improve the cross-sectional particle distribution were performed on angled lifters. A single lifter was used and the mass-transfer rate examined as a function of angular lifter displacement. Analysis of the mass transfer characteristics of single lifters allowed performance comparisons and recommendations for lifter design.